Case Studies with Mathematical Modeling of Free-radical Multi-component Bulk/Solution Polymerizations: Part 1

Transcription

1 Ths s an Acceted manusct o the atcle ublshed by Taylo & Fancs n Jounal o acomolecula Scence, Pat A: Pue and Aled Chemsty, 5:9, 59-98, DOI:.8/ Case Studes wth athematcal odelng o Fee-adcal ult-comonent Bul/Soluton Polymezatons: Pat Woosung Jung, azeh ahnezhad, Thomas A. Dueve and Alexande Penlds* Insttute o Polyme eseach (IP), Deatment o Chemcal Engneeng, Unvesty o Wateloo, Wateloo, Ontao NL 3G, Canada * Autho o coesondence Abstact In at o ths sees o two extensve ovevews o mult-comonent olymezaton case studes, we esent mathematcal modellng esults wth exemental conmatons. The case studes ae om ee-adcal, bul and/o soluton olymezatons, coveng the ange om homo- to hexa-olymezaton at both egula and elevated temeatue levels,.e., wthout and wth ossble deoagaton stes. The model eventually tacles comlex olymezaton eatues, angng om conveson-tme hstoes to moe esotec mult-comonent comoston and/o sequence length oles. Pat o the sees wll descbe moe comlcated stuatons wth deoagaton and comoston contol olces, all elyng solely on a unque monome/olyme database o hysco-chemcal oetes and othe chaactestcs, wth no uthe aamete adustment. These database tems wll be cted n tables n at o the sees. Keywods: bul olymezaton, soluton olymezaton, ee-adcal olymezaton, mathematcal modellng, coolymezaton, teolymezaton

2 Intoducton In mult-comonent ee-adcal olymezaton, moe than two monomes atcate n chan gowth leadng to combned oetes o the ndvdual homo-olymes; the olymezaton s bascally comsed o comettve eactons between deent adcal/monome seces. As the numbe o monome seces nceases, the numbe o ossble eactons also sgncantly nceases and theeoe the olymezaton mechansm becomes comlcated. Notwthstandng ths, both the mathematcal modelng and the study o mult-comonent eces have attacted consdeable ndustal and academc nteest o seveal decades due to the added economc benets o enhanced olyme oetes and exanded alcatons va vaous combnatons o monomes. Ths ae stats wth an ovevew on model develoment and contnues wth vaous testng case studes o mult-comonent olymezatons. Thee has been a contnuous eot n ou gou o about thee decades towads the develoment, testng and enng o a bul/soluton mult-comonent olymezaton model/database (-4). It has been shown that the smulaton acage can act as a vey lexble and useul tool that could gude academc and ndustal eseach and develoment o homo-, co-, and teolymezatons. The obectves o the moe ecent exanson o the mathematcal modelng hase wee to extend and test uthe a mechanstc eacto model o mult-comonent (u to sx monomes) bul/soluton olymezatons unde batch/sem-batch eacto conguatons wth many useul eatues. A lot o eot was ut on seachng the lteatue o hyscal/netc aametes, modelng aoaches and exemental data. The sxmonomes o nteest nclude styene (Sty), n-butyl acylate (BA), butyl methacylate (BA), hydoxyethyl acylate (HEA), hydoxybutyl acylate (HBA), and acylc acd (AA), along wth deent emutatons. In ode to develo a lexble, comehensve, and use-endly model, the accomanyng model database was also exanded n aallel. Ths motant (and athe unque) database ncludes hysco-chemcal/netc chaactestcs/coecents o the ndvdual monomes and othe eacton ngedents,

3 such as solvents, ntatos, and chan tanse agents, and also chaactestcs o the ossble coolyme as o teolyme and (othe hghe) multcomonent combnatons (e.g., values such as eactvty atos, glass tanston temeatue chaactestcs, etc.). These database tems (moe detals on the database tems wll be cted n at o the sees) ae xed and do not change om smulaton case to smulaton case, thus coveng a vey wde ange o oeatng condtons, eces and modes o oeaton, and hence mang the model edctons moe cedble, thus nceasng one s condence n the model edctve caabltes and utue uses o ece desgn, eacto oeaton otmzaton and antcaton o ocess modcaton tends. Though an extensve lteatue seach o olymezaton models and netc nomaton, the smulaton model was develoed nto a genealzed and comehensve one whch coves the ange om homo- to hexa-olymezaton at both egula and elevated temeatue levels, n ode to exlan vaous olymezaton netc chaactestcs (ncludng deoagaton and bacbtng eacton eatues), and theeoe, to ovde quc and elable edctons o oductvty (eacton ate) and qualty (molecula weght, olyme comoston, sequence length, banchng, etc.) o mult-comonent olymes ove a wde ange o eacton condtons. odel testng was conducted wth exemental data n ode to vey the model s elablty. Due to lmted exemental data o hghe level mult-comonent olymezatons (wth a numbe o monomes hghe than two), the smulaton model could be tested wth homo- u to tetaolymezaton cases, whch omed the case studes o the ae. The model edcton lots thoughout the ae wee geneated elyng solely on a unque database o ndvdual monomes/ngedents and no aametes wee adusted uthe o selectvely n ode to obtan ageement wth exemental data. In addton, the model was uthe utlzed o nvestgaton o scenaos o contol o olyme comoston, whch s one o the most motant actos closely elated to mechancal/chemcal oetes o multcomonent olyme oducts. All these extensve model testng case studes nceased the ange o the model s alcablty as well as the use s condence n the model s elablty o the descton o vaous olymezaton eces and oeatng modes. 3

