Kinetics and Modeling of the Radical Polymerization of Acrylic Acid and of Methacrylic Acid in Aqueous Solution

Transcription

1 Kineics and Modeling of he Radical Polymerizaion of Acrylic Acid and of Mehacrylic Acid in Aqueous Soluion Disseraion zur Erlangung des mahemaisch-naurwissenschaflichen Doorgrades Docor rerum nauralium der Georg-Augus-Universiä Göingen im Promoionsrogramm Chemie der Georg-Augus Universiy School of Science (GAUSS) vorgeleg von Nils Friedrich Guner Wienberg aus Hamburg Göingen, 203

2 Bereuungsausschuss Prof. Dr. M. Bubac, Technische und Maromoleulare Chemie, Insiu für Physialische Chemie, Georg-Augus-Universiä Göingen Prof. Dr. P. Vana, MBA, Maromoleulare Chemie, Insiu für Physialische Chemie, Georg-Augus-Universiä Göingen Miglieder der Prüfungsommission Referen: Prof. Dr. M. Bubac, Technische und Maromoleulare Chemie, Insiu für Physialische Chemie, Georg-Augus-Universiä Göingen Korreferen: Prof. Dr. P. Vana, MBA, Maromoleulare Chemie, Insiu für Physialische Chemie, Georg-Augus-Universiä Göingen Weiere Miglieder der Prüfungsommission: Prof. Dr. G. Echold, Physialische Chemie feser Körer, Insiu für Physialische Chemie, Georg-Augus-Universiä Göingen Prof. Dr. B. Geil, Biohysialische Chemie, Insiu für Physialische Chemie, Georg-Augus- Universiä Göingen Jun.-Prof. Dr. R. Maa, Comuerchemie und Biochemie,Insiu für Physialische Chemie, Georg-Augus-Universiä Göingen Prof. Dr. A. Wode, Physialische Chemie I / Humbold-Professur, Insiu für Physialische Chemie, Georg-Augus-Universiä Göingen Tag der mündlichen Prüfung:

3 Meiner Familie

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5 Table of Conens Table of Conens Absrac... Inroducion Theoreical Bacground General Asecs of Radical Sabiliy and Reaciviy Ideal Polymerizaion Kineics of Radical Polymerizaion Formaion of Radicals and Iniiaion Proagaion Terminaion Seady Sae Kineics Addiional Reacions Transfer Reacions o Small Molecules Inermolecular Transfer o Polymer Inramolecular Transfer o Polymer Bacbiing β-scission Reacion Reardaion and Inhibiion Influences on Rae Coefficiens Temeraure and Pressure Concenraion Ionizaion Chain Lengh Conversion Comuer Modeling of Polymerizaions Maerials, Exerimenal Procedures and Daa Evaluaion Chemicals V

6 Table of Conens 3.. Monomers Solvens Iniiaors Inhibiors Subsances used o reare Buffer Soluions Ohers Purificaion Procedures NIR Seu Thermally iniiaed Polymerizaion in a Cuvee Phooiniiaed Polymerizaion in a Cuvee Degree of Monomer Conversion EPR Seu Organic Samles Aqueous Samles Deconvoluion of Secra Calibraion NMR Quaniaive H-NMR Quaniaive 3 C-NMR Polymerizaion in NMR Samle Tube Densiy Measuremen Viscosiy Measuremen Imoran Feaures of Polymer Soluions Polymerizaion in Viscosiy Measuremen Caillary Prearaion of Buffer Soluions SEC... 8 VI

7 Table of Conens 3.0 ESI-MS HPLC H-Meer High-Temeraure Polymerizaions Soed-Flow exerimens in High-Pressure Cell Polymerizaion in a Tubular Reacor Oher Seus for Polymerizaion L Auomaed Reacor Polymerizaion in a Heaing Bloc Polymerizaion in a Flas Polymerizaion in a Lined Flas Comuer Programs Curve Fiing Deerminaion of Join Confidence Regions Simulaion Error Esimae Mehacrylic Acid Chain-Transfer o 2-Mercaoehanol Chain Transfer Consans deduced by he Mayo Mehod Chain Transfer Consans deduced by he CLD Mehod Comarison of Mayo and CLD mehods Model develomen for Non-ionized Mehacrylic Acid Modeling Polymerizaion a Medium iniial Monomer Conen Modeling Polymerizaion a Low iniial Monomer Conen Acrylic Acid Model develomen for Non-ionized Acrylic Acid Iniiaor Kineics Evaluaion of s daa VII

8 Table of Conens 5..3 Evaluaion of and Viscosiy daa Deerminaion bb by 3 C-NMR BA as a Model for AA o esimae CCTA by EPR CCTA s of ME wih AA Deerminaion of for AA Macromonomers by H-NMR Modeling Polymerizaion a 35 o 80 C Modeling Polymerizaion a High Temeraure Model Develomen for Ionized Acrylic Acid of Fully Ionized AA and deendence on Ionic Srengh a Full Ionizaion bb a Full Ionizaion and deendence on Ionic Srengh Densiy Modeling he Polymerizaion of Fully Ionized AA The deendence of on he Degree of Ionizaion The deendence of on he Degree of Ionizaion The deendence of bb on he Degree of Ionizaion β-scission The KA of AA Modeling he Polymerizaion of Parly Ionized AA Acrylamide Closing Remars Aendix Abbreviaions and Symbols References VIII

9 Absrac Absrac The radical olymerizaion of mehacrylic acid, acrylic acid and acrylamide in aqueous soluion has been invesigaed. Deailed ineic models for boh acrylic acid, AA, and mehacrylic acid, MAA, have been develoed alying he rogram PREDICI TM. Good reresenaion of exerimenal conversion vs. ime rofiles and molar mass disribuions as well as, in case of AA, he branching level could be achieved. The olymerizaion of MAA has been sudied a 35 and 50 C wih focus on he influence of 2-mercaoehanol, ME, as chain ransfer agen, CTA, on reacion ineics. The rae coefficien of ransfer o CTA,, r,cta was measured for differen monomer levels by he Mayo and he chain lengh disribuion rocedure. The raio of r,cta o he roagaion rae coefficien,, is indeenden of monomer o waer raio while boh rae coefficiens increase by aroximaely one order of magniude in assing from bul o dilue aqueous soluion. I was found ha addiion of CTA reduces he rae of MAA olymerizaion by wo effecs on. A negligible monomer conversion, increases owards higher conen of CTA, because average chain lengh is reduced by he CTA. Chain-lengh deenden erminaion may be reresened by adoing he comosie model, which is a well-esablished heory o describe chain-lengh deendency of erminaion of macroradicals of idenical size. The comosie model could be alied o average chain lengh. The reducion of owards higher degrees of monomer conversion (Norrish Trommsdorff or gel effec) becomes weaer owards higher levels of CTA, which could be described by correlaing he inensiy of he gel effec o molar mass of olymer in soluion.

10 Absrac The olymerizaion of non-ionized AA in aqueous soluion has been sudied beween 35 and 80 C wih and wihou ME as CTA. Chain-lengh deenden erminaion was aen ino accoun for modeling as for MAA. During AA olymerizaion a,5- hydrogen shif (bacbiing) aes lace ransforming he secondary roagaing radical, SPR, ino a eriary midchain radical, MCR, he ineics of which were included ino he model. The bacbiing reacion was quanified via 3 C-NMR, he oher MCR reacions were esimaed from conversion vs. ime rofiles. By measuring he MCR fracion during buyl acrylae, BA, olymerizaion via elecron aramagneic resonance, EPR, i could be shown ha he ransfer of MCRs o CTA is no an imoran reacion ah. BA can be used as AA model comound so ha he same finding should also aly for AA olymerizaions in aqueous hase. Chain ransfer of SPRs of AA was measured by he Mayo mehod. The model was exended owards high-emeraure olymerizaion of AA beween 90 and 70 C, where -scission and roagaion of macromonomers need o be considered. Moreover, a model for he olymerizaion of ionized AA was develoed, which aes numerous deendencies of rae coefficiens on ionizaion and ionic srengh ino accoun, e.g., roagaion is reduced by ionizaion of monomer, bu o a higher exen for lower monomer concenraion. Moreover, roagaion of ionized monomer augmens owards higher ionic srengh. MCRs were found during acrylamide olymerizaion via EPR revealing he bacbiing reacion o aly for his monomer as well. Thus, he ineic scheme is he same as for AA olymerizaion. Pars of his hesis have already been ublished: Wienberg, N. F. G.; Bubac, M.; Sach, M.; Lací, I. Macromol. Chem. Phys. 202, 23, Wienberg, N. F. G.; Bubac, M.; Huchinson, R. A. Macromol. Reac. Eng. 203, 7,

11 Inroducion Inroducion Polymer chemisry began wih he ioneering research by Saudinger, [,2] who discovered he chain srucure of olymers consising of chemically bonded monomeric unis. Baeeland s invesigaions leading o Baelie TM[3] formed from an eliminaion reacion of henol wih formaldehyde sared he age of commercial synheic olymers over 00 years ago. Since hose early imes, olymer roducion grew raidly and became a major field of he chemical indusry. In 202, he olymer roducion in Germany had a roducion value of 27.7 billion euro, which is 9.5 % of he chemical and harmaceuical indusry. [4] Polymers may be synhesized via olycondensaion, olyinserion (caalyic), caionic, anionic or radical olymerizaion. All of hese mehods have secial advanages and disadvanages and are used in indusry o differen exen. Radical olymerizaion is a robus and versaile echnique, which is alied o roduce e.g. olyehylene, olysyrene, olyacrylaes, olymehacrylaes, and corresonding coolymers in high quaniies. The hysical roeries of a olymer derive from he funcionaliies of is monomer unis, bu also from is molecular mass disribuion (MMD) and microsrucure. Thus, wih he same monomer (comosiion) he roducion of quie differen olymers is ossible. Provided he srucure-roeries relaionshi is nown, modeling of he olymerizaion rocess can be alied o simulae olymerizaion and redic he roeries of he resuling olymer. Kineic models are uilized as an 3

12 Chaer addiional ool for lanning new indusrial rocesses or imroving esablished ones, e.g., reducing consumion of resources or enhancing roduc qualiy. They also find alicaion for a more accurae rocess conrol (online use). For recise models, accurae nowledge of all rae coefficiens of he rocess including heir various deendencies is essenial. Rae coefficiens are no easily deermined and are ofen no nown wih sufficien accuracy. The inroducion of ulsed-laser olymerizaion, PLP, echniques led o a grea advancemen in nowledge of rae coefficiens. The roagaion rae coefficien can be measured recisely by he PLP SEC mehod, invened by Olaj e al. [5] based on he older roaing secor echnique. PLP is combined wih subsequen analysis of he formed olymer by size-exclusion chromaograhy, SEC. The erminaion rae coefficien including conversion deendence is accessible via he SP PLP NIR echnique, inroduced by Bubac e al. [6] The decline in monomer concenraion afer a single laser ulse, SP, iniiaion is moniored via ime-resolved near infrared, NIR, secroscoy. Elecron aramagneic resonance, EPR, secroscoy allows for direc measuremen of radical concenraion; combinaion wih ulsed laser olymerizaion led o he SP PLP EPR echnique inroduced by Bubac e al. [7] The echnique rovides access o chain-lengh deendence of he rae coefficien of erminaion and differen yes of radicals may be disinguished. During olymerizaion of acrylae ye monomers a,5-hydrogen shif (bacbiing) aes lace ransforming he secondary roagaing radical, SPR, ino a eriary midchain radical, MCR, he ineics of which are quie differen from SPR ineics and have o be accouned for in a ineic model. The olymerizaion of waer-soluble monomers is of indusrial imorance, as he associaed olymers find various alicaion as suerabsorber maerial, e.g., ar of hygiene and cosmeics roducs as well as in acaging and soil imrovemen, or as hicener, disersan and emulsifier, e.g., alied in wasewaer reamen, mining, exile, and aer indusry. Kineics in aqueous soluion are more comlex due o he srong deendence of he rae coefficien of roagaion on monomer concenraion, and hus degree of monomer conversion. [8-0] For monomers feauring ionizable moieies, ineics are aricularly challenging. The influences of ionizaion and ionic srengh are no limied o effecs on he srucure of he olymer in soluion; hey have a grea imac on olymerizaion ineics as well, e.g., he rae coefficien of roagaion of mehacrylic acid a low monomer concenraion in aqueous soluion declines by 4

13 Inroducion abou one order of magniude from he non-ionized o ionized monomer. [] Addiion of more ionizing agen, e.g., NaOH, o fully ionized mehacrylic acid, i.e., increasing ionic srengh, leads o a ronounced enhancemen of olymerizaion rae. [2] 5

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15 Theoreical Bacground 2 2 Theoreical Bacground This chaer summarizes he heoreical bacground of he research resened in his hesis. Esecially he general asecs were already resened in several oher wors and are herefore given briefly only. Aferwards aricular asecs imoran, e.g., for he olymerizaion of acrylic monomers, effecs of high emeraure, and ionizaion of monomer are resened. Chain-lengh and conversion deendency are also imoran asecs for he modeling resened in his hesis and are consequenly oulined in more deail. 2. General Asecs of Radical Sabiliy and Reaciviy In order o undersand reaciviy in radical olymerizaion, one has o consider he facors ha deermine sabiliy of organic radicals. The sabiliy of one radical is ineresing in absolue erms, bu mosly relaive o oher radicals. A his, one has o consider how easily a radical is formed. I is equiollen o loo uon he conribuion of he srengh of he bond, which has o be broen o form he radical, and he inrinsic sabiliy of he radical. Firs, he elecronegaiviy of he aom where he radical is essenially locaed has o be considered. In general, carbon-cenered radicals are more sable han nirogencenered ones, which again are more sable han oxygen-cenered ones. Tha is why carbon-cenered radicals are mos common in organic chemisry. Due o his facors ransfer o carboxyl grous of acrylic acid and mehacraylic acid (wo monomers, on 7

16 Chaer 2 which his hesis focuses,) can be excluded. Furhermore, ransfer of he radical funcion from a growing chain o he solven waer need no be considered. Neverheless, his effec may be overcomensaed by oher facors, e.g., TEMPO (2,2,6,6-eramehylieridine -oxyl) is a sable radical. The bond srengh beween a carbon and a hydrogen aom is srongly influenced by hybridizaion: s 3 is more sable han s 2 which again is more sable han s. This can be exlained, firsly, by an increasing s-characer of he bond, which decreases bond lengh, and secondly, by sabilizaion of he radical by alihaic subsiuens. A his, he radical is sabilized by hyerconjugaion beween he -orbial of he radical and he C-H -bond of vicinal carbons. This effec is addiive. Alinyl and benzyl radicals are raher exoic. The only radical olymerizaion ha feaures rimary radicals is he olymerizaion of ehene (ehylene), which is only erformed a high emeraures. A major ar of his wor is abou he ineics of secondary and eriary radicals; heir difference in reaciviy originaes from heir difference in sabiliy (subchaer 2.3.3). Delocalizaion by conjugaion o double bonds or aromaic rings causes esecially srong sabilizaion of ca. 2 cal mol (vinyl and henyl grou). A good examle for he imac of his sabilizaion is he roenyl radical formed by ransfer o monomer during radical olymerizaion of roene. During his olymerizaion, ransfer is so oen ha only oligomeric roduc can be roduced. For rare alinyl radicals conjugaion o only one -bond is ossible, because he oher one is orhogonal. Heeroaoms can sabilize radicals by conjugaion o a lone elecron air. In his case, he effec srenghens he more elecron densiy can be ransferred o he radical funcion. Amino grous sabilize more han hydroxyl grous because nirogen has a lower elecronegaiviy. A negaive charge on he oxygen leads o a beer sabilizaion. This is imoran for monomers wih a carboxylae moiey, which are reaed in subchaer 5.2. Boh donor and acceor subsiuens sabilize radicals and for caodaive radicals he effecs (mos ofen) add u insead of comensaing each oher, or ye cause an even more enhanced sabilizaion. Radicals show a endency o comensae elecron shorage and abundance, resecively, i.e. radicals wih a revailing influence of donors reac raher wih double bonds under he influence of acceors and vice versa. This is very imoran for reaciviy raios in coolymerizaion, bu also for he iniiaion se (see subchaer 2.2.). 8

17 Theoreical Bacground Charges and olariy, resecively, have a srong influence on reaciviy as hey lower he energy of he ransiion sae. They always reduce he enroy of he ransiion sae hus acceleraion he reacion. [3] The formaion of radical anions and caions is also ossible. I Soluions of radical anions are quie sable as long as hey remain oxygen free and no roonaion sources are available (Birch reducion). Radical anions are someimes used as iniiaors, e.g., in BuNA (buadiene rubber) roducion. Radical caions are less sable and do no lay a role in radical olymerizaion. Furhermore, seric effecs are imoran. Srong van-der-waals reulsion by moieies nex o he radical cener sabilizes he radical funcion and reduce is reaciviy. This is he reason why,2 subsiued monomers are raher uncommon. Due o reulsion of moieies in he corresonding olymeric roduc, growh of he chain is slow and he ceiling emeraure (he emeraure, above which he olymer is hermodynamically less sable han he corresonding monomer) hereof is low. Seric effecs are also very imoran for regioseleciviy. Radicals add o a,- subsiued double bond a he C2 side; his even holds for monosubsiued double bonds. Only for a few monomer, e.g., vinyl aceae, head-head-roagaion becomes significan a high emeraure. 2.2 Ideal Polymerizaion Kineics of Radical Polymerizaion During radical olymerizaion, he reacive radical secies can undergo various reacions. For a simle reamen some assumions are made: All reacions are irreversible. All saring radicals are only generaed by iniiaor and consumed by iniiaion. Monomer is solely consumed by roagaion. Radicals exclusively so growing by muual deacivaion. All rae coefficiens are indeenden of chain-lengh and concenraions. These basic reacions and deducions are described in he following subchaers. I Here, radical ion refers o comounds ha carry a conneced charge and radical funcion. This should no be mixed u wih radicals ha also have charges somewhere else. Under basic condiions, a growing chain of AA is a olycaion and a radical bu no a radical caion, because he radical funcion is searaed from he charge. 9

18 Chaer Formaion of Radicals and Iniiaion In rincile, all reacions generaing radical secies can be used for radical olymerizaion; his includes, e.g., ionizing radiaion, suersonic and elecrochemical reacions. Neverheless, more common is he addiion of an iniiaor. Iniiaor decomosiion is induced eiher by UV-rays (hoo iniiaion) or hermically (chemical iniiaion). Anoher commercially imoran iniiaion sysem is redox iniiaion, e.g., hydroeroxide and iron(ii) reac o hydroxide, hydroxyl radical and iron(iii). Common hooiniiaors are eones ha undergo -cleavage afer hooexciaion of he carbonyl funcion. This is he Norrish ye I reacion. [4] For hooiniiaors, he rae of decomosiion is usually indeenden of emeraure. Due o higher coss, his mehod of iniiaion is used more ofen in research han in indusrial roducion. Common chemical iniiaors are eroxides and azo-comounds, because boh he oxygen-oxygen-bond and he nirogen-carbon-bond can undergo homolyic bond cleavage raher easily. The former are cheaer and hus of higher indusrial imorance. In order o reduce he acivaion energy of he decay reacion, eroxides are someimes combined wih a reducing agen forming a redox iniiaion sysem. Iniiaion may also occur by reacions beween comonens in he reacion mixure oher han roer iniiaor. A well nown examle are wo mechanisms of hermal auo iniiaion of monomer syrene. [5,6] The hiol-ene reacion is anoher examle of iniiaion by non-iniiaor comounds wihin he reacion mixure. [7] The normal hoo and chemical iniiaors follow he reacion scheme: I f d 2R 0 The iniiaor, I, decomoses ino wo growing chains of chain lengh zero. This ignores he iniiaor fragmen comleely. Someimes he iniiaor fragmen a he end of he chain is couned as one monomer uni leading o he following scheme insead: 0

19 Theoreical Bacground I f d 2R The decay of he iniiaor aes lace as a firs-order reacion wih he rae coefficien d. Merely a fracion of iniiaor fragmens is available o iniiae radical olymerizaion. This fracion is given by he correcion facor, f, which is he iniiaor efficiency. Is value deends on viscosiy of solven and effecive size of he fragmens; usually i varies beween 0.4 and 0.9. Afer he decay of he iniiaor he fragmens boh being radicals may recombine as long as hey remain ogeher in he solven cage. Only afer one of hem has lef i by diffusion, immediae recombinaion is revened. In addiion, side reacions of he iniiaor radicals may furher reduce he share of radicals available for iniiaion decreasing f even more. The rae of formaion of radicals, which describes he buil u of he radical concenraion, c R, from iniiaor concenraion, c, wih ime,, can be exressed by I eq. (2.). dc d 2 f c R d I (2.) These newly roduced radicals reac wih a monomer molecule, M, o iniiae chain growh wih he rae coefficien i. This se is usually very fas and herefore ignored, because in his case i is negligible for overall rae of olymerizaion. R M R i 0 Iniiaor decay reduces iniiaor concenraion and i may haen ha iniiaor is decomosed comleely rior o comlee monomer conversion, which is referred o

20 Chaer 2 as dead-end olymerizaion. In indusrial racice, ofen mixures (cocails) of iniiaors wih differen raes of decomosiion are used. I is imoran o ee in mind ha even in he more robus radical olymerizaions no each iniiaor is able o iniiae effecively. Deending on he sabiliy of he iniiaing and he resuling radical, iniiaion can be slow and he corresonding iniiaor would be considered unsuiable for his olymerizaion. In case of hoochemically iniiaed olymerizaion induced by a shor (a few ns) UVlaser ulse, as used in ulsed laser olymerizaion, PLP, echniques, creaion of radicals can be considered as insananeous, because he formaion of radicals is fas in comarison o a subsequen reacion ses. In rinciel, he radical concenraion roduced uon alying a laser ulse a ime 0 zero, c R may be deermined by eq. (2.2), which conains quanum yield (fracion of absorbed hoons leading o decomosiion),, iniiaor efficiency, quaniy, n, of absorbed hoons, and irradiaed samle volume, V. 0 n cr 2 Φ f (2.2) V According o he Beer Lamber Bouguer law, [8-20] he amoun of absorbed hoons can be calculaed from he oal amoun of hoons hiing he samle by eq. (2.3); n n E 0 E c l I absorbed oal 0 (2.3) is he radian ower (inensiy) a a cerain wavenumber,, he index 0 means: in fron of he cell. E denoes energy, a his, an index of refers o laser ulse, an index of omolar energy of hoons a given laser wavelengh. is he molar decadic absorion coefficien, and l he ah lengh wihin he samle cell. In racice, deermining all hese values roves virually imossible and measured direcly (see subchaer 3.4). 0 c R is 2

21 Theoreical Bacground Proagaion Polymer chains grow by adding monomer, M, hus increasing chain lengh, i, by one. This rocess is called roagaion. R M R i i The rae of monomer consumion by roagaion is described by eq. (2.4). The corresonding rae coefficien is. dc d M c M c (2.4) R Terminaion The rocess of chain growh ends wih he erminaion of he radical (or wih ransfer, v.i.). Chain erminaion is characerized by he reacion of wo radicals eliminaing boh radical funcions. I roceeds eiher by disroorionaion, he ransfer of a -hydrogen from one radical o he oher forming an unsauraed chainend, or by combinaion, i.e., a formaion of a covalen bond beween he acive ceners of roagaing radicals. In case of combinaion, he degree of olymerizaion, i + j, of he resuling macromolecule, P i j, is he sum of he degrees of olymerizaion i and j of he wo rimordial growing chains, while disroorionaion does no change he degrees of olymerizaion of he reacans.,comb Ri R j Pi j R R P P,dis i j i j 3

22 Chaer 2 The overall erminaion rae coefficien is he sum of he rae coefficiens of combinaion,,comb, and of disroorionaion,,dis. Which of he mechanisms revails is mosly deermined by he srucure of he monomer, seric hindrance favoring disroorionaion. To some degree, higher emeraure suors disroorionaion. The fracion of disroorionaion is given by. The rae of consumion of radicals is described by a second-order rae equaion. To describe he rocess eq. (2.5) including a facor of 2 is used hroughou his wor, as recommended by IUPAC. [2] dc R 2 2 cr (2.5) d Seady Sae Kineics Under coninuous iniiaion, a quasi-saionary sae (Bodensein rincile) is reached quicly. Thus, he raes of generaion and consumion of radicals are equal, hence eq. (2.) and eq. (2.5) can be combined o eq. (2.6). Furher combinaion wih eq. (2.4) leads o eq. (2.7), which gives he rae of olymerizaion, r P. f c c (2.6) 2 d I R dc M r olym c M d f c I d (2.7) Liewise consideraions allow for calculaing he average number of monomer unis added o an iniiaing radical unil i erminaes. This is called he ineic chain lengh,, and can be calculaed according o eq. (2.8) as he rae of he overall reacion divided by he rae of he iniiaion reacion. 4

23 Theoreical Bacground c M f c d I (2.8) 2.3 Addiional Reacions The reacions given in subchaer 2.2 are generally considered o be he mos imoran ones, bu deending on reacion condiions and desired accuracy of he descriion of he rocess oher reacions need o be aen ino accoun. They are described in he following subchaers. The growing radicals are very reacive and can basically reac wih all oher subsances in he reacion mixure. The so-obained radicals may reiniiae quicly. This rocess is called ransfer. I can occur wih small molecules as described in subchaer Transfer o olymer has differen asecs and is reaed searaely. Inermolecular (see subchaer 2.3.2) and inramolecular ransfer (see subchaer 2.3.3) are differen in ineics and in heir imac on roduced olymer. A higher emeraure, -scission becomes imoran for olymerizaion, esecially as a follow-u rocess of ransfer o olymer. If he small molecular ransfer roduc iniiaes slowly or no a all, his rocess is called reardaion or inhibiion, resecively (see subchaer 2.3.2) Transfer Reacions o Small Molecules In he conex of radical olymerizaion ransfer reacion always means ransfer of he radical funcion. The following schemes illusrae ossible reacions. Transfer reacion: 5

24 Chaer 2 r,x Ri X Pi X The radical funcion is ransferred from he growing chain, R i, wih chain lengh i o an arbirary secies, X, forming he new radical X corresonding rae coefficien and X. Reiniiaion: and dead olymer, P i. The r,x is correlaed wih he raio of sabiliies of R i i,x X M R By adding monomer, M, he newly formed radical roduces anoher growing chain, R, of chain lengh uniy. This aes lace wih he rae coefficien of reiniiaion by X, i,x. Terminaion:,X Ri X Pi Insead of iniiaing, X rae coefficien is concenraion and hus rae. can also undergo erminaion reacions. The corresonding,x. If his rocess is of imorance, i reduces radical Usually, he only ransfer rae coefficiens ha is of ineres is r,x. Tyically, no he rae coefficien iself bu is raio o, called chain ransfer consan of ransfer o X, C X, is considered, see eq. (2.9). Sricly seaing, i is no a real consan, bu mosly he wo coefficiens change in he same way under differen condiions, e.g., uon change of emeraure, hus leaving C X unouched. The acivaion energy (comare subchaer 2.4.) of C is yically raher small (0 J/mol) or X imerceible, resecively. [22,23] Overall, here are surrisingly few sudies abou he acivaion energy of chain ransfer. Neverheless, his assumion of C X being a 6

25 Theoreical Bacground consan may no hold under all condiions, e.g., he value can change wih solven comosiion. [24] C X r,x (2.9) Chain ransfer can occur o all secies in a reacion mixure, e.g., iniiaor, monomer, solven. Every chain-ransfer even reduces molar mass of roduced olymer. Thus, he ineic-chain lengh does no give he degree of olymerizaion. A ransfer erm has o be added yielding eq. (2.0). i cm f c c (2.0) d I r,i i i Comonens ha easily undergo ransfer may be added o a olymerizaion sysem in order o conrol molar mass. They are called chain-ransfer agens, CTAs. If he rae of chain ransfer is so high ha only oligomer is roduced, he rocess is called elomerizaion and insead of CTA he addiive is called elogen. Tyically, halogenaed alanes or hiols are used as CTAs wih high chain ransfer consans and aldehydes or alcohols are used as weaer CTAs. The facile cleavage of he S-H bond in hiols is associaed wih large chain-ransfer rae coefficiens. [25] The sulfur-cenered radical roduced by hydrogen ransfer may add o monomer raidly. Transfer reduces chain lengh bu does no influence radical concenraion direcly. Thus, he CTA should no influence olymerizaion ineics. Laer in his wor, i will be shown ha his assumion has only limied validiy (see subchaer 4.2) 7

26 Chaer 2 Deerminaion of Chain-Transfer Consans The mos widesread echnique for deerming C X is he Mayo mehod. [26] A more recenly develoed echnique is referred o as CLD mehod. [27] In addiion, here is a hird scarcely used mehod: O Brien and Gornic [28] showed, based on consideraions of Mayo, [26] a way o deermine chain ransfer-consans wihou he necessiy o measure molecular masses. In rincile, he Mayo and CLD echnique should wor equally well. Noneheless, here has been quie some disue abou he mehod of choice. [22,23,29,30] Boh mehods require olymer from reacion o low conversion under seady-sae condiions, which is subsequenly analyzed for molar-mass disribuion, MMD. Under aricular condiions C X may also be deduced from ulsed laser olymerizaion. [22,3] The Mayo rocedure refers o eq. (2.). If only one chain ransfer rocess is of ineres, eq. (2.2) can be used. The inverse of he number-average degree of olymerizaion, i n sloe o a sraigh-line fi yields he number and weigh averages,, is loed vs. he raio of CTA o monomer concenraions. The C X. Commercial SEC conrol rograms direcly yield M and n M w, resecively. From M, n i n is simly obained by dividing by monomer mass, which maes he Mayo mehod easily alicable. Eq. (2.) is ransformed ino eq. (2.2) defining in he absence of he CTA. 0 i n as he degree of olymerizaion c r, R j j i n c (2.) c c M j M c C i (2.2) n CTA CTA 0 c M in c R and c M refer o concenraion of radical and monomer, resecively. Guillemes indicae: chain-lengh averaged. c j is he concenraion of an arbirary secies j, o which ransfer occurs wih he rae coefficien r, j. 8

27 Theoreical Bacground The CLD mehod uses eq. (2.3) and (2.4). [23,29] Ploing he logarihm of olymer mass disribuion, P, as a funcion of mass, m, should yield a sraigh line wih m sloe for large molar masses, i.e., for m aroaching infiniy Wihin a second se, he roduc of and negaive molar mass of he monomer, M, is loed vs. he raio of CTA o monomer concenraions, c CTA sloe o he so-obained sraigh line yields he ransfer consan, / c. According o eq. (2.4), he M C CTA. cr r, d ln Pm i c i lim m d m M cm i c (2.3) M ccta 0 λ M C λ M (2.4) M CTA M c M I has been ariculaed ha he CLD mehod is less sensiive owards roblems wih SEC calibraion and signal analysis. [23] The mehod of O Brien and Gornic [28] emloys eq. (2.5). A double logarihmic lo of he raio of iniial concenraion o concenraion of CTA and monomer a any conversion should give a sraigh line, he sloe of which is C CTA. The echnique wors wih non-caalyic CTAs only. For end-grou analysis usually H-NMR or iraion is used. This mehod may also used o measure CTA concenraion. 0 0 c CTA c M ln C CTA ln ccta cm (2.5) Inermolecular Transfer o Polymer Insead of ransfer of he radical funcion o a small molecule, i can also be ransferred o olymer in he reacion mixure, following his scheme: 9

28 Chaer 2 r,p Ri Pj R j Pi Commonly, he newly formed radical is no of he same ye as he original one, because he rae coefficien of ransfer o olymer is higher if he newly formed radical is more sable. Naurally, he reaciviy of he more sable radical is smaller. During olymerizaion of acrylae-ye monomers he secondary roagaing radical, SPR, may reac o he more sable eriary radical midchain radical, MCR, by a ransfer rocess. The ransfer consan varies a lo wih he monomer ye. Under mos condiions, he effecive rae of inermolecular ransfer o olymer is oo low o have a noable ineic effec. Transfer o olymer can have a srong effec on olymer roeries. Long-chain branching oins are formed by ransfer o olymer and subsequen addiion of olymer, or subsequen erminaion. Already a small number of long chain branching oins has a srong effec on he hysical roeries of he olymer. Transfer o olymer ofen becomes imoran a high conversion when he concenraion of olymer is elevaed. This reacion broadens he MMD. If he olymerizaion emeraure is sufficienly high, scission (see subchaer 2.3.) becomes an imoran follow-u reacion Inramolecular Transfer o Polymer Bacbiing A growing olymer chain may ransfer he radical funcion bacwards along he chain. This reacion is called bacbiing. The rae coefficien of bacbiing, bb, is higher, in case ha more sable radicals are formed. I was firs described for ehene olymerizaion. [32] Here a,4-,,5-, and,6-hydrogen shif aes lace. During olymerizaion of acrylic monomers, only bacbiing via a -5-hydrogen shif is significan. [33] As for inermolecular ransfer, his shif ransforms a secondary ino a eriary radical, also called MCR. The higher sabiliy of he eriary radical maes bacbiing an enhalically-driven rocess. In Figure 2- he mechanism of bacbiing is deiced, which occurs via an inermediae six-membered ring. 20

29 Theoreical Bacground Figure 2- The mechanism of bacbiing is shown for a growing chain in acrylic acid olymerizaion. Firs, he radical funcion (mared red) is locaed a he end of he chain (mared urquoise). Then a six-membered ring is formed and one elecron from he bond of he hydrogen aom aached o he carbon aom five bonds bac in he chain (mared green) forms ogeher wih he elecron of he original radical funcion a new bond beween he hydrogen aom and he end of he chain. By his rocess a new radical funcion is formed a he osiion of he rimordial hydrogen bond. The only difference beween MCRs formed by iner- and inramolecular chain ransfer is he osiion in he chain, o which he radical funcion is ransferred. If necessary o secify, in his wor, shif and s MCR denoes an MCR formed by an,5-hydrogen l MCR hose wih he radical funcion somewhere in he chain. MCRs can add monomer and hus be reransformed ino SPRs. This is shown in Figure 2-2. Noe ha i was calculaed for BA, ha he newly formed SPR reacs wih differen rae coefficiens as normal SPRs. [34] This should be rue for all acrylae-ye monomers. Figure 2-2 The mechanism of MCR-roagaion is shown for an MCR of acrylic acid. By adding monomer, an MCR is ransformed bac ino an SPR, which has an addiional shor branch (mared urquoise). 2

30 Chaer 2 Significan bacbiing maes reacion ineics more comlicaed. Firs, he bacbiing iself has o be considered: R SPR, i bb R MCR, i Addiionally, roagaion has o be disinguished: R M R s SPR, i SPR, i R M R MCR, i SPR, i And he same alies o erminaion: R R P P P ss SPR, i SPR, j i j i j R R P P P s SPR, i MCR, j i j i j R R P P P MCR, i MCR, j i j i j Bacbiing has a srong effec on rae of olymerizaion and roduc roeries. The laer effec led o is discovery. [32,35] MCRs are more sable han SPRs and hus roagae much slower, e.g., in AA olymerizaion a 50 C he raio s o is [36,37] This means R P is slowed down by he bacbiing reacion and eq. (2.4) has o be ransformed ino eq. (2.6), which resuls in an effecive value defined by eq. (2.7). 22

31 Theoreical Bacground dc d M s s cm c x R SPR c M c x R MCR c M cspr c M c MCR (2.6) s effecive x (2.7) SPR The reducion of effecive roagaion leads o lower olymer molecular mass. If a seady-sae assumion is made: dc MCR /d = cons. (comare subchaer 2.2.4) and ransfer o monomer lus scission (see subchaer 2.3.) is ignored, he fracion of MCRs may be esimaed by eq. (2.8). [38] x c MCR bb MCR s cspr cmcr cm 2 cmcr 2 cspr bb (2.8) Major simlificaion may be achieved wih he so-called long-chain hyohesis, i.e., i is much more robable for an MCR o add o a monomer molecule han o erminae s or undergo ransfer reacions cm r,m cm 2 cmcr 2 cspr : x MCR bb M bb c (2.9) There is some indicaion ha he radical funcion of an MCR formed by bacbiing can move furher bac along he chain, ransforming ino an MCR, which is similar o hose formed by inermolecular ransfer. [34,39] There is no enhalical gain by his rocess, bu acivaion energy has been calculaed o be raher low for BA, maing i a relevan mechanism. [34] I was calculaed ha an bacbiing again, because is geomery favors i. [34] s MCR is liely o undergo 23

32 Chaer 2 Huchinson e al. [40,4] found ha bacbiing can be influenced by he choice of solven. They hyohesize ha hydrogen bond ineracions beween he growing chain and solven molecules siffen he chain hence hindering is bacward movemens reducing he rae of bacbiing. Shor-chain branching has consequences for olymer roeries ha differ from he ones of long-chain branching β-scission Reacion The -scission means he breaage of he C-C-bond in -osiion o he carbon aom bearing he radical funcion. Therefore, a scission of he carbon bacbone of he olymer chain aes lace. If his haens o an SPR, he reacion is he reverse of roagaion, forming a monomer and a olymer chain shorened by one; his is why i is called deroagaion. Deroagaion has a higher acivaion energy han roagaion. The emeraure, a which he rae of deroagaion becomes as fas as he rae of roagaion, is called ceiling emeraure. As he rae of roagaion deends on monomer concenraion, he ceiling emeraure also deends on i. Above he ceiling emeraure, olymerizaion is no longer ossible. If he sli comes abou for an MCR, i is convered ino an SPR and a dead olymer chain wih an unsauraed end-grou. Wih is erminal double-bond i can funcion as a monomer, hus i is called macromonomer, MM. -scission can go o boh sides. s This is esecially imoran for MCR, because here, deending on he side of scission, eiher a real MM or a hree-monomer-uni-mm can be buil. Labeling he laer macromonomer may be acually misleading. Ye, in his wor, hey are sill called MM for reasons of coninuiy. 24

33 Theoreical Bacground Figure 2-3 The mechanism of -scission is shown for an MCR of acrylic acid. -scission of MCRs can have a srong effec on reacion ineics and roduc roeries. Follow-u reacions are as follows. An MCR formed by bacbiing may undergo -scission in eiher direcion. denoes he rae coefficien of -scission: R R MM R MM s MCR, i SPR, i2 2 SPR,3 i3 An SPR can add o an MM and form an MCR wih he radical funcion somewhere on he chain:,mm R MM R i j l MCR, i j This radical can aferwards add monomer (or erminae) consequenly forming a long-chain branching oin: R M R i j l MCR, i j SPR, Bu i can also undergo -scission again: 25

34 Chaer 2 R R MM R MM l MCR, i j SPR, i j SPR,j i Polymerizaion ineics of BA a high emeraure including -scission and follow-u reacions have been modeled successfully. [42,43] Reardaion and Inhibiion If he radical funcion is ransferred o a small molecule and he roduc reiniiaes very slowly or no a all, he former rocess is called reardaion and he laer inhibiion. The chemical secies are called reardan and inhibior, resecively. Reardans decrease he rae of olymerizaion. Inhibiors reven he olymerizaion from aing lace unil hey are used u (inducion eriod). I should be noed ha his designaion is no handled very consequenly. Transfer o olymer which can slow down he rae of olymerizaion a lo (vide sura) is called ransfer noneheless. There are no only ransfer-ye reardans and inhibiors, bu also addiion-ye reardans and inhibiors. A ransfer-ye inhibiion: r,x R X P X i i An addiion-ye inhibiion: r,x R X P- X i i Boh radicals formed in hese reacions do neiher roagae nor iniiae. Ofen hey sill erminae. 26

35 Theoreical Bacground Kineics may become very comlicaed, because under differen condiions chemical secies may lay differen roles. From he earlies days of olymerizaion research i is nown ha oxygen iniiaes olymerizaion. [44] On he oher hand i is he mos abundan of he addiion-ye inhibiors. I adds o growing chains raidly. This reacion is robably diffusion conrolled. [45,46] The so-formed eroxide radical does no roagae. Peroxides or hydroeroxides formed by his rocess dissociae a high emeraure forming radicals, which can iniiae radical olymerizaion. For ha reason, here is even a second mechanism of iniiaion. Peroxides ha do no decomose during he olymerizaion rocess remain in he roduc reducing is qualiy. Hence oxygen lays an ambiguous role in olymerizaion ineics. [47] Usually, i is aemed o remove i comleely from he reacion mixure. Ofen unwaned imuriies funcion as inhibiors or reardans. Inhibiors are added o all monomers o ee hem from olymerizing during sorage and ransor. In his conex, hey are someimes called sabilizers. In indusrial racice, inhibiors are usually no removed bu jus comensaed for by addiional iniiaor. Common inhibiors are, e.g., quinone, hydroquinone, which is oxidized o quinone by oxygen, and hydrochinone monomehyl eher. The laer is only effecive in combinaion wih oxygen. 2.4 Influences on Rae Coefficiens In his subchaer differen influences on rae coefficiens are discussed. Lie all chemical reacions he sub-ses of radical olymerizaion deend on emeraure and ressure (see subchaer 2.4.). For some chemically conrolled reacions, here is a disinc deendence of rae coefficiens on concenraion. This is above all rue for aqueous sysems (see subchaer 2.4.2). In general, hese sysems exhibi more comlicaed olymerizaion ineics han organic sysems. By ionizing or roonaing comonens heir elecronic srucure and hus chemical reaciviy is alered; moreover, diffusion rae is modified as well (see subchaer 2.4.3). 27

36 Chaer 2 Some sub-ses of radical olymerizaion are no governed by he chemical reacion iself. To undersand his i has be o be aen ino accoun ha all chemical reacions wih moleculariy oher han uniy are receded by muual aroach of he reacans by diffusion. This way he rae coefficien can be sli ino a diffusiondeenden erm and a chemical-reacion erm as given by eq. (2.20). (2.20) diffusion chemical reacion If he firs erm of eq. (2.20) RHS redominaes, he reacion is considered o be diffusion conrolled. If he second erm redominaes, he reacion is considered o be chemically conrolled. Terminaion, iniiaor efficiency [48], inhibiion and caalyzed chain ransfer [49] are generally considered o be diffusion conrolled, while iniiaor decay, iniiaion, roagaion and ransfer are generally considered o be chemically conrolled. The diffusion se may be described by he Smoluchowsi equaion: [50] X Y 4 N D D r r (2.2) A c,x c,y X Y Here N denoes he Avogadro consan, D and D are he diffusion coefficiens A of he reacing secies X and Y, and r c,x and r c,y are he caure radii of X and Y, resecively. Therefore, he corresonding rae coefficien of he diffusive se is roorional o he sum of he diffusion coefficiens of he wo reacing molecular secies. Under he assumion of negligible ionic ineracion, he individual diffusion coefficiens may be aroximaed by he Soes Einsein equaion: [5] 28

37 Theoreical Bacground D T B S (2.22) 6 rh, X sands for he Bolzmann consan, T for he hermodynamic emeraure, r B h,x for he hydrodynamic radius of X, is he dynamic viscosiy of he soluion. Diffusion rae is decreased owards larger size and owards higher viscosiy of medium. Ofen in chemisry caure radii and hydrodynamic radii are of similar size. Thus canceling ou each oher afer combining eq. (2.2) and eq. (2.22).However, his is no rue for growing olymer chains, which have one disinc cenre of reaciviy, he radical funcion, ha does no change in size, while he res of he molecule vary a lo. This chain-lengh deendence is discussed in subchaer Eq. (2.22) conains viscosiy as well, which in many cases augmens dramaically during he course of olymerizaion. Thus, rae coefficiens will no say consan wih increasing conversion. Effecs of varying concenraion and ionizaion also maer wih he reamen of conversion deendence. This is addressed in subchaer There are a lo of henomena ha influence and deending on solven differen ones are of imorance. A good overview, also on asecs no imoran in his wor, is given elsewhere. [0] 2.4. Temeraure and Pressure The mos widesread mehod o describe he emeraure deendence of rae coefficiens is eq. (2.23), he Arrhenius equaion, derived by van Hoff [52] and Arrhenius [53] based on hermodynamic heory: E R T A Aex (2.23) 29

38 Chaer 2 The rae coefficien deends on a emeraure indeenden re-exonenial facor, A, he acivaion energy, E A, he gas consan, R, and he absolue emeraure, T. For diffusion-conrolled reacions, E A is he same as for fluidiy, he reverse of viscosiy (comare eq: (2.2) and eq. (2.22)). The laer is assumed o be a fracion of he energy of vaorizaion. For molecules ossessing sherical symmery, i is /3, for nonsherical molecules i is less, usually /4. [54] If hydrogen bonds are resen in he solven, he acivaion energy decreases owards higher emeraure due o reduced srengh of he hydrogen bonds. [55] In fac acivaion energy is ressure deended, bu as a convenion, ressure deendence is u ino he re-exonenial facor, A. Following his, a ressureindeenden re-exonenial facor, A, can be defined (eq. (2.24)) A low isohermal comressibiliy or in case of firs-order reacions boh emeraure and ressure deendence may be reresened by he raher simle eq. (2.25), which is an exension of eq. (2.23). V A A ex R T (2.24) A ex E A V R T (2.25) A ambien ressure, acivaion energy and can be negleced. V is normally lower han he error of measuremen of Concenraion For ideal olymerizaion ineics, rae coefficiens are considered o be indeenden of he concenraions of comunds. Ofen, his is assumed for real olymerizaions as well, bu for boh diffusion-conrolled and chemically-conrolled olymerizaion reacions, he rae coefficiens may vary significanly wih concenraion. 30

39 Theoreical Bacground A differen comosiion obviously leads o a differen viscosiy. Hence, all diffusion-conrolled raes (erminaion, iniiaor efficiency, inhibiion and caalyzed chain ransfer) are affeced. Following eq. (2.22) and eq. (2.2) heir rae coefficiens increase and decrease wih fluidiy. Someimes a small change of one comonen has a large imac on viscosiy. Less obvious is he concenraion deendence of chemically conrolled rae coefficiens. Iniiaor decay can be influenced a lo by oher comonens in a hardly redicable way, e.g., rae of decomosiion of sodium ersulfae is increased by a facor of u o seven in he resence of acrylic acid, bu deending on concenraion and ionizaion of monomer i can also be decreased. [56] A secial case, which will be discussed in greaer deail, is he rae coefficien of roagaion,. In he lae 90ies i was begun o measure roagaion rae coefficiens for olymerizaions in aqueous soluion by PLP SEC (ulsed laser olymerizaion size exclusion chromaogrohy) a mehod suerior over he older roaing secor echnique. I has been found ha deends on monomer concenraion. Several exlanaory aroaches were made for hese asonishing resuls: Firs, waer-soluble monomers lie acrylic acid and mehacrylic acid (wo of he earlies examined monomers) end o associae wih each oher forming a variey of differen dimers u o oligomers. Changes in he solven o monomer raio necessarily lead o differen amouns of he various associaions of monomer. Under he assumion ha hese monomer associaions show differen reaciviies, he rae has o deend on monomer concenraion. [57] This would mean ha reaciviy in olar organic solvens, e.g., ehanol or dimehyl sulfoxide changed in a similar way as in waer, bu his is no he case. [58] This heory has been discarded. Second, he local concenraion may be differ from overall concenraion. Usually, i is assumed ha overall monomer concenraion is idenical o he local monomer concenraion in close roximiy o he radical cenre. If overall and local monomer concenraions are differen, following eq. (2.4) will aear higher han he same facor as he local concenraion is higher as he overall concenraion. However, in case of olymerizaions in aqueous soluion, his assumion requires an enormously large difference a facor of en. A low monomer concenraions almos all monomer molecules would have o be siuaed in he direc viciniy of macroradicals. As a consequence, he reacion soluion consiss of a few radicals wih associaed monomer molecules dissolved in almos ure waer. [59] In addiion olymer in he reacion mixure does no influence. [9] If he olymer colleced monomer from he 3

40 Chaer 2 soluion o achieve he elevaed local concenraion, addiional olymer would reduce he measured.this heory is now considered dismissed. Third, he corresonding reacion is chemically conrolled and hus he rae coefficien can be described by he Eyring equaion, eq. (2.26), which assumes he reacans o go hrough a ransiion sae (TS) as he highes oin of he ass. [60,6] If i is a genuine ineic effec, i can be exlained by his equaion. T Q E 0 h Q Q B T B ex M R (2.26) Q sands for he ariion funcions of secies, denoes he ransiion sae. is he ransmission coefficien ( or less), h he Planc consan, and E 0 he zero-oin energy difference beween educs and ransiion sae. The ransmission coefficien is indeenden of he concenraions of he comonens in he reacion mixure. Thus, here remain only wo ossibiliies. Eiher he ariion funcions are influenced consequenly shifing he Arrhenius refacor (comare eq. (2.23)) or he zero-oin energy difference and he acivaion energy (comare eq. (2.23)), resecively. Deailed examinaion of he emeraure deendence of of MAA has shown ha E is almos in A sensiive owards a variaion of monomer conen wihin a large concenraion range and i is rimarily A ha varies. [59] Consequenly, he ariion funcions have o be influenced by he solven environmen. Gilber e al. [62] calculaed ha he effec is due o differen exens of hindrance o inernal roaion (vibraion wih an acivaion energy in he order of magniude of a roaion) in he ransiion sae (TS) srucure for roagaion. The solven molecules in he surrounding area of he acivaed comlex may imose a hindrance o he inernal roaion of he acivaed comlex deending on how srong hey are aached and how big hey are. The sronger inermolecular ineracions of he acivaed comlex wih an environmen ha basically consiss of monomer molecules resul in a lower mobiliy of side grous and hus lead o a reduced re-exonenial facor owards higher monomer conen. [9,59]. The same grou [63] has found in a newer invesigaion again hrough calculaion ha a differen solven field causes a differen acivaion energy. They found for he 32

41 Theoreical Bacground roagaion of AA ha he acivaion energy in oluene reresening non-olar solvens is as in he gas hase while i is considerably reduced in a waer environmen. The level of accuracy, however, was no sufficien for quaniaive accuracy. The variaion of E was ascribed o beer resonance sabilizaion of he A TS in he olar solven, and beer mixing of he molecular orbials of he reacans, assising in he ransfer of elecrons from he monomer o he growing chain. In anoher calculaion of he olymerizaion of MAA and AA he exerimenal finding was confirmed ha he rae acceleraion of boh olymers in waer is mainly due o enroic raher han elecrosaic effecs. Degirmenci e al. also calculaed he difference of he s of MAA and AA arises mainly from seric hindrance of he mehyl grou and no from difference in elecronic srucure. [64] For AAm, calculaions ha comare roagaion in gas hase wih hose in aqueous hase conclude ha acivaion energy is reduced. [65] Exerimenal resuls for - vinylyrrolidin-2-one [66] and N-vinylformamide, [67] sugges as well ha E varies A wih solven conen, alhough no in a way ha could exlain he deendency of on c. M Overall, he influence on in aqueous soluion is mosly based on an aleraion of he enroy of he ransiion sae, bu here is an also a smaller effec on subchaer 5..2, his is discussed in deail including new resuls for. E. In A Ionizaion Shifing he H of a reacion mixure away from is naural value by addiion of acid or base can have an enormous influence on reacion ineics. Boh diffusion and chemically conrolled reacions are affeced by various mechanisms. The effec of ionizaion on he rae of olymerizaion has been invesigaed by several grous. The bes invesigaed monomers are acrylic acid and mehacrylic acid. [,2,68-80] Alhough, mos grous did no now a he ime of ublicaion ha acrylic acid undergoes bacbiing (see 2.3.3) during olymerizaion. To characerize he ionizaion of monomer and olymer, he degree of ionizaion,, is defined by eq. (2.27). 33

42 Chaer 2 n ionizing agen (2.27) n ionizable grous Firs, densiy changes wih ionizaion. Therefore, a differen concenraion alies for he same mole raio of monomer o solven. Ionized molecules are referably locaed near o conrary charged ions, hus he local concenraion of charged monomer near o charged monomer or a charged growing chain is lower han he overall concenraion. If he monomer has ionizable funcionaliies, he corresonding olymer has hem as well. The K and A K value of he olymer B are differen from he values of he monomer. [8,82] Thus, olymerizing wih iniially arly ionized monomer, he degree of ionizaion of monomer and olymer is differen for he same H and change during olymerizaion. In dealing wih olyions, in addiion o H, anoher facor has o be aen ino accoun, he ionic srengh, I, given by eq. (2.28). I c z 2 2 i i (2.28) i z is he charge number of he ion. The degree of ionizaion of olymer and ionic srengh have an enormous effec on he srucure of olymer. [82-87] As more and more side grous become ionized, Coulomb reulsion leads o a widening of he olymer coil. However, higher ionic srengh, hus more couner ions, weaens his effec. Screening by couner ions may even lead o a olymer srucure of he ionized olymer lie he one of he non-ionized olymer. [84,85,87] Addiion of sals mos ofen increases viscosiy, which can be calculaed raher easily. [88] However, ionized monomer and olymer mae he redicion of soluion viscosiy more comlicaed. The equaions used in he revious subchaers o calculae he influence of viscosiy on diffusion-conrolled reacions (eq: (2.22) and eq. (2.2)) are insufficien in his case, because diffusion of charged secies canno be described ignoring Coulomb ineracion. 34

43 Theoreical Bacground The invesigaion ino he olymerizaion of ionizable monomers has been focused on he wo commercially mos imoran ones: acrylic acid and mehacrylic acid. All wors agree in ha he iniial rae of olymerizaion decreases owards higher degree of ionizaion of monomer (AA and MAA) and increases again wih even higher degree of ionizaion, alhough he increase by overiraion is higher for AA. II[2,68-75,78-80] The same rend was found for molar masses of olymer roduc. Mos grous found his minimum a full ionizaion, bu Cuié e al. discovered ha he minimum of rae of olymerizaion is shifed owards lower degrees of ionizaion wih higher emeraure. [80] In addiion, he differen exerimenal sudies differ a lo wih resec o he magniude of he decrease of he rae of olymerizaion wih higher. The sronges effec was found by Kabanov e al. [2] who observed a 50-fold decrease in overall rae from olymerizing non-ionized AA o olymerizing fully-ionized AA. III Comarison of raes of olymerizaion wihou undersanding he deendencies of individual reacions can be roblemaic. The H value or he ionizaion of monomer can have surrising effecs on chemically conrolled reacions lie he iniiaor decay. One examle ha may illusrae he roblems, which iniiaors can cause, shall be given here: In an early wor, Kachalsy and Blauer [83] reored ha monomers wih a carboxyl grou did no olymerize if his funcion were ionized. This way hey exlained he decline in rae of olymerizaion hey found wih higher H. Laer i was oined ou by Pinner [72] ha heir iniiaor of choice (hydrogen eroxide) does no wor under oo basic condiions. Afer his was ublished, Blauer erformed more exerimens wih a differen iniiaor (AIBN and 4 % ehanol o mae i soluble) and olymerized fully ionized MAA successfully u o H 2. [73] Only a few auhors ried o undersand he olymerizaion ineics in deail. An ousanding exceion is he ah breaing wor by he grou of Kabanov. [2,69] They exlained boh he reducion of overall rae and he decrease of molar masses of olymer wih increasing by a reducion of hrough Coulomb reulsion of he ionized growing chain and he ionized monomer. The finding of increasing rae and molar mass wih overiraion was exlained as a -effec as well. They concluded ha an ion air mechanism increases roagaion. A couner ion,, e.g., a sodium caion, can bring a monomer anion and he end of he olyanion, i.e. he growing chain, ogeher having one of hem a each side so hey may reac. As he number of II The reader should noe ha he degree of ionizaion is defined here in a way ha a value of more han one is ossible. Addiional neuralizing agen afer full ionizaion is couned as well. III Their overview grah (Fig. in he aer cied) of iniial rae of olymerizaion for AA and MAA as a funcion of H beween and 4 is reroduced in many oher wors. Unforunaely, in he English ranslaion from he Russian original he labels in he grah were swaed (No. is AA and no MAA). 35

44 Chaer 2 couner ions rises, his effec becomes more and more imoran enhancing. This is suored by heir finding ha addiional sal has qualiaively he same effec as overiraion. The quaniy of he effec deends on he naure of he couner ion (v.i.). Furhermore, hey found an increase of aciciy of he newly roduced olymer in he same way as hey found an increase of rae wih overiraion, i.e. more sal had a sronger effec on fully ionized monomers and differen couner ions varied in heir effeciveness, e.g., 2-mehylroan--aminium lead o a higher ercenage of syndioacic riads in MAA han ammonium (u o 87 %). This was exlained by van-der-waals ineracion beween mehyl grous. Moreover, lower emeraure led o higher aciciy. By olymerizing a he highes ionic srengh, hey even roduced crysalline AA ha had he same inerlanary disances as AA roduced by hydrolysis of syndioacic oly (isoroyl acrylae). Measuring has gained recision in comarison o he roaing secor mehod by he develomen of he PLP SEC mehod (ulsed laser olymerizaion carried ou in conjuncion wih size-exclusion chromaograhic), u forward by Olaj e al. [5,89] SEC of olyacids may be erformed afer eserficaion [57,90] or direcly by aqueous hase SEC. [9] The laer being he referred mehod. This mehod has been emloyed o measure values of MAA and AA as a funcion of concenraion and degree of ionizaion direcly. [,76,92] The bes invesigaed monomer considering he influence of degree of ionizaion and concenraion is MAA. As he influence of ionizaion seems o be he same for boh MAA and AA, [] only MAA is discussed here. The rae varies enormously as a funcion of boh monomer concenraion and degree of ionizaion [9,,58,59,9,92] e.g., decrease by abou one order of magniude in assing from dilue aqueous soluion of non-ionized MAA o eiher bul olymerizaion of nonionized MAA (as discussed in subchaer 2.4.2) or o fully ionized MAA in dilue soluion. Lací e al. [] have develoed an emirical equaion, eq. (2.29), ha incororaes boh influences over a broad range and covers a wide emeraure range as well ex 0.08 ( 0.08) ex5.3 w T /K 2 w w (2.29) 0 ;0.05 w 0.40;6 80 C 36

45 Theoreical Bacground Their findings for MAA olymerizaion should be ransferable o he olymerizaion of oher monomers (no only AA) in ionized or arly ionized form in aqueous soluion a leas for similar monomers. The lo of eq. (2.29) is given in Figure 2-4 o visualize he comlex relaionshi. The variaion of wih monomer conen is weaer for arially ionized MAA and may even be reversed wih fully ionized MAA. A broader range han he sric validiy of he equaion (0.05 < w < 0.4) is loed. In addiion, for MAA olymerizaions a differen degrees of ionizaion (0 ) no effec by addiion of sodium chloride (increasing ionic srengh and number of couner ions, resecively, wihou increasing he degree of ionizaion) was found. [] Figure 2-4 The rae coefficien of roagaion of MAA as a funcion of boh weigh fracion of monomer and degree of ionizaion as given by eq. (2.29). Please noe ha alhough he full range of w is loed he equaion was only derived for 0.05 < w < 0.4. There is scarce exerimenal daa on he influence of degree of ionizaion on he rae of erminaion. Because of viscosiy increase and addiional reulsion, a reducion of he rae coefficien mus be assumed. Based on he observaion ha screening of couner ions can lead o a srucure lie he non-ionized olymer chain, one may 37

46 Chaer 2 assume ha screening of couner ions can increase of ionized growing chains may be even u o he oin ha he reducion by Coulomb reulsion becomes comensaed. Exerimenal daa, e.g., by Kabanov [2] e al. did no resen his effec. Laer, Anseh e al. [78] found a reducion of wih ionizaion of olymer, which could be arly comensaed by an increase of he number of couner ions. However, as heir measuremen of / was done afer s of dar ime, one should be raher cauious wih hese exerimens. In a more recen se of exerimens [36] i was shown for non-ionized AA ha radical concenraion has faded ou comleely afer s (SPR) and 0.6 s (MCRs) dar ime, resecively. In a new sudy, radicals during olymerizaion of fully ionized AA were invesigaed direcly by EPR. [77] was found o decrease by abou a facor of 5 from 0 cg g AA o 20 cg g sodium acrylae (NaA) Chain Lengh The influence of chain lengh is ignored in ideal olymerizaion ineics. Nowihsanding, i would be more correc o wrie he rae coefficiens for roagaion and erminaion as and, resecively. The guilleme indicaes ha he rae coefficiens are chain-lengh averaged. Ofen i is omied for reasons of convenience. Chain-lengh deendence of roagaion and erminaion is of comleely differen naure, as he former coefficien is chemically conrolled while he laer is diffusion conrolled. Chain-lengh deendency of erminaion resuls from an increase of he hydrodynamic radius (see eq. (2.22)) while he caure radius says he same or changes slighly only (see eq. (2.2)). This is no a all rivial. The hydrodynamic radius is a funcion of olymer ye and chain lengh as well as solven and emeraure. The caure radius may be influenced by more or less effecive shielding by he long unreacive chain aached o he reacive radical cener. Diffusion coefficiens of olymers usually follow a ower-law exression. [93,94] To illusrae his, one examle is given in Figure 2-5. The diffusion coefficiens of AA are loed for differen molar masses ( M, weigh average molecular mass) and are bes reresened by he exression: w D 2. 0 M cm s. The reader may w noe he similariy o eq. (2.30) which will be inroduced nex. 38

47 Theoreical Bacground If jus one chain lengh, i, is reaed, he chain-lengh-deenden erminaion (CLDT) may be given by a ower.law funcion, which follows he form found for diffusion of olymers hrough a soluion i ii, 0 l (2.30) denoes he rae coefficien of erminaion of wo radicals of idenical chain ii, 0 lengh i. Here, is he rae coefficien of erminaion direcly exraolaed from long-chain regime o boh chain lenghs being uniy. l describes chain-lengh deendency. 0-6 D / cm 2 s M w / g mol Figure 2-5 The selfdiffusion coefficiens of AA for differen molar masses are loed. AA is fully ionized and 0.0 mol L NaCl is added. The solid viole line is he bes ower-law fi. The exonen is Daa is aen from lieraure: red circles, [82] blue squares. [95] There is usually a disribuion of chain-lenghs and wo chains erminaing mosly will have differen chain-lenghs. There are hree ways under discussion, by which erminaion of radicals of arbirary size is described bes. These are he diffusion mean, eq. (2.3), he geomeric mean, eq. (2.32), and he harmonic mean, eq. (2.33). 39

48 Chaer 2 (2.3) 2 0 i,j l l i j l i,j 0 2 (2.32) ij 2 i j i j i,j 0 l (2.33) In case of i j all hree equaions are ransformed bac ino eq. (2.30). Under many condiions, he resuls from eq. (2.3), eq. (2.32), and eq. (2.33) are very similar and a condiions, under which he exressions redic quie differen -values, he rae coefficien is difficul o measure wih he required accuracy. [96] The geomeric mean model is comuaionally less demanding. The diffusion mean is he hysicochemically mos lausible. If eq. (2.30) reresened he chain-lengh deendence of correcly, i would be ossible o measure chain lengh deendency in he domain of long chains and exraolae bac o chain lengh uniy or vice versa as his can be done wih diffusion coefficiens. I was found ha such exraolaion does no wor. In order o exlain his, he comosie model was develoed. [97] I saes ha erminaion follows ure cenre-of-mass diffusion only u o a cerain chain-lengh he crossover chainlengh, i c, afer which enanglemen becomes imoran. In his second region segmenal diffusion is dominan. Thus, wo differen equaions are needed deending on he chain lengh of he erminaing radicals. These are given as eq. (2.34). For chains wih i below i c, a differen exonen alies han for chains wih i above han i c. i i i ii,, s c i i i i i ii,, sl l 0 l c c (2.34) 40

49 Theoreical Bacground, reresens he coefficien for wo chains wih chain lengh uniy. The essenial, 0 message is ha is no, he coefficien from direc exraolaion from long chain o chain lengh uniy. is he exonen of chain-lengh deendency in he s region of shor chains. I is in he range of 0.5 o.0. For larger radicals wih chain lenghs above he crossover chain lengh, i c, which is in he range of 30 o 00 i, i monomer unis, he decrease of wih is less ronounced wih he exonen, l, being in he range of 0.6 o This model was confirmed exerimenially for all monomers sudied so far by differen echniques. Mos noable of hese is single ulse ulsed laser olymerizaion in conjuncion wih elecron aramagneic resonance secroscoy (SP PLP EPR). The majoriy of exising SP PLP EPR sudies has been carried ou on mehacrylae-ye monomers. [7,98-03] as given by he comosie model is loed in Figure 2-6 wih yical values. 0.6 is he heoreical value of l for wo radical ceners locaed a he end of he chain in good solvens. [04-06] If he wo radical ceners are no locaed a he end of heir chain wih one being siuaed somewhere in he middle, he heoreical value of l will become 0.27, and if boh of hem are somewhere in he chain, i will become [06] So far, here is no exerimenal daa o suor he laer wo coefficiens, while he firs is in close agreemen wih values found exerimenally. [7,99,00,07,08] A good overview of measured values for in general and also of values for chainlengh deendency is given elsewhere. [07] 4

50 Chaer 2 0 8, = 0.6 / L mol s i c =00 = cener-of-mass diffusion is dominan segmenal diffusion is dominan i Figure 2-6 The rae of erminaion for wo chains of idenical lengh following he comosie model (eq. (2.34)) is loed as solid line and he bac exraolaion from long-chain region (eq. (2.30)) is loed as dashed line. The wo lines merge a he crossover chain lengh, ic. Tyical arameers for a good solven are chosen. The comosie model may exlain he raio of long-chain of syrene o long-chain of mehyl mehacrylae (MMA). [09] The diffusion coefficien of MMA is slighly above he one of syrene. Thus, one would exec ha of MMA were higher as well. Surrisingly, comaring he long chain behavior, of syrene is higher by more han a facor of wo. Deailed ineic analysis o he shor-chain region has revealed ha MMA exhibis a higher i c and a higher s. The combinaion hereof leads o lower long-chain -values even wih a higher,. On he oher hand, he wo monomers exhibi very differen values. Hence, he comarison of long-chain -values is conduced beween wo quie differen chain lenghs, his migh as well exlain he difference. This quesion will only be solved finally, afer of syrene will have been measured wih sufficien recision., i and, c s The diffusion-conrolled naure of ossible value for allows for an esimae of he maximum given by eq. (2.2) and eq. (2.22), which is called he diffusion, limi. A his, one more asec has o be considered: When he wo radical ceners 42

51 Theoreical Bacground reac, he affeced wo radicals combine, which resuls in one of hree ossible rile saes or one ossible single sae. [0] Only he single leads o a sable molecule. I is ossible (bu unliely) ha iner-sysem crossing aes lace and i is ossible ha sins fli hrough sroes o neighboring molecules while he wo radical ceners are sill ogeher in he solven cage. They hi each oher and he surrounding molecules around 00 o 000 imes before hey leave he solven cage again. Thus, he value of from he diffusion limi has o be correced by a facor beween 0.25 and. The acual values of are always even lower han he diffusion limi, because seric hindrance may reduce he effecive caure radii. CLDT has been roughfully sudied a low degrees of monomer conversion. No clear icure on CLDT a moderae and high conversion has emerged so far. Wor abou chain-lengh deendency varying wih conversion is scarce. Alying he SP PLP NIR mehod, i was found for buyl mehacrylae and er-buyl mehacrylae, ha says consan u o a cerain degree of monomer conversion (ca. 0.3 in case of erbuyl mehacrylae), hen increases linearly by abou a facor of 4 u X = 0.5; aferwards boh 0, which has sayed consan ha long, and decrease linearly; reaches 0 a abou X = 0.7. [08] However, SP PLP NIR does no rovide direc access o CLDT. Moreover, he rocedure is edious. [] The combined deendence on chainlengh and conversion was also invesigaed by he RAFT CLD T mehod. I was found ha chain-lengh deendence becomes more and more ronounced owards higher conversion and ha i declines wavelie. [2] An exended comosie model was roosed, in which here is in addiion o he crossover chain-lengh anoher urnover oin for even higher chain lengh. This chain-lengh mars he onse of he gel oin. A his oin, jums from a value of abou 0.6 o abou uniy. [3-5] The RAFT CLD T mehod suffers from he inheren roblem ha he RAFT agen influences he ineics. The resuls found for low conversion, which region is quie well invesigaed, are in some cases conradicory o exerimens wihou RAFT agen and hus he resuls for higher conversion may be wrong as well. Preferable would be a more direc measuremen, e.g., by EPR, bu his has no been aemed so far. The emeraure deendence of fluidiy (inverse dynamic viscosiy); i c, o be emeraure indeenden. [7,98-00] As, scales wih he emeraure deendence of l have exerimenally been found i is assumed o deending on chain s, and flexibiliy, is lac of emeraure deendence is raher surrising and fuure exerimens covering an even broader emeraure range are required. Exerimenal roof for chain-lengh-deenden roagaion (CLDP) has been found indirecly by ulsed laser olymerizaion size exclusion chromaograhy (PLP SEC) c 43

52 Chaer 2 exerimens [6] and ulsed laser olymerizaion marix-assised laser desorion ionizaion ime-of-fligh mass secromery (PLP MALDI ToF MS) [7] hus excluding SEC arifacs. The basic idea is ha he reacive cener a he end of he chain canno see he res of he chain; accordingly, here canno be a chain lengh deendence for chemically conrolled reacions exce for very shor chains. In case of high chain ransfer or very high rae of iniiaion, his siuaion may aly. I has been roosed by Smih e al. [8] o reresen CLDP by his equaion: ln / 2 i ex i /2 i (2.35) i The rae coefficien of roagaion a chain-lengh i,, decreases from he highes value a chain lengh uniy,, wih a half-life chain lengh, /2 i, o reach he normal value i.e. he value of he rae coefficien of roagaion for log chains,., 6x / L mol s s / L mol s 5x0 3 4x0 3 3x0 3 2x0 3 x i 0 3 / L mol s 0 9 i /2 i c l i Figure 2-7 In order o illusrae he difference beween CLDT (red) and CLDP (blue) boh have been loed for mehyl mehacrylae bul olymerizaion a 25 C. Boh ordinaes are 44

53 Theoreical Bacground scaled o cover wo orders of magniude o mae he curves more comarable. In he region of very shor chains, decreases less wih chain lengh han bu i ees declining, while says consan afer a few addiions. The rae coefficien of erminaion has been loed according o eq. (2.30) (simle exonenial, shor dash) and eq. (2.34) (comosie model, solid line). The values were aen from lieraure: [03,9], = L mol s ; s = 0.63; ic = 200; l = 0.7. The rae coefficien of roagaion has been loed as consan (value a high chain lengh, shor dash) and according o eq. (2.34) (exonenial decay, solid line). The values were aen from lieraure: [6,8] = L mol s ; = 5.8 ; s = 0.63; i/2 =.2. Eq. (2.34) is loed in he inser wih axes scaled linearly. In order o comare he effecs of CLDT and CLDP boh ogeher for MMA bul olymerizaion a 25 C in Figure 2-7. and were loed I should be noed ha no all calculaions suor a higher for he firs addiion ses, e.g., for buyl acrylae and vinyl chloride even a sligh increase or a o and fro over he firs four ses was comued, resecively. [34,39] Conversion During he course of conversion, all effecs of concenraion as discussed in subchaer aly as he concenraion of monomer declines wih conversion and in case of arially ionized or roonized monomer he degree of ionizaion of monomer may change wih conversion, which has consequences on he ineics as discussed in subchaer Aar from ha, viscosiy increases during he course of olymerizaion, which is deal wih in his subchaer. As all chemical reacions wih moleculariy oher han uniy are receded by muual aroach of he reacans by diffusion and diffusion rae is decreased owards higher viscosiy of medium, diffusion conrolled reacions become slower and non-diffusion-conrolled reacions may run under diffusion conrol. This can be undersood by combining he Smulochwsi (eq. (2.20)), and he Soes-Einsein equaion (eq. (2.2)) as discussed reviously in his wor (inroducion 2.4). I is imoran o undersand ha macroscoic viscosiy and he effecive viscosiy which alies for he growing radicals are no necessarily he same., a negligible conversion scales wih dynamic viscosiy,, i.e. if he value in one soluion 45

54 Chaer 2 is nown, he value in a differen solven can be rediced easily by scaling of wih he raio of recirocal soluion viscosiies: [02],,, soluion A soluion B (2.36) soluion B soluion A, Bu does no decrease by addiion of olymer o he same degree as fluidiy. This is demonsraed in Figure 2-8 (urle riangles). The same is rue for (red diamonds, blac squares, and magena riangles). 0 0 (w MAA ) / (w MAA = 0) (w MAA ) / (w MAA = 0) w Polymer / g g Figure 2-8 To comare he influence of olymer conained in he reacion mixure on and, exerimenal daa for MAA/MAA is loed. Values are given as raio o he value a zero olymer conen. Green sheres: relaive fluidiy [20], red diamonds: <> SP-PLP NIR echnique, wmaa 0 = 0.6; [2] blac squares: <> SP PLP NIR echnique, wmaa 0 = 0.6; [2] urle riangles:, SP PLP EPR echnique, wmaa = 0. olymer-remix; [20] magena riangles: <> SP PLP EPR echnique, wmaa = 0., olymer-remix. [20] I should be noed ha he olymer roduced during laser exerimens is of smaller size han he olymer used for remix and viscosiy measuremens. 46

55 Theoreical Bacground In he following secion, viscosiy and is influence on erminaion are discussed. I urns ou ha and are influenced by he resence of olymer o differen exen (Figure 2-8). The growing chains are no influenced by olymer coils around hem in he same way as wih he solven, wih which hey sand in direc conac. The exac relaionshi is no nown. In order o characerize he change in viscosiy over conversion, relaive viscosiy,, is defined as he raio of viscosiy a a cerain conversion X, X, o viscosiy a r 0 zero conversion : X r 0 (2.37) The erminaion reacion of wo macroradicals roceeds in a hree-sage mechanism according o Benson and Norh. [22,23] Firs, boh macroradicals have o come ino conac by ranslaional (cener-of-mass) diffusion (TD). Subsequenly, he radical funcionaliies have o come ino immidiae roximiy (a few Å) by segmenal diffusion (SD). The hird and final se is he chemical reacion (CR) roceeding eiher by combinaion or disroorionaion. Hence he rae coefficien of diffusion-conrolled erminaion,,d, is given by: (2.38),D,SD,TD,CR Anoher mechanism, by which wo radical ceners of growing chains can aroach each oher is reacion diffusion (RD), where radical sies advance owards each oher no by movemen of he olymer chain, bu by growing in he direcion of he oher radical cener. This erm has o be added: 47

56 Chaer 2,D,RD (2.39) A low degree of monomer conversion, segmenal diffusion mosly dominaes. The associaed rae coefficien,sd is conrolled by he ye of olymer and he viscosiy of he monomer-solven mixure. As he former is conversion-indeenden and he laer does no change much,,sd remains more or less consan, which resuls in a laeau value of u o moderae degree of monomer conversion. A higher conversion, sars o decrease noably, when TD becomes slower han SD and consiues he bole nec hus conrolling he mechanism. The,TD corresonding rae coefficien,, scales wih he inverse viscosiy of he 0 olymerizing medium. can be exressed relaive o, he heoreical,td erminaion rae coefficien under ranslaional diffusion conrol a conversion zero, and relaive viscosiy. The sar decrease of wih saying consan leads o an augmen of boh rae of olymerizaion and molar mass of olymer roduced. This is called he Norrish Trommsdorff or gel effec. [24,25] Towards even higher conversion, cener-of-mass diffusion of macroradicals essenially ceases and erminaion runs under RD conrol. Terminaion under RD condiions scales wih via he reacion-diffusion consan, C RD, which is enhanced by chain flexibiliy. Sudies ino he erminaion ineics of ehene indicaed ha he reacion-diffusion consan may be esimaed wih he hel of he volume-swe-ou model which considers he diameer of he macroradical and he jum disance. [26-28] Tyically, CRD is indeenden of emeraure, bu decreases owards higher ressure. [29,30] I should be noed ha, in his wor, TD C RD is defined differenly from some oher ublicaions, where bul olymerizaions have been analyzed and RD was correlaed wih conversion, X, via a consan C RD (see eq. (2.40)). The,TD exression of he resen wor ino soluion olymerizaion uses monomer concenraion (eq. (2.4)).,RD RD C X (2.40),RD C RD cm (2.4) 48

57 Theoreical Bacground A very high conversion and hus high viscosiy even roagaion may run under diffusion conrol. This is esecially he case for bul olymerizaions. As erminaion by reacion diffusion is roorional o roagaion, from his oin on boh and begin o decline raidly and radicals remain frozen in he olymer marix. This is called he glass effec. Diffusion conrolled may be scaled o viscosiy alying a diffusion conrolled,d 0 rae coefficien of roagaion a zero conversion,,d, and relaive viscosiy,, r which changes wih conversion. This leads o modificaion of eq. (2.20) ino eq. (2.42). (2.42) r 0 0,0,D Including diffusion-conrolled roagaion and assuming ranslaion-diffusion conrolled and reacion-diffusion-conrolled erminaion o occur in arallel, yields Equaion (8) for he overall erminaion rae coefficien of bul olymerizaion. [23,30] * CRD X r r 0 0 0,SD,TD,0,D (2.43) Informaion abou he effecive reduced viscosiy in olymer soluion is hardly available (v.s.). The variaion of relaive viscosiy has been aroximaed by an exonenial relaion conaining one single arameer C : [90] X r exc X (2.44) Combining eq. (2.42) wih eq. (2.44) yields: 49

58 Chaer 2 0 0,0,D ex C X (2.45) Combining eq. (2.43)(2.42) wih eq. (2.44) yields: * CRD X exc X exc X 0 0 0,SD,TD,0,D (2.46) These wo equaions are loed in Figure SD / L mol s gel effec TD RD 0 0 glass effec X Figure 2-9 The conversion-deendence of and loed for MMA bul olymerizaion according o eq. (2.46) and eq. (2.45). The regions of dominan segmenal diffusion, ranslaional diffusion, and reacion diffusion are mared by SD, TD, and RD, resecively. Rae coefficiens are aen from lieraure. [30,36] 50

59 Theoreical Bacground If iniiaor decay is a ruly unimolecular reacion, i should no be influenced by viscosiy. An iniiaor sysem wih higher moleculariy, e.g., a redox iniiaor can become diffusion conrolled. Iniiaor efficiency decreases as he viscosiy increases. The wo newly formed radicals remain near one anoher, i.e. in he solven cage, for a longer eriod, so hey have more ime o erminae or undergo side reacions. The ime san beween addiion of wo monomer molecules also increases wih conversion, because a very high conversion here is less monomer available. Exerimenal confirmaion for a ronounced decrease of f a high conversions has been obained from comarison of bul and emulsion olymerizaion of MMA. [3] Furhermore EPR sudies found his effec. [32-35] 2.5 Comuer Modeling of Polymerizaions The hysical roeries of a olymer derive from he funcionaliies of is monomer unis, bu also from is molecular mass disribuion (MMD) and microsrucure. Thus, wih he same monomer (comosiion) he roducion of quie differen olymers is ossible. This is one of he reasons why even hough los of new monomers have been develoed over he las decades, redominanly he same monomers as in he beginning of large-scale indusrial alicaion of olymerizaion are used. New requiremens on roducs were raher me by modificaion of roducion rocesses of exising monomers han by alicaion of new monomers. This may demonsrae he imorance of meiculous oimizaion of indusrial olymerizaion rocesses. Modeling can be used o simulae olymerizaion, e.g., conversion and hereby hea roducion, bu also all roeries of he resuling olymer as hey are deermined by he rocess. I is a more sohisicaed aroach han jus doing exerimens o see how modificaion of one arameer, e.g., emeraure, affecs ohers, e.g., M w. As far as ossible, all relevan reacions wih all heir individual deendencies are regarded searaely. Hence, secial exerimens should be carried ou o yield individual rae coefficiens. Modeling can be used o es hyohesis abou mechanisms, i.e. checing if hey lead o correc redicions, or o lan exerimens. In addiion, a model may be used for evaluaion and inerreaion of a comlex exerimen. Thus, modeling may lead o a beer undersanding of he underlying ineics. 5

60 Chaer 2 Kineic models are alied as an addiional ool for lanning new indusrial rocesses or imroving esablished ones, e.g., reducing consumion of resources or enhancing roduc qualiy. They also find alicaion in rocess conrol (online use). If i is nown, how he sysem will reac o aleraion of arameers, due o a woring model, seering also considers he develomen o come. This maes oeraion more recise hus enhancing roduc qualiy and safey of he lan. The use of deailed ineic models for inelligen rocess conrol becomes more and more widesread. Mahemaically he model consiss of a se of differenial equaions and is inegraed numerically. For a very accurae icure, i is ossible o use Mone Carlo calculaions. Mone Carlo means figuraively hrowing dice as he numerical inegraion wors wih a random number generaor. I usually requires much comuaion ime and enormous memory caaciies. These calculaions yield informaion abou individual chains wih heir secific srucure are calculaed. Mone Carlo is used, if hese secial informaion is desired. In conras o very slow Mone Carlo, he use of momens equaions is he quices way o solve he roblem, bu in his case i is no ossible o calculae disribuions and use chain-lengh deenden rae coefficiens. Calculaing including disribuions gives more informaion and allows for chain-lengh deendency, bu needs more comuaional effor. There are several mehods o achieve his. The mos wide sread sofware acage is PREDICI TM, which is also he one used in his wor. I uilizes discree Galerin mehods and allows for modeling, which involves an arbirary number of secies and chain-lengh disribuions and any number of chain-lengh deenden reacion ses; moreover here are no resricions on he form of MWD and equilibria may be involved. [37] These facors slow comuaion down and he limiaions of calculaion arise eiher from ime-consumion or from he insabiliy of he rogram. 52

61 Theoreical Bacground 53

62

63 Maerials, Exerimenal Procedures and Daa Evaluaion 3 3 Maerials, Exerimenal Procedures and Daa Evaluaion 3. Chemicals 3.. Monomers Acrylamide Acrylamide (AAm, IUPAC: ro-2-enamide, Flua, urum, 98.0 %, sabilized wih Cu 2+, IV CASRN: , M 7.08 g mol ) was used as received or recrysallized from aceone where remared. urum IV echnical informaion given by Sigma-Aldrich GmbH on inquiry 55

64 Chaer 3 Acrylic acid Acrylic acid (AA, IUPAC: ro-2-enoic acid, Merc, 99 %, anhydrous, sabilized wih hydroquinone monomehyl eher, CASRN: , used as received or urified by disillaion (v.s.) where remared. M g mol ) was AA has a Michael sysem and undergoes,4-michael addiion wih iself. Diacrylic acid (DiAA, 2-(acryloyloxy)aceic acid) is formed. Waer conaminaion and higher emeraure romoe his reacion. [38,39] Thus, sorage sabiliy of AA is limied and H-NMR was done in regular inervals o ensure DiAA concenraion being below 0.0 mol mol. Buyl acrylae Buyl acrylae (BA, IUPAC: ro-2-enoic acid buyl eser, Flua, urum, 99 %, sabilized wih hydroquinone monomehyl eher, CASRN: , M 27.7 g mol wih inhibior remover (v.i.). ) was urified by assing he monomer hrough a column filled Mehacrylic acid Mehacrylic acid (MAA, IUPAC: 2-mehylro-2-enoic acid, Merc, 99 %, anhydrous, sabilized wih hydroquinone monomehyl eher, CASRN: , M 00.2 g mol ) was used as received or urified by disillaion (v.s.) where remared. 56

65 Maerials, Exerimenal Procedures and Daa Evaluaion Sodium acrylae Sodium acrylae (NaA, IUPAC: sodium ro-2-enoae, Aldrich, urum, 97 %, sabilized wih 40 m hydroquinone monomehyl eher, V CASRN: , M g mol ) was used as received. Polymerizaion during longer sorage of several monhs was observed. H-NMR was carried ou before a se of exerimens o ensure ha monomer is no conaminaed by olymer Solvens Demineralized waer Demineralized waer (CASRN: , inernal cycle. M 8.02 g mol ) was aen from an Deuerium oxide Deuerium oxide (Aldrich or Deuero, 99.9 %, CASRN: , M g mol ) was used wihou furher urificaion. Dimehyl sulfoxide Dimehyl sulfoxide (DMSO, Grüssing, für analyische Zwece 99.5%, CASRN: , M 78.3 g mol ) was used wihou furher urificaion. o -Xylene o -Xylene (IUPAC:,2-dimehylbenzene, Sigma-Aldrich, uriss, > 99.0 %,CASRN: , M 06.7 g mol ) was used as received. V echnical informaion given by Sigma-Aldrich GmbH on inquiry 57

66 Chaer 3 Toluene Toluene (IUPAC: mehylbenzene, Flua, uriss, > 99.7 %, CASRN: , M 92.4 g mol ) was used wihou furher urificaion Iniiaors 2-[(E)-2-(-carbamimidoyl--mehylehyl)diazen--yl]-2-mehylroanimidamide dihydrochloride 2-[(E)-2-(-carbamimidoyl--mehylehyl)diazen-yl]-2-mehylroanimidamide dihydrochloride, alernaively labeled 2,2 -azobis-(2-mehyl roionamidine) dihydrochloride (V-50, Aldrich, 97 %, CASRN: , M used as received g mol ) was 2,2'-Azobis[2-mehyl-N-(2-hydroxyehyl)roionamide] 2,2'-Azobis[2-mehyl-N-(2-hydroxyehyl)roionamide] (VA-086, Wao, s grade, > 98 %, CASRN: , M g mol ) was used as received. 58