4 Exemental. Peamble Ths ae contans extensve mathematcal modellng esults and exemental data. The exemental data come om many souces and they eesent a mx o eseach laboatoy and lot-lant data. As such, actual exemental detals can be ound unde the esults and Dscusson secton, when deent data souces (and the coesondng lteatue eeences) and data behavou ae dscussed and comaed to model edctons. Due to ths extensve mathematcal modellng, and beoe we stat the dscusson o the obtaned esults, a be bacgound on mult-comonent olymezatons along wth the mathematcal modellng s n ode.. Be Bacgound on ult-comonent Polymezaton.. Lteatue evew Numeous modelng studes and exemental wo on homo- and mult-comonent olymezaton have taen lace ove the last 3 yeas o so, and ctng them all hee s beyond the scoe o ths ae. Fo detaled evews on mult-comonent olymezaton, see (5). Gao and Penlds () evewed souces o lteatue wth useul exemental data o seveal monome systems n the extensve ae, along wth a summay o modelng eots. They also showed model edctons ove a vey wde ange o monome systems and condtons, usng a comehensve database o hysco-chemcal monome chaactestcs (WATPOLY). Conmatons and addtonal extensons wee gven n (3-4) and (-7). Usng the smulaton acage, Fusawa and Penlds (8) consdeed modelng wo egadng thee classes o co-olyme comoston contol stateges n a sem-batch eacto, and dscussed the nluence o these olces on olymezaton ate, comoston, molecula weght, banchng, etc. Based on the above eots, the extended veson o the mult-comonent model has been develoed ncludng vaous smulaton eatues and otons whch wll be dscussed late n ths ae (sequence length dstbuton, deoagaton, and moe comlex olymezaton scenaos). 4

5 Deoagaton has been nown snce ccomc (9) dscoveed exementally that alha-methyl styene (AS) does not olymeze above and veed the elaton between themodynamc equlbum concentaton and celng temeatue. Lowy () assumed thee cases n whch one o the two monomes undegoes evesble oagaton and suggested the coesondng co-olyme comoston equatons. Late on, seveal eots to develo a moe geneal equaton too lace. Wttme (), o nstance, added some coecton actos whch comensated o adcal eects wth deent temnal sequence dstbutons, nto the ayo-lews equaton (). The deoagaton model o co-olyme comoston by Küge et al. (3) was consdeed moe geneal and stable wth bette convegence oetes than eale ones, and ths was dscussed by Palme et al. (4-5) wth examles om AS/methyl methacylate (A) bul and soluton (toluene) batch co-olymezatons at to 4. They estmated equlbum constants and coss-deoagaton atos as well as eactvty atos, and obtaned exemental data egadng conveson, comoston, and molecula weghts though the ull conveson ange. Usng these data, Cheong and Penlds () showed easonable model edctons, and Leamen et al. (7-8) envestgated ths monome system o moe ened aametes and uthe exanded the studes to AS/butyl acylate (BA)/A te-olymezaton. All deoagatng models mentoned above wee based on temnal model netcs. On the othe hand, combnatons o deoagatng eects wth the enultmate model wee consdeed n butyl methacylate (BA)/BA co-olymezaton (9-), Sty/BA coolymezaton (), and Sty/dodecyl methacylate (DA) co-olymezaton (). Anothe motant asect ncluded n modelng eots s ntamolecula chan tanse (bacbtng), shot chan banchng, and agmentaton (scsson) dung BA olymezaton. antow et al. (3) conducted batch eacto modelng wth deoagaton usng the mlct enultmate unt eect model, and good ttng esults wee obtaned by L et al. (). 5

6 .. ult-comonent Polymezaton Knetcs ult-comonent adcal olymezaton ollows the egula ee-adcal olymezaton stes: ntaton, oagaton, temnaton, chan tanse to small molecules such as monome, solvent, chan tanse agent (CTA) etc., tanse to olyme, and temnal/ntenal double bond olymezaton. Addtonal eacton stes at elevated temeatues, such as deoagaton and themal ntaton, ae also consdeed when aoate. BA monome s seconday eacton stes egadng tetay adcals elated to shot chan banchng along wth othe model eatues and addtonal case studes ae gong to be dscussed n a late secton. Intaton d I () n n,, () The ntaton ste nvolves two eactons. Fst, commecally motant azo o eoxde ntatos usually yeld a a o may adcals by themal homolytc cleavage. Not all may adcals can atcate n uthe eactons. Ate ntato decomoston, the adcals ae taed n the eacton mxtue due to the cage eect. Wthn the cage, some adcals may ecombne, eact wth each othe o wth monome, o duse out to ntate olymezaton. Uon extng, some adcals lose the eactvty and become stable. Ths s descbed by the ntato ecency (usually n the ange o.3 to.75), whch s essentally the acton o adcals that successully lead to gowng chans. Themal Intaton th n m byoducts (3) Styencs can undego ntaton wthout necessaly the esence o an added chemcal ntato. Ths ntaton ate s neglgble comaed to the contbuton va chemcal ntato decomoston, howeve, t becomes sgncant at elevated temeatues (hghe than ). Ths uely (auto)themal o sel-ntaton ollows a Dels-Alde mechansm (4). Poagaton,

7 ,, (4) adcals gow by addton o successve monome seces (tycally, hundeds o thousands). It should be noted that the hghe eactvty a monome seces has, the moe t can ncooate nto a olyme chan. Ths s an motant eatue o mult-comonent olymezaton that allows the synthess o an almost unlmted numbe o deent oducts by vaatons n the natue and elatve amounts o the monome seces n the eed. Accodng to the temnal model based on a st ode aov ocess, the eactvty o a oagatng adcal deends only on the monome unt at the gowng adcal end and s ndeendent o chan comoston. The oagaton ste s motant n a multcomonent olymezaton because the comoston and aangements eventually encounteed n a olyme molecule ae mostly deendent on eactvty deences between adcal seces and monome seces. Deoagaton,, (5) At elevated temeatues chans may evesbly undego deoagaton leadng to chan length decease. In the mult-comonent case, deoagaton aects not only the ate o olymezaton but also olyme comoston, sequence length dstbuton and molecula weghts. Thee ae seveal models that can be used to edct comoston o a evesble co-olyme system. Among them, Küge s obablstc aoach (3, 8), extended to the mult-comonent case, s moe oweul and obust than othe models (e.g., Lowy () and Wttme ()), and wll be dscussed n moe detal late. Temnaton tc, s, P s (combnaton/coulng) () td P P, s, s (dsootonaton) (7) Chan gowth stos and dead olyme molecules ae obtaned om the eacton o two adcals, ethe by combnaton o dsootonaton. In temnaton by combnaton 7