67 Maerials, Exerimenal Procedures and Daa Evaluaion 2-Hydroxy-2-mehyl--henylroan--one 2-Hydroxy-2-mehyl--henylroan--one (D73, Aldrich, > 97 %, CASRN: , M g mol ) was used as received. 2-Mehyl-4 -(mehylhio)-2-morholinoroiohenone 2-Mehyl-4-(mehylhio)-2-morholino-roiohenone (MMMP, Aldrich, > 98 %, CASRN: , M g mol ) was used wihou furher urificaion. Di-er-buyl eroxide Di-er-buyl eroxide (DTBP, IUPAC: 2-(er-buyleroxy)-2-mehylroane, CASRN: , M g mol ) was used wihou furher urificaion. Sodium ersulfae Sodium ersulfae (NaPS, IUPAC: disodium O-[(sulfonaoeroxy)sulfonyl] oxidanidolae, CASRN: , M 238. g mol ) was used wihou furher urificaion. 59

68 Chaer Inhibiors Hydroquinone monomehyl eher Hydroquinone monomehyl eher (MeHQ, IUPAC: 4-Mehoxyhenol, Flua, CASRN: , M 24.4 g mol ) was used as received. N,N -Di-sec-buyl--henylenediamine N,N -Di-sec-buyl--henylenediamine (IUPAC: N,N 4 -di-(2-buyl)benzene-,4- diamine, Aldrich 94.0 %, CASRN: , M g mol ) was used wihou furher urificaion Subsances used o reare Buffer Soluions Ciric acid Ciric acid (IUPAC: 2-hydroxyroane-,2,3-ricarboxylic acid, Sigma-Aldrich, 99 %, CASRN: , M 92.2 g mol ) was used as received. Hydrochloric acid sandard soluion Hydrochloric acid sandard soluion ( mol L, Flua) was used as received. 60

69 Maerials, Exerimenal Procedures and Daa Evaluaion Poassium dihydrogen hoshae Poassium dihydrogen hoshae (oassium hoshae monobasic owder, suiable for cell culure, suiable for insec cell culure, suiable for lan cell culure, Sigma, 99.0 %, CASRN: , M g mol ) was used as received. Poassium chloride Poassium chloride (for molecular biology, Sigma, 99.0%, CASRN: , M g mol ) was used as received. Sodium hydroxide volumeric soluion Sodium hydroxide volumeric soluion ( mol L, Flua) was used as received Ohers 2,2,6,6-Teramehylieridine -oxyl 2,2,6,6-Teramehylieridine -oxyl (TEMPO, Aldrich, > 99 %, CASRN: , M g mol ) was used for ESR calibraion wihou furher urificaion. 2-Mercaoehanol 2-Mercaoehanol (ME, IUPAC: 2-sulfanylehan--ol, Aldrich, 99 %, CASRN: , M 78.3 g mol ) was used as CTA wihou furher urificaion. 6

70 Chaer 3 Argon Argon ( %, CASRN: ) was used as received. Formic acid Formic acid (Flua, eluen addiive for LC-MS, ~98 % CASRN: , M g mol ) was used as roonaing agen wihou furher urificaion. Inhibior remover Inhibior remover (Aldrich, relacemen acing for removing hydroquinone and monomehyl eher hydroquinone ) was used o free monomer from MeHQ. Iso-buyric acid Iso-buyric acid (IBA, IUPAC: 2-mehylroanoic acid, Flua,.a., > 99.5 %, CASRN: , M 88. g mol ) was used as sauraed monomer analog wihou furher urificaion. Nirogen Nirogen ( %, CASRN: ) was used as received. Polyvinylyrrolidone Polyvinylyrrolidone (VP, Aldrich, CASRN: , 5 M w g mol, was used as received. 4 M n g mol ) 62

71 Maerials, Exerimenal Procedures and Daa Evaluaion Sodium chloride Sodium chloride (Merc,.a., > 99.5 %) was used as received. 3.2 Purificaion Procedures Monomers may come ino conac wih ground glass joins during urificaion and sorage. In order o reduce imuriies, PTFE rings (Dr. Diemar Glindemann, Glindemann TM PTFE sealing rings) were used insead of grease o seal ground glass joins and PTFE sococs were used for column chromaograhy. The chemical subsances were sored according o insrucions of sulier. Monomer free of inhibior was sored a 20 C. Inhibior Remover Inhibiors ha are more olar han he monomer can be removed by assing he mixure hrough a column filled wih inhibior remover. By his rocedure MeHQfree BA of was obained. Disillaion In order o remove imuriies, e.g., inhibior, monomer was disilled over a 20 cm Vigreux column a 8 mbar. Fine coer wire was laced in he sill o and he lower ars of he column o reven olymerizaion. This is esecially imoran for AA. 3.3 NIR 3.3. Seu Secra were recorded wih he FTIR secromeer IFS TM 88 (Bruer Oi). A waer-cooled cell holder was used o reduce hea ransfer from he cell o secromeer comonens. The oical sysem was ermanenly urged wih comressed air, dried by an adsorion dryer (ZANDER Aufbereiungsechni). The 63

72 Chaer 3 oical configuraion consised of a ungsen halogen lam (Gilway Technical Lam, L747A, 2 V, 50 W), a silicon-coaed calcium difluoride beam slier (model T840), and a liquid-nirogen-cooled InSb deecor (InfraRed Associaes, model D43, mm in diameer). The samle comarmen was searaed from he oical sysem by calcium difluoride windows. Cuvees were conneced o he heaed/refrigeraed circulaing bah F3-K (Haae) oeraed wih an aqueous ehane-,2-diol soluion (50 ercen by volume) used as hea ransfer fluid. Daa acquisiion and daa analysis were erformed using he sofware OPUS (Bruer Oi, version 4.2 or 6.0) Thermally iniiaed Polymerizaion in a Cuvee All comonens were mixed and filled ino a cylindrical, hermosaed oical cell (65.4/Q, oical ah lengh, if no saed oherwise 0 mm, Secrosil, Sarna) and urged wih argon for 4 minues. The cell was osiioned ino he secromeer (v.s.) and brough o he desired emeraure. The ime required for heaing o olymerizaion emeraure was in mos cases shorer han he inhibiion eriod. This iniial range of negligible degree of monomer conversion was cu off in he conversion-ime rofiles, which were subjeced o modeling. A few reacion mixures led o significan degree of monomer conversion before he final emeraure had been reached. Change in emeraure was checed via he shae of he broad waer ea (v.i. Figure 3-2.). In hese aricular cases he daa oins from before final emeraure were removed and he remaining rofile was exraolaed o correc he ime. These rofiles were no used for modeling, bu only o comare wih he redicions of he final model. NIR secra were aen in shor inervals (of 3 o 60 s) unil monomer conversion was comlee, which oo u o several hours. The absence of residual monomer was addiionally checed by H-NMR. Cleaning of he cell can become edious, esecially for measuremens wihou CTA. Leaving he devices for exended ime eriods (several hours o days) in sauraed NaHCO 3 soluion urned ou o be he bes mehod for recleaning hem. 64

73 Maerials, Exerimenal Procedures and Daa Evaluaion Phooiniiaed Polymerizaion in a Cuvee All comonens were mixed and filled ino a cylindrical, hermosaed oical cell (Sarna 65.4/Q/ oical ah lengh, if no saed oherwise 0 mm, Secrosil TM, Sarna). D73 was used as hooiniiaor. The iniial mixure was urged wih argon for 4 minues. Afer heaing o reacion emeraure, he olymerizing mixure was irradiaed for 40 o 80 s wih an Osram Ulra-Vialux TM 300 W lam osiioned a a disance of 8 cm, unil a degree of monomer conversion of a few ercen had been reached, which was moniored via NIR secroscoy (v.s.). Polymerizaion was soed by adding MeHQ o he reacion mixure, which was aferwards cooled o 20 C Degree of Monomer Conversion absorbance wavenumber / cm Figure 3- NIR absorbance secrum showing he signal of he firs overone of he C H sreching recorded during a olymerizaion of 0. g g AA in D2O. The arrow indicaes he direcion of change wih reacion ime. Only he ea around 75 cm is used for calculaion of conversion. 65

74 Chaer 3 The firs overone of he C H-sreching mode a he C=C double bond was used o quaniaively measure degree of monomer conversion as a funcion of olymerizaion ime. This mehod wors in boh organic and aqueous soluions. [30,40,4] A yical se of lines for differen degrees of monomer conversion (from zero o full) during AA olymerizaion is deiced in Figure C absorbance room emeraure wavenumber / cm Figure 3-2 Shown is a ar of he broad waer signal also deiced in Figure 3-3 for a series of secra aen every 5 s during he iniial eriod of a olymerizaion of 0. g g AA in D2O. The arrow gives he direcion of change wih ime. Final emeraure is reached aroximaely afer he fourh secrum. For AA, he absorbance of he C H mode was inegraed beween 6250 and 620 cm agains a baseline fied via a olynomial assing hrough he absorbance daa oins a 6370, 6280, 63 and 6085 cm. Ionizaion of monomer shifed he signal. For NaA, he absorbance of he C H mode was inegraed beween 626 and 6053 cm agains a baseline fied via a olynomial assing hrough he absorbance daa oins a 6284, 6255, 6062 and 605 cm. mode was inegraed beween 6275 and 6092 For MAA, he absorbance of he C H cm agains a baseline fied via a olynomial assing hrough he absorbance daa oins a 630, 6274, 6088 and 6065 cm. As he shif resuling from ionizaion is no very srong and oher 66

75 Maerials, Exerimenal Procedures and Daa Evaluaion influences migh inerfere, he NIR signal was no used o calculae he degree of ionizaion of monomer for differen degrees of conversion. The olymer signal (C H-sreching mode a he sauraed carbon aom) is much weaer and osiioned a smaller wavenuber (Figure 3-3 c) comared o he corresonding monomer signal. The low wavenuber region of monomer ea overlas o a small exen wih high wavenuber region of he olymer ea (Figure 3-3 d). As no he full bu raher he high wavenuber ar of he signal was used, his did no affec he daa evaluaion described above. As shown in Figure 3-2, he shae of he broad ea associaed wih waer is esecially sensiive owards emeraure. Such being he case, he waer ea was used o chec emeraure and ensure ha only daa oins were used afer final emeraure was reached. Moreover, i was secured ha reacion enhaly of olymerizaion did no lead o significan emeraure increase and he whole rocess remained isohermal. For he urose of imroving signal-o-noise qualiy, DO was used as he solven 2 insead of H2O. [4] For a yical monomer weigh fracion of 0. g g he monomer signal is jus a small ea on he flan of he HO ea (Figure 3-3 a), whereas he 2 bacground absorion of DO is a smaller wave numbers han he one of 2 HO in 2 he =C H region under invesigaion (Figure 3-3 b). No noable solven isooe effec on he olymerizaion ineics is execed o occur. [4] This assumion has been verified by comarison wih reored conversion vs. ime rofiles for HO being he solven. [90] In recies of PREDICI TM simulaion 2 weigh was correced by raion of densiies aen from ref. [42] 67

76 a b c 0.75 d absorbance wavenumber / cm Figure 3-3 Tyical NIR secra.wih imoran lines being mared: dar blue square: H2O; medium blue square: D2O; red circle: monomer; green riangle: olymer; condiions: a: 0.0 g g AA in H2O, oical ah 2 mm; b: 0. g g AA in D2O, low conversion, oical ah 0 mm; c: same as b, bu full conversion; d: difference beween b and c

77 Maerials, Exerimenal Procedures and Daa Evaluaion 3.4 EPR 3.4. Seu EPR secra were recorded on an EPR CW/Transien Secromeer Sysem Elexsys- II TM 500T (Bruer Biosin) or an Elexsys TM E500 (Bruer Biosin) boh oeraing wih he X-band. The resonaor, Oical Transmission Caviy (Bruer), was oen or equied wih a grid, o allow for irradiaion. Temeraure was se by a 43VT uni (Bruer) urging he samle caviy wih nirogen. Samles were irradiaed inside he caviy by a 500 W mercury arc lam (LAX 450, Müller Eleroni; HBO 500 W/2, Osram). I was checed ha secra aen wih a cu-off filer WG335 (Scho) had he same raio of EPR line inensiies. As he weaer UV radiaion wih filer imaired S/N raio, samles from measuremens wihou filer were used for daa rocessing Organic Samles Monomer in solven was by several freeze-um-haw cycles and CTA in solven was degassed by several freeze-um-haw cycles as well.the following rearaion was carried ou in a glove-box under an argon amoshere. Then he wo soluions were mixed giving a monomer concenraion of 0.02 mol mol, i.e. iniiaor concenraion of 3.04 mmol L, or 0.05 mol mol, i.e..52 mol L wih eiher 7.60 mmol L, and an 6 mmol L. An EPR quarz ube of 5 mm ouer, and 4 mm inner diameer (Bruer) was filled wih 200 L reacion mixure. The samle ube was closed wih a lasic ca and sealed wih PARAFILM TM. The samles were measured direcly aferwards o avoid side reacions, e.g., he hiol-ene reacion occurred. Oimized measuring condiions were: single scan: 83.9 s, widh: 00 G; ime consan: 0.24 ms; aenuaion: 3; receiver gain: 60; microwave ower: 0 mw; modulaion amliude: 3 G. 69

78 Chaer Aqueous Samles Measuring EPR in waer is esecially challenging. A secial EPR-cell consruced for measuremens in waer was used, he ER 65FCVT-S-Q, also called WG-808-S-Q, (WilmadLabGlass/Rooec-Sinec) made of Surasil TM o guaranee a clean bacground. The measuring secion is beween wo lanar laes maximizing he filling facor. I has a volume of 50 L and is filled comleely. No liquid is lef above his secion as his would reduce S/N-raio. D73 (iniiaor) weigh fracion 3 was g g. Oimized measuring condiions were: single scan: 0.0 s, widh: 00 G; ime consan: 0.0 ms; aenuaion: 3; receiver gain: 70; microwave ower: 0 mw; modulaion amliude: 3 G Deconvoluion of Secra Secra were simulaed using Simfonia TM v..25 (Bruer). Couling consans and line broadening were firs adjused for secra measured a emeraures where one radical secies dominaes, i.e. SPRs a 50 C and MCRs a 70 C. Simulaion of he secra was carried ou by Dr. Taiana Sergeeva. For deails see ref. [0] The simulaed secra were used o fi he comlex secra alying Excel TM solver and gain fracion of differen radical secies Calibraion Radical concenraions were obained by calibraion wih TEMPO. The double inegral of he signal and radical concenraion are correlaed linearly. The double inegral of secra a differen concenraions of TEMPO are loed agains radical concenraion and fied o a sraigh line, he sloe of which is he calibraion consan. I has o be measured for each comosiion of he reacion mixure and emeraure. This is only ossible for BA-oluene mixures, because ME and TEMPO undergo a redox reacion. Calibraion wih TEMPO was carried ou by Dr. Johannes Barh. For deails see ref. [43,44] 70

79 Maerials, Exerimenal Procedures and Daa Evaluaion Secra were subjeced o double inegraion o obain absolue radical concenraion by mulilying wih he calibraion consan. In rincile, boh he measured secrum and he fied secrum should yield he same resul. However, he baseline has o be correced. I can be sraigh and jus iled, bu also slighly curved. The more lines in a secrum he more difficul i is o correc he baseline wihou erasing signal. Analysis of SPR dominaed secra (few lines) gave he same resul for original and simulaed secra. Analysis of secra wih many lines from boh SPR and MCR gave lower radical concenraion for measured (and baseline-correced) secra. As his could be raced bac o signal being cu off, simulaed secra were used for analysis. 3.5 NMR H-NMR secra were recorded in hin-walled ubes (e.g. Scho S, Norell TM 508-u) a solue mass concenraions of abou 0.06 g g. Secra for qualiaive analysis were deermined a room emeraure wih an Avance TM III (300 MHz, Bruer). In order o imrove S/N-raio, 6 or 32 FIDs were co-added. Secra for quaniaive H-NMR analysis were deermined by a Uniy TM 300 or Mercury TM 300 (300 MHz, Varian) Quaniaive H-NMR Oimum H-NMR measuring condiions for quaniaive analysis were aen from Schrooen. [45] The relaxaion of he hydrogen aom aached o he -carbon is unusually slow. Baseline (Bernsein olynomial fi) and hase (manual) were correced. 7

80 Chaer 3 Table 3- Oimum condiions for quaniaive H-NMR measuremen. VI Ref. [45] arameer AA AA measuring emeraure 35 C ulse angle 0 84 reeiions 32 acquisiion ime / s 3.28 relaxaion delay / s Quaniaive 3 C-NMR FIDs were rocessed by he MesReNova TM sofware acage. Baseline (Bernsein olynomial fi or mulioin baseline correcion) and hase (manual) were correced. Exonenial aodizaion of he FID was done o imrove S/N. I was checed for he samles ha exhibi a raher inense quaernary carbon ea ha aodizaion does no influence he resuls. VII Secra for quaniaive 3 C-NMR analysis were deermined wih an Inova 500 equied wih a cryo-robe (500 MHz, Varian). Because of he cryo-robe, as i is oversauraed in he very beginning of recording, bacward linear redicion (u o 22 oins, Toeliz) was necessary. VI NMR measuremens were erformed a he Insiu für Organische und Biomoleulare Chemie (Georg-Augus-Universiä Göingen) by R. Machine. VII Aodizaion may cause higher inensiy for eas of aoms wih a shorer relaxaion ime. 72

81 Maerials, Exerimenal Procedures and Daa Evaluaion Figure 3-4 Tyical FID of a 3 C-NMR of AA. Oimum 3 C-NMR measuring condiions for quaniaive analysis were deermined in his wor. Differen measuring arameers were esed. A samle wih very high branching was chosen (olymerizaion condiions: waer, 70 C, X = 85 %) o abain a good S/N-raio. 0. g g AA, 0.02 g g VA-086, in The wo quesions were, which delay is needed o ge comlee relaxaion of all crucial nuclei, and which delay is necessary for he nuclear Overhauser effec, NOE, buil u during acquisiion, o recede. In order o minimize NOE, measuremen was carried ou wih inverse gaed decouling, i.e. i was only decouled during acquisiion. Differen combinaions of acquisiion ime, a, and relaxaion delay, rd, were ried. Acquisiion should no be oo long because of NOE buil-u, on he oher hand no oo shor, because oherwise signal migh be cu off and his o a differen exen for differen nuclei. Thus, looing a he FID, shown in Figure 3-4, he value should no be smaller han 0.5 s and no bigger han.0 s. The relaxaion delay should be so long furher exension hereof has no more influence. To allow for shorer delays, he ulse angle was reduced. 73

82 Chaer 3 Baseline correcion and subsequen inegraion were carried ou wih he rogram Origin. The secra were aen wih he same secromeer and samle sraighaway one afer anoher and hus should be direcly comarable. Figure 3-5 shows he signal of he quaernary carbon of branching oins, Figure 3-6 he corresonding eriary one of monomer unis ha do no have a branching oin. The inegrals are given in Table 3-2; he raio hereof in Table 3-3. inensiy / a.u a / s rd / s / m Figure 3-5 The line of he quaernary carbon (mared red in he AA srucure) a branching oins as measured wih differen seings. a: acquisiion ime; rd: relaxaion delay. As i urns ou, NOE is a bigger roblem han relaxaion ime a longer acquisiion ime leads o he signal of he Cq being reduced relaive o he C.The S/N-raio is clearly beer for he shorer acquisiion ime while he resul (raio) is consisen wihin an error range of 3. %. In addiion wih.0 s acquisiion ime a longer delay seems o be required, which goes wih execaion. 74

83 Maerials, Exerimenal Procedures and Daa Evaluaion Summing u, an acquisiion ime of 0.5 s gives a beer signal and requires only a relaxaion delay of 2.5 s. Therefore, hese measuring condiions are he oimal ones, summarized in Table 3-4. inensiy / a.u. 3.5x0 4 a / s rd / s x x x0 4.5x0 4.0x x / m Figure 3-6 The line of he eriary carbon (mared red in he AA srucure), a which branching oins can occur, as measured wih differen seings. a: acquisiion ime; rd: relaxaion delay. Table 3-2 Inegrals of he eas shown in Figure 3-5 and Figure 3-6. measuring condiion range / m Inegral / a.u. Deviaion / % a 0.5 rd a 0.5 rd a 0.5 rd a 0.5 rd

84 Chaer 3 a.0 rd a.0 rd a.0 rd a 0.5 rd a 0.5 rd a 0.5 rd a 0.5 rd a.0 rd a.0 rd a.0 rd Table 3-3 Raio of he inegrals of he eas shown in Figure 3-2 and Figure 3-3. measuring condiion raio quaernary o eriary line deviaion raio of 0.5 rd 5 s / % from a 0.5 rd a 0.5 rd a 0.5 rd a 0.5 rd a.0 rd a.0 rd a.0 rd

85 Maerials, Exerimenal Procedures and Daa Evaluaion Table 3-4 Oimum condiions for quaniaive 3 C-NMR measuremen of AA VIII w P 0.3 ofen no ossible due o viscosiy and homogeneiy issues measuring emeraure 50 C or higher decouling n n y decouling wih an NOE as low as ossible ulse angle 36 comromise beween maximum inensiy and a measuring ime as shor as ossible reeiions acquisiion ime relaxaion delay s 2.5 s for highly branched olymer for samle wih minimal branching Polymerizaion in NMR Samle Tube The reacion mixure was filled ino an NMR ube and urged wih argon hrough a hollow needle for 6 minues. The samle ube was closed wih a lasic ca and sealed wih PARAFIM TM. The ube was e in he heaed/refrigeraed circulaing bah F3-K (Haae) oeraed wih an aqueous ehane-,2-diol soluion (50 ercen by volume) used as hea ransfer fluid for he desired ime. The olymerizaion was quenched by addiion of MeHQ and oxygen (air) lus cooling o 0 C (ice bah). VIII NMR measuremens were erformed a he Insiu für Organische und Biomoleulare Chemie (Georg-Augus-Universiä Göingen) by R. Machine. 77

86 Chaer Densiy Measuremen A densiy meer based on he oscillaing U-ube rincile was used. I consiss of a daa acquisiion uni, DMA 60 (Anon Paar), a measuring uni, DMA 602TP (Anon Paar), and a high-emeraure cell, DMA 602 H (DURAN TM 50, 0 50 C, Anon Paar). Temeraure monioring inside he U-ube was carried ou by means of a digial hermomeer (Volcraf 302 K/J Thermomeer). Heaing was erformed by a waer bah circulaor (Haae, D2-L). To reduce overheaing, he waer bah circulaor was conneced o a waer circulaion cooler (Lauda Dr. R. Wobser, WK 500). The measuremen is only correc, if he U-ube is filled comleely and here are no bubbles inside i. This became a roblem esecially for measuremens a higher emeraure, because solubiliy of gases decreases. Therefore, soluions were firs heaed o desired emeraure and filled ino he caillary aferwards. 3.7 Viscosiy Measuremen If no saed oherwise, viscosiy was measured by an AMVn TM insrumen (Anon Paar GmbH) using Rheolus TM (Anon Paar GmbH) as he analysis sofware. I is a falling/rolling shere viscosimeer, which uses four differen caillaries o cover a range from 0.3 o mpa s. The caillaries were filled by sucing in he soluion ino i wih a syringe from he oher end. IX In a few exerimens, inemaic viscosiy,, was measured wih an Ubbelohde viscomeer (SCHOTT, 0a, inside diameer of 0.53 mm) and correced via he Hagenbach Couee rocedure. The viscomeer was mouned inside a clear-view hermosa (Lauda Dr. R. Wobser, D40) filled wih waer. I remained inside for a leas 900 s before measuremen o allow for hermal equilibraion. The waer emeraure was deermined by a P00 conneced o a PID conroller (Euroherm, 2460). The PID conroller regulaed a universal relay box (Lauda Dr. R. Wobser, R3), which conrolled he ower suly of an immersion heaer. IX Some of he viscosiy and densiy measuremens were carried ou by Roman Kremring during his bachelor hesis. 78

87 Maerials, Exerimenal Procedures and Daa Evaluaion Dynamic viscosiies,, were deermined via combinaion of he measured inemaic viscosiy and densiy,, by: (3.) 3.7. Imoran Feaures of Polymer Soluions 60 / mpa s ime / s Figure 3-7 A samle of 0.06 g g MAA was measured a 25 C by an AMVn (falling/rolling shere viscosimeer) wo imes. Firs, he caillary was filled quicly and wih high sheer force (red sars), second, he caillary was filled gingerly wih lower sheer force (blue riangles). The arrow indicaes hree singular measuremens, during which a iny bubble in he caillary slowed he shere down hence giving a oo high value of. Polymer soluions are non-newonian fluids, viz., when sressed hey become eiher less viscous over ime (hixoroy), or hey become more viscous over ime 79

88 Chaer 3 (rheoecy). Boh he Ubbelohde viscomeer and he falling/rolling shere viscosimeer cause sheer forces on he samle during filling and measuring. For he laer hese can be minimized by choosing a small angle, hus slowing down he shere. If no saed oherwise, viscosiy was measured a an angle of 20. Figure 3-7 shows how he filling rocedure increases viscosiy and i slowly decreases aferwards. Therefore, he sheer forces during measuremen are very small, if he righ condiions have been chosen. Filling he caillary gingerly reduces sheer-induced rise in viscosiy. Neverheless, i aes ime for viscosiy o decrease. Samles were filled and lef for o s before measuremen. Anoher roblem is occurrence of bubbles as hey slow down or even bloc he movemen of he shere. Measuremens ha gave indicaion of bubbles or oher inerferences were discarded. Bubbles became a roblem esecially for measuremens a higher emeraure, because solubiliy of gases decreases. For ha reason, soluions were firs heaed o desired emeraure and filled ino he caillary aferwards Polymerizaion in Viscosiy Measuremen Caillary All comonens were mixed, urged wih argon for 8 minues, and direcly suced ino he measuring caillary by a syringe a he oher end. The caillary was osiioned ino he viscosimeer (v.s.) and brough o he desired emeraure. Iniiaors ha roduce gas, e.g., azo-iniiaors are unsuiable for his exerimen. A 0.05 g g monomer soluion changes densiy by less han %, his effec was ignored. 3.8 Prearaion of Buffer Soluions Buffer soluions were reared based on ref. [46] Main comonens, e.g., ciric acid, were chosen following he recie given. Aqueous soluions (.0 mol L ) of sodium hydroxide or hydrochloric acid, resecively, were added under sirring unil he desired H value had been reached. During his rocess, he H value was moniored online. 80

89 Maerials, Exerimenal Procedures and Daa Evaluaion 3.9 SEC The enire se of size-exclusion chromaograhy, SEC, analysis was carried ou in aqueous hase by I. Lací, DSc, and M. Sach, PhD, and co-worers a he Polymer Insiue of he Slova Academy of Sciences according o rocedures deailed elsewhere. [59,9,47] 3.0 ESI-MS The olymer was dissolved, e.g., in waer/ehanol o give a soluion of ca. Two secromeers were used o measure ESI-MS. X 0. g L. An Ion-ra LCQ TM (Thermo Finnigan) conneced o an HPLC seu (v.i.) was oeraed wih an elecrosray volage of 4.5 V and a caillary emeraure of 200 C. I had a measuring range of m/z. In order o imrove S/N-raio ca. 200 secra were coadded. A microtof TM (Bruer) was oeraed wih an elecrosray volage of 3.8 V and a caillary emeraure of 80 C. I had a measuring range of m/z. In order o imrove S/N-raio ca. 200 secra were coadded. Secra were analyzed by OriginPro TM 8.5 (OriginLab). 3. HPLC Seu The high-erformance liquid chromaograhy, HPLC, seu consised of an AS 555 TM auosamler (Jasco), degasser 3492 (Konron), a 57 Synergi TM MAX RP column (Phenomenex), and a Surveyor TM PDA UV-deecor (Finnigan) oeraing X ESI-MS analysis was erformed a he Insiu für Organische und Biomoleulare Chemie (Georg-Augus-Universiä Göingen) by Dr. H. Frauendorf. 8

90 Chaer 3 from 200 o 800 nm. XI The HPLC seu was conneced o an ESI-MS secromer (Finnigan, Ion Tra LCQ TM ), v.i. Samle rearaion Aqueous samles wih mg g XII iniiaor were sirred unil dissoluion was comlee. They were e a he desired emeraure for a defined ime analogously o eiher olymerizaion in a heaing bloc or olymerizaion in a ubular reacor (v.i.). In he laer case, residence ime was correced analogously o olymerizaion (v.i.). Aferwards samles were cooled down raidly in an ice bah. Measuremen The injecion volume was 5 L, he flow rae 5 L s. The saring eluen was waer 4 wih 5 0 g g formic acid. Wihin 900 s he eluen changed gradually o mehanol 4 wih 5 0 g g formic acid. Eluaion was coninued wih he laer for 420 s. The signal aeraining o non-decomosed iniiaor could be assigned o a line found afer 360 s via ESI-MS. Inegraion of he corresonding UV signal gave he concenraion of he iniiaor. 3.2 H-Meer A S47 SevenMuli dual meer H / conduciviy (Meler-Toledo, H , 0.00 S cm c 000 ms cm ) was used o deermine as H values. XI HPLC analysis was erformed a he Insiu für Organische und Biomoleulare Chemie (Georg-Augus-Universiä Göingen) by Dr. H. Frauendorf. XII For some samles a higher iniial weigh fracion was chosen and he samles were dilued rior o HPLC measuremen. 82

91 Maerials, Exerimenal Procedures and Daa Evaluaion 3.3 High-Temeraure Polymerizaions Figure 3-8 The seu for high emeraure exerimens is shown schemaically. I could be oeraed in wo modes. Figure 3-8 deics he seu schemaically. XIII The reacion mixure sared from he reservoir conainer locaed on a balance (Omnilab, OL 300-P), which was conneced o a comuer o calculae mass flow in s inervals. The reacion mixure flowed via a PTFE ube (inner diameer mm) o he degasser (Ercaech AG, ERC-325α) and furher o an HPLC um (buil by he mechanical worsho of he Insiu für Physialische Chemie, Georg-Augus-Universiä Göingen). The um gave a ressure of 200 bar and from here on connecion was by a sainless seel caillary (AD: /6 ) wih an inner diameer of 0.5 mm. Then i enered a double line ube ( m) o ge a emeraure of 50 C., which was no enough o induce significan monomer conversion bu reduced emeraure difference o reacion emeraure. In he nex se he reacion mixure flowed ino he ubular reacor locaed in a heaing bah (Haae, N3) filled wih silicone oil. The sainless seel, ubular reacor consised of wo (Nova Swiss, AD: /6, ID: 0.5 mm). I was siral-shaed, had a lengh of 050 cm, an inner diameer of 0.5 mm ± 0.05 mm, and hus a geomeric volume of 2.06 ml ± 0.4 ml. Temeraure was measured by CIA S250 Chromel/Alumel hermocoule and ressure by a P3MB (HBM). Aferwards he reacion mixure was cooled o 50 C in a double line ube ( m). Then i flowed ino a high-ressure cell (described in more deail elsewhere [45,48] ) heaed elecrically o 50 C and locaed in he FTIR secromeer IFS 88 (Bruer Oi). A conrolling XIII The high-emeraure olymerizaions were all carried ou by Daniel Weiß. [48] under cosuervision of Dr. H.-P. Voegele. 83

92 Chaer 3 valve followed o se he velociy of he flow. The las ar of he seu was a collecing vessel. The seu allowed for wo differen modes of oeraion described in wha follows Soed-Flow exerimens in High-Pressure Cell The ubular reacor was byassed and olymerizaion oo lace in he high ressure cell. The reacion mixure flowed wihou rior warming hrough he cell unil saionary condiion was reached. Then he valves of he high-ressure cell were closed and he cell was used as a bach reacor. Polymerizaion was followed by NIR as described in subchaer 3.3. The uer emeraure limi for measuremens wih his mode of oeraion was se by iniiaor decay. A emeraures above 40 C, VA-086 decayed so fas ha significan X had already been reached a he saring oin. Wih his seu, i was no ossible o draw samles during olymerizaion. The rocedure is described in more deail here. [48] Polymerizaion in a Tubular Reacor Polymerizaion was carried ou inside he ubular reacor. Residence ime,, was se by flow rae and was calculaed from mass flow, densiy of he reacion mixure and geomeric volume of he reacor. This heoreical value had o be correced (v.i.). The lower and uer emeraure limis for measuremens wih his mode of oeraion were se by iniiaor decay. A emeraures above 70 C, VA-086 decayed so fas ha high final monomer conversion was reached even a he highes flow rae. Measuring a conversion vs. ime rofile is no ossible under hese condiions. A emeraures below 30 C, VA-086 decayed so slowly even for he lowes flow rae, which sill allowed for urbulen flow, high conversion could no be reached. Samles were aen a each flow rae. They were dried in vacuo a emeraures u o 90 C and measured by NMR (subchaer 3.5. and 3.5.2). 84

93 Maerials, Exerimenal Procedures and Daa Evaluaion Correcion of residence ime in he ubular reacor 0.2 inensiy / a.u ime / s Figure 3-9 Residence ime disribuion of he whole seu (red) and wihou he ubular reacor (blue) measured as ime-deenden signal inensiy (ulse-resonse) for residence ime exerimens alying marer (AA) as aroximae dela funcion. Residence ime of he ubular reacor was measured by flowing waer hrough he aaraus wih and wihou he reacor being included. AA was injeced as maring subsance as an aroximae dela funcion. Increase of he cener ea of he inerferogram (o increase ime resoluion) was used o measure he arrival of maring subsance. The resul is shown in Figure 3-9. The curves from exerimens wih he ubular reacor have, wihin exerimenal accuracy, he same shae as he curves from exerimens wihou he ubular reacor here is only a ime offse. Thus, no significan broadening by he highressure cell can be observed. The curves were inegraed o obain, see Figure 3-0. The rue residence ime of he ubular reacor was calculaed as he difference beween residence ime including he ubular reacor and residence ime no including he reacor. 85

94 Chaer F() ime / s Figure 3-0 Sum funcions of he curves shown in Figure 3-9. This is used o comue he rue residence ime of he ubular reacor as he difference beween residence ime including he ubular reacor (red) and residence ime no including he reacor (blue). This was done for differen flow raes and he residence ime calculaed from mass flow, densiy of he reacion mixure and geomeric volume of he reacor. This heoreical value, calc, was loed agains he rue residence ime,. This is shown in Figure 3-. A linear relaionshi was found and an emirical correcion funcion was deermined, eq. (3.2), wih which all exerimenal resuls given laer have been correced. / s / s (3.2) calc The rocedure is described in more deail elsewhere. [48] 86

95 Maerials, Exerimenal Procedures and Daa Evaluaion 6 2 / s calc / s Figure 3- Calculaed and direcly measured residence imes are comared (green squares). These values are fied o a sraigh line (red, eq. (3.2)). As i was only ossible o measure for high flow raes, for lower flow raes, and hus higher conversion, residence ime was correced via linear exraolaion, eq. (3.2). The ime has o be more recise for he beginning of he olymerizaion, as he rae of olymerizaion is highes here. The comarison of he conversion-ime rofiles of olymerizaion wih he soed-flow oeraion o conversion-ime rofiles from olymerizaion in he ubular reacor before and afer correcion sugges ha he correcion and even he exraolaion wors well. An examle is given in Figure 3-2. Small symbols give he resul from bach olymerizaion (soed-floe oeraion) used as reference here. Big oen symbols belong o a olymerizaion of he same reacion mixure in he ubular reacor. The rae of olymerizaion seems o be smaller for he ubular reacor. Correcion of residence ime of he ubular reacor via eq. (3.2) yields he big, solid symbols. The correced conversion-ime rofile of he olymerizaion in he ubular reacor agrees wih he one of he bach reacor, hus he raes of olymerizaion are he same. 87

96 Chaer X ime / s Figure 3-2 Conversion-ime rofiles of olymerizaion wih he soed flow oeraion (small symbols) is comared o conversion-ime rofiles from olymerizaion in he ubular reacor before correcion (big oen symbols) and afer correcion (big filled symbols) are comared. 0. g g AA was olymerized wih g g VA-086 in H2O a 40 C. 3.4 Oher Seus for Polymerizaion 3.4. L Auomaed Reacor A LabMax TM L auomaed, sirred reacor (Meler-Toledo) was conneced o a nirogen cylinder and oeraed by ic Sofware (Meler-Toledo). A mixure of waer and monomer was sirred under a nirogen blane for 800 s and heaed o desired emeraure. Then iniiaor and, if required, CTA were added in counercurren. Samles were drawn in increasing ime inervals. They were cooled immediaely afer having been aen from he olymerizing mixure and boh MeHQ and oxygen (air) were added. The decay of monomer and CTA concenraions was moniored by H-NMR and by gravimeric analysis. 88

97 Maerials, Exerimenal Procedures and Daa Evaluaion Polymerizaion in a Heaing Bloc The reacion mixure was filled ino a dar (roecion from UV ligh) wis-off-glass wih a seum inegraed in he ca. Argon was urged hrough he reacion mixure by a hollow needle. The samle was e in he Bloc Heaer 250 (Roilab) for he desired ime. In order o ensure good mixing, he heaer was sanding on a KS-5 shaer (Edmund Bühler GmbH) Polymerizaion was soed eiher by cooling he samle raidly wih liquid nirogen, which someimes caused he glass o brea, or by adding MeHQ and oxygen (air) and cooling he samle in an ice bah Polymerizaion in a Flas The reacor was a flas conneced o a Schlen line. A mixure of waer and solven was eiher urged wih argon for 30 minues or degassed by several freeze-umhaw circles and flooded wih argon aferwards. I was brough o desired emeraure. Then dissolved iniiaor and, if required, CTA were added by a syringe hrough a seum. Samles were drawn in increasing inervals. They were cooled immediaely afer having been aen from he olymerizing mixure and boh MeHQ and oxygen (air) were added. Laer, his rocedure was relaced by olymerizaion in a lined flas, which allows for beer emeraure conrol. Synhesis of arylic acid macromonomer The above described rocedure was modified o synhesize arylic acid macromonomer, MM(AA). 50 ml DMSO were urged wih argon and brough o 38 C g VA-086 was dissolved in 5.3 g DMSO. Half of he iniiaor soluion was added hrough a syringe g AA was added drowise. The res of he iniiaor was added slowly. Afer 2400 s he reacion mixure was cooled in an ice bah. No inhibior was added. The roduc of exracion from waer was dried in vacuo. 89

98 Chaer 3 90 ml o-xylol were urged wih argon and brough o 40 C. 0.6 g DTBP was added hrough a syringe, hen 0.79 g AA. Afer 8700 s he reacion mixure was cooled in an ice bah. No inhibior was added. The reacion roduc was dried in vacuo Polymerizaion in a Lined Flas The reacor was a lined flas wih is hose barbs conneced o a heaed/refrigeraed circulaing bah (Haae, F3-K) wih ehanol used as hea ransfer fluid. The flas was comleely covered wih aluminum foil. The reacion mixure was urged wih argon for 2400 s and brough o he desired emeraure. The foil was oened on one side and he flas was irradiaed by a 00 W mercury arc lam (LAX 00, Müller Eleroni; HBO 00 W/2, Osram) from ca. 40 cm disance. Aferwards a samle was drawn by a wide, hollow needle, cooled immediaely o 20 C, and sored in darness. This rocedure was reeaed unil final conversion was reached. 3.5 Comuer Programs 3.5. Curve Fiing Fiing of mahemaical funcions o exerimenal daa was conduced by he sofware OriginPro TM 8.5 (OriginLab), exce for curve fiing described in Linear fiing is carried ou alying he mehod of leas squares. For non-linear curve fiing he Levenberg Marquard algorihm is used for ieraive adjusmen of arameers Deerminaion of Join Confidence Regions The rogram Conour (A. M. van Her, version.8) was used o generae ellises corresonding o join confidence regions for Arrhenius acivaion energy and Arrhenius re-exonenial facor of. The deails of he rogram are given elsewhere. [49,50] 90

99 Maerials, Exerimenal Procedures and Daa Evaluaion Simulaion Simulaions were erformed by he rogram Predici TM v6.4.8 (Dr. Michael Wulow Comuing in Technology GmbH). 3.6 Error Esimae Densiy The densiy meer is secified o be accurae o g cm. ESI-MS Resuls are from he LCQ TM are recise by 0. m/z and resuls from he microtof TM are recise by m/z. Monomer Concenraion from FT NIR Reeaed recording of secra of he same samle shows slighly differen resuls. Errors may be inroduced by aodizaion and hase correcion, bu he main source of error seems o arise from uncerainies of he baseline. The error of he inegraed absorbance is esimaed o be less han ±2 %, bu rises for very low concenraions. NMR As correc measuring condiions were checed and resuls from differen daa rocessing were comared, values derived by H-NMR are esimaed o have a leas wo significan digis and hose from 3 C-NMR o have a leas one significan digi. H The inaccuracy of he H values is given by he manufacurer o be ± Saisical Error The errors of arameers which are deduced by curve fiing are deermined using saisical mehods. They are mosly given ogeher wih he resecive value in he ex. 9

100 Chaer 3 Temeraure For exerimens in cuvees as well as for viscosiy deerminaion, an error of ±0.5 C is esimaed on he basis of manufacurer s informaion. The emeraure in he H measuremens is recise o ±0. C. The emeraure in densiy measuremens is accurae wihin ±0. C. The emeraure in he nirogen flow o hermosa EPR ubes is recise o ±0. C. Viscosiy The error given by manufacurer of he AMVn is: accuracy (rueness) < 0.7 %, recision < 0.35 %. The accuracy of he oher viscosiy measuremens is slighly lower. Weigh For rearing he reacion soluions and gravimeric analysis, an analyical balance (CPA 3245, Sarorius) wih an accuracy of ±0. mg was used. 92

101 Maerials, Exerimenal Procedures and Daa Evaluaion 93

102

103 Mehacrylic Acid 4 4 Mehacrylic Acid The olymerizaion of MAA (mehacrylic acid, IUPAC: 2-mehylroenoic acid) is of indusrial ineres as he roduc is widely used, mos ofen as comonomer for olymers alied, e.g., in hygiene and cosmeics. These olymers are roduced by radical olymerizaion in aqueous hase. In addiion o soluion olymerizaion, emulsion olymerizaions are erformed in which carboxylic monomers such as mehacrylic acid may ac as in-siu sabilizer. Moreover, MAA is similar o AA, bu he ineics are simler due o lac of bacbiing. Knowledge abou MAA ineics may hel o beer undersand AA ineics. For modeling olymerizaion in aqueous soluion, deailed ineic and mechanisic nowledge is required. The roagaion rae coefficien is nown from PLP SEC analysis. [5,89,5] SEC on MAA may be erformed afer quaniaive mehylaion of he carboxyl moieies yielding PMMA [57,90] or direcly on MAA via aqueous-hase SEC. [9] The value of MAA varies enormously as a funcion of boh monomer concenraion and degree of ionizaion [9,,58,59,9,92] e.g., decreases by abou one order of magniude in assing from dilue aqueous soluion of non-ionized MAA o eiher bul olymerizaion of non-ionized MAA or o fully ionized MAA in dilue soluion. These effecs are no indeenden of each oher, i.e., he variaion of wih monomer conen is weaer wih arially ionized MAA and may even be reversed wih fully ionized MAA. [] I has been aemed o model soluion and emulsion olymerizaion from = 0 o =. [79] PLP SEC sudies on samles, o which MAA had been added, hus mimicing siuaions of differen degrees of monomer conversion, esablish ha i is 95

104 Chaer 4 essenially he raio of MAA-o-waer concenraions which is resonsible for he characerisic deendence of in aqueous-soluion. [9] For non-ionized MAA, boh he SP PLP NIR [2] and he SP PLP EPR echniques [20] have been alied in aqueous soluion. The exerimenal and values urned ou o be well suied for modeling aqueous-hase MAA olymerizaion ineics and olymer molar mass disribuion in he absence of efficien chain ransfer. [90] So far, modeling of MAA olymerizaion in aqueous soluion has no been addressed a echnically relevan CTA concenraions. This chaer describes olymerizaion ineics and modeling of MAA wih a secial focus on chain ransfer. Unlie o receding invesigaions, [90] he chain-lengh deendence of has o be exlicily aen ino accoun and he imac of CTA concenraion on he variaion of erminaion rae wih degree of monomer conversion has o be accouned for as well. Pars of his chaer have already been ublished: Wienberg, N. F. G.; Bubac, M.; Sach, M.; Lací, I. Macromol. Chem. Phys. 202, 23, Wienberg, N. F. G.; Bubac, M.; Huchinson, R. A. Macromol. Reac. Eng. 203, 7, Chain-Transfer o 2-Mercaoehanol Modeling olymerizaion under he influence of chain-ransfer requires nowledge of he corresonding rae coefficiens. Therefore, he chain-ransfer consan of 2-mercaoehanol for mehacrylic acid olymerizaion in aqueous soluion has been measured for varying MAA conen from 0.05 o 0.3 g g a 50 C. The analysis has been carried ou via boh he Mayo and he chain lengh disribuion, CLD, mehod. XIV Anoher quesion o be answered is, wheher r in aqueous soluion varies wih MAA conen as does or says consan as is he case wih convenional XIV CLD sands for chain lengh disribuion, while CLDT sands for chain-lengh deenden erminaion. While a lile confusing, hese are he common abbreviaions in lieraure. 96

105 Mehacrylic Acid monomers in organic solvens. I urns ou ha C CTA is indeenden of monomer concenraion. Thus, r,cta exhibis he same srong decrease wih monomer concenraion as has been reored for. The quesion was easier o answer wih ME being he CTA, as he associaed C CTA is large and may be accuraely measured. [28,52] Non-ionized MAA was seleced as monomer, because is already nown. [9,59] Moreover, in conras o acrylae-ye monomers, where secondary chain-end radicals may undergo bacbiing reacions o roduce eriary midchain radicals, in MAA olymerizaion only one ye of roagaing radical occurs. The simulaneous resence of hese wo yes of radicals adds comlexiy o he ineic analysis, [33,0,53] as addressed in chaer Chain Transfer Consans deduced by he Mayo Mehod <i n > c ME / c MAA Figure 4- Mayo lo of roduc from olymerizaion of 0.30 g g MAA a 50 C in aqueous soluion a differen levels of hooiniiaor (D73):.3 mmol L (red), 6.56 mmol L (blac), and 32.8 mmol L (green). The corresonding bes fis o a sraigh line are given as doed lines and he concaenae fi as blue solid line. Due o dominance of chain ransfer as chain soing even, he individual sloes are almos idenical. 97

106 Chaer 4 The Mayo mehod requires olymerizaions o be dominaed by chain ransfer as soing even. In order o demonsrae he fulfillmen of he necessary condiions, olymerizaions were carried ou a differen iniiaor concenraions, bu oherwise idenical condiions. The resul of he Mayo rocedure, eq. (2.2), yielding C CTA is shown in Figure 4- for he hree differen iniiaor concenraions. Five imes more and five imes less iniiaor conen han used for he oher exerimens resened laer resuled in almos he same sloe of he Mayo lo i n M n M M <i> n i n M w 2 M M c ME / c MAA Figure 4-2 Inverse of he number average degree of olymerizaion for MAA samles loed as a funcion of he raio of CTA (here ME) o monomer (here MAA) conen. Polymer was roduced by reacion o low degrees of monomer conversion for 0.30 g g MAA in aqueous soluion a 50 C and 6.56 mmol L D73 added as hooiniiaor; daa oins are eiher deduced from Mn (red squares) or from Mw (blue circles). The doed, red line is fied o he daa from Mn (eq. (4.)) and he sraigh, blue line is fied o he daa from MW (eq. (4.2)). The number-average degree of olymerizaion, i n, may be deduced eiher from M n or M w. The qualiy of M deerminaion may be affeced by uncerainies of SEC n analysis a lower molar masses. I hus aeared recommendable o deermine from M w, he value of which is accessible wih beer accuracy han M. In case of n M n 98

107 Mehacrylic Acid ransfer-conrolled olymerizaion, as wih ME being he CTA, disersiy Mw/ M n is close o 2, which allows for an esimae of M from M n w. [23,29] Figure 4-2 shows a yical Mayo lo for MAA olymerizaion in aqueous hase wih i being deduced from SEC curves eiher via eq. (4.) or via eq. (4.2). n i n M M n (4.) M i n M w (4.2) 2M M w (lg (M / g mol )) c ME /c MAA = c ME /c MAA = * c ME /c MAA = lg (M / g mol ) Figure 4-3 Shown are hree yical MMDs of olymer roduced by reacion o low degrees of monomer conversion for 0.5 g g MAA in aqueous soluion a 50 C, cme/cmaa = 0.03 (dashed line) (solid line) (doed line), and 6.56 mmol L D73. The MMD reresened by a doed line has a second maximum mared by an aseris. This occurred only for a few samles of olymerizaions wih high ME conen and was robably caused by oserior iniiaion by ME. The hiol-ene reacion as a ossible mechanism of iniiaion is shown a he o. Analysis was sill ossible (see ex). 99

108 Chaer 4 The daa from boh M and n qualiy of SEC analysis and also suggess ha w n M w are in close agreemen, which demonsraes he M / M is close o 2, as is execed in case of chain ransfer o ME being he dominan chain-erminaing even. As he scaer on he daa from M w is smaller, only hese numbers have been fied by he sraigh line. From he sloe o his line C CTA = 0.6 ± 0.00 is obained. According o he same rocedure, C CTA has been deermined for oher MAA weigh fracions and hooiniiaor concenraions. The so-obained numbers are lised in Table 4-. Using M w for analysis has an addiional advanage. Among he Mayo daa a few resuls of olymerizaions wih high ME concenraion are included where he MMDs of he MAA samles were bimodal robably from subsequen iniiaion by ME (see Figure 4-3). As waer evaoraes faser han MAA and ME, he concenraion of boh laer secies increase during drying and he hiol-ene reacion (Figure 4-3 o) may become imoran. For hese MMDs, he daa oins obained from M (eq. (4.)) deviae from a sraigh line deduced by fiing he values of n monomodal MMDs only. This does no hold rue for fiing via eq. (4.2). The soobained i n values all closely fi o a sraigh line. This is shown in Figure <i n > c ME / c MAA Figure 4-4 Mayo lo of olymer roduced by reacion o low degrees of monomer conversion for 0.5 g g MAA in aqueous soluion a 50 C. Daa oins are eiher deduced from Mn (red squares) or from Mw (blue circles); he blue line is fied o he daa from MW (eq. (4.2)). Daa oins corresonding o bimodal MMDs are mared by an arrow. 00

109 Mehacrylic Acid 4..2 Chain Transfer Consans deduced by he CLD Mehod The CLD mehod esimaes C CTA according o eq. (2.4), which requires he sloe of ln P vs. M lo, eq. (2.3), o be nown. SEC yields he weigh fracion of he M olymer of molar mass M, w M. From w he quaniy M P is obained via M eq. (4.3). [54] ln (P M ) -24 M n M w x x x x0 5 M / g mol Figure 4-5 CLD lo for deerminaion of he chain-ransfer consan according o eq. (4.3) and (4.4); he daa refers o olymer roduced by reacion o low degrees of monomer conversion for 0.30 g g MAA in aqueous soluion a 50 C, cme/cmaa = 0.007, and 6.56 mmol L D73 being added as he hooiniiaor; he sloe o he sraigh line is used for deerminaion of he chain-ransfer consan CCTA (see Figure 4-6). The region of fiing is indicaed by solid line. Mn and Mw are given for orienaion. w M PM (4.3) 2 M 0

110 Chaer 4 w M 2 ln λ M M (4.4) The so-obained ln P vs. M correlaion for MAA from olymerizaion of M 0.30 g g MAA in aqueous soluion a 50 C is shown in Figure 4-5. Sraigh-line behavior is no seen over he enire range of MAA masses. According o eq. (2.3), he daa for very high molar mass should be considered for deducing he sloe, in aricular in cases where erminaion becomes significan. [23,29] The resuling dilemma is illusraed in Figure 4-5 by indicaing he osiions of M n and M w, which are in he region of maximum signal inensiy. In his region, molar mass is no sufficienly high as o allow for deerminaion of he chain-ransfer consan. On he oher hand, he very high molar mass region, e.g., above g mol, is oo oor in signal qualiy as o rovide a reliable esimae of he sloe The CLD mehod has hus been alied in his examle o molar masses around g mol (Figure 4-5, solid line), o which he sraigh line is fied. In general, he region used was a comromise beween choosing he highes molar masses, and sill having sufficien signal inensiy. The region of maximum RI inensiy is no suiable for CLD analysis in his examle. An examle of a final lo yielding Figure 4-6. C CTA from he CLD mehod is deiced in 02

111 Mehacrylic Acid (M M ) c ME / c MAA Figure 4-6 The aseris symbols reresen he resuls from CLD fiing according o eq. (4.4). The doed line reresens he sloe aen from he Mayo lo in Figure 4-2 for he same exerimenal condiions: 0.30 g g MAA in aqueous soluion a 50 C, and 6.56 mmol L D73. This line has almos idenical sloe as one from fiing he aseris symbols o a sraigh line, which yields CCTA from CLD mehod (Table 4-). The daa oin mared by he arrow is he one deduced from he sloe o he fied line in Figure Comarison of Mayo and CLD mehods Daa obained for C CTA from he CLD mehod are reresened by he aseris symbols in Figure 4-6. The resuls from he Mayo rocedure (see Figure 4-2) are given by he doed line. The CLD resuls exhibi a significanly larger scaer han he Mayo ones. The C CTA values from he wo rocedures are comared in Table 4-. Wihin he larger scaer of he CLD daa, good agreemen beween he Mayo and CLD mehod is found. The uncerainy is slighly larger a he lowes MAA conen (0.05 g g ). I should furher be noed from Table 4- ha he CLD mehod yields unusually high C CTA a he larges hooiniiaor concenraion, which is mos liely due o he occurrence of smaller radicals and hus o a larger imac of erminaion 03

112 Chaer 4 affecing CLD analysis. Wih he exceion of his aricular C CTA value, he daa in Table 4- indicae ha C CTA a 50 C is more or less indeenden of boh MAA and hooiniiaor concenraion. The boom enry in Table 4-, liss he resul from an exerimen a 90 C. Comarison wih he associaed exerimen a 50 C ells ha he Mayo and CLD mehods yield oosie rends for he emeraure effec on which may be undersood as an indicaion of C CTA, C CTA no being deenden on emeraure o a significan exen, as execed (see subchaer 2.3.). The Mayo mehod aears o rovide simle bu accurae access o he ransfer consan in case of high CTA aciviy wih olymerizaion in aqueous soluion..25 C CTA / C CTA,w = /,w = w MAA Figure 4-7 Relaive CCTA and (wih resec o he associaed value for wmaa = 0.05). The CCTA/CCTA(wMAA = 0.05) daa refers o MAA olymerizaion a 50 C, blue riangles oining righ: Mayo mehod, aqua riangles oining lef: CLD mehod. The daa oins scaer more for lower concenraions. The daa is aen from ref. [59,2] The essenial resul of he resen sudy is illusraed in Figure 4-7, in which boh C CTA and are loed relaive o he resecive values a w MAA 0.95 g g. Whereas C CTA is indeenden of monomer conen, exhibis he well-nown srong decrease uon enhancing MAA concenraion. This observaion says ha he genuine ineic effec associaed wih hindrance o roaional moion in he 04

113 Mehacrylic Acid ransiion sae srucure by he molecular environmen is rimarily due o characerisics of he radical chain-end and hus is more or less idenical for roagaion and for ransfer o he CTA. The imoran consequence of his finding is ha he nown enormous variaion of wih monomer concenraion, and hus wih conversion, also alies o chain ransfer, which may easily be aen ino accoun by adoing consan C CTA for a wide range of monomer concenraion. This finding robably holds for oher ransfer reacions, e.g., ransfer o monomer, as well. I was found for modeling MAA olymerizaion in aqueous soluion ha ransfer o monomer had o be included and boh he r / consan and he consan aroach were esed. [90] The firs aroach gave a slighly beer r reresenaion of he exerimenal MMDs, alhough, wihin exerimenal accuracy i was no ossible o decide wheher he rae coefficien of ransfer is affeced in he same way by he monomer-o-waer raio as is. The findings of he resen wor indicaes ha he r / consan aroach is correc. Table 4- Chain-ransfer consans, CCTA, of ME in MAA olymerizaions in aqueous soluion a differen MAA concenraions, cmaa, and iniiaor concenraions, cd73, a 50 and 90 C deduced via he Mayo and he CLD mehod. The uncerainies are esimaed as wice he saisical error of each underlying exerimenal series. The weighed mean value were calculaed. C CTA (Mayo) C CTA (CLD) variaion of MAA (50 C, D73 / mmol L 6.56 ) (5 w.%) 0.38 ± ± (5 w.%) 0.25 ± ± (30 w.%) 0.6 ± ± 0.05 mean value 0.2 ± ± 0.02 variaion of c D73 / mmol L (50 C, MAA / mol L 3.60 ) ± ± ± ± ± ± 0.02 mean value 0.2 ± ± 0.02 variaion of emeraure / C ( MAA / mol L 0.600, D73 / mmol L 6.56 ) ± ± ± ±

114 Chaer Model develomen for Non-ionized Mehacrylic Acid Bach radical olymerizaion of non-ionized mehacrylic acid, g g in aqueous soluion, has been sudied beween 35 and 50 C a ambien ressure wih 2-mercaoehanol as he chain-ransfer agen. Iniial olymerizaion rae decreases wih CTA concenraion, which has been varied u o ncta / nm In order o illusrae he influence of CTA, hree conversion vs. ime rofiles of olymerizaions wih differen level of CTA conen (bu oherwise idenical condiions) are deiced in Figure 4-8. Kineic modeling is resened, which includes chain-lengh-deenden erminaion and uses an emirical funcion o accoun for he deendence of erminaion rae on boh monomer conversion and molar mass of he olymeric roduc. In conjuncion wih PREDICI TM simulaion, hese models afford for an adequae reresenaion of he measured monomer conversion vs. ime rofiles and MMDs. The ineic models consider iniiaion, roagaion, erminaion, ransfer o monomer and ransfer o a CTA. Using a highly efficien CTA, such as ME, reduces chain lengh o an exen ha requires he deendence of on radical chain lengh and on he molar mass (disribuion) of he roduced olymer o be aen ino accoun. The reacion scheme is resened in Table 4-2, where I2 reresens he iniiaor, which decays hermally wih he rae coefficien d and exhibis a growh efficiency, f, of rimary radicals I. Wihin a firs addiion se, a growing chain P of lengh uniy is formed from I and one monomer molecule M. The radical chain grows by addiion of monomer molecules wih he rae coefficien. Terminaion of wo radicals may occur via combinaion, wih rae coefficien c, roducing a (dead) macromolecule D, or via disroorionaion, which roceeds wih rae coefficien by hydrogen ransfer and resuls in he formaion of wo macromolecules. Chain growh also ceases uon ransfer o monomer or o a CTA. The chain lengh of olymeric secies is given by he indices i, j, or. Radical secies are mared by a do, e.g., P i. The values of he individual rae coefficiens, are summarized in Table 4-3 and Table 4-4, resecively d 06

115 Mehacrylic Acid no CTA c ME /c MAA = c ME /c MAA = 0.03 X 0.50 c ME /c MAA = g g MAA ime / s Figure 4-8 Polymerizaion of 0.30 g g MAA in aqueous soluion wih 0.00 g g V-50 as iniiaor a 50 C. The relaive CTA conen is given for each rofile in he grah. The azo-iniiaor V-50 was used, as eroxides and hiols may form a redox iniiaion sysem. [55] Moreover, iniiaor decay should be indeenden of H, which is he case wih V-50. [56] V-50 decomoses according o a firs-order rae law wih a half-life of abou 0 hours a 50 C. [56] This slow iniiaor decay ensures almos consan iniiaor conen during he reacion and avoids dead-end olymerizaion. Iniiaor efficiency was assumed o be f = 0.8, which is a yical value ha has successfully been used for modeling. [90] The variaion of densiy was considered in he simulaion by assuming ideal mixing. The emeraure deendence of he densiy of monomer and solven was fied by a hird-order and a second-order olynomial, resecively. [57] I was checed ha he hiol-ene reacion does no lay a significan role for he sysems under invesigaion. 07

116 Chaer 4 Table 4-2 Individual reacion ses used for modeling radical olymerizaion of non-ionized mehacrylic acid in aqueous soluion. iniiaor decomosiion I2 f d 2I chain iniiaion I M R roagaion Ri M Ri erminaion by combinaion by disroorionaion c R R P i j i j d R R P P i j i j chain ransfer o monomer o CTA r,m Ri M Pi R r,cta Ri CTA Pi R 0 The variaion of as a funcion of iniial MAA weigh fracion, w MAA, of degree of monomer conversion, X, and of emeraure, is nown from lieraure;,max in Table 4-3 refers o roagaion in highly dilued aqueous soluion. [2] There are indicaions of being chain-lengh deenden u o i = 0. [8] This deendence needs o be considered under condiions of exreme chain ransfer, as wih caalyic chain-ransfer agens. [49] For he resen sysem no need for incororaion of his effec was found. C CTA for ME is 0.22, wih his number being insensiive owards MAA-o-waer conen and emeraure (4.). Transfer o monomer is nown from lieraure [90] and as C CTA was found o be consan, he same was assumed for C. M xx The fracion of erminaion by disroorionaion,, was assumed o be 0.8, which is a yical value for mehacrylaes. [90] The comosie model is used for reresenaion of chain-lengh-deenden erminaion. Informaion abou as a funcion of MAA concenraion and of radical chain lengh is available from SP PLP EPR exerimens. [20] To avoid he high comuaional effor associaed wih considering individual reacions beween wo radicals of chain lenghs i and j, resecively, erminaion is scaled via he number-average radical size. The chainlengh deendence of has been imlemened ino PREDICI TM via he comosie 08

117 Mehacrylic Acid model wih he relevan chain lengh being given by he number-average size. This rocedure is associaed wih only modes addiional comuaional effor. This rocedure is based on he fac ha averaged over all chain lenghs,, has been shown o be equal o he of he average chain lengh of ha disribuion, i n, imes a correcion facor, d, which is usually close o uniy as given in eq. (4.5). [07,58-6] The correcion facor resuls from he fac ha shorer chains conribue more o overall erminaion. Eq. (4.5) is valid in case of erminaion being dominan. d l l 2 l l (4.5) In case of ransfer being dominan eq. (4.5) ransforms ino eq. (4.6) yielding almos he same resul. [6] d 2 l (4.6) 0 l d i n (4.7) Beyond chain-lengh deendence, he variaion of wih monomer conversion has o be incororaed. Such informaion is available from SP PLP NIR measuremens. Wihin he resen sudy, he effecs of chain lengh and conversion on erminaion rae are boh aen ino accoun o allow for simulaion of MAA olymerizaion in aqueous soluion wihin a wide range of CTA concenraions and u o comlee degrees of monomer conversion. 09

118 Chaer Modeling Polymerizaion a Medium iniial Monomer Conen The enries in Table 4-3 demonsrae ha a large body of ineic informaion on MAA radical olymerizaion in aqueous MAA soluion is available from indeenden exerimens. I is essenially erminaion ineics a differen levels of ME concenraion, which remains o be deermined via simulaion of he exerimenal monomer conversion vs. olymerizaion ime daa. Under condiions of highly efficien chain ransfer, e.g., wih ME, he disribuions of radical size and of olymer molar mass are conrolled by roagaion and ransfer raes. 0 8 s = 0.62 < > / L mol s s = 0.6 i c = 68 i c = 00 l = 0.66 l = M n (R) / g mol Figure 4-9 Dar blue squares: Iniial values deduced as mean values from he conversion range 0 < X < of MAA olymerizaions (0.30 g g in aqueous soluion) a varying cme/cm u o 0.2. The abscissa values are simulaed number-average values of growing olymer chains. Solid blue line: fiing according o he comosie model; daa oins for Mn below 5852 g mol were used for fiing he shor-chain behavior, whereas daa a higher average molar masses are subjeced o fiing he long-chain behavior. Red dashed line: i,i and s from SP PLP EPR wor on MAA; [20] in dashed line: exraolaion wih ic of MAA and l from heoreical consideraions. [06,9] To deermine he effec of radical chain lengh on wihou inerference of conribuions from olymer-induced viscosiy changes, raes a differen ME 0

119 Mehacrylic Acid concenraions and low degrees of monomer conversion, i.e., below 2.5 ercen were esimaed under he assumion of being indeenden of monomer conversion. The so-obained values are loed as a funcion of he number-average size of growing olymer chains, wih hese laer values being deduced from simulaion. A double-log lo of he resuling vs. he number-average radical size is shown in Figure 4-9. CTA concenraion has been widely varied which resuls in he broad range of radical sizes. In addiion o from simulaion of measured MAA conversion vs. ime races ii, (oen square symbols), values of deduced from SP PLP EPR exerimens [20] are reresened by he dashed line in Figure 4-9. The EPR exerimen is highly insaionary, bu refers o a narrow disribuion of radical chain lenghs. Terminaion occurs beween wo radicals of aroximaely he same size, which increases linearly wih ime afer ulsing. The square symbols refer o erminaion under saionary condiions wih he reacing radicals exhibiing a broad disribuion of chain lenghs. The number-average size of radicals, M n, is obained as he mean value over a broad disribuion of radical sizes, whereas he abscissa value for he SP PLP EPR daa refers o a narrow disribuion of radical chain lenghs. In view of his fundamenal difference, he daa from he wo exerimens are remarably close o each oher in sloe, hus in, s bu also in absolue value. ii, The close comarison also holds for exraolaed o longer radical chain lenghs, which values are illusraed by he in dashed line in Figure 4-9. This line is consruced by adoing he cross-over chain lengh of mehyl mehacrylae (MMA) for MAA and aing he ower-law exonen l from heory. [06,9] From SP PLP EPR, he value of s for MAA was deermined o be 0.62 ± 0.06, [20] which is close o s 0.6, he corresonding number from he resen sudy. I should however be noed ha he laer s is based on only hree daa oins. For MMA bul olymerizaion, has been obained from SP PLP EPR measuremens s o be 0.63 [03] and from RAFT-CLDT o be [9] So far, no value of eiher i c or has been measured for MAA by he SP PLP EPR echnique because of oor signal inensiy. [20] The values for MMA are close o i c = 00 [07] and l l = 0.6. [06] The corresonding numbers deduced wihin he resen sudy from he <> vs. Pn correlaion in Figure are: i c 68 and l 0.7. In Figure 4-9, an offse is seen beween he dashed and he solid line, which corresonds o, from saionary exerimens being by a facor of 0.7 below he SP PLP EPR value. However, according o heory, [6] his facor should be.27 (calculaed from eq. (4.6), eq. (4.5) gives.2). Closer insecion ells ha he wo lines corresond o differen sysems, 0. g g MAA in H2O and 0.3 g g MAA in

120 Chaer 4 D2O boh a 50 C. Viscosiy measuremens for hese wo soluions a ambien ressure resuled in he values and.2064 mpa s, resecively. The associaed raio of viscosiies is In conjuncion wih he heoreical facor of.27 he raio of, values hus should be = 0.704, which is in erfec agreemen wih he measured difference. The close comarison demonsraes he, dominan effec of viscosiy on. The saisfacory agreemen of he wo yes of reresenaions (Figure 4-9) rovides suor for alying he comosie model o he correlaion of he low conversion chain-lengh-averaged erminaion rae coefficien wih average radical chain lengh, i, according o he full line in Figure. Below M n n = 5852 g mol, which corresonds o i c = 68, he exression for shor-chain radicals, eq. (4.8), has been used, whereas eq. (4.9) has been alied for long-chain radicals. In wha follows, always refers o he chain lengh averaged rae coefficien; for reasons of convenience, chevrons are omied. i i i (4.8), s,cld n n c, s l l 0 l,cld c n n n c i i i i i (4.9) Afer focusing on CLDT, he variaion of erminaion rae wih monomer conversion will now be addressed. A low degrees of monomer conversion, segmenal diffusion (SD) oeraes, which is conrolled by he viscosiy of he monomer-solven mixure. Over an iniial range of monomer conversion, he associaed coefficien,sd remains more or less consan which resuls in a laeau value of u o moderae degrees of monomer conversion. A higher conversion, sars o clearly decrease, as erminaion ransiions o ranslaional diffusion conrol wih he associaed rae coefficien,td scaling wih he inverse viscosiy of he olymerizing medium. This ye of bul viscosiy includes he imac of he concenraion and of he ye of olymer roduced during he course of a aricular olymerizaion.,td is exressed 0 in erms of,td, he hyoheical erminaion rae coefficien under ranslaional 0 diffusion conrol rior o olymerizaion, and of r, he relaive viscosiy, r / 0 wih referring o he viscosiy of he iniial soluion rior o olymerizaion. Towards even higher conversion, cener-of-mass diffusion of macroradicals 2

121 Mehacrylic Acid essenially ceases and erminaion runs under reacion-diffusion (RD) conrol, which assumes wo radical sies o aroach each oher by roagaion of he chain ends in conjuncion wih mobiliy of chain segmens. Terminaion under RD condiions hus scales wih via he reacion-diffusion consan, C RD, which is enhanced by chain flexibiliy. The exression of he resen sudy ino soluion olymerizaion,td uses monomer concenraion, eq. (2.4). A very high conversion and hus high viscosiy even roagaion may run under diffusion conrol. (see subchaer 2.4.5) The variaion of relaive viscosiy has been described by an exonenial relaion conaining one single arameer C. [90] Adoing his noaion and assuming no o run under diffusion conrol, urns eq. (2.43) ino eq. (4.0), which has been successfully alied for modeling MAA olymerizaion in aqueous soluion. [90] * C RD X e XC,SD 0,TD (4.0) For an iniial MAA conen of 0.6 g g, he laeau value of consan (bu chainlengh deenden) he region of consan,sd holds u o abou X 0.. For an MAA conen of 0.3 g g,,sd is aroximaely wice as large and exends u o X 0.2 wih hese ranges, however, being affeced by he size and he srucure of roduced MAA. [2] As no bacbiing occurs during MAA olymerizaion, ideal olymerizaion ineics, XV eq. (2.7), has been used for esimaing monomer conversion vs. ime daa of all exerimens. Figure 4-0 illusraes as a funcion of X from exerimenal daa deduced via eq. (2.7) for wo olymerizaions in he absence of CTA. The differen regions of diffusion conrol, i.e., by SD, TD, and RD are clearly seen. Also resened in Figure 4-0 are conversion vs. ime rofiles measured a wo ME levels. The iniial laeau region which is assigned o SD, increases wih ME conen and exends over he enire exerimenal conversion range a he highes ME concenraion. A cme / cmaa 0.2, he laeau value for erminaion under SD conrol is significanly above a lower ME conen. The laeau value for MAA olymerizaion wih cme / cmaa is close o he one for XV Here, ideal refers o each single daa oin, i.e., overall consancy is no assumed. Moreover, CLD-T is no excluded. 3

122 Chaer 4 MAA olymerizaion wihou CTA. The conversion range of SD conrol is however larger han in he absence of ME. Moreover, he decline of in he TD region is less ronounced. The daa for chemically induced MAA olymerizaion wih cme / cmaa is remarably close o deduced from SP-PLP-NIR exerimens on 0.3 g g MAA in aqueous soluion wihou CTA. [2] The reason behind his agreemen robably is ha he high radical concenraion, which is insananeously roduced by he laser ulse, leads o similarly low molar masses as in chemically induced olymerizaions wih cme / cmaa CI, 0.2 c ME /c MAA log( / L mol s ) 7 6 SD 0.3 g g MAA TD CI, c ME /c MAA SPPLPNIR 5 CI, no CTA (wo exerimens) RD X Figure 4-0 Deendence of he erminaion rae coefficien on monomer conversion as derived from ideal olymerizaion ineics (eq. (2.7)) for four chemically iniiaed (CI) olymerizaions (0.30 g g in aqueous soluion) a ambien ressure; daa oins were smoohed; he aseris symbols are daa from SP PLP NIR exerimens (wmaa 0 = 0.30 g g, 50 C, 2000 bar), [2] which were exraolaed o ambien ressure wih eq. (2.25) via he acivaion volume of 2.4 cm 3 mol. The ME concenraions are given in he Figure. The noaions SD, TD, and, RD refer o conrol of erminaion by segmenal, ranslaional (cenre-of-mass), and reacion diffusion, resecively. Eq. (4.) has been conceived as an exression for, in which chain-lengh deendence and conversion deendence are merged ogeher. Asecs of conversiondeenden s [20] and [08] have already been discussed. Mos sudies ino CLDT l 4

123 Mehacrylic Acid refer o low monomer conversion, whereas sudies ino he conversion deendence ignore CLDT. No clear indicaions for a oenial deendence of s and of on l monomer conversion were found. Hence, boh ower-law exonens are assumed o be insensiive owards monomer conversion. In eq. (4.), he arameers,sd and 0,TD are relaced by sd,cld,sd 0 / and by d /,CLD,TD. The arameers sd and d accoun for he relaive conribuions of segmenal diffusion and ranslaional diffusion: η,cld e XC RD M sd d C c (4.) Transformaion of eq. (4.) ino eq. (4.8) and eq. (4.9), resecively, requires: sd + d = for X = 0. Analysis of he individual monomer conversion vs. ime rofiles by fiing o eq. (4.) via he Levenberg-Marquard algorihm yields numbers for sd, C RD d, C, and. The arameers sd = 0.96 ± 0.0 and d = 0.04 ± 0.0 urned ou o rovide an adequae reresenaion of for he enire se ( 0.3 g g MAA) of measured conversion vs. ime races. The conversion deendence of erminaion rae on ME concenraion is exclusively assigned o C. The imac of ME conen is hus conained in,cld and in C. The arameer C RD 20 was deduced from olymerizaion raes measured in he absence of ME. This value is in reasonable * agreemen wih he one of MMA, for which C RD = 93.5 was measured, which corresonds o C RD 0.3. [30] Assuming o be indeenden of chain lengh resuls in,rd being also insensiive oward chain lengh. Illusraed in Figure 4- are he individual conribuions of he erms in eq. (4.) o overall for MAA olymerizaion ( 0.3 g g ) in aqueous soluion wihou CTA being resen.,cld remains essenially consan over he wide conversion range, in which average chain-lengh dros only by a facor of 2.6. U o abou X = 0.6, he firs erm on he RHS eq. (4.) dominaes and RD lays no significan role. Above 0.74,,RD exceeds he firs erm. 5

124 Chaer 4 7 SD,CLD log( / L mol s ) 6 TD as realized in model RD 5,RD wihou,rd X Figure 4- Conribuions o overall according o eq. (4.) as a funcion of degree of monomer conversion. The noaions SD, TD, and, RD refer o conrol of erminaion by segmenal, ranslaional (cenre-of-mass), and reacion diffusion, resecively. The arameer C may be deduced by PREDICI TM fiing of he enire body of olymerizaion daa for a wide range of molar masses, which may be achieved by variaion of CTA conen. In Figure 4-2 he so-obained C values are loed as a funcion of he weigh average molar mass a X = 0.5, a value which is close o he mean molar mass aen over he enire conversion range. The enire se of exerimenal C vs. M w daa is fied by eq. (4.2) which resuls in he arameer values a =.4 and b = 0.5. Ineresingly, his value for b is similar o he ower-law exonen for self-diffusion of olymer in good solvens (see subchaer 2.4.4) and hus also similar o. l b C a M w (4.2) 6

125 Mehacrylic Acid Combinaion of eq. (4.) and eq. (4.2) relaces C by a and b. Thus, by using one addiional arameer, an adequae reresenaion of he measured conversion vs. ime races a widely differen olymer molar masses is achieved. The combined influence of M w of dead olymer in soluion and chain lengh of macroradicals (long-chain region) on is deiced in Figure 4-3 o. The weigh of he former is a X 0.5 much sronger. M w and X have he same influence on shown in Figure 4-3 boom. 2 0 C c sd d e,cld X C RD M C.4 M w 4. 8 C M w (P) / g mol Figure 4-2 Correlaion of C wih he weigh-average molar mass of MAA roduced u o X = 0.5 a differen levels of chain-ransfer agen ME. The symbols are deduced from PREDICI TM fiing of exerimenal conversion-ime daa. The obained fi arameers refer o eq. (4.2), which exends eq. (4.). Illusraed in Figure 4-4 is he imac on of ME concenraions u o c / c 0.2 according o eq. (4.) and eq. (4.2). The minor increase of uon ME MAA enhancing monomer conversion a he highes ME conen resuls from a wea decrease of radical chain lengh owards lower MAA conen, i.e., oward higher 7

126 Chaer 4 conversion. In addiion o he logarihm of, he square roo of is loed (in he lower ar of Figure 4-4). The inverse of he laer quaniy scales wih boh rae of olymerizaion and ineic chain lengh. The qualiy of he ineic model associaed wih he rae coefficiens summarized in Table 4-3 is illusraed by comarison of measured and simulaed monomer conversion vs. ime races in Figure 4-5. The model urns ou o adequaely reresen he olymerizaion ineics of 0.3 g g MAA in aqueous soluion a 50 C for ME conens beween zero and cme / cmaa 0.2. For 0, 0.05 and 0. ME conen, reea exerimens are included. They demonsrae ha he qualiy of simulaion is close o exerimenal reroducibiliy. A high monomer conversion, he model slighly overesimaes olymerizaion rae, which may be arly due o reduced iniiaor efficiency or o diffusion conrol of henomena are no included in he model. a very high viscosiy. These 8

127 Mehacrylic Acid Figure 4-3 The deendence of on molar mass of olymer in soluion and chain lengh of macroradicals a X = 0.5 is loed a he o. The deendence of on molar mass of olymer in soluion and degree of monomer conversion a <in> = 0 5 is loed a he boom. 9

128 Chaer / L mol s x ( / L mol s ) 6.0x x x X Figure 4-4 Deendence of overall erminaion rae coefficien,, and of 0.5 (lower figure) on monomer conversion, as esimaed from eq. (4.) and eq. (4.2) wih he arameer values being deduced from PREDICI TM fiing of he exerimenal MAA conversion vs. ime races for wmaa 0 = 0.30 g g and 50 C. cme/cmaa is indicaed a each curve. 20

129 Mehacrylic Acid X ime / s Figure 4-5 Comarison of measured and simulaed MAA conversion vs. ime los (for differen cme o cmaa raios as given for each grah) for MAA olymerizaions (wih 0.30 g g MAA) a 50 C, ambien ressure, and 0.00 g g V-50 as he iniiaor. Deiced as squares in blue are he exerimens and in cyan reea exerimens (for cme/cmaa = 0, 0.05 and 0.0). The simulaions hereof are indicaed by he red lines. 2

130 Chaer 4 Table 4-3 Summary of rae coefficiens and oher arameers used for modeling radical olymerizaion of 0.3 g g non-ionized mehacrylic acid in aqueous soluion a 50 C. reacion se rae exression ref. iniiaor decomosiion d / s ex ( T / K) [56] f 0.8 [90] roagaion erminaion ,max L mol s ex T /K wmaa X ex 0,max wmaa X 0 0. wmaa X / bar ex wmaa X T /K 3, L mol s ex XVI i 68 : L mol s i, n, X =0 n T /K 0.6 i 68 : L mol s 68 i, n, X =0 n C M w.4 g mol 0.5 XC X 0.66 L mol s e 20 c, =0 M [2] [20] his sudy his sudy ransfer densiy c L mol s 0.8 d C C L mol s 0.8 [90] r, M 5 r,m [90] r,cta CTA.22 0 [62] 4 MAA / C / C 5 HO g ml / C / C g ml / C.32 0 [57] XVI The value is already correced for a disribuion of chain lenghs. 22

131 Mehacrylic Acid Modeling Polymerizaion a Low iniial Monomer Conen In his subchaer he erminaion behavior of comared o he daa for 0. g g MAA is deal wih and 0.3 g g iniial weigh fracion of monomer. Under condiions of efficien chain ransfer, as wih ME, he disribuions of radical size and of olymer molar mass are conrolled by roagaion and ransfer raes. Furhermore, i is demonsraed ha he decline of wih conversion caused by he resence of olymer also deends on he amoun of monomer being resen a he same ime. A slow rae of iniiaion and in he absence of CTA, ransfer o monomer becomes he essenial chain soing even. Modeling olymerizaion of MAA a lower iniial monomer concenraion was carried ou analogously o he modeling rocedure described in subchaer XVII The enries in Table 4-3 demonsrae ha a large body of ineic informaion on MAA radical olymerizaion in aqueous MAA soluion is available from indeenden exerimens. As wih he revious modeling roblem, i is essenially erminaion ineics a differen levels of ME concenraion, which remains o be deermined via simulaion of exerimenal monomer conversion vs. olymerizaion ime daa. In wha follows, refers o he chain-lengh averaged rae coefficien; for reasons of convenience, chevrons are omied. To deermine he effec of radical chain lengh on wihou inerference of conribuions from olymer-induced viscosiy changes, raes a differen ME concenraions and low degrees of monomer conversion, i.e., below 2.5 ercen were esimaed under he assumion of remaining consan. The so-obained values are loed as a funcion of he number-average size of growing olymer chains, wih hese laer values being deduced from simulaion. Wih accurae values for and C CTA being available, hese calculaed values should be recise. A doublelog lo of he resuling vs. he number-average radical size is shown in Figure 4-6. CTA concenraion has been widely varied which resuls in he broad range of radical sizes. This was done for hree ses of exerimens: 0. g g MAA 50 C, and 0.3 g g MAA a 50 C, 0. g g MAA 35 C. The values for 35 C were exraolaed o 50 C alying E A 22 J mol from li. [20] XVII Some of he conversion ime and MMD daa used for modeling in his subchaer were aen from revious wor. [47] 23

132 Chaer 4, Surrisingly, is, wihin exerimenal uncerainy, he same for 0. g g MAA. Thus, he reresenaion of chain-lengh deendency of raio of viscosiy for 0.3 g g and a negligible conversion, viz., he can be adoed from he revious subchaer. The 0.3 g g and suggess ha should be higher for 0. g g MAA conen ( /.5) MAA 0.3 wmaa 0. w 0. g g MAA conen by a facor of.5. This may indicae an influence of MAA conen on he olymer coil dynamics. 0 8 / L mol s M n (R) / g mol Figure 4-6 Symbols: Iniial values deduced as mean values from he conversion range 0 < X < of MAA olymerizaions in aqueous soluion a varying cme/cm u o 0.2. The abscissa values are simulaed number-average values of growing olymer chains. Blue squares: wmaa = 0.30 g g, wv-50 = 0.00 g g, 50 C; circles: wmaa = 0.0 g g, wv-50 = 0.0 g g, 50 C; riangles: wmaa = 0.0 g g, 35 C exraolaed o 50 C alying EA from li. [20] Line: fiing of he 0.30 g g daa according o he comosie model; daa oins for Mn below 5852 g mol were used for fiing he shor-chain behavior, whereas daa a higher average molar masses are subjeced o fiing he long-chain behavior. The chain-lengh deendency of for 0.0 g g and 0.30 g g is in good agreemen. As no bacbiing occurs during MAA olymerizaion, ideal olymerizaion ineics, XVIII eq. (2.7), has been used for esimaing as a funcion of X from XVIII Here, ideal refers o each single daa oin, i.e., overall consancy is no assumed. Moreover, CLD-T is no excluded. 24

133 Mehacrylic Acid exerimenal monomer conversion vs. ime daa in he same way as for higher MAA concenraion. The resul for hree CTA concenraions is shown in Figure 4-7. The mos ronounced decrease of occurs for olymerizaions wihou CTA. The reroducibiliy is very good. The daa oins in blue and cyan, belonging o exerimens under osensibly he same condiions, show close agreemen (see Figure 4-7). The reducion of owards higher degree of monomer conversion becomes less ronounced as he ME conen increases. The iniial value of increases wih higher ME conen, as has been discussed for Figure 4-9 and Figure 4-0, resecively. A cme / cmaa 0.2, is significanly higher han a lower ME conen and does no change wih X. 8.0 log( / L mol s ) no CTA (wo exerimens) c ME /c MAA = 0.2 c ME /c MAA = X Figure 4-7 Deendence of he erminaion rae coefficien as deduced by adaing ideal olymerizaion ineics (eq. (2.7)) for olymerizaion of 0.0 g g MAA in aqueous soluion wih 0.0 g g V-50 a ambien ressure. The realive ME concenraions are given in he figure. In Figure 4-8, he deendence of on ME conen and degree of monomer conversion is comared for w 0 0. g g and w g g. For he 0.3 g g MAA MAA he iniial laeau region of, which is assigned o SD, increases wih ME conen MAA 25

134 Chaer 4 and exends over he enire exerimenal conversion range a he highes ME concenraion. The decline of in he TD region is less ronounced, he higher he ME conen. The iniial value of increase owards higher ME conen, which becomes visible a high levels of CTA. For he 0. g g MAA, he Norrish Trommsdorf effec is much weaer, due o he wea increase of olymer conen owards higher monomer conversion. For CTA-free olymerizaion, he concenraions, bu a X = 0.8 he value a X = 0 is he same for he wo iniial MAA value for w g g is by one and a half MAA 0 orders of magniude below he one for w MAA 0. g g. Aside from ha, here are no ronounced SD and TD dominaed regions for low MAA conen. The form may be described as a iled laeau. Bubac e al. [90] also found for olymerizaions wihou CTA and MAA conen of 0. g g, 0.2 g g, and 0.3 g g ha he Norrish Trommsdorf effec becomes weaer owards low iniial monomer conen. The daa was more scaered and all olymerizaions were modeled wih only varying wih resec o reacion diffusion. In his wor, a more fundamenal reamen of erminaion ineics is carried ou. The general effec of adding CTA is he same for boh Towards higher ME conen, ME MAA 0. g g and 0.3 g g MAA. is larger and varies less wih conversion. A c / c 0.2, he value for erminaion is he same for boh iniial weigh fracions over he enire range of conversion (see Figure 4-8). Analysis of he individual monomer conversion vs. ime rofiles of 0. g g MAA (wihou addiion of ME) by fiing o eq. (4.), via he Levenberg-Marquard algorihm, yields numbers for sd, d and, C. The rocedure was he same as alied for 0.3 g g MAA. The arameer C RD is 20, as for 0.3 g g MAA. The arameers sd = 0.00 ± 0.0 and d =.00 ± 0.0 urned ou o rovide he bes reresenaion of for he enire se of measured MAA conversion vs. ime races a 0. g g MAA. Eq. (4.) is urned ino eq. (4.3). Differences in he conversion deendence of erminaion rae on ME concenraion are exclusively assigned o C. The imac of ME conen is hus conained in,cld (v.s.) and in C (v.i.). C c (4.3),CLD RD M η e XC 26