8 (coulng), two adcals mae one dead olyme. In dsootonaton, a hydogen atom n the beta oston o one o the adcal centes s tanseed to anothe adcal and a temnal double bond s omed. Chan Tanse to Small olecules (monome, solvent and CTA) mt, T P T (8) adcal tanse s a chan-beang eacton. adcal actvty can tanse om a gowng chan to any exstng o added substance, such as monome, solvent, and chan tanse agent (CTA) ollowng a smla mechansm. Ths (sde) eacton eectvely stos the gowth o the ognal adcal chan. As a esult, a olyme s chan length and hence ts molecula weght wll be deceased. Chan Tanse to Imuty (etade/nhbto) Z, Z P Z (uneactve) (9) Imuty can be any comound whch not only educes chan length, but also suesses the olymezaton ate. It convets adcals to uneactve o less eactve seces, and the olymezaton stos comletely (nhbto) o slows down (etade) untl the mutes ae consumed. Chan Tanse to Polyme (Long Chan Banchng, LCB), Ps, P, s, () As conveson nceases, tanse to olyme becomes sgncant. Ths esults n the abstacton o a hydogen atom om the dead olyme by the gowng adcal and a new adcal ste oms somewhee on the olyme bacbone nstead. onome can now add to ths ntenal adcal cente, and a banched olyme s oduced (t-unctonal banchng). Tanse to olyme boadens the molecula weght dstbuton (ncease o olydsesty) and nceases the weght aveage molecula weght consdeably, but does not nluence the numbe aveage molecula weght. Unle othe ate constants, measung the tanse to olyme ate constant s nheently dcult. Because o ths, thee ae elatvely ew elable aamete values/souces avalable n the lteatue. 8

9 Temnal Double Bond Polymezaton (LCB) *, Ps, s () Ths s anothe mechansm o omng long chan banchng (LCB). Temnal double bonds on a dead olyme molecule ae obtaned by ethe temnaton va dsootonaton o esecally tanse to monome eactons. Once the concentaton o these temnal double bonds becomes comettve, a adcal can also attac the temnal double bond and one lage banched macoadcal s ceated. Eventually, ths nceases both the numbe and weght aveage molecula weghts and boadens the molecula weght dstbuton consdeably. Intenal Double Bond Polymezaton (Cosslnng) **, Ps, s () Cosslnng o netwo olyme omaton s due to the esence o a d-unctonal monome, such as,3-butadene, an motant monome wdely used n the ubbe ndusty. Addton o a adcal to ths monome yelds an allylc adcal wth two ossble easonance stuctues. Ths adcal eacton oceeds va oagaton at ethe the, cabon o,4 cabon stes. Both dead olyme molecules that may om have an unsatuated (endant o esdual) double bond ntenally and ths wll eact wth anothe adcal to cause cosslnng (o teta-unctonal long chan banchng)...3 odel Develoment n a Batch/Sem-batch eacto onome Balances I ully evesble, a sx-comonent olymezaton nvolves 3 oagaton eactons ( homo-oagatons and 3 coss-oagatons) and 3 deoagaton eactons ( homodeoagatons and 3 coss-deoagatons). Assumng monome consumton s lagely due to oagaton stes o oducng long chans (Long Chan Aoxmaton o LCA o tye I), monome balances ae as ollows: dn F, n V (3) dt 9

10 whee N, F,n, and stand o the moles, the mola nlow ate, and the ate o consumton o monome seces, esectvely, and V s the volume o the eacton mxtue. In a batch eacto, F,n becomes zeo. s exessed n tems o ate constants, and adcal and monome concentatons, as shown below, when deoagaton s neglgble. (4),,, whee,, and ae the total monome and adcal concentatons, and the mole acton o monome seces and adcal seces, esectvely. adcal Balances: No Deoagaton Intato (NI) and muty (NZ) balances ae needed to buld the ull adcal balance. adcals ae geneally geneated by ntato decomoston and consumed n temnaton o n eactons wth mutes. dn dt I F, N (5) I n dnz FZ, n znz () dt whee d and z ae the ntato decomoston ate constant and muty eacton ate constant, esectvely. The total adcal concentaton s calculated usng the ollowng balance: d d V N V dt I z Z I (7) whee t s the oveall temnaton ate constant (t = tc + td), and I, the ntaton ate, wll be dened late n Equaton 5. Usng the steady state hyothess (SSH) o adcals, based on Equaton 7, the total adcal concentaton s calculated as: t z ( N z t / V ) ( I / V ) 4 t / z ( N z t / V ) (8)

11 ultlyng ths wth the coesondng adcal actons gves the ndvdual adcal concentatons. In ode to calculate, adcal balances ae omulated by assumng that coss-oagaton ates o two adcals ae equal and theeoe, SSH o adcals n mult-comonent olymezaton s also vald (Long Chan Aoxmaton o LCA o tye II). In a sx-comonent case, o examle, 3 coss-oagaton eacton constants should be consdeed. ) ( ) ( dt d (9) whee s the eacton ate o a adcal (endng n monome ) wth monome. adcal actons can now be solved om a genealzed system (set) o equatons. eaangng nto a matx om, Equaton 9 can be exessed as = b () whee = ) ( ) ( ) ( ) ( = 5 4 3, b = Snce, substtutng and eaangng agan, the ollowng exesson s obtaned:

12 = ( ) ( 3) = 3 4 5, b = ( 4) ( 5) Fnally, adcal actons ae calculated by = - b; ndvdual adcal concentatons can be obtaned by multlyng the total adcal concentaton n Equaton 8 by each adcal acton. adcal Balances: Deoagaton In the deoagaton case, adcal concentaton calculatons become moe comlcated. Thee ae 7 eactons n total ncludng 3 oagatons and 3 deoagatons whch need to be consdeed o a sx-monome system. () Theeoe, Equatons 4 and 9 should be moded to nclude homo- and cossdeoagaton tems usng the extended Küge s sx-comonent model. () d dt ( ) ( ) (3)