135 Mehacrylic Acid 8 log( / L mol s ) SD TD w 0 MAA w 0 = 0.3 MAA c ME /c MAA = 0.2 w 0 = 0. MAA w 0 MAA = 0., no CTA = 0.3, no CTA RD X Figure 4-8 Deendence of he erminaion rae coefficien as derived from ideal olymerizaion ineics (eq. (2.7)) for hree olymerizaions (0.30 g g MAA wih 0.00 g g V-50, (blue/darblue) and 0.0 g g MAA wih 0.0 g g V-50 (cyan/ale cyan) in aqueous soluion). The relaive ME concenraions are given in he Figure. The noaions SD, TD, and, RD refer o conrol of erminaion by segmenal, ranslaional (cenre-ofmass), and reacion diffusion, resecively. Given he iniial laeau of for w 0 MAA 0.3 g g and considering olymer conen, one may exec consan for w 0 0. g g over almos he whole conversion MAA range. However, he olymer conen for w 0 0. g g a X = 0.6 is he same for w 0.3 g g a X = 0.2, bu he value of he former is lower by a facor of five. 0 MAA This asec will be addressed in wha follows. Imuriies ha funcion as rearders lead o an increased aaren. As hey are consumed during he course of olymerizaion, heir effec on aaren decreases, which means ha he aaren decreases as well. Given he iniial values of he olymerizaion wih w 0 MAA 0. g g being he same as he ones of he olymerizaion wih w g g, a reardaion of he former olymerizaion MAA aears raher unliely (see Figure 4-8). In order o chec wheher such imuriies affec he olymerizaion a MAA 0. g g iniial weigh fracion of MAA, a wo-se exerimen was carried ou. The reacion mixure was reared as before, bu rior o chemically iniiaed olymerizaion

136 Chaer 4 UV-laser ulses were alied. XIX Azo-comounds can be used as boh chemical and hooiniiaors. The high energy laser ulses cause V-50 o decay and, wih each ulse, high radical concenraions are achieved. They do no lead o significan monomer conversion, because of high erminaion rae. Comonens ha reac wih growing chains faser han does he monomer are used u o a significan exen. Afer he laser cleaning, wihin he second se, a chemically iniiaed olymerizaion was carried ou as wih he oher samles. Due o a high iniiaor concenraion in he beginning, high radical roducion by he laser ulses is combined wih he iniiaor concenraion being reduced slighly only X X ime / s ime / s Figure 4-9 Comarison of wo olymerizaions of 0.0 g g MAA wih 0.00 g g V-50 as he iniiaor in aqueous soluion a 50 C and ambien ressure. Red riangles: chemically iniiaed olymerizaion; Blue sars: Firs, hooolymerizaion leading o high radical concenraion and o X = Second, chemically iniiaed olymerizaion; ime zero was correced. In he inser he region of low conversion is deiced enlarged. Laser cleaning was carried ou by a LPXro 240 (Coheren), 200 ulses were alied (00 Hz, 74.3 mj er ulse) XIX This se was carried ou wih he hel of Dr. Jens Schrooen. 28

137 Mehacrylic Acid The conversion-ime rofiles of a olymerizaion wih laser cleaning is comared o a olymerizaion under he same condiion, bu wihou laser ulses being alied, in Figure 4-9. Laser iniiaion led o X = 0.03; he ime zero of he rofiles was correced accordingly. The wo conversion-ime rofiles, wih and wihou laser cleaning, are in erfec agreemen u o X = 0.4. Hence, imuriies funcioning as rearders rovide no exlanaion for he decrease of wih monomer conversion. A higher degree of monomer conversion, he Norrish Trommsdorf effec is weaer for olymerizaion wih laser ulses being alied in he beginning. The reason for his robably is ha he oligomeric maerial roduced by laser ulsing reduces viscosiy. Beyond he laeau region, he olymerizaion of 0. g g and 0.3 g g iniial weigh fracion of monomer, resecively, exhibi differen a he same level of olymer conen. I should be noed ha he monomer conen for a given olymer conen is hree imes higher for 0.3 g g MAA. Thus, he monomer may affec he sabiliy and ermeabiliy, resecively, of he olymer-waer soluion weaening he Norrish Trommsdorf effec. The daa indicaes ha a higher MAA conen in he reacion mixure, and hus in he solven-swollen olymer coils, enhances segmenal mobiliy. This observaion would be in line wih he unexeced finding of he same iniial values for 0. g g and 0.3 g g MAA (v.i.). I may also exlain he differen exend of he Norrish Trommsdorf effec seen in Figure 4-9. In order o verify his assumion, a olymerizaion was carried ou wih isobuyric acid, IBA, being added as non-olymerizing monomer analog. The effec of IBA addiion on is he same as monomer addiion. [9] The idea is ha IBA, while no olymerizing, will have he same effec as monomer on he olymer-waer marix, and hus on. A reacion mixure of 0. g g MAA and over almos he enire range o he iniial laeau region of 0.2 g g IBA corresonds found for he olymerizaion of 0.3 g g MAA. The values derived by ideal olymerizaion ineics are deiced in Figure Wih 0.2 g g IBA in he reacion mixure, does no decrease wih X. On he conrary, a sligh enhancemen is seen, which migh resul from being a lile higher wih IBA relacing MAA. The abovemenioned exlanaion for he decrease of wih conversion found for w 0 0. g g is suored by his exerimen as well. This observed variaion of MAA uon addiion of IBA is no ye fully undersood and should be subjec o furher research. I needs o be considered whenever secies are added o MAA olymerizaion in aqueous hase. 29

138 Chaer 4 8 w 0 MAA = 0. + w IBA = 0.2 log( / L mol s ) 7 6 w 0 MAA = 0.3 w 0 MAA = X Figure 4-20 Deendence of he erminaion rae coefficien as derived from ideal olymerizaion ineics, eq. (2.7), for hree olymerizaions: 0.30 g g MAA wih 0.00 g g V-50, (blue/darblue), 0.0 g g MAA wih 0.0 g g V-50 (cyan/ale cyan), and 0.0 g g MAA wih 0.0 g g V-50 and 0.20 g g IBA as non-olymerizing monomer analog in aqueous soluion. Differences in he conversion deendence of erminaion rae on ME concenraion are exclusively assigned o C. The imac of ME conen is hus conained in,cld and in C. The arameer C was deduced by PREDICI TM fiing of he enire body of olymerizaion daa for a wide range of molar masses, which may be achieved by variaion of CTA conen. In Figure 4-2 he so-obained C values are loed as a funcion of he weigh average molar mass a 0.5 degree of monomer conversion, a value which is close o he mean molar mass aen over he enire conversion range. The C values derived for w 0 MAA 0. g g are smaller han he ones for w g g, because d is smaller for w g g. The enire se of MAA exerimenal C vs. MAA M daa, including boh emeraures and he heoreical daa w oin of ( ) for a olymerizaion roducing olymer of chain lengh uniy only and hus exhibiing no conversion deendence, was fied by eq. (4.2) which resuls in he arameer values a = 0.27 and b =

139 Mehacrylic Acid X C,CLD RD M e C c (4.3) C 0.27 M (4.2) 0.9 w C M w (D) / g mol Figure 4-2 Correlaion of C wih simulaed weigh-average molar mass of MAA a X = 0.5 for olymerizaion a differen levels of chain-ransfer agen ME. The symbols are deduced from PREDICI TM fiing of exerimenal conversion-ime daa. The obained fi arameers refer o eq. (4.2), which comlemens eq. (4.). Boh equaions are also given in he grah. Blue symbols refer o 50 C and cyan symbols refer o 35 C. The heoreical daa oin for a olymerizaion roducing olymer of chain lengh uniy only and hus exhibiing no conversion deendence ( ) is no shown, bu was included ino he fiing of daa. Viscosiy measuremen were carried ou, in order o invesigae how he emirical exonenial funcion feauring he arameer C deending on M w is relaed o acual conversion deendence of viscosiy. The relaive viscosiy of remixed soluions of waer, MAA, and MAA simulaing differen degrees of monomer conversion are loed in Figure XX For comarison, he funcion used in he model is scaled and loed as a line. Good agreemen is observed, which, however, does no mean ha measuremen may be relaced by viscosiy measuremens, XX There are wo roblems o be e in mind: Premixed soluions do no have exacly he same viscosiy as he genuine reacion mixure a a given degree of conversion and he Ubbelohde mehod may cause roblems wih non-newonian liquids, even hough low flow raes were chosen. 3

140 Chaer 4 bu i is ineresing o observe, as he exac relaionshi beween and viscosiy of olymer soluions is unnown (see subchaer 2.4.5). Furhermore, he relaive viscosiy shows he same emeraure deendence a 35, 50, 65, and 80 C, which suors he finding of C being emeraure indeenden. 3 2 r X Figure 4-22 Relaive viscosiy of remixed soluions of waer, MAA, and MAA simulaing differen degrees of monomer conversion (wmaa 0 = 0. g g ) is given for 35 C (in), 50 C (urle), 65 C (green), and 80 C (blue). The funcion used in he model (red line) is loed for comarison. Samles were measured by Ubbelohde mehod. The qualiy of he ineic model associaed wih he rae coefficiens summarized in Table 4-4 is illusraed by comarison of measured and simulaed monomer conversion vs. ime races in Figure 4-23 for 50 C and in Figure 4-24 for 35 C. The model urns ou o saisfacorily reresen he olymerizaion ineics of 0. g g MAA in aqueous soluion a boh 35 and 50 C for ME conens beween / MAA 0 cme c and ME MAA c / c 0.2. For comarison, some reea exerimens are included. They demonsrae ha he qualiy of simulaion is close o exerimenal reroducibiliy. 32

141 Mehacrylic Acid MMDs have been measured for differen emeraures (35, 50, and 65 C) and for differen levels of iniiaor concenraion (0.0, 0.00, and C r,m g g ). Wih 5 aen from ref. [90] MMDs were rediced oo high. The deviaion was sysemaically higher owards lower rae of iniiaion, i.e., low iniiaor concenraion and low emeraure. Therefore, ransfer o monomer had o be 4 increased and C 0 r,m yields simulaed MMDs being in saisfying agreemen exerimenal ones. In Figure 4-25 some MMDs are comared o he redicion of he PREDICI TM model. Measured MMDs exhibi a in slighly below 6 0 g mol. This is a calibraion arifac. Measured and rediced MMDs are in good agreemen wihin exerimenal uncerainy, which is higher in his case due o he roblem of MMDs being arly ou of calibraion range. MMDs of olymerizaions a high levels of CTA are no shown, as heir redicion is raher rivial for nown and C r,cta being deduced from MMDs. 33

142 Chaer X ime / s Figure 4-23 Comarison of measured and simulaed MAA conversion vs. ime los. Blue lines: olymerizaion of 0. g g MAA wih 0.0 g g V-50 as he iniiaor a 50 C wih differen iniial cme o cmaa raios given for each grah; he simulaions are indicaed by he red lines; an indeenden reea exerimens for cme = 0 is included (cyan). 34

143 Mehacrylic Acid X ime / s Figure 4-24 Comarison of measured and simulaed MAA conversion vs. ime los. Blue lines: olymerizaion of 0. g g MAA wih 0.0 g g V-50 as he iniiaor a 35 C wih differen iniial cme o cmaa raios given for each grah; he simulaions are indicaed by he red lines; indeenden reea exerimens are included (cyan). 35

144 Chaer 4 35 C 50 C w (lg ( M / g mol )) C lg ( M / g mol ) Figure 4-25 Comarison of measured and simulaed MMDs. Blue line: olymerizaion of 0. g g MAA o full conversion wih 0.00 g g V-50 and a differen emeraures given for each grah. Very high molar masses were reached and a significan amoun of olymer was beyond he limis of SEC calibraion. This resuled in a in as a calibraion arifac. Red line: simulaion. To es and furher verify his model, olymerizaions wih a comleely differen seu and lower monomer concenraion were carried ou. As demonsraed by Figure 4-26, he model develoed wih conversion ime daa from exerimens in small scale reacors and wih deuered waer as solven is well suied for redicions of larger scale ( L). In addiion, he agreemen shows he absence of isooe effecs. Figure 4-26 also shows ha he model is caable of redicing conversion of CTA correcly. 36

145 Mehacrylic Acid C CTA of 2-mercaoehanol for MAA olymerizaion in aqueous soluion has been deermined o be 0.2 ± 0.0 a 50 C. The Mayo and he CLD mehod were alied for analysis of he aqueous-hase SEC daa. Boh mehods yield more or less idenical resuls wih he Mayo mehod being slighly more robus when alied o a sysem under condiions of srong chain-ransfer aciviy and wih SEC analysis being difficul. C CTA urned ou o be indeenden of MAA conen, which means ha he chain-ransfer rae coefficien largely decreases from dilue o concenraed aqueous soluion of MAA as does. The measured consancy of C CTA largely faciliaes modeling of aqueous-soluion radical olymerizaions once he variaion of wih monomer conen has been maed ou and a reliable C CTA value is nown. Bach radical olymerizaion of 0. g g non-ionized MAA in aqueous soluion has been invesigaed beween 35 and 65 C for a wide concenraion range of 2-mercaoehanol, which acs as he chain-ransfer agen. The measured monomer conversion vs. ime rofiles and MMDs may be adequaely simulaed via PREDICI TM using a hysic-chemically based model which includes ineic informaion from indeenden laser-induced exerimens. Efficien chain ransfer of ME affecs boh he iniial rae of erminaion, due o he deendence of on radical chain lengh, and erminaion u o high degrees of monomer conversion, due o bul viscosiy being uned by he imac of ME conen on olymer molar mass. Chain-lengh deendency of could be well described by alying he comosie model, which was originally develoed for one redominan chain lengh. During olymerizaion of 0.3 g g MAA wihou CTA shows clearly defined regions of SD, TD, and RD. For 0. g g MAA his is no he case, i is more a iled laeau. The develomen of wih degree of monomer conversion can be described by hree arameers sd, d, and C. These arameers are differen for 0. g g and 0.3 g g MAA, while he low conversion values were found o be he same for boh concenraions. For modeling monomer concenraions in beween, e.g., 0.2 g g MAA linearly inerolaed values may be used, bu his should be subjec of furher research. Polymerizaions wih an iniial monomer conen below 0. g g MAA can be rediced by he model quie well, as Figure 4-26 demonsraes. Neverheless, he gel effec becomes weaer owards lower iniial MAA conen. C deends on molar mass of olymer in soluion, bu aears o be emeraure indeenden beween 35 and 80 C. The model should redic conversion vs. ime rofiles and MMDs for olymerizaions u o 80 C wihou roblems. 37

146 Chaer 4.0 degree of conversion MAA ME x x x0 3.2x0 4 ime / s Figure g g MAA were olymerized wih 0.05 mol mol ME and g g V-50 in H2O a 50 C inside a L sirred reacor. Degree of monomer conversion was moniored by H-NMR (cyan squares) and gravimerically (blue riangles); he simulaion hereof is given as a blue, solid line. Degree of CTA conversion was moniored by H-NMR (red circles); he simulaion hereof is given as a red, solid line. Table 4-4 Summary of modified rae coefficiens used for modeling radical olymerizaion of 0. g g non-ionized mehacrylic acid in aqueous soluion from 35 o 50 C and 65 C for MMDs, resecively. This able comlemens Table 4-3. reacion se rae exression ref., X =0 L mol s 20 c XC M η e erminaion ransfer C C M w 0.27 g mol r,m 0 r, M his sudy his sudy 38

147 Mehacrylic Acid 39

148

149 Acrylic Acid 5 5 Acrylic Acid The olymerizaion of AA (acrylic acid, IUPAC: roenoic acid) is of grea indusrial imorance. Polyacrylic acid, AA, is he mos imoran suerabsorber maerial, e.g., ar of hygiene and cosmeics roducs as well as in acaging and soil imrovemen. AA is widely used as hicener, disersan and emulsifier. I is alied, e.g., in wasewaer reamen, mining, exile, and aer indusry. Each monomer uni of he olymer bears an ionizable moiey maing AA a olyelecrolye. AA is a wea elecrolye, hus is degree of ionizaion varies vigorously wih H. Soluions of AA have ineresing roeries as he srucure of he olymer varies a grea deal wih degree of ionizaion and ionic srengh as well as he naure of counerions. [82,84-87,63-66] The influences of ionizaion and ionic srengh are no limied o effecs on he srucure of he olymer in soluion; hey have a grea imac on olymerizaion ineics as well. In subchaer 5., olymerizaion ineics and modeling of AA a is naural H is discussed. Ionizaion and ionic srengh are addressed in subchaer 5.2 The effec of ionizaion on overall olymerizaion ineics of AA has been sudied by several grous. [2,68,70,74,80,83,67] Proagaion has been examined searaely by PLP SEC, for boh non-ionized [37,57,9] and arly as well as fully ionized monomer. [76] Coolymerizaion, e.g., wih AAm has been sudied and a ronounced deendence on H was found. Boh reaciviy raios vary wih degree of ionizaion, so does he rae of olymerizaion. [75,68] Theoreical esimaes of for non-ionized monomer have been carried ou o exlain he concenraion effec [63,64] (see subchaer 2.4.2) as well 4

150 Chaer 5 as he influence of ionizaion. [69] Terminaion, bacbiing and roagaion of MCRs have been sudied by modeling radical concenraion vs. ime races from SP PLP EPR of boh non-ionized [36] and fully ionized [77] AA. 5. Model develomen for Non-ionized Acrylic Acid Bach radical olymerizaion of non-ionized acrylic acid, 0. and 0.3 g g in aqueous soluion, has been sudied a ambien ressure beween 35 and 80 C under variaion of iniiaor concenraion and uon addiion of differen levels of 2-mercaoehanol as CTA. Furhermore, high-emeraure exerimens were carried ou beween 90 and 70 C a 200 bar a differen levels of iniiaor concenraion in a bach and in a ubular reacor. XXI Iniial olymerizaion rae decreases wih CTA concenraion, which has been varied u o ncta / nm Accurae ineic modeling of hese olymerizaions requires chain-lengh-deenden erminaion as has been shown for MAA (see subchaer 4.2). An overview of he relevan reacions and associaed rae coefficiens is given in Table 5-. The basic ineic scheme given in he firs ar of Table 5- is similar o he one for MAA olymerizaion given in Table 4-2. Because of bacbiing aing lace wih AA, he scheme has o be exended by MCR ineics resened in Table 5- second ar. The MCR relaed reacions have been described in subchaer Modeling a high emeraure requires even more reacions aen ino accoun. They are lised in he las ar of Table 5-. The associaed reacions are discussed in subchaer XXI The high-emeraure olymerizaions in a ubular reacor device have been carried ou by Daniel Weiß. [48] 42

151 Acrylic Acid Table 5- Individual reacion ses used for modeling radical olymerizaion of non-ionized acrylic acid in aqueous soluion. Basic ineics iniiaor decomosiion I f d 2R 0 chain iniiaion i R0 M RSPR, SPR-SPR erminaion roagaion of SPRs R M R s SPR, i SPR, i ss ss by combinaion by disroorionaion R R P SPR, i SPR, j i j R R P P ss ss SPR, i SPR, j i j chain ransfer of SPRs o monomer o CTA s r,m R M P R SPR, i SPR, i i SPR, s r,cta R CTA P R i SPR, MCR ineics bacbiing R SPR, i bb R MCR, i SPR-MCR erminaion MCR-MCR erminaion roagaion of MCRs R M R MCR, i SPR, i s s by combinaion by disroorionaion R R P SPR, i MCR, j i j R R P P s s SPR, i MCR, j i j by combinaion by disroorionaion R R P MCR, i MCR, j i j R R P P MCR, i MCR, j i j chain ransfer of MCRs o monomer o CTA r,m R M P R MCR, i MCR, i i SPR, r,cta R CTA P R i SPR, 43

152 Chaer 5 Addiional high emeraure reacions -scission of s MCR R s R MCR, SPR, i 2 MM2 RSPR,3 MM i i3 l MCR R l R MCR, SPR, i MM j RSPR, j MM i j i SPR adding MM roagaion of l MCR R MM R s,mm SPR, l MCR, i j i j R M R l MCR, i j i j SPR, Table 5-2 summarizes he numerous rae coefficiens, almos all of which have been deermined or modified in his wor. Iniiaor decay, roagaion of SPRs, erminaion of SPRs, ransfer o CTA, and bacbiing are available from indeenden exerimens. Chain-lengh deendency of erminaion rae was included, because olymerizaion under addiion of CTA was modeled as well. Transfer o monomer was obained raher indeendenly from he MMDs of he roduc of olymerizaion wih low rae of iniiaion. MCR ineics is less cerain and was subjec o fiing. As simulaion resuls are s raher insensiive owards MCR erminaion he main fiing facor was /. Table 5-2 Summary of rae coefficiens and of oher arameers used for modeling radical olymerizaion of non-ionized acrylic acid in aqueous soluion u o 90 C a ambien ressure. reacion se rae exression ref. decay of V-50 decay of VA d / s ex ( T / K) [56] f 0.8 [90] d / s.24 0 ex ( T / K) his sudy f 0.38 [70] 44

153 Acrylic Acid roagaion s 8 w / L mol s ex exw exw 9.9 ex R / J mol K T / K [37] his sudy erminaion s 234 / 2.4 ex T /K 3,,ss L mol s.9 0 ex XXII i n,, X =0 n n 30 : L mol s i i 30 : 0.8 L mol s 30 i T /K, 0.64, X =0 n,, 0. g g w 0.6 w.3.22 w w.76 w,, 2 3 AA AA AA,,ss his sudy [36] his sudy [7,72] his sudy / 0. his sudy s ss 0.5 [07] L mol s 0.05 L mol s 0.05 L mol s 0.4 L mol s 0.4 L mol s 0.8 L mol s 0.8 ss ss c ss ss d s s c s s d c d, X =0 L mol s 20 c XC M η e 3.7 C 360 w 0 w AA his sudy his sudy bacbiing 5020 T /K 9 bb / s ex his sudy ransfer o monomer C his sudy s s r,m 5 r,m s XXII The value is already correced for a disribuion of chain lenghs (comare subchaer 4.2). 45

154 Chaer 5 ransfer o ME densiy AA HO 2 C C s CTA r,m 5 r,m C CTA s r,cta s r,cta g ml / C g ml / C / C / C his sudy [57] 5.. Iniiaor Kineics According o ideal olymerizaion ineics (see subchaer 2.2), rae of iniiaion enhances he rae of olymerizaion and lowers molar mass by a square roo deendence. The simle ineic scheme does no sricly aly for AA olymerizaion, bu should be valid o a good aroximaion. Even hough iniiaor decay is generally undersood as a firs order reacion, i is ofen influenced by he concenraion of oher comounds (see subchaers 2.2. and 2.4 esecially 2.4.3). The iniiaors used for chemical iniiaion of olymerizaions resened here are he azo comounds V-50 and VA-086. The slow iniiaor decay ensures almos consan iniiaor conen during mos of he reacions and avoids dead-end olymerizaion. Furhermore, a slow rae of olymerizaion is imoran in ha he emeraure of he olymerizaion mixure may be e consan. Azo comounds were seleced for iniiaion, as hiols and eroxides may form a redox iniiaion sysem. [55] Moreover, iniiaor decay should be indeenden of H, which requiremen is more or less fulfilled by V-50 [56] and erfecly holds for VA-086, as will be resened below. The iniiaor efficiency of V-50 was assumed o be f = 0.8, which is a yical value, ha had been successfully used for modeling before. [90] The iniiaor efficiency of VA-086 has been reored o be [70] 46

155 Acrylic Acid c VA-086 / c 0 VA H ime / 0 4 s Figure 5- Exonenial fi via eq. (5.), of ime-deenden relaive iniiaor concenraion a 90 C. Buffer soluions have been reared o simulae differen degrees of ionizaion of monomer; H =.2 (square), 4.8 (circle), 3.99 (diamond),.49 (riangle). Symbols: measured daa, dashed line: fi; solid line: concaenae fi. The decay of VA-086 has been measured for differen H in buffer soluions (see subchaer 3.8) reared o simulae differen degrees of ionizaion of monomer. Samles were heaed in a heaing bloc and analyzed by HPLC subsequenly (see subchaer 3.). The resuling relaive concenraions as a funcion of ime are shown in Figure 5-. The exonenial fi, eq. (5.), yields. d Indeenden fis for each H value (.2, 4.8, 3.99, and.49) yield idenical resuls of good d, 90 C s, which is in 5 reroducibiliy. The concaenae fi gives: fair agreemen wih manufacurer. [56] d, 90 C s 5, which is he value rovided by he 0 / ex d c c (5.) 47

156 Chaer 5-3 ubular reacor, 70 C ln ( d / s ) heaing bloc, 90 C T / 0 3 K Figure 5-2 Squares: measured d; solid line: bes fi o sraigh line yielding eq. (5.3), red, doed line: lo wih Arrhenius arameer rovided by he sulier, eq. (5.2). [56] d was also measured a he highes emeraure of he ubular reacor exerimens, 70 C. Analogously o he olymerizaion rocedure, an iniiaor soluion was heaed a differen flow raes and he soluion was measured by HPLC 2 aferwards. Eq. (5.) yields: d, 70 C s. The measured d values and he Arrhenius lines according o equaion, eq. (2.23), wih values from he sulier, eq. (5.2), as well as he bes fi o he measured daa oins, eq. (5.3), are loed in Figure 5-2. The laer equaion is used for modeling. The acivaion energy of realisic han he sulier value of 23 J mol associaed wih eq. (5.3) aears o be more 05 J mol d / s ex ( T / K) (5.2) 48

157 Acrylic Acid d / s.24 0 ex ( T / K) (5.3) 5..2 Evaluaion of s daa Boh rae of olymerizaion and molar mass scale wih, herefore accurae values of are essenial for modeling. In his subchaer, he evaluaion of boh ublished [37] and unublished PLP SEC resuls from Lací e al. for non-ionized AA is resened. XXIII Moreover, he monomer concenraion effec on resecively, in aqueous soluion is discussed. The and s, s values discussed here refer o negligible conversion, while modeling was carried ou for olymerizaions u o full conversion. Polymer in he reacion mixure is no included for calculaion of w in he model, as i has been shown for MAA olymerizaion ha only refers o he monomer o waer raio. [9] The mos robable combinaion of A and E A is given in Figure 5-3 for differen weigh fracions of monomer. Join 95 % confidence inervals are resened for he high monomer conens ( 0 g g ) w, whereas for he less accurae daa a low AA conen join 75 % confidence inervals are given. A srong deendence of A on monomer conen can be observed. A smaller deendence of E A on monomer conen canno be ruled ou. Two aroaches have been considered o fi an exression for s as a funcion of emeraure and weigh fracion of monomer. Deending on he desired accuracy, he deendence of E A on AA conen may be ignored. In his case, he maximum of s around w 0.03 g g can be ascribed enirely o A and an averaged E, A.6 J mol, deduced from he daa for 0.2 g g and 0.4 g g AA may be used, as he olymerizaion of his amoun of monomer is of highes ineres. A values may be calculaed and fied o an equaion of he same form as has been used before o s obain a good reresenaion of wihou maximum. [2] This rocedure yields he firs erm of eq. (5.4) RHS. Calculaing he difference beween A values from XXIII s Thus, all measuremens were carried ou he Lací grou. 49

158 Chaer 5 measured s and he firs erm of eq. (5.4) RHS and fiing hose exonenially yields he second erm of eq. (5.4) RHS. Eq. (5.4) rovides a good reresenaion of beween 0 and 60 C. However, for low AA conen( w 0.06 g g ), eq. (5.4) s RHS s erm underesimaes of a low monomer conen s a 0 C and overesimaes i a 60 C. If he value s ( 0.06 g g ) w is no of ineres, he firs erm of s eq. (5.4) RHS will be sufficien for an adequae esimaion of. s / L mol s.94 0 ex T /K ex ex ex 59 w T /K w (5.4) 8 E A / J mol E A / J mol A / 0 8 s A / 0 8 s Figure 5-3 Join confidence inervals of he Arrhenius arameers for of non-ionized AA (lines) and he mos robable combinaion (symbols) for differen weigh fracions of AA. Join 95 % confidence inervals (solid lines) are given for monomer concenraions u o w = 0. and, as accuracy of he daa of lower concenraion is noably lower, join 75 % confidence inervals (dashed line) are deiced for lower AA conen. w = 0.0 (blac), 0.02 (red), 0.03 (green), 0.05 (blue), 0. (aqua), 0.2 (magena), 0.4 (yellow), 0.6 (brown); symbols: bes values. Daa for high w is also shown enlarged. 50

159 Acrylic Acid I is highly desirable o have an adequae reresenaion for he enire range of concenraions and emeraures under invesigaion. Moreover, for exraolaion owards high emeraure, e.g., he modeling resened in subchaer 5..9, i is essenial o use an acivaion energy as recise as ossible. Given his, deendency of E A on monomer conen was included in he modeling resened. The A values aen from Figure 5-3 are deiced as a funcion of weigh fracion in Figure 5-4, wih he accuracy of values corresonding o lower monomer conen s being lower as has been shown before. As he effec of monomer conen on arises mosly from a difference in enroy of he resecive ransiion saes, he course of A is very similar o he one of, ye, i does no exhibi a maximum. Accordingly, he A values are fied in he same form as s s, bu wihou a maximum[2] yielding eq. (5.5). This equaion allows for a good reresenaion of daa, which can be observed in Figure 5-4. s 8 / L mol s ex 7 w A (5.5).2x x0 7 A / L mol s 6.0x x w / g g Figure 5-4 Squares: The Arrhenius re-exonenial facor shown in Figure 5-3 as a funcion of weigh fracion of monomer. Line: Bes fi, eq. (5.5). 5

160 Chaer 5 Alhough less variable han he re-exonenial facor, he acivaion energy seems o be a funcion of weigh fracion of monomer as well, as is shown in Figure 5-5. The big sar symbols denoe E values from he original fiing resened in Figure 5-3. Furhermore, A A E values were calculaed from measured s values by combining eq. (5.5) for A wih he Arrhenius equaion, eq. (2.23). This is deiced by he small sar symbols, which were fied emirically yielding eq. (5.6) loed in Figure 5-5 as line. s 2.6 E A/ J mol 6.7 exw ex w 9.9 (5.6) 6 E A / J mol w / g g Figure 5-5 Big sars: Acivaion energy shown in Figure 5-3 as a funcion of AA weigh fracion. Small sars: Acivaion energy derived from values and eq. (5.5). Red line: Bes fi of EA (small sars), eq. (5.6). 52

161 Acrylic Acid The combinaion of eq. (5.5), eq. (5.6), and eq. (2.23) yields eq. (5.7), which allows for an imroved reresenaion of he measured daa and should be suiable for exraolaion. s 8 w / L mol s ex exw exw 9.9 ex R / J mol K T / K (5.7) In Figure 5-6, is loed as a funcion of emeraure and AA weigh fracion s s on w is seen. Moreover, a can be observed over he enire emeraure range, which shifs according o eq. (5.7). A mared deendence of maximum of s owards smaller w uon increasing emeraure. Figure 5-6 Plo of eq. (5.7) wihin he boundaries of sric validiy. 53

162 Chaer 5 s Eq. (5.7) is used for modeling u o high emeraure. Therefore, he imlicaions of he exraolaion should be considered. The lo of he equaion wihin he emeraure range of modeling is shown in Figure 5-7. Over such a broad emeraure range, he deendency of E A on w has a mared effec. The values of a low concenraion increase faser owards higher emeraure han he ones a s high concenraion. Hence, he seeness of he increase of s from concenraed aqueous AA soluion owards higher diluion increases from 35 C u o 70 C. Ineresingly, he maximum fades ou and is rediced o disaear above aroximaely 50 C. Figure 5-7 Plo of eq. (5.7) wihin he emeraure range used in his wor (including exraolaion). Discussing he behavior of in aqueous medium A infinie diluion, he environmen of a growing chain consiss of waer molecules only. Towards higher monomer concenraion, waer molecules are relaced by monomer molecules. Hindrance of inernal roaion of he ransiion-sae srucure for increases. Finally, he environmen of a growing chain in bul consiss exclusively of monomer molecules. The aleraion in surroundings of he radical cenre is no linear, bu is mos ronounced in he beginning and declines gradually. 54

163 Acrylic Acid Generally, his is in agreemen wih exerimenal findings of soluion. However, a maximum of in aqueous is difficul o reconcile wih his simle aroach. The analysis resened here may hel o unraveled he fac of a maximum of being resen a abou 0.03 g g. Boh A and E A deend on monomer conen, he former o a larger exen, bu neiher of he deendencies exhibis a maximum. Insead, he maximum resuls from he combined deendency of on A and E. A This elucidaes ha deailed analysis is crucial and a small deendency lie he one of E A (Figure 5-5) may no be ignored when rying o undersand ineic behavior. More deailed sudies are needed, lie, e.g., calculaions of solven fields ha consis of waer and monomer in differen raios. So far, only calculaions wih a surrounding of ure waer and oluene have been carried ou (and only by reaing he surrounding as a coninuum or one waer molecule and a coninuum). [63,64,69] 5..3 Evaluaion of and Viscosiy daa Because of is diffusion-conrolled naure, scales wih inverse viscosiy (fluidiy, see subchaer 2.4), hence, measuremens of and viscosiy are comared in his secion. Fluidiy of waer-aa mixures and of he wo ure subsances are loed in Figure 5-8 as a funcion of AA conen a 30 C. The daa oins were fied o a cubic funcion, which is used in he model o accoun for comosiion deendency of a zero conversion. The correcion facor for he influence of differen monomer conen on,, is inroduced by eq. (5.8). w 2 3 w.3.22 w AA w AA.76 w AA (5.8),, 0. g g w (5.9) 55

164 Chaer / mp s w AA / g g Figure 5-8 Triangles: fluidiy of waer/aa mixures as a funcion of AA conen a 30 C. Daa aen from ref. [7,72] Line: bes cubic fi used for eq. (5.9). Exerimenal, values for 0. g g and 0.5 g g AA as well as he comosie model (eq. (2.34)) arameers s and i c are available from lieraure. [36] The heoreical value of in good solvens, 0.6, was used in he model. [04-06] However, l his daa is for SPR-SPR erminaion. MCR erminaion ineics is discussed furher below. The raio of he, value for 0. g g o associaed raio of fluidiies is.8. [7,72] The 0.5 g g AA is 6., whereas he 0. g g value was used and slighly adjused for modeling, eq. (5.9) and eq. (5.0), as he corresonding and coefficiens aeared o curae. The correcion facor for a disribuion of chain lenghs (comare subchaer 4.2) is already included. bb 3,,ss L mol s.9 0 ex T /K (5.0) 56

165 Acrylic Acid Chain-lengh deendency of erminaion was included in he model, because i is needed for olymerizaions wih CTA added o he olymerizaion mixure (see subchaer 4.2). Comosie-model arameers have neiher been measured of MCR- SPR erminaion nor of MCR-MCR erminaion. Considering ha i c reresens he oin, a which conrol by cener-of-mass diffusion is relaced by conrol via segmenal diffusion, i may be smaller han he value for SPR homoerminaion. However, he ic value for SPR homoerminaion is already raher low, so he SPR value was adoed for modeling of MCRs. For he same reason, he SPR s value is also used for MCR erminaion. The heoreical value of is differen if radicals are locaed somewhere in he chain. [06] For l s MCR his is no he case, because hey are locaed almos a he end of he chain. Furhermore, EPR exerimens wih BA (see subchaer 5..5) sugges ha chain-lengh deendency of MCRs should be he same as for SPRs. i n,, X =0 n n 30 : L mol s i i 30 : 0.8 L mol s 30 i, 0.64, X =0 n 0.6 (5.) There is no lieraure daa for homoerminaion of MCRs. For crosserminaion a chain-lengh averaged value is available, which has been derived by modeling SP PLP EPR daa under neglec of homoerminaion of MCRs, [36] Under he assumion of he geomeric mean, eq. (2.3), for crosserminaion and he above-menioned comosie model arameers, he values from ref. [36] yield averaged 0.8 for he raio of he (hyoheical) o,,,,ss. Slighly beer reresenaion of exerimenal conversion vs. ime daa is obained wih his coefficien being reduced (down o 0.0), bu his low value aears far oo small. Thus, 0. was chosen as raio for modeling, as exressed by eq. (5.2). Because of he diffusion conrolled naure of,, is acivaion energy should be he same as for fluidiy. A difference in,,ss,, acivaion energy beween and would be difficul o reconcile wih his fac. Thus, he raio of he wo coefficiens is assumed o be emeraure indeenden. Overall, for he daa modeled in his wor, roagaion of MCRs roved o be more influenial han erminaion. 57

166 Chaer 5 / 0. (5.2),,,,ss For he fracion of disroorionaion in SPR homoerminaion a yical value for he olymerizaion of acrylae ye monomers, homoerminaion ss was used and for he MCR 0.05, 0.8 was adoed from olymerizaion of mehacrylae-ye monomers. [73] For crosserminaion an inermediae value of s 0.4 was chosen. Temeraure deendency of was negleced in he model. A decrease owards higher emeraure is execed. [73] Chain-lengh deendency of [73] was negleced as well. The diffusion mean, eq. (2.3), was assumed for crosserminaion yielding eq. (5.3). s ss 0.5 (5.3) The Norrish Trommsdorff effec is less ronounced during olymerizaion of AA han for MAA. For 0.2 g g and 0. g g no conversion deendence of was found, while for 0.3 g g a sligh conversion deendence was noed in agreemen wih lieraure. [44,57] As no measuremens were done wih monomer conen sufficienly high o deermine C, a reasonable value of RD C RD 20 was assumed. The conversion deendence of was modeled by esimaion of C in he same way as described for MAA in subchaer leading o eq. (5.4). As only few conversion vs. ime rofiles were used for esimaing he relaionshi given by eq. (5.5), his equaion should be validaed by furher exerimens. For olymerizaions of can be se o zero. 0. g g AA, C, X =0 L mol s 20 c XC M (5.4) η e C 360 w 0 AA w 0.3 (5.5) 58

167 Acrylic Acid For he olymerizaion of 0.2 g g AA a 70 C no Norrish Trommsdorff effec was observed ( C 0), which can be exlained by he lower molar mass of olymer roduced under hese condiions (see subchaer 4.2) Deerminaion bb by 3 C-NMR The rae coefficien of bacbiing during olymerizaion of non-ionized AA is available from modeling SP PLP EPR daa, [36] where a decrease by a facor of.9 from 0. g g owards 0.5 g g AA conen was found. In he resen wor, a more direc aroach is used. bb is derived from he fracion of branching oins, x, i.e., he raio of monomer unis ha exhibi a branching BP oin o he oal number of monomer unis. The mehod of measuremen was 3 C-NMR. A his, i is imoran o choose arameers ha allow for quaniaive analysis of srecra. These were examined as described in subchaer A negligible influence of ransfer, scission, and erminaion by disroorionaion, every bacbiing even leads o a branching oin. Hence, he number of branching oins is given by he raio of rae of bacbiing o he rae of roagaion: x r c x bb bb R SPR BP s r c M c x R SPR c M c x R MCR (5.6) The conribuion of MCRs o growh is negligible, i.e., c c x c c x, which simlifies eq. (5.6) ino eq. (5.7). s M R SPR M R MCR x BP bb s cm (5.7) s Eq. (5.7) has he advanage of being accuraely nown. 59

168 Chaer g g AA in waer were hooolymerized in a lined flas wih.6 0 g g 4 D73 as he iniiaor. A low monomer concenraion was chosen o maximize branching T /K 9 bb / s ex (5.8) ln ( bb / s ) T /K 9 bb / s ex 433 T /K 8 bb / s ex 3925 T /K 7 bb / s ex 3 70 C 00 C 50 C 0 C T / K Figure 5-9 Arrhenius lo of bb. Red, solid line: AA, 3 C-NMR, his wor; blue, dashed line AA (0. g g ), SP PLP EPR, from ref; [36] doed magena line BA, 3 C-NMR, from ref. [74] The corresonding equaions are given in he same color. The Arrhenius arameers were deermined beween 20 and 74 C from 3 C-NMR analysis of AA roduc from low conversion (A more deailed descriion is given furher below). The associaed equaion, eq. (5.8), is loed in Figure 5-9. The Arrhenius equaion from he SP PLP EPR daa [36] for 0. g g AA deermined beween 5 and 40 C as well as he equaion for BA [74] are loed for comarison. The daa for bb of AA obained by he wo sraegies are in good agreemen. AA exhibis a slighly higher E A han BA wih also he absolue values being higher 60

169 Acrylic Acid beween 50 and 00 C. However, branching levels will be lower for AA a idenical s condiions because of he higher value of of AA. The EPR sudy indicaed a decrease of bb by a facor of.9 from 0. g g owards 0.5 g g AA conen. [36] In his sudy, from 0.03 g g owards 0.3 g g AA conen a 74 C, a sligh increase by he facor of.2 was found. The lower bb value a higher, monomer conen in he EPR sudy may be a consequence of he value being relaively lower a ha concenraion. I was esimaed o be lower han he change in fluidiy. Furhermore, wihin he EPR-exerimen, bb is couled o erminaion and. The laer migh have been underesimaed quaniaively. The resul from he NMR exerimen is indeenden of hese coefficiens. This suors he idea ha he, of 0. g g AA should be more reliable (see subchaer 5..3). The assignmen of signals of he 3 C-NMR secrum of AA is nown from lieraure. [75] Noneheless, in order o ensure line assignmen in addiion o normal secra (bu wih condiions allowing for quaniaive evaluaion, see subchaer 3.5.2) a de-35 (disorionless enhancemen by olarizaion ransfer 35 degree) secrum and an a (aach roon es) secrum were measured. In Figure 5-0 he secion of he 3 C-NMR secrum corresonding o he bacbone of he chain and he enire 3 C-NMR secrum (inser) are given. The carboxyl funcion gives signals beween 70 and 90 m, which could in rincile be used for evaluaion of branching, bu as line assignmen was easier for he bacbone and disincion of lines is more difficul for he carboxyl signals, his was no done. Around 30 m he observed signal of residual monomer aears quie srong due o weaer broadening. Moreover, signals from macromonomer endgrous can be observed, bu for evaluaion of hese endgrous H-NMR was used because of is suerior S/N raio. Towards higher field, he signals of he bacbone and of endgrous aear. This region is shown enlarged in Figure 5-0. Here, in conras o he full secrum, an a (red) and de 35 (eal) secrum are shown. For boh echniques, eriary and rimary carbon aoms give negaive signals and secondary ones give osiive signals. The difference beween he echniques is ha quaernary carbons show in he a, bu no in he de, which roves he signal a 50 m o originae from quaernary carbon. I also becomes clear ha he hree signals beween 4 and 47 m belong o eriary carbon aoms. 6