13 Küge (3) calculated the enultmate adcal concentaton usng the obablty that a monome o tye s attached to a (enultmate) adcal endng n, P., P (4) whee P Equatons and 3 can be ewtten usng Equaton 4 as ollows: P (5) d dt ( ) P ( ) P () Assumng SSH, the let sde o Equaton becomes zeo. On the othe hand, the obablty P n Equaton 4 s exessed n tems o ate constants and seces concentatons. P l l l l l l l l l l l P (7) P Equaton 7 ntoduces nonlneates and hence, Equatons and 7 should be solved smultaneously by a numecal method. l In ou examle o hexa-olymezaton, thee ae 3 obabltes and adcal actons that need to be calculated. Theeoe, the equed numbe o (nonlnea) Equatons and 7 becomes 4 and they can be solved by an aoate numecal method (e.g., ethe Newton s o tust egon technque). Othe Imotant Balances I a chan tanse agent (NCTA) and/o solvent (NS) ae esent n the eacto, they wll decease molecula weght and the ollowng balances should also be ncluded: dncta FCTA, n CTANCTA (8) dt 3

14 dns FS, n S NS (9) dt whee CTA and S eesent chan tanse ate constants to CTA and solvent, esectvely. Due to the change n densty om monome to olyme, the volume o the olymezng mxtue wll shn dung the eacton accodng to the ollowng exesson: dv dt F, n w, monome, monome olyme w V whee w, ρ,monome, and ρolyme ae the molecula weght and the densty o monome seces, and the densty o olyme, esectvely. (3) Anothe motant balance s necessay o the moles o each monome n the eacto whch ae bound as olyme. In a batch eacto, whee thee s no nlow/outlow o olyme om the eacto, the amount o consumed monomes s equal to that o the geneated olyme accodng to LCA I, and conveson/olyme comoston calculatons can be obtaned dectly om the monome balances n Equaton 3. Howeve, n a sembatch eacto, addtonal balances ae needed o the nlow o monomes that ae ncooated n the mult-comonent olyme n ode to calculate conveson/olyme comoston oles oely: dp dt F, V (3) n whee P and F,n ae the moles and mola nlow o monome seces bound as olyme. Conveson, Comoston, Sequence Length Indcatos and Tad Factons The total mola conveson o monomes to mult-comonent olyme s gven by X (3) N P P 4

15 Smlaly, atal conveson o monome seces s X P (33) N P Conveson vesus tme oles ndcate how ast olymezaton oceeds (olyme oductvty). The nstantaneous olyme comoston, the oveall mole acton o monome ncooated nstantaneously n the olyme, s calculated as dn F (34) dn Equaton 34 coves all nds o mult-comonent cases (and educes to homoolymezaton). When educed to smle cases wthout deoagaton, t becomes dentcal wth the ayo-lews (co-olyme) equaton (), Aley-Goldnge (teolyme) model (5), and Wallng-Bggs (te- and hghe) equatons (). Comang these nstantaneous olyme comostons wth the ones om Valvasso-Sato (7) and Hocng-Klmchuc (8) comoston equatons, whch ae deved om a smled LCA II, the deences ae not sgncantly lage elatve to tycally encounteed exemental eos (5). The accumulated olyme comoston, the aveage mole acton o monome ncooated nto the olyme at a cetan conveson level, s detemned by F P (35) P Co-olyme comoston n a batch eacto usually exhbts the so-called comoston dt. Polyme comoston s an motant ndcato closely elated to the olyme s mechancal, chemcal and otcal oetes. Theeoe, t should be contolled to oduce a desed oduct. Polyme comoston contol wll be dscussed late n secton 3. as a case study. 5

16 Estmaton o eactvty atos s ey to calculatng olyme comoston as well as adcal actons mentoned eale. The denton o a eactvty ato unde the temnal model s the ato o a homo-oagaton ate constant dvded by a coss-oagaton ate constant. ( ) (3) A sx-comonent system bascally eques 3 bnay eactvty atos o cossoagatons and ndvdual homo-oagaton ate constants. Futhemoe, the numbe o aametes wll be moe than that consdeng deoagaton. Theeoe, successul mult-comonent studes ely on the establshment o good homo- and co-olymezaton netc data. ult-comonent olyme comostons obtaned n Equatons 34 and 35 ae able to descbe the oveall macoscoc nstantaneous/accumulated mole ato o monome unts n the olyme chan. Howeve, they cannot gve a whole ctue egadng the dstbuton o monome sequences, o examle, n bloc co-olymes such as -AA--A- BB--B-AA-, and uely altenatng co-olymes such as -A-B-A-B-A-B-, havng the same comoston. Ths mcostuctual oety,.e., nomaton about the aveage numbe o monome unts comng om how they ae dstbuted along the olyme chan, can be evealed by the sequence length dstbuton. Because o electng ntamolecula homo(heteo)genety, aveage sequence length and sequence length dstbuton (SLD) can be motant ndcatos o mult-comonent olyme qualty/behavou, esecally when the ndvdual homo-olymes have wdely deng oetes. To llustate ths, a statstcal aoach (Koeng (9)) was ollowed. Assumng the olymezaton behavou ollows the temnal model wth ull deoagaton, the obablty, that a gowng adcal wth unt n ts end adds monome, n a sxmonome system s dened as: P l l l l l l l l l l l (37) P l l

17 7 whee ( ) The obablty s totally deent om (and not to be conused wth) P (catal lette) o deoagaton n Equaton 7, deste the algebac smlaty. Usng, the obablty dstbuton o havng n consecutve unts o monome, that s, a sequence o monome wth length n n a gowng chan, s: n n N ( ) (38) whee n n n n N ( ) The nstantaneous numbe and weght aveage sequence lengths o monome n hexaolymezaton ae calculated n Equatons 39 and 4, esectvely. 3 3 n n n n n n n n n n n n n n n n n n N N N nn N nn n (39) n n n n n n n n n n n n n n n n n N n n N n nn N n w 3 (4) In ode to detemne the cumulatve obablty dstbuton as a weghted comoste o the nstantaneous values, these nstantaneous values should be ntegated. The govenng equatons ae exessed as ollows, based on aoaches descbed n (3-3):