170 Chaer 5 Figure 5-0 Secion of he 3 C-NMR secrum corresonding o he bacbone of he chain and he whole 3 C-NMR secrum (inser). The samle consiss of he roduc of he olymerizaion of 0. g g AA wih 0.02 g g VA-086 in H2O a 70 C. Inser: The carboxyl funcion gives signals beween 70 and 90 m, around 30 m he signal of residual monomer can be observed, aearing sronger, because lines are less broadened, as well as wea signals from macromonomer endgrous. Furher owards high field he signals from he bacbone of he chain as well as endgrous aear. Large: Bacbone secion of he secrum. Here, in conras o he full secrum, an a (red) and de 35 (eal) secrum are shown. Using hese echniques, eriary and rimary carbon aoms give negaive signals, while secondary ones give a osiive signal. The difference beween he echniques is ha quaernary carbons show u in he a, bu no in he de roving he signal a 50 m o originae from a quaernary carbon. Anoher advanage of 3 C-NMR is ha shor-chain branching and long-chain branching may be disinguished. Figure 5- shows he secion of he 3 C-NMR secrum used for deerminaion of branching. This secrum is of he reacion olymerizaion roduc from reacion of 0. g g AA wih 0.02 g g VA-086 in H2O a 70 C. Because of he high emeraure, branching is high. The AA main chain is drawn wih a shor chain branch and a long chain branch. Here, ea assignmen is indicaed by arrows of he same color. There are he signals of he quaernary carbon aoms a a branching oin, C q, he eriary carbon aoms in he chain away from branching oins, C, he eriary carbon aoms in a long chain nex o a branching oins, C2, and, he eriary carbon aoms in a shor chain nex o a branching 62

171 Acrylic Acid oins, C 3. Assignmens were aen from lieraure. [75] No for all secra, he searaion of he eriary signals was as good as in Figure 5-. Figure 5- Secion of he 3 C-NMR secrum of he reacion roduc of olymerizaion of 0. g g AA wih 0.02 g g VA-086 in H2O a 70 C and a Lewis srucure secion of a AA molecule. The AA is drawn consising of he main chain (blac), a shor chain branch (blue), and a long chain branch (red). The signals of he quaernary carbon aoms a a branching oin (Cq, orange), he eriary carbon aoms in he chain away from branching oins (C, blac), he eriary carbon aoms in a long chain nex o a branching oins (C2, urle), and he eriary carbon aoms in shor chains nex o branching oins (C3, green) are mared accordingly. The corresonding osiions in he olymer chain are indicaed by arrows of he same color. (For C only one arrow is given o ee he grah lucid.) Assignmen of signals has been aen from ref. [75] In order o calculae x SCB from he four signals shown in Figure 5-, hree formulae were develoed: eq. (5.9), eq. (5.20), and eq. (5.2). As searaion of signals is difficul, i was checed ha resuls from all hree formulas agree, viz., ha he evaluaion of he secrum is consisen. For he examle given in Figure 5-, eq. (5.9), eq. (5.20), and eq. (5.2) yield 0.53, 0.46, and 0.52, resecively. x SCB C3 x SCB C q (5.9) 63

172 Chaer 5 x 3 C C 2 q SCB C q (5.20) x SCB C C2 2 C 3 C (5.2) For calculaion of x from he four signals shown in Figure 5-, eq. (5.22) and BP eq. (5.23) were develoed. Again, i was checed ha resuls from he wo formulas agree, viz., he evaluaion of he secrum is consisen. For he examle given in Figure 5-, eq. (5.22) and eq. (5.23) yield x BP and 0.053, resecively. x BP Cq C C 3 C C 2 q (5.22) x BP C2 xscb 3 xscb 2 C 2 C2 C C 2 x x 3 x 2 x 3 x 2 SCB SCB SCB SCB SCB (5.23) 5..5 BA as a Model for AA o esimae C CTA by EPR In revious wor, [47] a reardaion of he AA olymerizaion by ME as CTA has been found for low concenraions of CTA, which was exlained by a higher resuling from reduced of chain lengh. However, a even higher concenraions of CTA, an enhancemen of rae of olymerizaion was found relaive o he execed value considering CLDT, i.e., in going from no o high concenraion of CTA, r olym asses hrough a minimum. One exlanaion could be ha a higher CTA concenraion a significan amoun of MCRs undergo ransfer o CTA wih subsequen reiniiaion of 64

173 Acrylic Acid he CTA radical ha he rae enhancing effec of ransforming MCRs ino SPRs noably comensaes reardaion by enhancemen of erminaion. The olymerizaion ineics of BA (buyl acrylae) has been invesigaed wih focus on roagaion, erminaion, bacbiing and high-emeraure reacions. [40-43,49,0,07,76-8] BA olymerizaions have been successfully modeled for differen condiions. [42,43] Overall BA is one of he bes examined monomers. BA and AA show a similar general ineic behavior and even ineic coefficiens are of similar size. The main difference arises from solven, because BA is olymerized in organic solvens, while AA olymerizaion aes lace in aqueous soluion. For many monomers including AA, he rae coefficien of roagaion becomes a funcion of monomer concenraion (see subchaer and 5..2) when olymerized in waer, hus maing ineics more comlex. This does no affec he comarison made in his chaer, because C CTA is a good consan even in aqueous sysems (subchaer 4..). In his subchaer invesigaion ino he chain ransfer of MCRs o CTA are described and an aroximae value for C CTA is deermined. On he one hand, chainransfer consans of hiols o boh mehacrylae and acrylae monomers are close o each oher, i.e., beween 0.5 and 2. On he oher hand, i was found by Juners e al. [76] via mass secromery ha he amoun of -scission roducs is reduced a grea deal even in case ha small amouns of CTA (0.0 mol mol ) were added o he reacion mixure. The auhors concluded ha he CTA reaced so fas wih MCRs ha ransfer becomes he main reacion ahway of MCRs, i.e. he CTA aches MCRs hus reducing branching. So far, no exerimenal rocedure has been develoed o measure chains-ransfer of MCRs o CTA direcly. Agirre e al. olymerized BA wih erabromomehane added as CTA. [82] Terabromomehane was chosen, because in conras o hiols his CTA ransfers a bromine aom insead of a hydrogen aom, and hus he aching roduc is differen from he bacbone of he olymer. Mass secromery confirmed ha he amoun of -scission roducs was reduced, he aching roduc could no be found via 3 C-NMR analysis, which srongly suggess ha C CTA is raher low. As he wo yes of radicals, SPRs and MCRs, show differen hyerfine sliing, hey can be easily disinguished by EPR. In addiion, absolue radical concenraions can be obained. Unforunaely, EPR measuremens of aqueous soluions are difficul and can only be carried ou using secial equimen (see chaer 3.4.3). Waer has a raher high diole momen of.855 D. [83] In conras, oluene is an almos ideal solven for EPR exerimens, wih a diole momen of D. [83] This led o he idea of using BA as a model o ge a beer undersanding of AA ineics. 65

174 Chaer 5 In revious wor by Sergeeva e al. olymerizaion of.52 mol L BA olymerizaion in oluene was invesigaed by EPR. [0] Polymerizaion oo lace under consan UV iniiaion. Boh absolue radical concenraion and he fracion of MCRs were deermined as a funcion of emeraure in he range of 50 o 90 C. As he aim of his invesigaion was o fahom he effec of chain ransfer on MCR ineics, he same seu and exerimenal rocedure as in he earlier wor was used, wih he exceion of adding differen levels of ME as CTA. 3-line 7-line 4-line 68.7 % 20 G Figure 5-2 The simulaed 3-line secrum and he 7-line secrum assigned o MCRs and he 4-line assigned o SPRs are given in he uer ar. The double inegrals of he 3-line, he 7-line, and he 4-line secrum accoun for 0.9, 68.7, and 20.4 %, resecively, of he double inegral of he combined secrum, which bes reresens he measured secrum. Condiions:.52 mol L BA in oluene, 0.02 eq. ME, 30 C. The fracion of MCRs is obained by fiing he simulaed secra o he measured ones. The EPR secrum of SPRs acually consiss of six lines, bu due o line broadening a 4-line secrum is observed. The 7-line MCR secrum consiss inrinsically of nine lines resuling from couling wih wo non-equivalen grous of 66

175 Acrylic Acid wo -roons. The 3-line secrum resuls from slow roaion of macromolecules, as discussed in deail in ref. [0] In Figure 5-2, he hree-comonen fi is shown consising of he 4-line, 7-line, and 3-line secies. All hree simulaed secra (o) are combined o bes reresen he measured secrum. The comarison beween simulaed and measured secrum (boom) demonsraes good accuracy of he simulaion. Mos of he small deviaion resuls from he baseline of he exerimenal secrum being somewha iled. The raio of he double inegrals yields he raio of radical concenraions and hus he fracion of MCRs is given by: x MCR 3-line 7-line 3-line 7-line 4-line (5.24) Shown in Figure 5-3 is, o which exen MCRs are observed as a 3-line secrum deending on emeraure for differen CTA concenraions. The 3-line secrum is associaed wih a hindered roaion of he macroradical. [0] I is no observed wih model secies consising of a few monomer unis only. A reducion of he fracion of he 3-line secrum may indicae ha chain lengh is reduced ino he oligomeric region. The 3-line secrum is observed for olymerizaions wih 0.02 CTA XXIV o he same exen as wihou CTA. For 0.05 mol mol mol mol CTA his is aroximaely rue as well even hough he fracion of he 3-line secrum aears o some exen reduced. On he oher hand, his deviaion is wihin exerimenal uncerainy. Figure 5-4 shows he mole fracion of mid-chain radicals for BA olymerizaions from low emeraure, where SPRs redominae, o high emeraure, where MCRs redominae. Deending on emeraure, he mole fracion of MCRs is reduced slighly by CTA. For boh 0.02 be observed beween 0 and 60 C. mol mol and 0.05 mol mol he reducion can only XXIV CTA conen is given relaive o monomer conen. 67

176 Chaer line / (3-line + 7-line) / C Figure 5-3 The share of he 3-line secrum is given as a funcion of emeraure. Comaring olymerizaions wihou CTA (squares) aen from ref. [0] o hose wih addiion of 0.02 mol mol CTA (circles) he 3-line secra indicae no effec of CTA. Comarison wih olymerizaions, where 0.05 mol mol CTA (riangles) have been added, does no fully suor his; here aears o be a sligh lowering owards less 3-line signal. Oher han wih PLP, coninuous iniiaion ensures ha radical concenraion is (seudo) saionary. Thus, eq. (2.8) can be used o analyze olymerizaion wihou CTA. For olymerizaions wih CTA, a ransfer erm, r,cta c CTA, has o be added yielding eq. (5.25). Transfer o monomer may be ignored. Transfer o olymer was negligible because x MCR did no show any conversion deendence. x c MCR bb MCR s cspr cmcr cm r,cta ccta 2 cmcr 2 cspr bb (5.25) Bacbiing as well as roagaion of MCRs are indeenden of CTA. There are wo effecs of CTA ha influence x MCR. Firs, even small amouns of CTA reduce 68

177 Acrylic Acid average chain lengh dramaically, which leads o higher s and. A his, he former coefficien is much higher, and hus crosserminaion is he dominan reacion. Second, a new reacion ahway is oened. MCRs can ransfer o he CTA, which iniiaes as follow-u reacion, hereby convering MCRs ino SPRs x MCR / C Figure 5-4 The mole fracion of mid-chain radicals during olymerizaion of BA (.52 mol L in oluene) under coninuous hooiniiaion is shown as a funcion of emeraure. The CTA reduces he fracion of MCRs; his effec increases wih he amoun of CTA, bu he effec is small and no seen for every emeraure. All daa oins are averages of mulile measuremens. Squares: no CTA, circles: 0.02 mol mol, riangles: 0.05 mol mol. Saisical error is calculaed as correced samle sandard deviaion. Daa of olymerizaions wihou ME is aen from ref. [0] A lower emeraures, bacbiing and crosserminaion are conrolling for he acivaion energy of he former is by x MCR. As 27. J mol higher, he fracion of MCRs increases wih emeraure. The higher rae of erminaion for olymerizaions wih CTA leads o he reducion of MCRs. The difference in x MCR firs increases hen decreases again and disaears a ca. 60 C. A higher emeraure, erminaion loses imorance comared o roagaion of MCRs due o is 23.3 J mol lower acivaion energy. [44,84,85] Moreover, a high emeraure crosserminaion 69

178 Chaer 5 addiionally loses imorance, as here are only few SPRs lef for erminaion wih MCRs. s C CTA is aroximaely uniy. In he sysem BA wih hiols s C CTA is.5 and emeraure indeenden. [80] In general, chain-ransfer consans exhibi no or very low acivaion energy. Tha means ransfer becomes imoran when roagaion becomes imoran. Hence, a high emeraure, a reducion of x MCR caused by increased ransfer should be noable. This is no observed; he grahs merge a high emeraure. This henomenon needs o be discussed in furher deail. The wo ahways reducing MCR concenraion by ransfer o CTA and by roagaion are given by eq. (5.26) and eq. (5.27), resecively. r C c x c (5.26) r CTA CTA MCR R r c x c (5.27) M MCR R In order o esimae wheher ransfer is significan one has o loo a he raio of he wo reacion raes. Doing so leads o eq. (5.28). Wih 0.0 mol mol CTA, he chainransfer consan has o be 00 o ge a ransfer rae as fas as roagaion, which would be an uncommon value. To mae ransfer he dominan reacion an even higher value is needed. r r r c CTA C CTA (5.28) c M Under he assumion ha he long-chain aroximaion holds, eq. (5.29) is used o calculae he fracion of MCRs for 70 C, a emeraure, which lies in he region where erminaion is of less imorance. Sill, he differences are only a minimum value (v.i.). 70

179 Acrylic Acid x bb MCR cm r,cta ccta bb (5.29) The following Arrhenius arameers are used for calculaion: [44] bb 3.7 J mol ex s R T J mol R T ex L mol s In Table 5-3 he difference beween x MCR wihou ransfer o CTA and x MCR wih ransfer o CTA is given in ercenage oins. The log-chain aroximaion was used for calculaion and, due o shorer chains, erminaion is higher for olymerizaion wih CTA furher decreasing x. MCR Thus, he differences are only a minimum value. In he exerimen wih he higher CTA concenraion, a sronger effec is rediced. As he effec is reduced by conversion, values a zero and 50 % conversion are given.. Wihin exerimenal accuracy, no conversion effec could be observed. Wihou ransfer, a degree of monomer conversion of 0.9 would resul in one ercen oin increase of x, MCR eq. (5.29), which is wihin error range of x MCR measuremen. A 70 C, he measured difference of x MCR beween olymerizaion wihou CTA and wih 0.02 mol mol CTA is 0.6 ercenage oins and beween olymerizaion wihou CTA and wih 0.05 mol mol CTA is 3. ercenage oins. Adding exerimenal error of 2 ercenage oins, which is more han wice he correced samle sandard deviaion, gives 2.6 and 5., resecively. These values are already very close o.87 and 4.53, he calculaed differences for C and below 2.77 and 6.62, he calculaed values for CTA 5. CTA 0 C Besides, if he laer value of he consan were righ, a noable conversion deendence would aly. Thus, seems o be below 0 and is cerainly below 5. C CTA 7

180 Chaer 5 Table 5-3 The difference beween xmcr wihou ransfer o CTA o xmcr wih ransfer a 70 C is given in ercenage oins. Long-chain aroximaion is made, hus calculaed numbers are he minimum values. The iniial value and he one a 50 % is given, because he value is a funcion of conversion (boh monomer and CTA) 0.02 mol mol CTA 0.05 mol mol CTA C CTA X By calibraion wih TEMPO, absolue radical concenraions can be obained from he double inegral of he EPR signal. The overall absolue radical concenraions for differen condiions are given in Figure 5-5. Throughou he olymerizaion reacion, high saionary radical concenraions are observed. Addiion of CTA causes a reducion of he radical concenraion by abou a facor of 3. The reducion does no increase linearly wih CTA conen. From 0.02 he reducion is only abou 30 %. mol mol o 0.05 mol mol The difference in radical concenraion beween he hree reacion mixures may, o some exen, be exlained by he difference in resuling from differen chain lenghs. GPC analysis of a samle from olymerizaion wihou CTA a 20 C gave an M of n assuming g mol (Ð = 2.2). Alying he Mayo equaion, eq. (2.2), and s C CTA.0, he addiion of 0.02 mol mol CTA reduces chain lengh from 282 o 50. Wih l 0.2 he comosie model, eq. (2.34), yields an associaed reducion of by a facor of.4. According o eq. (2.6) seady-sae radical concenraion is roorional o he recirocal square roo of. Thus, he reducion of c R is by a facor of.2. Furher reducion of he radical concenraion may arise 72

181 Acrylic Acid from erminaion by CTA radicals. For olymerizaions wih a smaller rae of iniiaion and herefore a lower rae of erminaion leading o longer chains he imac of a CTA would be sronger. I would be ineresing o do he same exerimen wih low radical concenraion resen beyond EPR measuring range. 8 (0 mol L ), bu hese condiions are a 6 c R / 0 6 mol L / C Figure 5-5 Overall radical concenraions (SPRs and MCRs) of olymerizaions wih differen concenraions of CTA are shown as a funcion of emeraure. Blac squares: no CTA, red circles: 0.02 mol mol, blue riangles: 0.05 mol mol. Daa of olymerizaions wihou ME is aen from ref. [0] The radical concenraions in he hree reacion mixures exhibi exacly he same emeraure deendency. The radical concenraion slighly increases wih higher emeraure. Then i increases from 0 o 30 C, and aferwards decreases again, bu slowly or says consan. The rae of iniiaion is he same, because in case of hooiniiaion he energy for decomosiion of iniiaor is no sulied hermally. Terminaion increases wih emeraure, bu only slighly, as he acivaion energy of is as low as 73

182 Chaer J mol. [44,84,85] Hence, wih a consan fracion of MCRs a sligh decrease of he radical concenraion wih higher emeraure would be execed, bu his is no he case. In he emeraure region under invesigaion a dramaic shif in x MCR aes lace. Due o MCRs erminaing more slowly, a higher fracion of MCRs allows for a higher radical concenraion. The fac ha he inflecion oins of he curves in Figure 5-4 and Figure 5-5 are a he same emeraure also suors MCRs ineics as being he reason c R / c R (20 C) x MCR / C Figure 5-6 Overall saionary radical concenraion (SPRs and MCRs) is loed in olive as a funcion of emeraure scaled o he radical concenraion a 20 C. For comarison he fracion of midchain radicals is loed in in. (uer half filled squares: no CTA, righ half filled circles: 0.02 mol mol, lower half filled riangles: 0.05 mol mol ) In order o beer visualize boh he relaionshi beween radical concenraions during olymerizaion wih differen CTA conen and how hey are relaed o he fracion of MCRs, boh quaniies are loed ogeher in Figure 5-6. A his, radical concenraion is scaled o he value a 20 C which is near he inflecion oin. The radical concenraion curves of he hree reacion mixures are on o of each oher 74

183 Acrylic Acid and hey are also (hough somewha more scaered) on o of he curves fir he MCR fracion. The fac, ha he hree curves have, wihin exerimenal error, he same shae even hough chain lengh of boh MCRs and SPRs are quie differen oins owards MCRs and SPRs showing he same chain-lengh deendency of. In his subchaer i has been shown ha he chain-ransfer consan of MCRs canno be significanly higher han he chain-ransfer consan of SPRs. Even wihou considering higher erminaion rae for olymerizaions wih CTA, s C CTA sill canno be above 5, which would be oo low o mae ransfer of MCRs a major reacion ahway. Thus, effecs so far aribued o high ransfer of MCRs o CTA have o be exlained differenly, e.g., a reducion of -scission roducs may be he resul of increased erminaion. Moreover, an enhancemen of rae of olymerizaion may resul from addiional iniiaion by he hiol-ene reacion. Furhermore, i was demonsraed how erminaion increases and overall radical concenraion dros by a facor of hree uon addiion of 0.02 mol mol CTA. However, he reducion of he fracions of MCRs by higher crosserminaion is only small C CTA s of ME wih AA The chain-ransfer consan of SPRs o ME during olymerizaion of AA was deermined by he Mayo lo, which has been develoed for sysems wih only one growing radical secies. In he following, i will be shown ha he Mayo rocedure can be used for his sysem wih MCRs being resen o deermine C relaed o a deailed analysis of MCR ineics by Niiin e al. [38] s. CTA This is The basic idea of he Mayo equaion is ha he average chain lengh is deermined by he raio of growh of chains o he raes of erminaion and ransfer, eq. (5.30). i n r r r r (5.30) 75

184 Chaer 5 The wo soing evens of he chain growh can be searaed, eq. (5.58) i n r r (5.3) r r r In case of SPR-MCR ineics, he firs erm of eq. (5.3) RHS need no be considered furher, bu he second has o be. Transfer o growh of boh radical secies may be exressed by eq. (5.32). r c c x c c x s r r,cta CTA R SPR r,cta CTA R MCR s M R SPR M R MCR r c c x c c x c x x c x x s CTA r,cta SPR r,cta MCR s M SPR MCR (5.32) A simlified reamen of he denominaor of eq. (5.32) RHS has already been discussed in subchaer (see eq. (2.7)). The same reamen can be made for he numeraor, bu only under he condiion: x x. In s r,cta SPR r,cta MCR subchaer 5..5, i has been shown ha he chain ransfer consan of MCRs does no exceed he corresonding one for SPRs. Thus, r,cta s r,cta is a much larger han and eq. (5.33) can be used for good aroximaion. For sysems, in which eq. (5.33) is valid, he Mayo lo yields C s. CTA r c s r CTA r,cta s M r c (5.33) The Mayo lo for he roduc of he olymerizaion of 0.0 g g AA a 50 C in aqueous soluion wih 6.56 mmol L of hooiniiaor D73 is given in Figure

185 Acrylic Acid The daa oins were deduced from M w via eq. (4.2), because his was found o give beer resuls for he MAA/ME sysem (see subchaer 4..). The bes fis o a sraigh line according o eq. (2.2) yields: s C CTA (5.34) s The value of C CTA of AA and ME in aqueous soluion is higher han C CTA he value for MAA and ME in aqueous soluion, which may be exlained by he sabiliy of MAA macroradicals being higher han he sabiliy of AA macroradicals (comare subchaer 2.2.) < i > n c ME / c AA Figure 5-7 The Mayo lo, eq. (2.2), of he olymeric roduc of he olymerizaion of 0.0 g g AA a 50 C in aqueous soluion wih 6.56 mmol L of hooiniiaor D73 o low conversion. Daa oins (blue circles) were deduced from MW via eq. (5.25). The corresonding bes fis o a sraigh line is given in red. 77

186 Chaer Deerminaion of for AA Macromonomers by H-NMR Above 90 C, macromonomers, MM, are formed during AA olymerizaion by bacbiing and subsequen -scission o a significan exen. They can roagae, which leads o he formaion of MCRs, which may undergo -scission again forming MMs (see subchaer 2.3.). Hence, he searaion of he corresonding coefficiens is difficul. The roblem was circumvened by synhesizing MM a high emeraure (subchaer 3.4.3) and observing heir roagaion a lower emeraure so ha - scission (and hus formaion of MM) as follow-u reacion can be excluded. Figure 5-8 H-NMR secrum ( 300 MHz) of AA macromonomers, MM(AA), synhesized in DMSO a 38 C. The osiions of he roons are aribued o he signals via blue arrows. The MM lines are: H-NMR (D2O): =.73 (bs, 2H), 2.36 (bs, H), 5.69 (bs, H), 6.8 (bs, H). The redicion of he shif by ChemDraw TM is.75, 2.35, 5.95, and 6.54, resecively. In Figure 5-8, he H-NMR secrum of MM(AA) synhesized in DMSO a 38 C is given. The osiions of he roons are aribued o he signals via arrows. The chemical shif of he wo roons of he erminal double bond 5.69 (bs, H) and 6.8 (bs, H) canno be assigned o roduc from disroorionaion, as he shif of such 78

187 Acrylic Acid roons would be differen. Moreover, vicinal couling is yically very small, while geminal rans-couling is always observed in high-resoluion H-NMR secroscoy Figure 5-9 shows he ESI-MS secrum of he samle, of which he H-NMR is deiced in Figure 5-8. The signals mared by heir m / z values are muliles of AA monomer mass. The corresonding Lewis srucure of he MM(AA) is given as well. The molecule wih u consiss of eleven monomer unis, hus mosly oligomeric MMs have been roduced. Furhermore, no disroorionaion aerns (wo lines of equal heigh wih he difference of 2.02 u) were found in he mass secrum giving addiional suor for synhesis of MMs. Figure 5-9 ESI-MS secrum (negaively charged ions; mehanol and waer) of MM(AA) synhesized in DMSO a 38 C. The signals mared are muliles of AA monomer mass. The srucure of he MM(AA) is given as well. The molecule wih u consiss of eleven monomer unis. The smaller signals in beween are mosly from mulible-charged olymer. In Figure 5-20, he olymerizaion of MM(AA) synhesised in o-xylene wih AA in aqueous soluion is deiced. The olymerizaion was carried ou in NMR ubes. Boh he degree of AA conversion and he raio of MM(AA) o AA was measured via H-NMR. The olymer signal is small a low conversion and in broad. Calculaing X 79

188 Chaer 5 from he raio of monomer and olymer signal would be raher imrecise, even more so, as he MM already gives a olymer signal (comare Figure 5-8). By use of he aromaic signal of residual o-xylene as reference he measuremen becomes more accurae X c MM / c M ime / s Figure 5-20 MM(AA) and AA were olymerized in NMR ubes. The degree of AA conversion was measured by H-NMR (squares), as was he raio of MM(AA) o AA (sars). Consumion of monomer and macromonomer is he same, as he raio says consan owards higher conversion of AA. The doed line indicaes he iniial raio. The synhesis of MMs had been carried ou in o-xylene and he aromaic signal of residual o-xylene was used as reference. caa = mol L, cmm(aa) = 0.02 mol L (firs momen), cv-50 = mol L, in aqueous soluion a 50 C. Because of seric hindrance, roagaion of MCRs wih MMs was assumed negligible. Differen iniial raios around : were olymerized o observe boh AA and MM(AA) wih similar accuracy. The coefficien of roagaion of an SPR wih an s MM,,MM, was esimaed via PREDICI TM simulaion of rofiles he X and he c / c rofiles as a funcion of ime. The resul is given by eq. (5.35). Considering MM M he higher sabiliy of he eriary radical, i aears reasonable ha he addiion of an MM o an SPR is favored. 80

189 Acrylic Acid s,mm (5.35) s In case ha MCRs also add MMs, he reaciviy raios should be uniy as cmm / c M is indeenden of X Modeling Polymerizaion a 35 o 80 C The revious subchaers describe he ineic informaion available from indeenden exerimens aen eiher from lieraure or from his sudy. The basis for modeling olymerizaion of AA beween 35 C and 90 C were mosly conversion vs. ime rofile. XXV Furhermore, MMDs XXVI of olymerizaions beween 35 C and 65 C were used. was scaled o s and esimaed for each conversion vs. ime rofile of olymerizaions wihou addiion of CTA. The corresonding Arrhenius lo is shown in Figure 5-2. Daa from olymerizaions wih V-50 being he iniiaor are in good agreemen wih hose from olymerizaions wih VA-086 being he iniiaor. The concaenae, bes fi o a sraigh line yields eq. (5.36) s 234 / 2.4 ex T /K (5.36) According o eq. (5.36) he difference in acivaion energy beween s E A E A 9.2 J mol calculaed from ref. values [36,37] and higher han E E, which is in good agreemen wih reored for BA. [42] and s is 20.5 J mol A A.2 J mol s XXV Some of he conversion ime daa used for modeling in his subchaer were aen from revious wor. [47] Moreover, hree conversion vs. ime rofiles were a couresy of Paric Drawe. XXVI The Lací grou (Polymer Insiue SAV, Slovaia) did he SEC analysis. 8

190 Chaer C ln ( / s ) C T / K Figure 5-2 Arrhenius lo of he raio of o s. The values were esimaed from conversion vs. ime rofiles by PREDICI TM. Red circles: V-50 was used as iniiaor; blue riangles: VA-086 was used as iniiaor. The concaenae, bes fi o a sraigh line is given in urle. The so-obained difference in EA of and s is in agreemen wih lieraure. [36,37] MMDs have been measured for differen emeraures (35, 50, and 65 C) and for differen levels of iniiaor concenraion (0.0, 0.00, and C r,m g g ). Wih 5 aen from ref. [90] MMDs were rediced oo high. The deviaion was sysemaically higher owards lower rae of iniiaion, i.e., low iniiaor concenraion and low emeraure. Therefore, ransfer o monomer had o be 4 increased and C 0 r,m yields simulaed MMDs being in saisfying agreemen exerimenal ones. 0. g g AA in waer were olymerized a 35, 50, and 65 C u o comlee conversion wih V-50 as iniiaor a levels of 2 0, 4 0, and 0 g g. Molar mass 3 was found o vary only slighly wih iniiaor concenraion. Wihou considering ransfer o monomer MMDs were rediced oo high. The deviaion was sysemaically higher owards lower rae of iniiaion, i.e., low iniiaor concenraion and low emeraure. In order o illusrae he influence of C, r,m wo 82

191 Acrylic Acid measured MMDs are loed ogeher wih he corresonding simulaion no feauring ransfer o monomer in Figure A relaively high rae of iniiaion (lef) he deviaion beween exerimen and simulaion is raher wea, bu a low rae of iniiaion he deviaion is srong. Therefore, simulaion of MMDs required s C r,m being: C (5.37) s s r,m 5 r,m s C M = 0 w (lg ( M / g mol )) lef: 0 2 g g 65 C righ: 0 3 g g 50 C lg ( M / g mol ) Figure 5-22 Comarison of measured and simulaed MMDs wihou considering ransfer o monomer shows deviaion, which is was sysemaically higher owards lower rae of iniiaion. Blue line: olymerizaion of 0. g g AA o full conversion (iniiaor concenraions and emeraures given for each grah). Very high molar masses were reached and a significan amoun of olymer was ouside of SEC calibraion. This resuled in a in as calibraion arifac. Red line: simulaion. In Figure 5-23, measured MMDs are comared o redicions by he PREDICI TM model. The measured MMDs feaure a in slighly above 6 0 g mol. This is a calibraion arifac due o end of direc calibraion a his oin as for MMDs from MAA olymerizaion (subchaer 4.2.2). Wih ransfer o monomer being included, measured and rediced MMDs agree wihin exerimenal uncerainy, which is 83

192 Chaer 5 higher in his case due o said roblem of MMDs being arly ou of calibraion range. MMDs of olymerizaions wih CTA are no shown as heir redicion is raher rivial, rovided ha and C r,cta are nown wih high accuracy. For olymerizaions wih higher monomer conen, only a few conversion vs. ime rofiles were measured. Eq. (5.4) leads o acceable reresenaion of measured daa, bu esecially for 0.3 g g AA a clear deviaion in shae is seen. Probably an equaion of he form eq. (4.) (see subchaer 4.2.) would lead o beer resuls. For an evaluaion lie his, more daa would be needed. In Figure 5-24, he comarison of measured and simulaed AA conversion vs. ime los of olymerizaion of 0. g g AA a emeraures from 35 o 80 C demonsraes he qualiy of he model in his emeraure range. The agreemen of measured and simulaed AA conversion vs. ime los of 0. g g AA olymerizaion a emeraures from 65 o 80 C uon addiion of CTA from small o very high amouns can be observed in Figure 5-24 and Figure The qualiy of he redicion does no reach he level as obained for olymerizaion wihou CTA, bu is sill saisfacory, esecially when one considers he lower exerimenal reroducibiliy of exerimens involving CTA. The conversion vs. ime rofiles of olymerizaions wih highes ME conen show good agreemen wih he simulaion (Figure 5-25). For some oher olymerizaions wih very high ME conen (no shown here) a drif owards higher rae of olymerizaion was found, i.e. a high CTA conen furher increase of CTA level did no lead o furher decrease of olymerizaion rae bu o a sligh increase again. This effec migh originae from addiional iniiaion by he hiol-ene reacion, he rae of which could no be quanified. I may no be exlained by high ransfer of MCRs o CTA, because for he s model sysem BA/ME i was found ha C CTA canno be much higher han C CTA (see subchaer 5..5). The arameers of he model for he olymerizaion of non-ionized AA are summarized in Table

193 0 2 g g 65 C 0 2 g g 50 C 0 2 g g 35 C 0 3 g g 65 C 0 3 g g 50 C 0 3 g g 35 C 0 4 g g 65 C 0 4 g g 50 C Figure 5-23 Comarison of measured and simulaed MMDs. Blue line: olymerizaion of 0. g g AA o full conversion (iniiaor concenraions and emeraures given for each grah). Very high molar masses were reached and a significan amoun of olymer was ouside of SEC calibraion. This resuled in a in as calibraion arifac. Red line: simulaion.

194 g g V C 0 3 g g V C 0.2 g g AA 0 3 g g V C 0.3 g g AA X g g V C g g V mol mol ME 50 C 0 2 g g V mol mol ME 50 C g g V C g g VA C ime / s g g VA C Figure 5-24 Comarison of measured and simulaed AA conversion vs. ime los. Blue symbols: olymerizaion of 0. g g AA (if no saed oherwise) wih iniial cme o cmaa raios given if alicable; iniiaor concenraions and emeraures are secified for each grah; he simulaions are indicaed by he red lines; indeenden reea exerimens are included (cyan and dar blue). Daa for 90 C is given in subchaer 5..9.

195 X cmol mol ME 65 C 2.6 cmol mol ME 65 C 4 cmol mol ME 65 C cmol mol ME 65 C cmol mol ME 80 C 2.6 cmol mol ME 80 C cmol mol ME 80 C cmol mol ME 80 C ime / s 22 cmol mol ME 80 C Figure 5-25 Comarison of measured and simulaed AA conversion vs. ime los. Blue symbols: olymerizaion of 0. g g AA wih g g and g g VA-086 as he iniiaor a 65 C and 80 C, resecively. The aricular iniial cme o cmaa raios given for each grah. The simulaions are indicaed by he red lines; indeenden reea exerimens are included (cyan).

196 Chaer Modeling Polymerizaion a High Temeraure For olymerizaions a high emeraure, which means for his sysem above 90 C, addiional reacions have o be considered leading o an even more comlex reacion scheme. -scission of MCRs may ae lace building macromonomers. These roagae o form l MCR s, which may add monomer and hus grow furher or undergo -scission again. The corresonding scheme is shown in Table 5-4 o. The imlemenaion of he addiional high-emeraure reacions ino PREDICI TM can be simlified. Niiin e al. [42] modeled BA olymerizaion u o 70 C wih a reduced number of reacions. They condensed he reacion scheme in Table 5-4 o ino he reacion scheme in Table 5-4 boom inroducing he comounded rae coefficiens defined by eq.(5.38) and eq. (5.39). This sraegy was adoed for he resen modeling wor. s,mm 2 c M (5.38) s,mm 2 M 2 c c M (5.39) Table 5-4 The addiional reacions ha have o be aen ino accoun for high emeraure olymerizaion are shown in he uer ar. For modeling of BA olymerizaion u o 70 C as has been shown by Niiin e al. [42] a simlified aroach is ossible o accoun for -scission of MCR l, MM roagaion, and MCR l roagaion. The corresonding scheme is shown in he lower ar. Addiional high emeraure reacions -scission of s MCR R s R MCR, SPR, i 2 MM2 RSPR,3 MM i i3 l MCR R l R MCR, SPR, i MM j RSPR,j MM i j i SPR roagaing wih of MM roagaion of l MCR R MM R s,mm SPR, l MCR, i j i j R M R l MCR, i j i j SPR, 88

197 Acrylic Acid Simlified Treamen RSPR, i MM j RSPR, j MMi 2 RSPR, i MM j RSPR, i j For modeling olymerizaion a inermediae emeraure u o 90 C, was scaled o wih he raio being emeraure deenden (see subchaer 5..8). s Exraolaion of his raio u o 70 C gave reasonable resuls, as will be shown below. Deermining he influence of and on rae of olymerizaion, molar mass, and branching is no rivial. Their resecive influence also deends on oher arameers. Higher leads o higher olymerizaion rae, bu has no direc influence on branching level. also increases olymerizaion rae, esecially if is relaively low and comarison. However, he effec of high. reduces branching, esecially if bb is low in and on molar masses is reverse. The final coefficiens were obained by eeing he Arrhenius exression for derived from moderae emeraure olymerizaions and adjusing for bes reresenaion of measured conversion vs. ime rofiles and molar masses. The resuling Arrhenius lo is given by eq. (5.36) / s.9 0 ex T /K (5.40) The corresonding acivaion energy is energy of 27 J mol, which is close o he acivaion 25 J mol found for during hermal degradaion of olyehylene. [86] The acivaion energy is significanly higher han 63.9 J mol, he acivaion energy found for he -scission of BA. [42] The absolue value of in he considered emeraure range is also bigger han he value found for BA. These comarisons sugges ha his value of migh be oo high. In order o obain beer reresenaion of exerimenal daa (conversion vs. ime rofiles, molar masses, branching level) by simulaions of he model, he arameers / and s / as well as comosie model arameers of MCRs have been,,,,ss widely varied. MCRs ineics do no have a large imac on he simulaion. A sligh 89

198 Chaer 5 variaion of bb has been aemed, bu as he redicion of he branching level is in good agreemen wih measured daa, his coefficien aears o be accurae. The,,ss value measured for AA [36] aears raher high in comarison o oher monomers, which suggess ha a lower value migh lead o beer modeling resuls.,,ss Neverheless, lowering by a facor of hree he virual deendence of / on iniiaor conen a 90 C remains (see Figure 5-2). Higher and lower values for his coefficien (by a facor of 0) were aemed, bu he accuracy of he simulaion could no be imroved. Differen values for and / led o a beer reresenaion of conversion vs. s ime rofiles, bu o a redicion of higher molar masses han have been measured, which is discussed furher below. s In Figure 5-26 o, he concenraion of branching oins, c, BP is deiced as a funcion of conversion and emeraure. c BP increases owards higher emeraure and owards higher conversion. The branching level can be rediced very well by he model over he enire range of emeraure and conversion. In Figure 5-26 boom, he fracion of shor-chain branching is loed as a funcion of conversion and emeraure. The simulaed values of x SCB decrease owards higher emeraure and owards higher conversion. The exerimenal values are much lower han simulaed ones. This may be exlained by furher bacbiing of MCRs moving he radical funcion bacwards along he olymer chain (see subchaer 2.3.3), a reacion ha is no ye included in he model. I should be noed ha long-chain branching does only mean ha he branch is a leas one monomer uni longer han a shor-chain branch of wo monomer unis. Measured and simulaed molar mass are comared in Figure 5-27 (o: M n ; boom: M w ). While M n decreases noably a high conversion, M w says relaively consan. Molar mass decreases owards higher emeraure, which is mosly he consequence of iniiaor decay being more raid. The exerimenal resuls for molar mass are somewha scaered. The model can redic hem over he whole range of emeraure and conversion very well. The conversion vs. ime rofiles of olymerizaions beween 90 and 70 C and he according simulaions are shown in Figure Exerimenal resuls are from wo differen modes of oeraion of he ubular reacor seu (see subchaer 3.3). The resuls from he soed flow exerimens, in which he ubular reacor is byassed 90

199 Acrylic Acid and he high-ressure cell is used as a bach reacor, are deiced as small symbols. for 90 o 40 C. The resuls from olymerizaion in he ubular reacor are deiced as big symbols and are resen from 30 o 70 C. Three differen iniiaor concenraions were used. They are disinguished in Figure 5-28 by differen colors. A 90 C he simulaion is good agreemen wih exerimenal resuls for medium iniiaor conen, for high iniiaor conen he rae is somewha underrediced and for low iniiaor conen overrediced. For 0 and 20 C, he rae of olymerizaion is rediced oo low by he model. A higher emeraure, he agreemen of exerimenal conversion vs. ime rofiles wih he simulaion is saisfacory. Comaring he simulaion and exerimenal resuls from olymerizaion in he ubular reacor i aears ha rae of olymerizaion is underrediced a low conversion and over rediced a high conversion. This may no be an inaccuracy of he model bu an arifac of residence ime correcion. The same difference can be observed comaring exerimenal resuls from bach exerimens and olymerizaion in he ubular reacor. The model gives a good reresenaion of exerimenal resuls from olymerizaion beween 30 and 70 C, shown in Figure Table 5-5 gives he rae coefficiens added for high-emeraure reacions. The oher rae coefficiens are lised in Table 5-2, as hey have also been used for modeling olymerizaion a moderae emeraure. Table 5-5 Summary of addiional rae coefficiens and of oher arameers used for modeling radical olymerizaion of non-ionized acrylic acid in aqueous soluion a C. The values given in his able were obained oimizing based on boh conversion vs. ime rofiles and molar masses. reacion se roagaion of MMs -scission rae exression s,mm 8 / s.9 0 ex s + ref his sudy.5 0 T /K 4 his sudy 9

200 Chaer 5 Figure 5-26 Comarison of simulaed (small red and in symbols) and measured (big blue symbols) branching level (o) and he fracion of shor-chain branching (boom) of he reacion roduc from 0. g g AA wih 0.02 g g VA-086 in waer. 92

201 Acrylic Acid Figure 5-27 Comarison of simulaed (small red and in symbols) and measured (big blue symbols) molar mass of he reacion roduc from 0. g g AA wih 0.02 g g VA-086 in waer. 93

202 C C C X C 30 C C C C 70 C ime / s Figure 5-28 Comarison of measured (symbols) and simulaed (line) conversion vs. ime los of he olymerizaion of 0. g g AA wih 0.0 g g VA-086 (red circles), g g VA-086 (green riangles), g g VA-086 (blue and cyan squares). The mode of oeraion was eiher soed flow (bach exerimen) given by small symbols or olymerizaion in he ubular reacor deiced as big symbols.