18 N n X N n dx n X dx n X N n F dx n X F dx n X n X F dx F dx X n X F dx F dx (4) whee n N n X n X n F dx F dx X X F dx F dx X X F dx F dx (4) The cumulatve numbe-aveage sequence length o monome s calculated as N n n N n n N n X n n X n F dx F dx X X F dx F dx X X F dx wheeas the cumulatve weght-aveage sequence length o monome s gven by W X n n n 3 N Nn n N X n n Nn n F dx N F dx X X X n n n X N F dx / F dx / X X F dx F dx F dx F dx X X F dx F dx F dx (43) (44) Anothe way to nvestgate olyme mcostuctue s the calculaton o dyad, tad, o entad actons. Among them, tad acton calculatons, beng moe equently used, have agan been extended heen to sx-comonent olymezatons as an examle. The tad actons ae descbed by the obablty unctons o Equaton 37. Geneally, thee ae thee attens o tad actons, gven n Equatons 45 to 47. A (45) 8

19 A A (4) A (47) whee, = {,, 3, 4, 5, } (thee ae dstngushable cases out o total tads). Consdeng all dstngushable monome -cented tad actons, the summaton should equal, as shown n the samle calculaton that ollows: A A A A A A A A A A A A A A3 A3 A33 A34 A35 A3 A4 A4 A43 A44 A45 A4 A5 A5 A53 A54 A55 A5 A A A3 A4 A5 A A A A3 A4 A5 A A A A3 A4 A5 A A3 A3 A33 A34 A35 A3 A4 A4 A34 A44 A45 A4 A5 A5 A35 A45 A55 A5 A A A3 A4 A5 A A A A33 A44 A55 A A A3 A4 A5 A A3 A4 A5 A A34 A35 A3 A45 A4 A (48) Accumulated tad actons ae obtaned by the usual ntegaton o the coesondng nstantaneous oetes ove conveson, such as: A X A X F F dx dx (49) 9

20 Pseudo-ate Constant ethod The seudo-ate constant method enables a comlcated mult-comonent olymezaton system to be vewed as a vtual homo-olymezaton. The monome and adcal actons obtaned above ae used n the seudo-ate constant calculatons o the multcomonent case. Indvdual ate constants ae oely weghed nto the oveall seudoate constant, deendng on the secc eacton ste. The ate o ntaton n mult-comonent olymezaton can be wtten n the same way as o homo-olymezaton: I l I (5) whee l denotes the numbe o ossble ntatos used n the ece; each ntato has ts own decomoston ate constant, ecency acto and concentaton, d, and I, esectvely. d The ate o mult-comonent olymezaton s the ate o dsaeaance o monome seces n the system. d P, seudo (5) dt The seudo-oagaton ate constant can be exessed as P, seudo (5) The ate o temnaton s gven by t, seudo t t t ( ) (53) t whee, when =, t becomes the homo-temnaton ate constant, wheeas when, t s the coss-temnaton ate constant (t = t). The seudo-temnaton ate constant s

21 (54) t, seudo t The seudo-ate constants o chan tanse eactons ae as ollows: (55) m, seudo m F (5), seudo CTA, seudo CTA, S, seudo S, Z, seudo (57) Tanse eactons deally aect molecula weghts but not olymezaton ate. In Equatons 55 and 5, the coss-tanse eacton constants may also be needed, alcable, based on the eacton mechansm. Howeve, snce these values have scacely been eoted, they stll eman uncetan. I needed, and o all actcal uoses, they can be dened as m m (58) (59) Z olecula Weght Calculatons The nstantaneous numbe- and weght-aveage molecula weghts (n and w, esectvely) o lnea mult-comonent olymes can be calculated as we n,. 5 whee e 3 w () w w e w w F CTA td CTA S Z m, S Z tc Equaton s dentcal wth the homo-olymezaton case excet o the use o the seudo-eectve molecula weght and seudo-ate constants. The nstantaneous weght

22 acton o olyme o chan length at some conveson level X, and hence nomaton about the nstantaneous molecula weght dstbuton, ae gven as ollows: w, X () The cumulatve numbe-/weght-aveage molecula weghts and weght acton o olyme o chan length ae gven by n X X n dx, w wdx X X () X w(, X ) w X dx X, (3) The equatons cted above ae vald o lnea (non-banched) systems. When addtonal eactons such as tanse to olyme and/o temnal/ntenal double bond olymezaton ae sgncant, banched o cosslned olyme molecules ae obtaned, and hence the method o moments should be aled o the adcal and dead olyme dstbutons. The th moments o the lve adcal dstbuton (λ) and dead olyme molecule dstbuton (μ) ae dened as, P (4) In ode to deve moment equatons, oulaton balances o lve adcal and dead olyme molecules ae equed. As an examle, consdeng the basc eacton stes n homo-olymezaton o smlcty (ntaton, oagaton, temnaton, and chan tanse to monome and solvent), the balances o adcals o chan length and, and dead olyme molecules o chan length, ae: d dt m d I ( S S tc m td ) S S (5) d dt ( ) ( tc td ) m S S ()

23 3 S dt P d S m td s s s tc (7) The zeoth moment o lve adcals s calculated as ollows: ) ( ) ( ) ( ) ( ) ( ) ( ) ( td tc d td tc d S m td tc d S m td tc S m S m td tc d I I S I S S S I dt d dt d dt d dt d dt d (8) snce, The zeoth moment λ s dentcal wth the total adcal concentaton. The st and second moments o lve adcals subsequently become Equatons 9 and 7. ) ( ) ( ) ( ) ( ) ( ) ( S I S I S S S I dt d dt d dt d dt d dt d S m td tc d S m td tc d S m td tc S m S m td tc d (9)

24 4 snce, ) ( ) ( ) ( ) ( ) ( ) ( S I S I S S S I dt d dt d dt d dt d dt d S m td tc d S m td tc d S m td tc S m S m td tc d (7) snce Smlaly, the moments o dead olyme molecules can be wtten as ollows: S S dt P d dt d S m td tc S m td s s s tc (7) snce