203 Acrylic Acid Alernaive values for and The unexeced high value for and he raher low qualiy of olymer samles from high-emeraure exerimens subjeced o molecular mass analysis led o he idea ha molar mass may be ignored and insead conversion vs. ime rofiles may have rioriy for oimizaion of he model. This led a similar value as found for of BA and / became even more similar o he value reored for BA han wih s he aroach including oimizaion wih resec o molar masses / s.3 0 ex T /K (5.4) The corresonding acivaion energy is energy of 65 J mol, which is close o he acivaion 63.9 J mol found for he -scission of BA. [42] The Arrhenius reexonenial facor is slighly lower han.5 found for he -scission of BA. [42] s 382 / 0.38 ex T /K (5.42) The corresonding difference in acivaion energy beween s E A E A.5 J mol, which is lower han ref. values, [36,37] bu surrisingly similar o E E for BA. [42] and s is 20.5 J mol calculaed from s A A.2 J mol reored The agreemen beween simulaions and exerimenal conversion vs. ime rofiles sill varies wih iniiaor concenraion, bu he underredicion of olymerizaion rae a 0 and 20 C is much weaer for his aroach and in general he reresenaion of exerimenal conversion vs. ime rofiles is beer. s The alernaive / exression, eq. (5.42), was no develoed for simulaion of AA olymerizaion beween 35 o 80 C. 95

204 C C C X C 30 C C C C 70 C ime / s Figure 5-29 Comarison of measured (symbols) and simulaed (line) conversion vs. ime los of he olymerizaion of 0. g g AA wih 0.0 g g VA-086 (red circles), g g VA-086 (green riangles), g g VA-086 (blue and cyan squares). The simulaions show here were done wih differen values for and han in Figure 5-28.

205 Acrylic Acid Table 5-6 gives alernaive values for he rae coefficiens added for highemeraure reacions. The oher rae coefficiens are lised in Table 5-2, as hey have also been used for modeling olymerizaion a moderae emeraure. Table 5-6 Summary of alernaive rae coefficiens, which were obained by oimizaion based on conversion vs. ime rofiles only, ignoring molar masses. reacion se rae exression ref. roagaion of MCRs -scission s 382 / 0.38 ex T /K / s.3 0 ex T /K his sudy his sudy 5.2 Model Develomen for Ionized Acrylic Acid Ionizaion of monomer and olymer alers rae coefficiens. For olymerizaion of fully ionized monomer, reacions beween ionized and non-ionized secies need no be considered, bu even in his case he level of comlexiy rises in comarison o olymerizaion of non-ionized monomer, as rae coefficiens of ionized secies deend s on ionic srengh. The effec of ionic srengh on, e.g., is considerable, as will be shown in subchaer 5.2. For olymerizaion of arly ionized monomer comlexiy is furher increased, because reacions of ionized wih non-ionized secies have o be considered and as he K values of monomer and olymer differ (see subchaer 5.2.0), he degree of A ionizaion of boh monomer and olymer changes wih conversion. The ineic scheme for he olymerizaion of ionized AA is rincially he same as for non-ionized AA, as no addiional reacions occur. Thus, he ineic scheme used for modeling consiss of he ineic scheme given in he uer ar of Table 5- and includes ineics of MCRs (Table 5- middle). High-emeraure reacions of ionized AA have no been modeled. The se of rae coefficiens and oher variables, e.g., densiy, was aen from modeling of he non-ionized monomer (Table 5-2) and exended as is summarized in Table 5-7 for fully ionized AA and summarized in Table 5-8 for arly ionized AA a he end of his secion. 97

206 Chaer 5 Some ineic informaion on he effecs of ionizaion is nown from lieraure, bu mos deendencies have no ye been sudied in deail. For modeling, a combinaion of re-evaluaion of daa reored by oher grous and new exerimens XXVII were analyzed. The level of comlexiy for modeling he olymerizaion non-ionized AA (see subchaer 5.) already being higher han for MAA (see chaer 4) is furher increased in his sysem. As modeling of he olymerizaion of fully ionized AA is easier, firs a summary of he rae coefficiens for his sysem is given wih he corresonding modeling wor following in subchaer Aferwards he asecs of he arly ionized sysems are discussed and redicions of he so-assembled model are shown in subchaer of Fully Ionized AA and deendence on Ionic Srengh s of fully ionized AA has been measured via PLP SEC only for one concenraion (0.05 g g a 6 C). [76] s However, he deendence of of fully ionized AA on monomer conen should be similar o he deendence of of fully ionized MAA on monomer conen. [] of fully ionized MAA is overall less deenden on monomer conen han he of non-ionized MAA and owards dilue soluion a decrease of insead of an increase as for he non-ionized monomer was found. [] The deendence s of of AA on w and AA is discussed in subchaer The resul wih resec o w a full ionizaion is given by eq. (5.43). AA s / L mol s.94 0 ex T /K ex 3.7 w.6 w 0.04 (5.43) There is no value available for of arly ionized AA and only one value for of fully ionized AA, which was obained by arameer esimaion from SP PLP EPR radical concenraion vs. ime rofiles. [77] The lieraure value was esimaed under he assumion ha MCRs do no erminae, whereas in he resen sudy he erminaion of MCRs is aen ino accoun. XXVII Paric Drawe carried ou he exerimens wih V-50 as iniiaor and fully ionized AA. 98

207 Acrylic Acid I aears reasonable ha is influenced by ionizaion in he same way as The same assumion has been made for he deendence of on AA conen and gave good resuls (see subchaer 5.). As a consequence, is higher han he value esimaed uon neglec of MCR erminaion. [77] The aroach used for his modeling wor leads o good reresenaion of exerimenal daa (v.i), whereas he lower value from ref. [77] leads o underredicion of he rae of olymerizaion. s. Figure 5-30 Rae of olymerizaion of 0.05 g g AA ( = ) wih 2 mmol L V-50 as he iniiaor in waer wih differen amouns of added NaCl a 50 C and ambien ressure. The rae of olymerizaion augmens linearly wih amoun of added sal. Reea exerimens show good agreemen. This grah is a couresy from Paric Drawe. s Eq. (5.38) describes as a funcion of monomer conen, emeraure and degree of ionizaion, bu does no consider he effec of ionic srengh on olymerizaion ineics. The rae of olymerizaion of 0.05 g g AA ( = ) wih 2 mmol L V-50 as he iniiaor in aqueous soluion a 50 C is shown in Figure 5-30 for differen amouns of added NaCl. The rae of olymerizaion augmens linearly wih he added amoun of sal. This increase should be associaed wih an increase of, 99

208 Chaer 5 since variaion of all oher rae coefficiens should resul in a decrease of olymerizaion rae a higher I, as will be discussed below. Kabanov e al. [2] roosed an ion-air mechanism as he cause for a higher owards increase of I. Their idea was ha he carboxylae uni a he chain-end of he macroradical ineracs wih a caion, e.g., Na, which in urn ineracs wih he carboxylae moiey of a monomer molecule hus handing i over o he radical cener and hus increases rae of roagaion. These auhors did no consider MCRs, as bacbiing was no nown for AA olymerizaion a he ime of ublicaion. The deendence of s on boh monomer conen and degree of ionizaion can be exlained via he ransiion sae srucure. The rends found exerimenally are reroduced by calculaion. [69] s So far, no aems have been made o calculae for ionized acrylic acid based on ransiion sae heory wih differen amouns of caions being resen around he radical cener. If an ion-air mechanism increases he rae of roagaion, his effec should be sronger for MCRs aroximaely wice as large because hey have carboxylae grous on boh sides handing over monomer. Thus, he rae enhancing effec by addiion of couner ions should be sronger for condiions favoring MCRs, e.g., low monomer concenraion. Moreover, he rae enhancemen by addiional counerions should be sronger for NaA han for NaMA. Indeed, overiraion wih sodium hydroxide, which increases he number of couner ions, resuls in a sronger rae enhancemen of olymerizaion of NaA han of NaMA. [2] The enhancing effec being weaer for NaMA may also exlain, why i was no found in PLP-SEC exerimens of NaMA (see subchaer 2.4.3). By close insecion of he rofiles given in Figure 5-30, i can be seen ha he maximum of rae of olymerizaion slighly shifs o higher degrees of monomer conversion owards higher sal concenraion. This observaion suors he idea of a sronger imac on MCRs, because heir fracion increases owards higher X. However, he variaion of x MCR is wea and more exerimens under condiions, which favor MCRs o differen exen, should be carried ou. As he addiion of sal should have an influence on all coefficiens robably wih exceion of iniiaor decay, an aem was made o sill find a good descriion for he influence of added sal based on daa given. Addiional counerions should increase he erminaion and bacbiing rae, and hus decrease he rae of olymerizaion. However, as an enormous augmenaion of he rae of olymerizaion was found, he amlifying effec on roagaion seems o be dominan. For modeling urose, he effec of higher I on was assumed o aly s wice as srong for. Consequenly, is mulilied wih he facor of 200

209 Acrylic Acid s enhancemen of roagaion, I, and scaled o he already enhanced is also mulilied wih I, viz., he roagaion of MCRs is augmened by 2 I. I was esimaed via PREDICI TM from conversion vs. ime rofiles corresonding o he daa shown in Figure 5-30 including he effec of I on bb, bu ignoring he effec on (see subchaer 5.2.2) resuling in eq. (5.44). 0 0 I c c 0.99 Na AA (5.44) a Full Ionizaion As discussed in deail in subchaer 5.2.7, viscosiy increase by ionizaion of monomer and Coulomb reulsion of ionized macroradicals as well as increased siffness of he olymer chain owards ionizaion hereof and hindered movemen of ionized macroradicals lead o a decrease of. The comosie-model arameers s,, and i l c a full ionizaion are assumed o be he same as for he non-ionized monomer. [77], In conras, he effec on is large: ss is reduced by a facor of ca. 5, s and are reduced oo much as o be easily measured by SP PLP EPR. [77] The facor of 5 was adjused down o 2 via PREDICI TM esimaion: ss, ss, 0 (5.45) 2, was obained via PREDICI TM fiing. The decrease of ss sronger han for, as was found exerimenally (v.s.)., owards ionizaion is,, 0 (5.46) 40 20

210 Chaer 5 I should be noed ha smaller reducion of led o a less accurae reresenaion of measured conversion vs. ime rofiles. was calculaed by he diffusion mean, eq. (2.3), as for he modeling of he non-ionized AA. The effec of higher I on s was no included ino he model, because no direcly measured daa is available and analysis of conversion vs. ime rofiles of olymerizaions wih differen I suggess ha he influence of I on is much weaer han he influence on and bb (see subchaer 5.2.). This migh be exlained by he effecs on by increasing viscosiy and by screening of addiional couner ions comensaing each oher. Oherwise, a decreased rae of olymerizaion would have been found wih NaCl being added o he reacion mixure (see subchaer 5.2.6). Fuure wor should be direced a measuring he influence of addiional counerions on direcly, e.g., by SP PLP EPR bb a Full Ionizaion and deendence on Ionic Srengh So far, he influence of ionic srengh on bacbiing has no been measured. However, bacbiing may be scaled o he flexibiliy of olymer chains (see subchaer 2.3.3), which is well undersood, as he srucure of AA coils in aqueous soluion has been sudied as a funcion of boh and I. [82,84-87,63-66] The deendence on is discussed in subchaer The ersisence chain lengh, l, is a common measure for he rigidiy of chains and may be subdivided ino he ersisence chain lengh wihou elecronic influence, l, 0 and he increase by ionizaion, he elecronic ersisence chain lengh, l e, as given by eq (5.47). l l 0 l e (5.47) 202

211 Acrylic Acid l / 0 0 m (I / mol L ) /2 Figure 5-3 The ersisence chain lengh of AA loed for = 0.6 (downward riangles), 0.4 (uward riangles), 0.2 (circles), 0.03 (squares) as a funcion of he square roo of ionic srengh and associaed sraigh line fis. Daa was aen from ref. [84,87] Daa of he ersisence chain lengh of AA as a funcion of square roo of ionic srengh was aen from ref. [84,87] and loed in Figure 5-3. Daa oins for = 0.6, 0.4, 0.2, and 0.03 were fied o resecive sraigh lines. The influence of is discussed in subchaer Considering l m aen from ref. [84,85] he so-obained sloes were fied as a funcion of (sars in Figure 5-38)o develo an equaion ha reresens he deendence of simlifies ino eq. (5.48). l on and I. A full ionizaion, i l I m (5.48) Comarison of eq. (5.48) wih he yields eq. (5.49). bb values of non-ionized and fully ionized AA 203

212 Chaer ex T /K bb /s I (5.49) Densiy Wih he rae equaions being formulaed in erms of concenraion, he densiy of he olymerizaion mixure should be nown. Aqueous sysems including ionizaion reclude he assumion of ideal mixing. The Debye Hücel heory [88] is commonly used o describe he behavior of ions in highly dilued soluion. For simlificaion, ionic srengh is used as reference (see eq. (2.28)). Densiy can be derived from he molar volumes, V, of individual comonens. For highly dilued soluions, he laer may be exraolaed from he molar volumes a 0 infinie diluion, V, by eq. (5.50). V V A I (5.50) D-H For higher concenraion, a series exansion is commonly made given by eq. (5.5). V V A I B I C I (5.5) D-H D-H D-H A can be derived by Debye Hücel heory, [89] while D-H B and D-H C are emirical. D-H By comarison of densiies of concenraed soluions wih may be calculaed for hese soluion by a simler formula (v.i.). 0 V i was found ha V 204

213 Acrylic Acid The aaren molar volume of AA in aqueous soluion (daa aen from ref. [90] ) was loed as a funcion of concenraion of monomer unis, MU. The daa was fied o sraigh lines (no shown). The so-obained values of he resecive sloes were loed in Figure 5-32 as a funcion of he degree of ionizaion of AA (ionizaion agen: NaOH). These daa were fied o a sraigh line as well, given by eq. (5.52). d V / dc (5.52) MU.2.0 sloe of V vs. c MU degree of ionizaion Figure 5-32 The aaren molar volume of AA in aqueous soluion loed as a funcion of concenraion of monomer unis (ref. [90] ) gives sraigh lines, he sloes of which (squares) increase wih degree of ionizaion of olymer (ionizaion agen: NaOH). The daa are fied o a sraigh line reresened by eq. (5.52). The sloes of he firs lo (squares in Figure 5-32) increase linearly wih ionizaion, a full ionizaion he sloe is aroximaely uniy. The volumes of non-ionized comonens are indeenden of I. Thus, molar volumes of AA and Na increase wih 0.5 I yielding eq. (5.53). 205

214 Chaer 5 0 V V 0.5 I (5.53) 0 The values of V for olymer and monomer a various are loed in Figure The resecive amoun of sodium caions is included (from ref. [9] ). One AA molecule aes u more volume han one monomer uni in AA. Ionizaion decreases he molar volume of olymer (from ref. [92,93] ) linearly. 70 monomer 60 V 0 / ml mol olymer Figure 5-33 Molar volume a infinie diluion as a funcion of degree of ionizaion for MU of AA and AA. The resecive amoun of sodium caions is included in he calculaion, aen from ref. [9] Monomer (circles) aes u more volume han olymer (sars) and ionizaion decreases molar volume, daa from ref. [92,93] These values were derived from highly dilued soluion by he Debye Hücel equaion, eq. (5.50). In order o chec eq. (5.53) derived in his modeling sudy, daa for highly concenraed olymer soluions (u o 8 mol L ) [90,94] was exraolaed o infinie diluion via his equaion (cyan). I can be observed ha molar volume of olymer decreases linearly owards higher degree of ionizaion. In order o verify eq. (5.53) derived in his sudy, daa for highly concenraed olymer soluions (u o his equaion. The so-obained values for 8 mol L ) [90,94] was exraolaed o infinie diluion via 0 V were comared o daa derived from 206

215 Acrylic Acid measuremens in highly dilued soluion via he Debye Hücel equaion, eq. (5.50). 0 As shown in Figure 5-33, values for V are in excellen agreemen. Therefore, he simlified aroach of eq. (5.53) seems o wor well and is used for modeling. The aroach is less accurae for very dilue soluions, bu he absolue error is low as densiies do no differ much from he one of he ure comound. The densiy of AA is calculaed in he model by eq. (5.54). No emeraure deendency of he imac of ionizaion was observed in his sudy. Daa is given in he aendix. V AA AA AA AA AA AA AA AA/AA AA AA V AA (5.54) Because of he linear deendency of molar volume on degree of ionizaion, a formula of he same form as for monomer, eq. (5.54), is used o calculae he densiy of olymer, eq. (5.55) V AA AA AA/AA AA AA AA AA AA AA AA V AA (5.55) The molar volume of ions in aqueous soluion is mosly negaive XXVIII a low concenraion and PREDICI TM canno calculae wih negaive molar volumes. Tha is 3 why, ions have he densiy of g cm in he model and heir acual densiy is used in he calculaion of densiy of waer, which is given by eq. (5.56) XXVIII Deending on effecive charge, hydraion of ions decreases he disance of surrounding waer molecules o one anoher, which resuls in an overall decrease of volume. This effec is sronger for dilue soluions. 207

216 Chaer 5 all m m m m virual H2O H2O virual all H2O H2O g mol all mall mall mh 2O m all mall m all H2O (5.56) Modeling he Polymerizaion of Fully Ionized AA Given he indeenden daa (subchaer 5.2.), as a nex se conversion vs. ime rofiles were comared o he simulaion in order o adjus he rae coefficiens wih highes uncerainy, as described above. Preferably, an iniiaor is used, he decay of which is indeenden of H or he resence of oher subsances. Oherwise, iniiaor ineics are hard o searae from monomer ineics. As discussed in subchaer 5.2., olymerizaions wihva-086 and NaPS have been carried ou, bu have no been used for modeling. V-50 has limied solubiliy in basic aqueous sysems and is decay, which is H indeenden a low H, shows some deendence on H a higher H. The deendence is rovided by he sulier given by eq. (5.57). [56] H d / s ex ex T/ K 4 3 (5.57) 0.05 g g AA neuralized wih NaOH o = was olymerized a differen levels of V-50 as he iniiaor and also under addiion of 0, 0.5,, 2, and 3 mol L amouns of NaCl a 50 C. XXIX The corresonding conversion vs. ime rofiles have been used for modeling. Simulaed and exerimenal rofiles are deiced in Figure There is some deviaion under variaion of iniiaor concenraion and for high amouns of added NaCl he iniial rae of olymerizaion is slighly overrediced. Neverheless, XXIX These exerimens were carried ou by Paric Drawe. 208

217 Acrylic Acid he overall close agreemen of simulaions and exerimenal daa is graifying o noe, aricularly in his case of numerous deendencies of rae coefficiens. Simulaed Ð values augmened a grea deal owards olymerizaions wih addiion of NaCl. This should be checed exerimenally. The addiional and modified, resecively, rae coefficiens and he oher arameers used for modeling radical olymerizaion of fully ionized acrylic acid in aqueous soluion are summarized in Table

218 Chaer mmol L V-50 no NaCl mmol L V-50 no NaCl X mmol L V mol L NaCl mmol L V-50.0 mol L NaCl mmol L V mol L NaCl mmol L V mol L NaCl ime / s Figure 5-34 Comarison of measured (blue) and simulaed (red) NaA conversion vs. ime los of olymerizaion of 0.05 g g AA neuralized wih NaOH o = wih differen levels of V-50 as iniiaor a 50 C and wih differen amouns of NaCl given for each grah; he simulaions are indicaed by he red lines; indeenden reea exerimens are included (cyan). The exerimenal ar was carried ou by Paric Drawe. 20

219 Acrylic Acid Table 5-7 Summary of modified rae coefficiens and of oher arameers used for modeling radical olymerizaion of fully ionized acrylic acid in aqueous soluion comlemening Table 5-2. reacion se rae exression ref. iniiaor decomosiion H d / s ex ex T/ K 4 3 [56] f 0.8 [90] roagaion erminaion bacbiing densiy s / L mol s.94 0 ex T /K ex 3.7 w.6 w 0.04 s s 0 0, c caa 0 I Na 0 0, c caa 0 I 2 Na 0 0 I c c 0.99 Na AA ss,, ss, 0 2, /K ex T bb /s V V 0.5 I I V AA AA/AA V AA AA AA AA V AA AA/AA AA AA AA V AA mh2o mall m virual H2O all H2O g mol m m all virual mall mh 2O mall H2O all mall mh2o deailed values given in he aendix all [,76], his sudy his sudy [77] his sudy [77,84,85,87] his sudy [90-94] his sudy 2

220 Chaer The deendence of on he Degree of Ionizaion Boh rae of olymerizaion and molar mass scale wih. Therefore accurae s nowledge abou is aricularly imoran. of AA a differen degrees of ionizaion has been measured via PLP SEC only for 0.05 g g a 6 C. [76] The s deendence of on w and on should be similar o he one of MAA, [] which is reresened by eq. (2.29) [] and holds for he range of 0.05 w Exraolaion o low AA conen a full ionizaion gives hysicochemically unrealisic negaive values (see subchaer 2.4.3, Figure 2-4). MAA.00 ( = 0) s () / s s s / 0 2 w w AA AA Figure 5-35 for a weigh fracion of 0.05 g g AA as a funcion of degree of ionizaion (by NaOH) is loed relaive o he value of he non-ionized monomer (blue sars, daa aen from ref. [76] ). The 3 rd facor of eq. (5.58) RHS reresening he deendence of on w and is given by he line; he corresonding formula is also given in he grah. Eq. (2.29) consiss of hree ars, which are concaenaed by mulilicaion: Firsly, a waa 0 and 0, secondly, a facor describing he decrease of s owards higher w a 0, and hirdly, a facor aing he combined deendence on AA w AA and ino accoun. A modificaion of eq. (2.29) has been develoed, in which he 22

221 Acrylic Acid firs wo erms were aen from subchaer In order o reresen he s deendence of on w a 0 as simly as ossible, eq. (5.4) RHS s erm, was AA s used as he basis. The maximum of and he deendence of E on monomer A conen were no included. No daa on he influence of ionizaion and ionic srengh on E is available for AA, bu MAA daa sugges ha only a wea influence A occurs. [] The 3 rd facor of eq. (2.29) has been modified considering boh he exising PLP SEC daa and esimaion via PREDICI TM for conversion-ime rofiles of olymerizaion of of 3, 2, and g g fully ionized AA a 50 C wih V-50 as iniiaor a levels mmol L. The general forma of eq. (2.29) was no changed, bu he arameers, which deermine he curvaure wih resec o ionizaion, were adjused yielding eq. (5.58). In Figure 5-35 he so-obained 3 rd facor of eq. (5.58) is loed s ogeher wih values of 0.05 g g AA a various degrees of ionizaion relaive o he value of he non-ionized monomer (daa aen from ref. [76] ) demonsraing he s good reresenaion of he deendence of on for 0.05 g g AA. s / L mol s.94 0 ex T /K ex 3.7 w 2 w w AA AA (5.58) s The redicion of according o eq. (5.58) for 50 C is deiced in Figure The resuling lo is similar o he one for he deendence of for MAA as a funcion of w and M (see Figure 2-4). There are, however, some imoran differences: Firsly, he overall s value of AA is higher han of MAA, which is reresened by he firs facor. Secondly, he seeness of he sloe a = 0 is higher for AA han for MAA, as reresened by he second facor. Thirdly, he curvaure a w = 0 is weaer s han in he MAA formula, esecially, for high. Hence, does no become negaive a high and low w. There is no value available for of arly ionized AA and only of one value available for of fully ionized AA, which was obained by arameer esimaion from SP PLP EPR radical concenraion vs. ime rofiles [77] and was no considered for modeling fully ionized AA (see subchaer 5.2.). I aears reasonable ha is s influenced by ionizaion and monomer conen in he same way as This aroach was used for modeling.. 23

222 Chaer 5 Figure 5-36 The rae coefficien of roagaion of AA as a funcion of boh weigh fracion of monomer and degree of ionizaion used in he model given by eq. (2.26). The lo is similar o he one for MAA (Figure 2-4), bu here are some imoran differences: he overall value is higher, he seeness a = 0 is higher, and he curvaure a w = 0 is weaer The deendence of on he Degree of Ionizaion The viscosiy of he reacion mixure increases owards higher. In addiion o he so-induced lowering of, Coulomb reulsion of ionized macroradicals furher decreases. I should be noed ha he acual viscosiy-induced reducion of is even higher han he reducion of fluidiy. Movemen of he charged macroradicals is furher decreased by larger effecive size from hydraion of he ionized secies and reulsion by surrounding counerions. As his effec deends on degree of ionizaion of olymer insead of degree of ionizaion of monomer, is conribuion is reresened in he model by he Coulomb facor. The viscosiy effec is increased owards higher ionic srengh, while he Coulomb conribuion o decrease of may be arly comensaed by screening of addiional counerions (see subchaer 2.4.3). Furhermore, ionizaion siffens he olymer chain, which should reduce segmenal diffusion, and hus decreases. The 24

223 Acrylic Acid flexibiliy of an ionized chain is increased by screening of couner ions; a high ionic srengh, he flexibiliy of he chain reaches he value of a non-ionized one. As discussed in subchaer given daa sugges ha he effecs from increased ionic srengh on mosly comensae each oher Figure 5-37 The viscosiy of 0.20 g g AA in aqueous soluion has been measured a differen emeraures (square: 35 C, circle: 65 C, riangle: 65 C, and sar: 80 C) and degrees of ionizaion. Ploing relaive viscosiy (referring o = 0) shows ha no emeraure deendence occurs irresecive of degree of ionizaion. Daa is aroximaed according o eq. (2.28) given as a line. The viscosiy of 0.20 g g AA in waer has been measured beween 35 and 80 C for differen degrees of ionizaion and is loed relaive o he viscosiy a = 0 in Figure No emeraure deendence could be found. For sae of simliciy, he daa is aroximaed by eq. (5.59) AA (5.59) 25

224 Chaer 5 Combinaion of eq. (2.36) and eq. (5.59) yields he correcion facor for aroximaing he influence of viscosiy under ionizaion,, according o eq. (5.60). 0.5 (5.60) AA The comosie-model arameers, s, and i l c are assumed o be unaffeced by ionizaion. [77], ss In conras, he effec on is large: is reduced by a facor of ca. s 5, and are reduced oo much as o be easily measured by SP PLP EPR. [77] The facor of 5 consiss of a facor of 2 due o viscosiy increase (eq. (5.60)) and a facor resuling from elecrosaic reulsion and decreased flexibiliy, viz., he influence of ionizaion of monomer on is reresened by one facor, which alies for boh SPRs and MCRs,, and a second facor ha reresens he influence of ionizaion of olymer on, which is differen for SPRs and MCRs. An exonenial funcion was used for inerolaion of for differen values of, as such an assumion allows for a good reresenaion of reored values as a funcion of, [78] alhough he absolue values in ref. [78] seem o be incorrec and have no been used for modeling (see subchaer 2.4.3). The facor of 7.5 was adjused down o 6 via PREDICI TM esimaion yielding in he correcion facor of Coulomb reulsion of ionized SPRs, correcion given by eq. (5.62) defined by eq. (5.6), which leads o an overall ss, C ss C AA ex.8 (5.6) ss ss ss, 0 C (5.62) An exonenial funcion was chosen for MCR homoerminaion as well. The exonen in eq. (5.63) was esimaed from conversion vs. ime rofiles (shown in subchaer 5.2.5) via PREDICI TM fiing. This rocedure yields he corresonding correcion facor, given by eq. (2.32), which leads o overall correcion given by, C 26

225 Acrylic Acid eq. (5.64). The decrease of found exerimenally (v.s.)., owards ionizaion is sronger han for ss as was C AA ex 3 (5.63),,, 0 C (5.64) The deendence of bb on he Degree of Ionizaion Bacbiing has only been measured for AA olymerizaions wihou ionizaion (see subchaer 5..4) and wih full ionizaion. [77] The influence of ionic srengh has been addressed in subchaer Bacbiing may be scaled o he flexibiliy of olymer chains (see subchaer 2.3.3), which is well undersood, as he srucure of AA coils in aqueous soluion has been sudied as a funcion of boh and I. [82,84-87,63-66] Considering l m aen from ref. [84,85] he sloes from fiing resened in Figure 5-3 were fied as a funcion of (sars in Figure 5-38)o develo eq. (5.65), which describes l of AA as a funcion of boh and I. AA 0 l m I (5.65) Comarison of eq. (5.65) wih he yields eq. (5.66). bb values of non-ionized and fully ionized AA 27

226 Chaer ex T /K bb /s AA I (5.66) Furher research should be direced owards measuring branching levels uon varying and I o chec eq. (5.66) exerimenally, rovided as a funcion of and I is nown wih high accuracy..5 deendence of l e on I Figure 5-38 The sloes of he sraigh lines shown in Figure 5-3 giving he deendence of ersisence chain lengh on I are deiced as sars. The fi o a consan imes he square roo of is deiced as line and given as formula. 28

227 Acrylic Acid β-scission No lieraure daa on he influenced of ionizaion on he -scission reacion of macroradicals is available. However, consideraions abou general radical sabiliy (see subchaer 2.) give a direcion. A vicinal carboxylae moiey sabilizes a radical cener beer han a carboxyl moiey. This effec is (aroximaely) addiive o oher influences on sabiliy, hus here need no be an influence of ionizaion, because boh SPRs and MCRs migh be sabilized o he same exen. If his sabilizing effec were slighly sronger for SPRs, -scission would be increased. Figure 5-39 Double-bond region of he H-NMR secrum of he roduc of he olymerizaion of xaa = 0.05 (0.2 g g ), = 0.7 wih 0.00 g g VA-086 in waer a 90 C. The wo broad signals aear o originae from MM(AA), he ohers from residual monomer. Double bonds from MM exceed hose from monomer residue by a facor of wo. The chemical shifs are differen from he ones given in Figure 5-8, because in his samle olymer and monomer are arly ionized. H-NMR of he roduc of 0. g g AA olymerizaion wih = 0.7 and.0 a 90 C suggess ha MMs were formed, bu MMs could no be deeced for lower under osensibly he same condiions. Figure 5-39 shows he double-bond region of he H-NMR secrum of he roduc of he olymerizaion of xaa = 0.05 (0.2 g g ), = 0.7 wih 0.00 g g VA-086 in waer a 90 C. The wo broad signals aear o 29

228 Chaer 5 originae from MM(AA)s, XXX he ohers from residual monomer. The chemical shifs differ from hose given in subchaer 5..7, because AA and AA are arly ionized. Deecion of MMs only a higher may sugges an increase of -scission by ionizaion. However, his finding may resul from being reduced (see 5.2.6). A longer ime san beween formaion of an MCR and growh hereof increases he robabiliy of a -scission even wih he. The -scission reacion was no included for modeling AA olymerizaion a 50 C, bu has o be considered a higher emeraure The K A of AA The nowledge of degree of ionizaion of olymer is essenial for calculaing he deendence of rae coefficiens, because, firsly, some rae coefficiens, e.g., deend direcly on AA and, secondly, is lined o AA AA via he associaed acidbase equilibria. Exensive measuremens on he deendence of he logarihmic acid dissociaion consan, K, of AA as a funcion of, AA average chain lengh, ionic srengh A bb (considering addiionally he ind of added sal) have been carried ou by De Sefano e al. [8] The unexeced resul ha he K of olymer changes significanly wih A chain lengh, even above he oligomeric region, was also found by Laguecir e al. [82] As he K value of AA is a funcion of of AA and vice versa, an analyic A soluion o calculae H is imossible. For modeling, he acid-base equilibrium of olymer is calculaed ogeher wih he acid base equilibria of monomer and waer by PREDICI TM. The comuaional effor for his is high. The roonaion consan, K H, is defined by eq. (5.70). XXX The signal a 5.3 m could be eiher a double exhibiing he roof effec or wo signals wih almos idenical chemical shif. If he signal were a double, i would mos robably originae from a double bond belonging o disroorionaion roduc. The oher signal a 5.7 m does no loo lie a double and does no exhibi a corresonding roof effec. Thus, i aears ha MMs have been formed, he srucure of which varies leading o slighly differen chemical shifs of he signals of he erminal double bond. 220

229 Acrylic Acid K H c c H-A + c H A (5.67) Assuming he concenraion of waer o remain aroximaely consan, leads o eq. (5.68). A H A K lg K lg K (5.68) One ossibiliy o reresen he relaionshi beween Henderson-Hasselbalch equaion, eq. (5.69). K and is he exended A H H lg K lg K h h lg AA AA (5.69) h is an emirical arameer. Anoher ossibiliy o reresen he relaionshi beween K and is he Högfeld A equaion, eq. (5.69). 2 K H 2 H H H AA K AA AA K m AA K 0 lg lg 2 lg lg (5.70) The Högfeld equaion was chosen for modeling, because i is more accurae esecially a very high and very low degree of ionizaion. [8] De Sefano e al. included he K value of AA for inerolaion of he chain-lengh A deendency of K ( exended Henderson-Hasselbalch equaion) over he oligomeric H h region. [8] From hysicochemical ersecive, a comarison wih he value for he sauraed monomer roanoic acid (4.87) is beer, [95] which is noably higher han he one of AA (4.25 ). [96] 22

230 Chaer enane-,3,5-ricarboxylic acid gluaric acid lg(k H ) roanoic acid lg(<i> ) Figure 5-40 The arameers of he Högfeld equaion, eq. (5.69), and he exended Henderson Hasselbalch equaion, eq. (5.70), are loed for AA a I = 0. and 25 C as a funcion of chain lengh. Daa is aen from ref. [8] Sars: Kh H, squares: K H (KA = ), solid riangles: Km H (KA = 0.5), circles: K0 H (KA = 0). For comarison and in order o exend he chain-lengh region covered by eq. (5.7) ino he oligomeric region, resecively, he values for roanoic acid, [95] gluaric acid [99] and enane-,3,5- ricarboxylic acid [97] are added. Lewis srucures of hese acids are given in he uer ar. The 2 nd KA value of roanoic acid lies beween K H and Km H (urle). The same fiing was done for I = 0.5,.0, 2.0, and 3.0. For comarison, Km H for I = 0.00 is aen from a differen ref: [82] oen riangles. Daa is fied according o eq. (5.7) and deiced as solid line of corresonding color. In his wor, fiing has been carried ou for he Högfeld equaion arameers by adoing he rocedure carried ou by De Sefano e al. [8] In order o exend he validiy ino he oligomeric region, he hree K values of enane-,3,5- A ricarboxylic acid [97] were used. I is a hree-monomer-uni oligomer (shor of one mehyl moiey). Is firs of lg H K value corresonds o A lg K 0, which has he meaning K of comleely non-ionized olymer, is second A K value corresonds o A H K, which has he meaning of K of half non-ionized olymer, and is hird A m 222

231 Acrylic Acid lg K, which has he meaning of K of he las nonionized monomer uni. The Lewis srucures of he acids are deiced in he A uer H K value corresonds o A ar of Figure In order o reresen he chain-lengh deendency of H K, K H m, and H K 0, he arameers were fied individually according o eq. (5.7). This was done for I = 0., 0.5,.0, 2.0, and 3.0, resecively. For enane-,3,5-ricarboxylic acid only values for I = 0. are available. For higher I, he K values of he small acid molecule A are ossibly indeenden of I. [98] Neverheless, he K values of oligomers a high ionic srengh calculaed by he aroach of his wor are less cerain. A lg H K x a0 a i a2 lg i (5.7) The so-obained arameers a 0, a, and a were fied by eq. (5.72), an equaion of 2 he same form as he exended Debye Hücel equaion discussed for densiy in subchaer a a a I a I (5.72) x x, x,2 x,3 The firs ar of he fiing rocess is illusraed in Figure The arameers of he Högfeld equaion, eq. (5.69), and of he exended Henderson Hasselbalch equaion, eq. (5.70), are loed for AA a I = 0. and 25 C as a funcion of chain lengh. The neuralizing agen was NaOH. Daa is aen from ref. [8] For comarison and in order o exend he chain-lengh range covered by eq. (5.7) ino he oligomeric region, resecively, he values for roanoic acid, [95] gluaric acid [99] and enane-,3,5-ricarboxylic acid [97] are added. Lewis srucures of hese acids are H given in he uer ar of Figure For comarison, K m for I = 0.00 (blue, oen riangles) is aen from ref: [82] Daa is fied as lines according o eq. (5.7). Wih he so-obained arameers, he degree of ionizaion of he olymer is calculaed during simulaion (see subchaer and aendix). 223

232 Chaer Modeling he Polymerizaion of Parly Ionized AA There are differen ossibiliies of including he effecs of ionizaion on reaciviy in he model. In rincile, individual reacions of non-ionized and ionized secies could be modeled searaely wih he resecive rae coefficiens; e.g., he addiion of an ionized monomer and a non-ionized monomer, resecively, o a macroradical wih a carboxylae moiey nex o he radical cener as well as he addiion of hese monomers o a macroradical wih a carboxyl moiey nex o he radical cener. Insead, i was decided o model he dynamic acid-base equilibria searaely and o use he resuling values for (average) degree of ionizaion of monomer and olymer, resecively, o calculae rae coefficiens corresonding o hese average values. Thus, he afore-menioned four reacions are reaed as one reacion. The roblem of he aroach wih individual reacions is ha a lo of individual rae coefficiens are needed, abou which no informaion is available, and which are generally difficul o obain; e.g., reaciviy raios of ionized olymer wih non-ionized monomer and nonionized olymer wih ionized monomer canno be measured as are reaciviy raios of coolymerizaions, because in his case, he resuling olymer does no yield any informaion abou ionizaion of moieies a he ime of monomer addiion. Furhermore, he K value of he carboxyl grou nex o he radical cener is A differen from he average K value of he olymer. Thus, aems o consider he A enulimae effec ose severe roblems, since he K value of he enulimae A carboxyl moiey srongly deends on he ulimae one being ionized or no. Moreover, acid-base equilibria are faser han he oher reacion ses under consideraion. Because of he von Grohuss mechanism, acid-base equilibria, lie oher reacions of H in waer, are even faser han he "normal" diffusion limi. [200] Hence, roonaion and deroonaion of a monomer may haen several ime during one addiion se. The dynamic acid-base equilibria are calculaed by PREDICI TM, which is imlemened ino he model by means of couner secies (more deails are given in he aendix). For each calculaion se, K AA of olymer is calculaed. Togeher wih he equilibria of AA and waer, his yields and AA for each calculaion se. AA Afer imlemenaion of indeenden daa ino he model, conversion vs. ime rofiles are he basis of oimizaion. A bes an iniiaor should be used, he decay of which is indeenden of H or oher subsances in he reacion mixure. Oherwise, iniiaor ineics are hard o searae from he monomer ineics. 224

233 Acrylic Acid VA-086 mees he requiremen of he decay being indeenden of H (see subchaer 5..), and hus aears o be an ideal iniiaor for his sysem. Conversion vs. ime rofiles have been measured for olymerizaion of (xm = 0.05) a 90 C wih 2 0, 0, 3 and 0 g g g g AA VA-086 a = 0, 0.3, 0.7, and (ionizing agen NaOH) given in he aendix. A he lowes iniiaor concenraion, dead-end olymerizaion is reached long before he uaive half-live of he iniiaor a s given by eq. (5.3). I was checed exerimenally ha a dead-end olymerizaion oo lace by resuming he olymerizaion by addiion of iniiaor. Moreover, olymerizaion of ionized and arly ionized monomer is faser han olymerizaion of non-ionized monomer, which is conradicory o he execaion on he basis of he rae coefficiens described above. Wih higher iniiaor concenraion, he rae of olymerizaion is in he beginning almos indeenden of AA ionizaion. Then a dead-end olymerizaion is reached again even before he uaive half-life of he iniiaor. The deviaion from he execed behavior is ouside exerimenal uncerainy and reroducibiliy of he exerimens is good, as reea exerimens show. A his sage, he only ossible exlanaion for his behavior is ha he decay of VA-086 is indeenden of H, bu deends heavily on he conen of ionized AA. Acceleraed iniiaor decay by ionized AA is suored by he fac ha unexeced low molar mass was found for he olymerizaion of fully ionized AA wih VA-086. Thus, iniiaor ineics seem o dominae overall ineics and he conversion-ime rofiles of ionized AA iniiaed by VA-086 have no been modeled. Furhermore, olymerizaions of 4 0, and 0 g g g g AA (xm = 0.05) a 90 C iniiaed by 3 0, sodium ersulfae, NaPS, a = 0, 0.3, 0.7, and (ionizing agen NaOH) were carried ou (conversion vs. ime rofiles given in he aendix). NaPS as iniiaor has he advanage of good solubiliy. Furhermore, i is of indusrial relevance for iniiaing olymerizaions in aqueous sysems. Is decay is influenced direcly by H [20] and also by AA deending on he degree of ionizaion. [56] The laer influence is alleged o be higher owards lower concenraion of monomer, [56] which was inerreed as raher high uncerainy of d measuremens. Modeling wih consan d gave reasonable resuls, bu as he exac deendency of d is unnown, he conversion vs ime rofiles have no be used for oimizaion of he model. The model should be caable of redicing conversion vs. ime rofiles for he olymerizaion a oher degrees of ionizaion and oher monomer concenraions. In Figure 5-4, simulaed conversion vs. ime rofiles of 0. g g and 0.2 g g AA a = 0, 0.2, 0.4, 0.6, 0.8, and are shown. The rae of iniiaion is idenical for all olymerizaions. A low degree of ionizaion is almos wihou influence on rae of 225

234 Chaer 5 olymerizaion. The highes difference in olymerizaion rae changing by 0.2 is observed beween = 0.6 and = 0.8. For olymerizaion rae is more ronounced han for 0. g g AA he influence of on 0.2 g g AA, which may be exlained by he difference of a = 0 and a = becoming larger owards lower monomer conen. For 0.2 g g AA and low X, he decrease of owards higher may be comensaed by decrease of. Simulaed molar masses (no shown) decrease similarly o simulaed olymerizaion raes. Cuié e al. found a higher difference in rae of olymerizaion already for a low degree of ionizaion, [80] bu in ha sudy NaPS was used as iniiaor, he decay of which is increased by he resence non-ionized AA. [56] Fuure wor should be direc owards checing of he model by acual measuremen of hese as well as MMD varying w and X g g AA 0.2 g g AA ime / s Figure 5-4 Simulaed conversion vs. ime rofiles of 0. g g AA (lef) and 0.2 g g AA (righ) a = 0, 0.2, 0.4, 0.6, 0.8, and. The arrow indicaes he direcion of higher. The recies conain 0.02 g g D73 as he iniiaor, he decay of which was se o he value of he seu described in subchaer 3.4.4, which resuls in a half-live of 625 s. The rae of iniiaion is idenical for all olymerizaions. 226

235 Acrylic Acid Table 5-8 Summary of addiional and modified, resecively, rae coefficiens and of oher arameers used for modeling radical olymerizaion of ionized acrylic acid in aqueous soluion comlemening Table 5-2. reacion se rae exression ref. iniiaor decomosiion H d / s ex ex T/ K 4 3 [56] f 0.8 [90] roagaion erminaion bacbiing acidiy of AA densiy s / L mol s.94 0 ex T /K ex 3.7 w 2 w w AA s s 0 0, c caa 0 I Na 0 0, c caa 0 I 2 Na 0 0 I c c 0.99 Na AA ss ss ss, 0 C, 0 C C ss C 0.5 ex 3 ex.8 AA AA ex T /K bb /s AA 2 H H 2 H AA lg K 0 lg 2 lg K A AA K AA AA K m lg I H K x a0 a i a2 lg i a a a I a I x x, x,2 x,3 deailed values given in he aendix 0 V V 0.5 I V AA AA/AA V AA AA AA AA AA [,76], his sudy his sudy his sudy [77] his sudy [77,84,85,87] his sudy [8,97] his sudy [90-94] his sudy 227