25 s s s S S dt P d dt d S m td tc S m td s s s tc (7) snce s s s S S dt P d dt d S m tc td tc S m td s s s tc (73) snce

26 s s s Now, consdeng all ossble eacton stes mentoned eale and ncludng chan tanse to olyme and ntenal/temnal double bond olymezaton, the moment Equatons 8 to 73 can be wtten as Z dt d Z t (74) ** * Z S CTA dt d Z P S m CTA t (75) 3 ** * 3 Z S CTA dt d Z P S m CTA t (7) ** * Z S CTA m td tc Z S CTA dt d (77) ** * Z S CTA m td tc Z S CTA dt d (78) 3 ** * 3 Z S CTA m td tc Z S CTA dt d (79)

27 In ode to calculate μ3 and avod oen-ended equatons, s 3 usually emloyed o moment closue. Usng the moment equatons above, the cumulatve numbe-/weght-aveage molecula weghts o a mult-comonent olyme ae calculated by: n w e (8) w w e (8) oment equatons o calculaton o molecula weght aveages aea n the lteatue n deent shaes and oms, oten ncludng only some o the evously cted eactons, and oten deved wth cetan smlyng (yet vald) assumtons. Fo nstance, as an examle, see deent yet equvalent vesons o these moment equatons n eeences (3-33). Fnally, as an ndcato o long chan banchng/cosslnng, the aveage numbe o t- /teta-unctonal banches e molecule can be comuted om the ollowng equatons (3-33): d B dt N 3 * (8) d( dt BN 4) (83) ** Duson Contol Knetcs The temnaton, oagaton, tanse eacton ate constants and the ntato ecency can all be aected by the esence o dusonal lmtatons thoughout the olymezaton and may show sgncant deceases. In bul and concentated soluton olymezatons, the eacton ate ses emaably at some conveson level between and 5%, and ths leads to sgncant nceases n olyme molecula weghts. Futhemoe, t has been equently obseved at hgh conveson that the eacton ate 7

28 alls adly and a lmtng conveson aeas n ste o sucent ntato/monome amounts stll uneacted. The ome henomenon s eeed to as autoacceleaton, Tommsdo-Smth-Nosh, o smly gel eect, whle the latte one s usually eeed to as the glassy eect. It s establshed that autoacceleaton haens due to dusonal (moblty) lmtatons o adcals and macomolecules. As olymezaton oceeds, the gowng entangled olyme chans ncease the eacton medum vscosty and the educed adcal moblty hndes uthe temnaton, whle ntato s contnuously decomosng nto adcals and the adcal chans ee oagatng (gowng). As a esult, the adcal concentaton nceases consdeably and so does olymezaton ate (and eventually molecula weghts). Seveal deent aoaches have been ntoduced to exlan the autoacceleaton and glassy eects as a uncton o othe ocess vaables. We nvoe the ee volume aoach, whch s a vey oweul and well-tested sem-emcal model. The ee volume equaton s exessed as: V n V V, ( T Tg, ) (84) V whee s a eacton mxtue comonent (monome, olyme, and solvent) V s ee volume o comonent at the glass tanston temeatue, s themal exanson coecent (deence) above and below Tg T s eacton temeatue Tg s glass tanston temeatue o comonent V, V ae volume o comonent and total eacton volume, esectvely. Fee volume theoy has suggested the unvesal values o.5 o V and. o, o monome(s) and solvent, and o.48 o the olyme. Howeve, whee aoate data exst, these aametes may be estmated o the secc system n, 8

29 queston. The glass tanston temeatue o the olyme (Tgoly) at some conveson level can be calculated usng Johnston s method: T goly w T g ( ) w w whee Tg s the glass tanston temeatue o the homo-olyme seces, Tg s that o an (deal) altenatng co-olyme comng om monomes and, w s the weght acton o monome bound n the olyme chans, and s the obablty o omng a dyad o monomes and, whch has been dened eale. T g (85) A decease o t wll be obseved st because temnaton s chemcally the astest ste and lage macoadcals ae nvolved (and ae hence moe vulneable to estctons o moblty). The duson contol o the oveall (seudo-) t s usually dvded nto thee ntevals: segmental, tanslatonal, and eacton-duson. Even at low convesons, the temnaton ate may be contolled by segmental duson, whch s descbed accodng to (3) as ollows: t, seg t, seudo c c (8) whee t,seudo s the chemcally contolled seudo-temnaton ate constant n Equaton 54 δc s a aamete deendent on molecula weght and solvent qualty c s the mass concentaton o accumulated olyme. In ths egon, when the eacton medum s a themodynamcally good solvent, the olyme col sze deceases and the temnaton ate constant may actually ncease untl the onset o tanslatonal duson. To eca, n the st (segmental duson) nteval, the oveall temnaton ate constant s equal to the segmental duson temnaton ate constant (t,seg) lus the eacton-duson temnaton ate constant (to be dscussed shotly), as e Equaton 87: t, oveall t, seg t, d (87) 9

30 The second nteval, tanslatonal duson o gel eect egon, s detemned by a gel eect aamete K3 suggested by aten and Hamelec (34): whee w c m A K 3 w ex (88) c V, c s a ctcal accumulated weght-aveage molecula weght o olyme V,c s a ctcal ee-volume A, m ae gel eect model aametes o the secc monome system ound n the monome database; usually, m =.5. Stcle et al. (35) eomed exements to detemne K3 values n A olymezaton and bult a temeatue-deendent Ahenus exesson o K3. In the mult-comonent case, we used the Ahenus om and calculated a seudo-k3, comosed o the ndvdual values o K3, va sueoston. EK, K3, AK, ex (89) T F K 3, seudo ex / (9) log ( K3, ) whee F s the cumulatve olyme comoston o monome seces. K3,seudo n Equaton 9 can be calculated o the olyme system n queston based on the chaactestcs o each monome n the seces database. In the model, the calculated K3,test (see Equaton 9) s comaed wth the edetemned K3,seudo o Equaton 9 as conveson vaes: m A seudo K 3, test w ex (9) V A seudo F A (9) 3

31 whee A and F ae the gel eect model aamete and nstantaneous olyme comoston o monome seces, esectvely. Fo A, see the dscusson aound Equaton 88. These A aametes ae combned nto a seudo-gel eect model aamete Aseudo o the mult-comonent case, as e Equaton 9. When K3,test becomes equal to o geate than K3,seudo, then the coesondng w and V (om Equaton 9) at the secc tme (conveson) ste become w c and V,c, esectvely. Ths sgnes the onset o the gel eect (tanslatonal duson egon) and the tanslatonally duson-contolled temnaton ate constant s now govened by Equaton 93: n w c t, tans t, c ex A seudo (93) V V, c w whee t,c s the oveall temnaton constant at the ctcal ont, and n s a aamete, usually equal to.75. Ths temnaton ate constant t,tans wll be obseved to decease sgncantly n ths egon. To eca, n ths second (tanslatonal duson) nteval, the oveall temnaton ate constant s equal to the tanslatonal duson temnaton ate constant (t,tans) lus the eacton-duson temnaton ate constant, as e Equaton 94: t, oveall t, tans t, d (94) At vey hgh conveson (usually, above 85%), t s exected that the chan moblty aected by tanslatonal duson wll decease so geatly that adcal chans cannot move any moe. Howeve, two macoadcal ends may move towad each othe by monome addton. Ths nal nteval, eacton-duson o esdual temnaton, s descbed as t, d 8 N A D (95) 3

32 / 3 V m (9) N A ns l D (97) whee NA s Avogado s numbe D s a eacton-duson coecent δ s a eacton adus Vm s the mola volume o monome ns s the aveage numbe o monome unts n a olyme chan l s the length o a monome unt n the chan s the oagaton ate constant s monome concentaton. In ths nal nteval, the oveall temnaton ate constant s the same as n Equaton 94. Stcle (3) and Stcle et al. (35) enhanced the netc model by addng t,d to t,tans n Equaton 94, thus achevng a vey good ageement between conveson data and model edctons n A olymezaton. Unde olymezaton condtons whee the eacton temeatue s lowe than the glasstanston temeatue o the olymezng mxtue beng syntheszed, even the moblty o small monome unts s lmted by duson n essentally a sold (glassy) olyme matx. Thus, even oagaton/tanse eactons become duson-contolled. The onset haens when the ee volume o the olymezng mxtue becomes lowe than an exementally detemned ctcal ee volume, and ths can be modeled smlaly to tanslatonal duson-contolled temnaton: ex B (98) V V, c, smallmolecule ex B (99) V V, c 3

33 whee and ae the chemcally contolled oagaton/tanse ate constants B s the glass-tanston eect model aamete V,c s the ctcal ee volume o duson contol o oagaton/tanse ate constants. In addton, the ntato ecency can also undego duson contol and begn to decease at hgh conveson, n a way smla to. When the ee volume o the eacton medum becomes less than an exementally detemned ctcal ee volume, ntato ecency s calculated usng ex C () V V, c3 whee s the ntal ntato ecency C s the ecency-elated model aamete V,c3 s the ctcal ee volume o duson contol o ntato ecency. 3 esults and Dscusson The mult-comonent olymezaton model has been wdely tested wth exemental data om vaous monome systems: o examle, homo-olymezatons o Sty, A, HEA, BA, and BA; co-olymezatons o Sty/acylontle (AN), A/BA, Sty/HEA, Sty/BA, Sty/BA, and AS/A; te-olymezatons o Sty/BA/hydoxyethyl methacylate (HEA), AS/A/BA, Sty/ethyl acylate (EA)/HEA, A/BA/vnyl acetate (VAc); and teta-olymezaton o Sty/ (EA)/HEA/AA. Ths testng s uthe to the extensve model and ngedent database testng descbed evously n eeences (-8). Testng ncludes a wde ange o olymezaton condtons and eces, wth both commonly emloyed and less equently encounteed monome systems. Samle exemental esults and model edctons ae esented n the subsectons below accodng to vaous eces and condtons. Ths motant execse clealy shows that the mult-comonent model can successully educe to smle cases, thus nceasng 33

34 one s condence n the elablty o the model and the accomanyng (unalteed) ngedent database. 3. Sty Homo-olymezaton Sty s a monome that has been extensvely studed by many eseaches. Fgue shows Sty bul homo-olymezaton (wth, -azo-bs-sobutyontle (AIBN) ntato) model edctons vs. exemental data (37). Pedctons and data show good ageement ove the ente conveson ange. The most dstnctve chaactestc o Sty s that t undegoes themal sel-olymezaton wthout ntato at hghe temeatues (ove ). Addtonally, chan tanse to themal ntaton byoducts can aect molecula weghts (4), accodng to: T.3 log X total ().5 whee td CTA CTA S S Z Z m, T s the eacton temeatue (K), and X s oveall conveson. Fgues and 3 ae examle lots o Sty bul themal olymezaton at 7, wth exemental data om (4). The model gves satsactoy edctons o both conveson and molecula weght aveages ( acc n Fgue 3 (and om hee on n othe gues that wll ollow) ees to an accumulated o cumulatve oety). 34

35 Conveson vs tme Conveson tme (mn.) Fgue. Smulaton o bul olymezaton o Sty at, AIBN =.4 Conveson vs tme Conveson tme (mn.) Fgue. Smulaton o bul themal olymezaton o Sty at 7 35

36 .9 x w (g/mol) n (acc.) w (acc.) Conveson Fgue 3. Smulaton o molecula weghts o Sty themal olymezaton at 7 3

37 3. A Homo-olymezaton A s anothe wdely studed monome. The model s tested wth the exemental data n (38), elated to bul olymezaton exements at 5, 7, and 9 usng two AIBN ntato concentaton levels (.58 and.548 mol/l). Fgue 4 eesents model edctons and exemental data o conveson at I =.58 mol/l. The exected temeatue eect on olymezaton ate s evdent and catued well by the model. Fgues 5 and show numbe-/weght-aveage molecula weght esults. The model edctons agan ollow the exemental data well n ths monome system. olecula weghts decease as eacton temeatue nceases, and the model successully exlans ee-adcal olymezaton tends. Conveson vs tme Conveson T = 5 degc. T = 7 degc T = 9 degc tme (mn.) Fgue 4. Smulaton o bul olymezatons o A at 5, 7, and 9, AIBN =.58 37