236 Chaer 5 V AA AA/AA AA AA AA V AA mh2o mall m virual H2O all H2O g mol m m all virual mall mh 2O mall H2O all mall mh2o deailed values given in he aendix all 228

237 Acrylic Acid 229

238

239 Acrylamide 6 6 Acrylamide The olymerizaion of AAm (acrylamide, IUPAC: 2-ro-eneamide) is of indusrial ineres as he roduc is widely used as hicener in, e.g., wasewaer reamen, gel elecrohoresis, aer roducion, and mining. The olymerizaion of AAm has been sudied overall. [55,202] The roagaion has been examined searaely by PLP SEC [45,67,203,204]XXXI and by heoreical calculaion, which gave ha waer as a solven (comared o vacuum and oluene) reduces acivaion energy of. [65] The erminaion reacion and ransfer o monomer have been sudied by -radiolysis relaxaion [205] and SP PLP NIR as well as chemical iniiaion. [45] Coolymerizaion, e.g., wih AA has been sudied and a ronounced deendence on H was found. Boh reaciviy raios vary wih degree of ionizaion, as well as he rae of olymerizaion [75,68] and chain ransfer o hiols. [52] The ineic behavior of AAm and is mehylaed derivaes (a he -carbon or one or wo imes a he nirogen) has been invesigaed and exensively discussed. [45] Bacbiing during homoolymerizaion of AAm has no been reored. This subchaer describes how bacbiing during olymerizaion of AAm has been verified. The mos sensiive and mos direc mehod o deec midchain radicals (MCRs) is EPR measuremen. MCRs can be formed during olymerizaion of AAm only by bacbiing and ransfer o olymer. The laer can only occur afer olymer is formed i.e. a significan conversion and esecially for higher iniial concenraion of monomer. Hence, by comarison of exerimens wih differen iniial monomer concenraions and considering how conversion influences he fracion of MCRs, is XXXI The reader may noe ha boh Pascal e al. and Seabroo e al. describe a now widely discarded exlanaion for concenraion deendence. 23

240 Chaer 6 source may be idenified. Accordingly, EPR is he mehod of choice o rove ha bacbiing occurs. I can also be used o quanify bacbiing i.e. measure he corresonding rae coefficien. By measuring under coninuous iniiaion, concenraion and fracion of MCRs can be obained. Anoher mehod o deec bacbiing is 3 C-NMR. As boh roagaion and erminaion (in case of combinaion only) of an MCR lead o a branching oin, he concenraion of branching oins allows for inference on bacbiing. The resuls from boh mehods are resened hereafer. 20 G Figure 6- The EPR secra of BA (aqua line) and AAm (red line) are quie similar. Shown are secra from condiions a which here are almos solely SPRs. The AAm secrum resuls from addiion of four secra o imrove signal-o-noise raio. Condiions AAm: hooiniiaion, g g monomer in H20, 273 K; BA: g g monomer in oluene, 223 K. The BA secrum is aen from ref. [0] The almos ure SPR secra of AAm and BA are comared in Figure 6-. The lines are nearly on o of each oher. Hence, couling consans and line broadening only deviae slighly. The similariy of he secra maes signal assignmen easy, as he assignmen for BA can be adaed. For deails of he assignmen of lines o SPRs and MCRs see subchaer

241 Acrylamide For oher acrylae ye monomers, e.g., BA, bb has a noably higher acivaion energy han he oher rae coefficiens wih which he fracion of MCRs, x MCR, decreases (,, and s ; comare eq. (2.8)). This is why, x MCR increases wih emeraure. Given his, olymerizaion emeraure was increased o chec for changes in he secrum resuling from an augmenaion of x MCR. The mos rominen new line aears in he cener and addiional smaller lines aear nex o he small ouermos lines of he SPR secrum. For BA his is discussed in deail here. [0] In Figure 6-2, secra from measuremens ha had olymer added o he reacion mixure in order o mae criical couling easier and imrove S/N-raio. In Figure 6-2 a he secrum for 273 K (red) loos he same as he one in Figure 6-. This shows ha ransfer o he added olymer is no significan, as indicaed in addiional exerimens a higher emeraure by measuring a reacion mixure ou of he olymer, iniiaor, and waer wihou he monomer and no finding a signal. a b I 5 G Figure 6-2 The EPR secra of AAm olymerizaion under coninuous UV iniiaion a differen emeraure are comared. a: 273 K (red) and 298 K (blue); b: 298 K (blue, same as a) and 323 K (green) This demonsraes how he fracion of MCRs increases wih emeraure. Condiions: 0.40 g g monomer in H20, g g olyvinylyrrolidone, addiion of wo secra o imrove signal-o-noise raio. 233

242 Chaer 6 Comaring he secrum recorded a 273 K (red) wih he secrum measured a 298 K (blue) in Figure 6-2 a reveals he changes execed for an increase of MCRs: A new line aears in he middle of he secrum and he ouer lines seem o broaden. The laer resuls from he fac ha he resoluion of he secrum is no sufficien o observe he wo lines searaely. Increasing emeraure furher leads o an enhancemen of he effecs menioned above. In Figure 6-2 b he secrum recorded a 298 K (blue) is comared o he secrum measured a 323 K (green). The middle line ges even more inense owards 323 K and has he same inensiy as he inner lines of SPR secrum which means he fracion of MCRs is ca. 0.4, which has been calculaed for BA for his raio. [0] Moreover, he ouer lines broaden more. Figure 6-3 Double-bond region of he H-NMR secrum of he reacion roduc of he olymerizaion of 0.05 g g AAm wih 0.02 g g VA-086 in H2O a 70 C is given. The MM lines are: H-NMR (D2O): = 5.4 (bs, H), 5.74 (bs, H). The redicion of he shif by ChemDraw TM is 5.49 and 5.89, resecively. The oher lines resul from monomer residue. In order o verify furher he finding of bacbiing haening during radical olymerizaion of AAm an indeenden, differen exerimen, NMR, was carried ou. Subjec o he o s raio, 3 C-NMR is a less sensiive mehod han EPR o 234

243 Acrylamide deec bacbiing. Such being he case, i was erformed on a olymer samle for which a relaive high concenraion of branching oins was execed. The olymerizaion was carried ou wih a low monomer conen ( 0.05 g g ), as well as low iniiaor conen ( 0.02 g g ), and a a high emeraure (70 C) o full conversion. A his high emeraure, -scission as follow-u reacion o bacbiing is execed o occur a a significan rae. Therefore, H-NMR was carried ou o find macromonomers. Figure 6-3 shows he lines of monomer and macromonomer in he H-NMR. The similariy o AA is obvious (see Figure 5-8 and Figure 6-3). The wo lines associaed wih macromonomer 5.4 (bs, H) and 5.74 (bs, H) canno be assigned o he disroorionaion roduc as he shif of is roons would be differen and he rans couling would be sronger. Furhermore, no disroorionaion aerns (wo lines of equal heigh wih he difference of 2.02 u) were found in he mass secrum (v.i.). The origin of he macromonomers can only be ransfer o olymer wih subsequen -scission. Since iniial monomer concenraion is very low, inermolecular ransfer o olymer should be insignifican. Thus, he finding of macromonomers confirms a high bacbiing rae of AAm a his elevaed emeraure. The 3 C-NMR secrum of AAm is very similar o he corresonding AA secrum (see Figure 5-0). Neverheless, in order o ensure line assignmen a normal secrum and a de-35 (disorionless enhancemen by olarizaion ransfer 35 degree) secrum were measured. In secra measured wih his echnique, eriary and rimary carbon aoms give negaive signals, secondary ones give a osiive signal, and quaernary carbons do no show. The secrum is given in Figure 6-4. The small ea of he quaernary carbon aom of he branching oin is shown enlarged in Figure 6-5. The quaernary naure is confirmed by he de-35 secrum. Comared o AA he line of he branching oin is shifed slighly owards high field. 235

244 Chaer 6 CH CH 2 amide moiey (quaernary carbon) monomer olymer bacbone / m Figure 6-4 The full 3 C-NMR secrum of he reacion roduc of he olymerizaion of 0.05 g g AAm wih 0.02 g g VA-086 in H2O a 70 C is given. The secrum is very similar o he corresonding AA/AA secrum. In order o ensure line assignmen a normal secrum (blue) and a de-35 secrum (red) are comared. In he laer eriary and rimary carbon aoms give negaive signals, secondary ones give a osiive signal, and quaernary carbons do no show. Peas are assigned accordingly. The signal of he quaernary carbon aom associaed wih branching is amlified in Figure 6-5. The concenraion of branching oins can be derived by inegraing 3 C-NMR eas of he quaernary carbon and he CH-bacbone eas (see subchaer 5..4, eq. (5.22)). The secrum acquired wih sandard arameers gives.5 % branching which can be considered as a minimum value. A secrum wih he same arameers as for quaniaive 3 C-NMR analysis of AA (see subchaer 3.5.2) leads o 2.9 % branching. The olymer of he laer measuremen had already been degraded; however, degradaion owards acrylic acid should no disor he resul, as he NMR secra are very similar and cyclizaion XXXII does no direcly involve he carbons used for calculaion. XXXII AAm is nown o undergo cyclizaion by eliminaion of waer and ammonia or by forming imido cycles. 236

245 Acrylamide C q / m Figure 6-5 Enlargemen of he wo secra shown in Figure 6-4. The small ea of he quaernary carbon (Cq) shows in he normal secrum (blue), bu no in he de-35 secrum (red). Under he assumions ha -scission has only marginal influence on branching, s and branching doubles from low o full conversion, aing from ref. [45] he following calculaion gives he bacbiing coefficien during AAm olymerizaion a 70 C as rough esimae: 8.6 J mol R T s 8 5 cg g.04 0 ex L mol s 5 cg g,70 C L mol s s 5 x 0.5 c L mol s 0.62 mol L s s 5 3 bb BP M This bb value is by a facor of 8.5 smaller han he according value for AA. If a high amoun of MCRs is erminaed by disroorionaion, he so-obained bb will be oo 237

246 Chaer 6 low. However, disroorionaion roduc could be found neiher by H-NMR nor by ESI-MS (v.i.). The yical high molar mass of AAm is no well suied for analysis by ESI-MS. Nonheless, he olymer from high-emeraure olymerizaion, which has been used for NMR analysis (v.s.), has shorer chains. Sill, much olymer has a molar mass ha is oo high for ESI-MS. This is why signal-o-noise raio is raher inferior. The ESI-MS analysis does no allow for confirmaion of branching. The molar mass is no alered by bacbiing if i is followed by roagaion. normalize abundance / a.u m/z Figure 6-6 Secion of an ESI-MS secrum (aceonirile, waer and a small bi of formic acid) of he roduc of he olymerizaion of 0.05 g g AAm in waer a 70 C wih 0.02 g g VA-086. The number of monomer unis is given for he main signals. They are muliles of monomer mass. The signals inbeween are mosly from more han one ime ionized olymer. The main olymer line is a muile of he monomer mass lus a sodium caion or a roon in case acid was added o he soluion. The laer gives a beer signal-o-noise raio and a yical secrum is shown in Figure 6-6. Boh he 238

247 Acrylamide -scission roduc and he ransfer o monomer roduc exhibi a molar masses ha fi he major signals. Considering he low molar mass of he corresonding olymer, i may be excluded ha his main signal is he -scission roduc. Thus, i may be assumed ha ransfer o monomer is he dominan chain-soing even a his high emeraure. Signals ha corresond o olymer wih one or wo iniiaor-fragmen endgrous could no be idenified. Mos robably he endgrous undergo various sidereacions. Anoher ineresing finding is ha he aaren isooe ea is much higher han execed (Figure 6-7). This can be exlained by degradaion of he olymer. The nucleohilic aac of waer or hydroxide ransforms an amide moiey ino a carboxyl grou, i.e. an acrylamide monomer uni is convered ino an acrylic acid monomer uni effecively changing he homoolymer ino a coolymer. Naurally his may also haen o monomer in he reacuion mixure consequenly maing i a coolymerizaion. The difference in m/z of he firs line of he wo monomer unis is.0256 u. The righmos ea in Figure 6-6 is shown enlarged in Figure 6-7. Deails of he ea and calculaed values for he 9 monomer uni homoolymer and he corresonding one wih one moiey hydrolyzed is given in Table 6-. In his examle, more han 5 % of he acrylamide monomer unis are hydrolyzed. The nex bigges ea found has an m/z raio, which is 34.0 u smaller han he main ea. This can be exlained by cyclizaion under eliminaion of waer and ammonia. This reacion is nown o occur wih AAm deending on emeraure and H. Again, he aaren isooe ea is oo big. This can be ascribed o hydrolysis of he amide funcion as discussed above. Furhermore, lines from double and mulile ionizaion are found. 239

248 Chaer 6 normalize abundance / a.u m/z Figure 6-7 Enlargemen of he 9 monomer uni ea given in Figure 6-6. m/z of he ea cener is given nex o he relaed ea. Table 6- Comarison beween he lines shown in Figure 6-6 and calculaion for corresonding olymer. found calculaed: calculaed: AAm 9 H 8 AAm AA H m/z normalized inensiy m/z normalized inensiy m/z normalized inensiy

249 Acrylamide 24

250

251 Closing Remars 7 7 Closing Remars The radical olymerizaion of mehacrylic acid, acrylic acid and acrylamide in aqueous soluion has been invesigaed by several differen mehods and seus. Kineic models for boh acrylic acid and mehacrylic acid have been develoed alying he rogram PREDICI TM. Good reresenaion of exerimenal conversion vs. ime rofiles and molar mass disribuions as well as he branching level in case of acrylic acid could be achieved. Boh he Mayo and he CLD rocedure reveal ha C CTA of MAA o ME is indeenden of monomer conen. As exhibis an increase uon decreasing MAA concenraion from bul o dilue soluion by abou one order of magniude, a consan raio of o r,cta hus means r,cta also varies by one order of magniude. This observaion may be undersood as he genuine ineic effec associaed wih hindrance o roaional moion in he ransiion sae srucure by he molecular environmen being rimarily due o characerisics of he radical chain-end and hus being more or less idenical for roagaion and for ransfer o he CTA. This finding robably holds for oher ransfer reacions as well, which should be checed by measuring he ransfer consans o differen molecules in aqueous soluion. Thereby waer as a solven has he advanage of ransfer o waer always being negligible. values from chemically iniiaed olymerizaion of MAA a negligible monomer conversion were evaluaed for a broad range of average chain lenghs. Excellen agreemen wih he comosie model was found alying arameers from lieraure. The influence of conversion on comosie-model arameers is sill a conroversial quesion. This rocedure may give low cos, low afford access o comosie-model 243

252 Chaer 7 arameers, a leas for he long-chain region, for olymerizaions a inermediae and higher conversion. Exerimens could be carried ou by mixing olymer of differen molar masses wih monomer, solven, iniiaor, and CTA. The redicamen would be ha he srucure of olymer coils in soluion is differen for dry olymer dissolved and olymer soluion direcly afer being formed by olymerizaion. A ossibly beer aroach would be o roduce he olymer in a firs se, add CTA o differen exen, and olymerize furher now wih differen chain lenghs deending on he amoun of CTA. For he second aroach secial care has o be aen o ensure accurae nowledge of iniiaor and monomer concenraion. The so-obained iniial values give comosie-model arameers for he corresonding X. Polymerizing under differen levels of CTA wih olymer added a he beginning may also give deeer insigh ino he Norrish Trommsdorff effec, which is esecially ronounced in case of MAA olymerizaion in aqueous soluion. The inensiy of he Norrish Trommsdorff effec decreasing owards higher CTA conen in he olymerizaion mixure could be correlaed o molar mass of olymer in soluion. The chain lengh of macroradicals and of dead olymer in soluion were no indeenden, as boh were correlaed o CTA conen. I would be ineresing o chec he deendence of on molar mass of olymer in soluion for differen chain lenghs of macroradicals, which could be achieved by he above-described olymerizaions wih olymer added o he reacion mixure. The relaionshi beween, and viscosiy of he reacion mixure is well undersood as long as no olymer is resen, i.e., a zero conversion. The relaionshi beween,td and viscosiy resuling from he resence of olymer someimes referred o as macroscoic viscosiy in conras o he microscoic viscosiy fel by he macroradicals is no well undersood. The influence of olymer in he reacion mixure on viscosiy is more ronounced han he influence on, bu he general correlaion is unnown. I would be desirable o gain a deeer undersanding of his relaionshi. Aems o correlae and viscosiy require accurae nowledge of viscosiy a a given conversion. The olymerizaion mixure ha has reached he desired conversion should be measured direcly and wihou delay, because he viscosiy of he reacion mixure changes wih ime. As viscosiy can be measured in a glass caillary, i is ossible o hooolymerize sewise wih analysis of degree of monomer conversion, e.g., by NIR and viscosiy for every se. The olymerizaion of 0.3 g g MAA exhibis an iniial laeau region of u o X = 0.22, while he olymerizaion of 0. g g MAA exhibis a decline of for he same range of olymer conen. I could be shown ha addiion of isobuyric acid as sauraed monomer analogue o he olymerizaion of 0. g g MAA eliminaes he 244

253 Closing Remars Norrish Trommsdorff effec, which oins o boh monomer and olymer conen being imoran for of a olymerizaion mixure. This eliminaion of he Norrish Trommsdorff effec may be ineresing for indusrial alicaions, as more consan reacion condiions may lead o beer roduc roeries. The daa indicaes ha a higher MAA conen in he reacion mixure, and hus in he solven-swollen olymer coils, enhances segmenal mobiliy and ermeabiliy of he olymer-waer soluion for macroradicals. The influence of oher small molecules on a differen X should be invesigaed sysemaically. The above-described aroach of sewise olymerizaion may also hel o undersand his henomenon, as an influence of hese molecules on he viscosiy of he olymer soluion migh be correlaed o heir influence on he Norrish Trommsdorff effec. Aqueous soluions of MAA exhibi very ronounced rheoecy, i.e. sheer force alied o he soluion resuls in an increase of viscosiy. I aears rewarding o invesigae, wheher sheer forces also decrease, and hus he rae of olymerizaion and he molar mass of olymeric roduc can be increased by inense sirring. Deailed analysis of daa of AA revealed ha he maximum found a abou 0.03 g g monomer conen may be exlained by boh A and E A deending on monomer conen. Taing he measured, wea deendence of E A on AA conen ino accoun, exraolaion o high emeraure suggess ha he maximum disaears above 50 C. For many monomers, he low monomer conen region has no been sudied by PLP SEC, bu for MAA no maximum was found. I would be ineresing o see wheher oher monomers han AA exhibi a maximum in he deendence of on he monomer conen as well. The influence of monomer conen on, was imlemened ino he model by correlaion o he effec of monomer conen on viscosiy. For an even more deailed analysis, viscosiy should be measured as a funcion of monomer conen u o high emeraure. There are some oen quesions abou erminaion ineics in general ha should be ss answered. The correlaion beween and as well as he way hese coefficiens are combined o yield should be sudied in more deail. I aears romising o s measure ure MCR erminaion in a model sysem, e.g., by SP PLP EPR, which consiss of MCR recursors of defined chain lenghs ha decay o MCRs (and a very raidly erminaing secies ha disaears quicly) afer UV-irradiaion. Such an aroach, alhough exerimenally challenging, may as well hel o sele anoher quesion. Comosie-model arameers of MCRs have never been measured. Neverheless, simulaion of conversion vs. ime rofiles and radical concenraions a 245

254 Chaer 7 differen chain lenghs in combinaion wih associaed MCR fracions sugges ha MCR exhibi he same chain-lengh deendency as SPRs, which should be verified in an indeenden exerimen. A difference in acivaion energy for and ss has been reored in lieraure. Differen acivaion energies for wo diffusion-conrolled reacions in he same sysem aear unliely and could only be exlained by seric hindrance of MCR- MCR erminaion being reduced owards higher emeraure. In his sudy, no indicaion for a difference in acivaion energy could be found, however, he reacion condiions under invesigaion made roagaion of MCRs, bu no erminaion, he imoran reacion ah. A seu o measure should be used o chec wheher acivaion energy of is higher han acivaion energy of fluidiy. Addiional informaion abou MCR ineics may be derived from deailed analysis, including simulaion, of coninuously iniiaed EPR exerimens, as boh absolue radical concenraion and he fracion of MCRs can be obained. Uilizing a recursor of wo differen chain lenghs may hel o answer he quesion wheher he diffusion mean, he geomeric mean, or he harmonic mean is he oimum rocedure for calculaing he erminaion beween wo chains of differen chain lengh. Mos robably, his quesion can only be answered by direc measuremen of he erminaion beween radicals of wo differen chain lenghs. The Norrish Trommsdorff effec is weaer for AA olymerizaion han for MAA olymerizaion. The conversion deendence of was modeled in he same way as described for MAA bu, as only a few conversion vs. ime rofiles were used for deriving he exression, validaion hereof, by measuring more conversion vs. ime rofiles of olymerizaions wih high AA conen, e.g., by H-NMR or NIR is desirable. Care has o be aen o ee emeraure consan, as high monomer conen leads o high hea of reacion. By measuring he fracion of MCRs during buyl acrylae olymerizaion via EPR, i could be shown ha he ransfer of MCRs o CTA is no an imoran reacion ah. Exension of hese exerimens owards higher emeraure, where he influence of erminaion is less imoran for x, MCR viz., he long-chain aroximaion gives a beer esimae, would be desirable. EPR measuremens of acrylae and CTA a high emeraure are ossible wih he combinaion of, e.g., nahhalene as solven (boiling oin: 28 C), dodecanhiol as CTA (boiling range: C), and ocadecyl acrylae (boiling oin: 400. C). Addiionally, EPR measuremen of 246

255 Closing Remars acrylae and CTA in highly viscous sysem, e.g., olyehylene glycol, would also lead o he long-chain aroximaion being a beer esimae. The bacbiing reacion of AA was quanified via 3 C-NMR. A deendence of bb on monomer-o-solven raio reored in lieraure, comaring could no be found in his sudy for 0.03 g g and 0. g g and 0.5 g g AA, 0.3 g g AA. A deailed sudy of bb over a broad range of monomer concenraions should be carried ou. The olymerizaion of macromonomers synhesized a high emeraure has been sudied a 50 C o searae roagaion of macromonomers from -scission. This aroach should also be used o chec he line assignmen of shor-chain branching and long-chain branching in 3 C-NMR. The AA model develoed for he emeraure range of 35 o 90 C was exended owards high-emeraure olymerizaion u o 70 C, where -scission and roagaion of macromonomers need o be considered. Quanificaion of -scission roved o be difficul because of he raher low qualiy of olymer samles from highemeraure exerimens subjeced o molar mass analysis. I is highly desirable o comare he simulaion o a second daa se of molar masses of roduc from highemeraure AA olymerizaion. A model for he olymerizaion of ionized AA was develoed, which aes numerous deendencies of rae coefficiens on ionizaion and ionic srengh ino accoun. This model should be checed by comarison o conversion vs. ime rofiles and MMDs from olymerizaion of AA under variaion of degree of ionizaion, ionic srengh, monomer, and iniiaor conen. Furhermore, he reduced erminaion rae found for olymerizaion of fully ionized AA should lead o radical concenraion during chemically iniiaed olymerizaion being high enough for EPR measuremen. A more ronounced enhancemen of roagaion by increased ionic srengh for MCRs han for SPRs could be observed by is influence on x. MCR Preferably, low concenraions of monomer should be invesigaed o maximize x MCR and hus radical concenraion, o ensure ha no gel effec alies, and o avoid roblems of solubiliy. Coefficiens used in he model for arly ionized AA should be measured by s indeenden exerimens. PLP SEC exerimens yielding should be carried ou under variaion of degree of ionizaion for higher weigh fracion of monomer o chec he equaion used in he model. Furhermore, he influence of counerions on 247

256 Chaer 7 s should be invesigaed sysemaically. Thereby he raio of counerions o monomer should be varied. I needs o be examined wheher he influence of ionic srengh on s is higher han on A ossible influence of he counerion on s. should be invesigaed as well. An ion-air effec as a ossible exlanaion for he s increase of should vary wih he srengh of coordinaion, size of he counerion, and charge number. I would be aricularly ineresing, wheher non-coordinaing caions also lead o an augmenaion of Moreover, an ion-air effec should aly for oher ionic monomers as well; i should be checed wheher he olymerizaion rae of oher ionic monomers can be maniulaed by addiion of sal. s As he deendence of on boh monomer conen and degree of ionizaion can be s exlained via he ransiion sae srucure, should be calculaed for ionized acrylic acid wih differen amouns of caions being resen around he radical cener based on ransiion sae heory. SP PLP EPR should be used o measure a inermediae degrees of ionizaion o chec he inerolaion used in he model. Aarenly, he effec of ionic srengh on is wea. An increase of s. caused by screening of counerions may be arly comensaed by increased viscosiy. Neverheless, for a more accurae icure, should be measured a full ionizaion under variaion of ionic srengh. In case of screening, he emeraure deendence of canno be execed o be he same as he emeraure deendence of fluidiy. bb should be quanified by 3 C-NMR analysis of low conversion roduc of he olymerizaion of AA under variaion of degree of ionizaion and of ionic srengh. Accurae nowledge of s a given, w, and I is essenial for he analysis. The mechanism of erminaion has o be checed by H-NMR, o examine wheher all bacbiing evens lead o branching oins. I should be examined wheher he K A of AA is indeenden of ionic srengh by measuring he H value of a dilue soluion of AA a = 0.5 under variaion of ionic srengh, e.g., by addiion of NaCl. MCRs were found during acrylamide homoolymerizaion in aqueous soluion via EPR revealing he bacbiing reacion o ae lace. Modeling he olymerizaion of AAm is a logical follow-u of he modeling of AA as he ineic scheme is he same. 248

257 Closing Remars 249

258

259 Aendix Aendix Daa of densiy and viscosiy measuremens of MAA soluions g g MAA g g MAA / g cm g g MAA g g MAA = 35 C = 50 C = 65 C X 0- Densiy of soluions of MAA in waer a differen emeraure. 25

260 Aendix / g cm / C X Figure 0-2 Densiy of 0. g g MAA/MAA in waer. Differen degrees of monomer conversion were simulaed by mixing monomer, olymer, and solven / mpa s / C X Figure 0-3 Viscosiy of 0. g g MAA/MAA in waer. Differen degrees of monomer conversion were simulaed by mixing monomer, olymer, and solven. 252

261 Aendix ln( X 0 0, 0,2 0,3 0,45 0,6 0, T /K Figure 0-4 Arrhenius lo of he daa resened in Figure X / mpa s ime / s Figure g g MAA were olymerized in waer wih g g NaPS as iniiaor a 50 C inside a viscosiy measuring caillary. Red sars give he consanly measured viscosiy; for comarison, he blue line gives he corresonding conversion-ime rofile (simulaion). 253

262 Aendix Figure 0-5 comares he develomen of viscosiy during a olymerizaion of g g MAA in waer wih g g NaPS as iniiaor a 50 C wih he develomen of degree of monomer conversion. The corresonding conversion-ime rofile was simulaed. They increase almos in arallel. The maximum in viscosiy occurs slighly before full conversion is reached; his migh be inaccuracy of he model. Ineresingly, viscosiy decrease afer he oin of aroximaely full conversion. This may originae from he fac ha olymer srucure in soluion changes wih ime. Direcly afer he olymer has been formed, he olymer-waer marix is no in is mos sable form. This effec can also be found when rearing olymer soluions from dry olymer and solven. Here, again viscosiy is a funcion of ime. Branching level and fracion of shor-chain branching Table 0- Measured branching levels and fracions of shor-chain branching. / C w I /% X DB_ex/% BP_ex/% x SCB _ex samle max

263 Aendix Densiy and viscosiy of AA soluions a differen degrees of ionizaion and emeraures Table 0-2 Densiy in g cm 3 of 0.2 g g AA in waer. / C Table 0-3 Viscosiy in mpa s of 0.2 g g AA in waer. / C Modeling Acid-Base Equilibria The couner secies for non-ionized, _AA, and ionized, _AA, monomer resecively, are se a ime zero by he schedule funcion according o iniial concenraion. For each roagaion se a monomer-o-olymer couner secies, +_AA, is generaed, which ransforms one monomer couner ino a olymer couner, _AA, in a fas reacion: 255

264 Aendix _AA +_AA _AA _AA +_AA _AA The equilibria are calculaed by PREDICI TM as hree differen equilibrium reacions, which are couled as hey all involve he H secies. w OH H H2OK AA AA _AA H _AA K AA _AA H _AA K K A his, auoroolysis of waer is given by K, w he equilibrium consans of AA and AA are denoed by K AA and K, resecively. The values for K AA AA was aen from ref. [96] and K AA is calculaed by PREDICI TM (v.i.). As he dynamic acid-base equilibria are calculaed by PREDICI TM, which is imlemened ino he model by means of couner secies (v.s.). These monomer and olymer couners do no have mass, so H has o be wihou mass as well, because oherwise mass would be creaed by deroonaion or vanish by roonaion. Consequenly, non-recie comonens mus have an incorrec mass. Mass and charge balance and all masses in recies are correc. The acual masses and masses used in he model are summarized in Table

265 Aendix Table 0-4 In order o ee mass balance correc, molar mass of H + was se o zero (bold). Molar masses of non-recie comonens were adjused accordingly (in ialics). All molar masses in he recies are correc. acual molar mass / g mol molar mass in model / g mol HO H.0 0 OH Na Cl AA NaA NaOH NaCl Values comlemening Table 5-8: V V V V V V V V / cm mol AA / cm mol AA / cm mol AA / cm mol AA / cm mol Na / cm mol H / cm mol Cl / cm mol OH 257

266 Aendix H H 2 H A, AA m 0 H K a0 a i a2 lg i K lg K 2 lg K lg K lg a I I a I I a I I lg H K 0 b0 b i b2 lg i b I I b I I c I I 2 lg 0 2 H K m c0 c i c2 lg i c I I c I I c I I 258

267 Aendix Conversion vs. ime rofiles for AA a various degree of ionizaion, which have no been used for modeling X g g VA g g VA g g VA086 and 0 and 0.7 and 0.3 and ime / s Figure 0-6 Measured conversion vs. ime rofiles from olymerizaion of 0.2 g g NaA (xm = 0.05) a 90 C wih differen levels of VA-086 as iniiaor (indiced in he grah) a differen degrees of ionizaion of monomer (given in he grah as well). 259

268 Aendix X g g NaPS g g NaPS g g NaPS and and ime / s Figure 0-7 Measured conversion vs. ime rofiles from olymerizaion of 0.2 g g NaA (xm = 0.05) a 90 C wih differen levels of NaPS as iniiaor (indiced in he grah) a differen degrees of ionizaion of monomer (given in he grah as well). 260

269 Aendix 26

270

271 Aendix Abbreviaions and Symbols A A Arrhenius re-exonenial facor ressure-indeenden Arrhenius re-exonenial facor A s Debye Hücel arameer (no emirical) D-H Å AA AAm a a 0 0 m acrylic acid acrylamide aached roon es (NMR echnique) acquisiion ime B 2 nd Debye Hücel arameer (emirical) D-H BA bb BP bs b buyl acrylae bacbiing branching oin broad single broad rile C x carbon, index : rimary, s: secondary, : eriary, q:quaernary y C x chain ransfer consan (x giving secies o which ransfer occurs, y giving of ye of radical: s secondary, eriary) C 3 rd Debye Hücel arameer (emirical) D-H y c x concenraion (x giving secies, y giving ime) ca. CLD circa, Lain: around/abou chain-lengh disribuion 263

272 CLDP CLDT chain-lengh-deenden roagaion chain-lengh-deenden erminaion X D diffusion coefficien of secies X Ð D73 disersiy 2-hydroxy-2-mehyl--henylroan--one de-35 disorionless enhancemen by olarizaion ransfer 35 degree (NMR echnique) DiAA DMSO DTBP E e.g. EPR e al. eq. f FID FT H-A HPLC h I i i diacrylic acid (2-(acryloyloxy)aceic acid) dimehyl sulfoxide di-er-buyl eroxide energy (an index of A refers o acivaion, an index of P o laser ulse, an index of omolar energy of hoons a given laser wavelengh) exemli graia, Lain: for examle elecron aramagneic resonance e alii / e aliae, Lain: and ohers equaion fracion of iniiaor fragmens available for iniiaion free inducion decay Fourier ransform acid (general) high-erformance liquid chromaograhy emirical arameer of he exended Henderson Hasselbalch equaion ionic srengh molecular secies chain lengh or running index; chevron indicaes: averaged, i.e. degree of olymerizaion, index of n indicaes: nuber-averaged

273 Aendix IBA i.e. j iso-buyric acid id es, Lain: ha is chain lengh or running index H K roonaion consan, subscri indicaes corresonding degree of ionizaion of olymer B y x l lg LHS M Bolzmann consan rae coefficien (x giving reacion: bb bacbiing, d (iniiaor) dissociaion, i iniiaion, roagaion, erminaion <may be furher secified afer comma D: diffusion, C: chemical reacion>, r,x ransfer o secies X; y giving ime or chain lengh of involved olymer secies or of ye of radical(s): s secondary, eriary), chevron indicae: chain-lengh averaged, suerscri zero denoes: a ime zero/zero conversion lengh, index : ersisence (chain) lengh, 0: ersisence (chain) lengh wihou elecronic influence, e: elecronic ersisence (chain) lengh decadic logarihm lef-handed side monomer M n number average molar mass M w weigh average molar mass M x MAA molar mass of secies x mehacrylic acid MALDI marix-assised laser desorion ionizaion MCR ME MeHQ MM midchain radical ( s : formed by an,5-hydrogen shif; l : no (direcly) formed by an,5-hydrogen shif ) 2-mercaoehanol hydroquinone monomehyl eher macromonomer 265

274 MMA MMD mehyl mehacrylae molar-mass disribuion MMMP 2-mehyl-4-(mehylhio)-2-morholino-roiohenone MS MU y n x NaA NaMA NaPS NIR NOE mass secromery monomer uni quaniy (amoun) of secies x a ime y sodium acrylae = fully ionized acrylic acid wih sodium couner ion sodium mehacrylae = fully ionized mehacrylic acid wih sodium couner ion sodium ersulfae near infrared nuclear Overhauser effec P i dead olymer chain wih a chain lengh of i P AA AAm BA PLP MAA olym VP radian ower (index 0 means: in fron of cell) roagaion ressure oly(acrylic acid) oly(acrylamide) oly(buyl acrylae) ulsed laser olymerizaion oly(mehacrylic acid) olymerizaion (used as index) olyvinylyrrolidone Q x ariion funcion of secies X (index of indicaes acivaed comlex)

275 Aendix R i R R r rd RHS RD SEC S/N SD SP SPR T growing olymer chain wih a chain lengh of i (do indicaes radical secies) res of he molecule no deiced for reasons of sace available (only used in drawings of molecules) universal gas consan rae relaxaion delay righ-handed side reacion diffusion size exclusion chromaograhy signal-o-noise segmenal diffusion single ulse secondary roagaing radical absolue emeraure (in elvin) ime TEMPO 2,2,6,6-eramehylieridine -oxyl TD ToF V ranslaional diffusion ime-of-fligh molar volume, index 0 indicaes exraolaed o infinie diluion V-50 2-[(E)-2-(-carbamimidoyl--mehylehyl)diazen--yl]-2-mehylroanimidamide dihydrochloride VA-086 v.i. viz. v.s. 2,2'-Azobis[2-mehyl-N-(2-hydroxyehyl)roionamide] vide infra, Lain: see below videre lici, Lain: i is ermied o see (namely) vide sura, Lain: see above 267

276 w x weigh fracion of x X arbirary secies (wih do: arbirary radical secies) X Y degree of conversion, index gives secies; wihou index i refers o monomer x Y z mole fracion of x arbirary secies (wih do arbirary radical secies) charge number degree of ionizaion l exonen of chain-lengh deendency in region of long chains s exonen of chain-lengh deendency in region of shor chains V acivaion volume ineic chain lengh chemical shif (only if referring o NMR) molar decadic absorion coefficien correcion facor for ; suerscri: s sands for secondary radical, sands for eriary radical; subscri: d sands for disribuion (correcing a value for one chain lengh o use i for a disribuion, which average chain lengh is he former one), w sands for correcion of viscosiy change wih differen monomer conen, sands for correcion of viscosiy change wih ionizaion, C sands for correcion of Coulomb reulsion of ionized macroradicals dynamic viscosiy, subscri r: relaive, suerscri X: a conversion X emeraure in C fracion of disroorionaion, index gives ye of radical erminaing: s:secondary, :eriary sloe of firs CLD lo wavenumber

277 Aendix inemaic viscosiy I correcion facor for influence of addiional sal on densiy ransmission coefficien residence ime, index: calc: calculaed from mass flow, densiy of he reacion mixure and geomeric volume of he reacor. radian ower (inensiy) a a cerain wavenumber 269

278

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291 Dansagung/Acnowledgemens Mein außerordenlicher Dan gil Herrn Prof. Dr. M. Bubac für die ineressane Themensellung sowie die see Disussionsbereischaf und Förderung dieser Arbei. Außerdem bedane ich mich bei Prof. Dr. P. Vana, MBA für die Übernahme des Korreferas. Secial hans go o Prof. Robin A. Huchinson (Queen s Universiy, Canada) for inviing me o Canada and inroducing me o modeling, los of helful discussions and suggesions, and alogeher a very fruiful cooeraion. I han Igor Lací, DSc, and Mare Sach, PhD, (Polymer Insiue SAV, Slovaia) for discussions roviding insigh ino challenging SEC analyses, and deerminaion of many MMDs. Conribuions of furher coworers a he Polymer Insiue of he Slova Academy of Sciences in Braislava are also graefully acnowledged. Ďaujem. I han Sandhya Sananarishnan, PhD, for hel wih Predici and showing me around a Queen s. I d lie o han Calisa Preusser (Queen s Universiy, Canada) for ineresing discussion and for sharing resuls. Ein besonderer Dan gebühr Dr. Jens Schrooen, Dr. Johannes Barh, Hendri Kaner, Henri Schröder und Paric Drawe für ihre unermüdliche Disussionsbereischaf und viele hilfreiche Anregungen.

292 Weierer Dan gil Herrn Dr. H.-P. Vögele für die sändige Hilfsbereischaf bei echnischen Fragen, besonders zu den IR-Seromeern. Bei Herrn R. Machine bedane ich mich für Raschläge zur NMR-Messung und aräfige Hilfe beim Finden der richigen Messbedingungen, sowie bei der gesamen NMR-Abeilung für die Messung von NMR-Proben. Herrn Dr. H. Frauendorf dane ich für die MS-ESI und HPLC Messungen sowie hilfreiche Anmerungen. I wish o han Dr. Taiana Sergeeva for discussions and suor regarding evaluaion of EPR secra as well as for sharing resuls. Ich dane Paric Drawe und Dr. Johannes Barh für das Teilen von Ergebnissen. Großer Dan gebühr Dr. Johannes Bubac für das Programm Predici Bach, eine exzellene Ergänzung des Programms PREDICI TM. Ich dane Daniel Weiß, dessen Maserarbei ich mibereu habe, für die gue Zusammenarbei und das Teilen von Ergebnissen. Ich dane Jusus B. Söllner und Roman Kremring, deren Bachelorarbeien ich bereu habe, für die Zusammenarbei. I han Dr. Hugo Vale (BASF SE) for helful discussions and suggesions. Herrn Prof. Dr. F. Meyer möche ich für die Bereisellung des ESR-Seromeers danen.

293 Thans are given o Prof. Dr. Alex M. van Her (Technische Universiei Eindhoven, he Neherlands) for roviding he rogram Conour. Den Miarbeiern der Insiuswersäen dane ich für ihre Hilfsbereischaf und zuverlässige Arbei. Ich möche mich bei Paric Drawe, Henri Schröder, Julia Möhre, Hendri Kaner, Nicolai Sörensen, Dennis Hübner und Jan-Hendri Schüz für das Korreurlesen dieser Arbei bedanen. Die Hilfe von Dr. Jens Schrooen bei der Bedienung des Lasers für PLP soll an dieser Selle danend erwähn werden. Ich dane Cahrin Conrad und Björn Söler dafür, dass sie Kaffeebohnen und Milch für die Abeilungen eingeauf haben ohne den Kaffee zwischendurch häe ich es nich geschaff ;-) Bei allen Migliedern der Arbeisreise Bubac und Vana bedane ich mich für die angenehme Arbeisamoshäre und die see Hilfsbereischaf, nich zu vergessen zahlreiche Frühsüce, Kuchen, Eis, aber auch gemeinsame Ausflüge zum Kanufahren oder Wandern. Bei der BASF SE möche ich mich für die finanzielle Unersüzung dieser Arbei bedanen. Ich dane dem Deuschen Aademischen Ausauschdiens (DAAD) für die finanzielle Unersüzung meines Aufenhales an der Queen s Universiy in Kanada.

294 Abschließend möche ich meinen Freunden, seziell der Reisegrue, für die moralische Unersüzung und die zahlreichen willommenen Ablenungen danen. Ich dane meiner Freundin, dass sie meisens ;-) an mich geglaub ha und immer für mich da is. Mein größer Dan gil meiner Familie. Für ihre Begleiung und Besärung, ihre Geduld und ihr Verrauen in mich bin ich ihnen zuiefs danbar.

295 CURRICULUM VITAE Personal Deails Name Dae and Place of Birh Ciizenshi Nils Friedrich Guner Wienberg 983/Nov/06 in Hamburg German Educaion 2009/Oc resen docoral disseraion research a Georg-Augus- Universiä Göingen, worgrou Prof. M. Bubac, Kineics and Modeling of he Radical Polymerizaion of Acrylic Acid and of Mehacrylic Acid in Aqueous Soluion 200/May 200/Jul research say a Queen s Universiy in Kingson, ON, Canada, worgrou Prof. R. Huchinson 2004/Oc 2009/Aug 2009/Aug/2 diloma sudies in chemisry a Georg-Augus- Universiä Göingen Chemie-Dilom (graduaion in chemisry) 2008/Oc 2009/Ar diloma hesis, worgrou Prof. M. Bubac, Iniiierung und Regelung bei radialischer (Meh)Acrylsäureolymerisaion in wässriger Lösung 200/May 200/Jul 2003/Jun/26 research say a Universiy of New Souh Wales in Kensingon, NSW, Ausralia, worgrou Prof. R. Read Abiur a he Gymnasium Rissen, Hamburg Scholarshis 200/May 200/July DAAD (Deuscher Aademischer Ausauschdiens) for a research say a Queen s Universiy in Kingson, ON, Canada