38 8 x 5 n(acc.) w(acc.) Cumulatve molecula weght vs conveson 4 w (g/mol) Conveson Fgue 5. olecula weght edctons o A olymezaton at 7, AIBN = x 5 n(acc.) w(acc.) Cumulatve molecula weght vs conveson w (g/mol) Conveson Fgue. olecula weght edctons o A olymezaton at 9, AIBN =.58 38

39 3.3 HEA Homo-olymezaton HEA homo-olymezaton ate constants could be estmated based on olymezaton netc data by Km (39). The mult-comonent model was also comaed n Fgue 7 wth exemental data (at thee deent temeatue levels (5,, and 7 ) wth.x -5 moles o BPO (benzoyl eoxde) ntato) collected by (4). Fast ates and no lmtng conveson ae obseved n the lot and cetan dsceances ae obseved at hgh conveson levels and hghe temeatues ( and 7 ), o ths lagely unstuded and vey ast-eactng monome that yelds hghly vscous olymezng mxtues (see also secton 3.8). Ths monome s used late n ths ae o uthe model testng o co-, te-, and teta-olymezatons. Conveson vs tme Conveson T = 5 degc. T = degc T = 7 degc tme (mn.) Fgue 7. Smulaton o bul olymezatons o HEA wth BPO 39

40 3.4 BA Homo-olymezaton Knetc and exemental nomaton on BA s not as eadly avalable as o Sty o A. Dubé et al. (4) eomed ull conveson ange exements o BA olymezaton usng a actoal desgn (T = 5 and, and AIBN =.,.5 ). BA olymezaton s a ast eacton chaactezed by a hgh value. eesentatve esults ae shown n Fgue 8. The glass tanston temeatue o BA olyme s low (about -5 ) and thee s sgncant banchng omaton va tanse to olyme and temnal double bond olymezaton (at ths ont, model testng has been conducted neglectng bacbtng eactons due to the lowe temeatues emloyed). The model ollows the exemental data well at low to medum conveson levels, but slght dsceances ae obseved at hgh conveson level. Due to comlete lac o data n the lteatue, the numbe-/weght-aveage molecula weght oles could not be comaed. Conveson vs tme Conveson AIBN =. AIBN = tme (mn.) Fgue 8. Smulaton o bul olymezatons o BA at 5 4

41 3.5 BA Homo-olymezaton odel edctons ae comaed wth exemental data eoted by (4), obtaned at usng, -azo-bs-sobutyontle (AIBN) ntato. Fgue 9 eesents bul olymezaton esults at deent concentaton levels o AIBN. The model edctons ae good. At ths stage o testng, deoagaton s not actve due to egula temeatue levels beng emloyed. Conveson Conveson vs tme AIBN =.89 AIBN =.45 AIBN =.97 AIBN =.7379 AIBN = tme (mn.) Fgue 9. Smulaton o bul olymezatons o BA at wth AIBN 4

42 3. A/BA Co-olymezaton Dubé and Penlds (43) nvestgated A/BA co-olyme systems as at o a A/BA/VAc te-olymezaton study. eactvty atos wee estmated as A-BA =.789 and BA-A =.97 (by the eo-n-vaables-model (EV) method). The eactvty ato values ndcate that o ths system thee s no azeotoc comoston and hence comoston dt s exected o all monome eed comostons. Fgue eesents conveson oles at a cetan BA eed acton (BA =.439) at wth two ntato levels (AIBN =.5 and. mol/l). Fgue shows the comoston dt o BA n the olyme. Sgncant dt s obseved and the dt s not aected by the ntato concentaton change. Fgue and 3 show the measued numbe-/weght-aveage molecula weghts and coesondng edctons at deent ntato levels. odel edctons gve easonable tends o ths system. Alb et al. (44) conducted BA/A soluton co-olymezaton wth 7 wt% o butyl acetate solvent and wt% o AIBN ntato at unde deent ntal monome eed atos (weght bass) usng an automatc contnuous onlne sectum-montong technque, whch enables the detemnaton o nstantaneous olyme comostons. Note that Fgue 4 eesents the nstantaneous (not cumulatve) comoston dt o BA as a uncton o conveson. Loong at the eactvty atos, t s evdent that A ncooaton nto the olyme s moe avoed ove BA, whch leads to lage comoston dt at hghe ntal BA/A eed atos, snce A s deleted eale than BA. Ths can also be veed va the coesondng deental co-olyme comoston dstbuton n Fgue 5. The values o the y-axs eesent the absolute values o the nntesmal change o total conveson dvded by the nntesmal change o nstantaneous olyme comoston o BA, namely, the values o the nvese sloes o Fgue 4. At the ealy stages o the co-olymezaton, moe A monome s ncooated nto the co-olyme than BA; the BA mole acton n the co-olyme does not change much. Theeoe, t s obseved that wth a hghe ntal A content n the system, the sloe dfba/dx becomes smalle n Fgue 4, whle the nvese sloe dx/dfba (the y-axs value o Fgue 5, calculated numecally as X/ FBA ) becomes 4

43 lage (the edcton oles ae also changng om J-shae to U-shae cuves). eye and Lowy (45) eoted that ths U-shaed deental co-olyme comoston dstbuton s consdeed as chaactestc o ncomatble co-olymezatons when deences between eactvty atos ae elatvely lage. Dung the ente eacton, a vtual homo-olymezaton o the moe eactve monome s avoued ntally, whle the homo-olymezaton o the less eactve monome taes lace dung the late o nal stages o the co-olymezaton. Conveson vs tme Conveson AIBN =.5 AIBN = tme (mn.) Fgue. Smulaton o bul co-olymezatons o BA/A, T =, BA =

44 Cumulatve comoston vs conveson AIBN =.5 AIBN =..38 Comoston(acc.) Conveson Fgue. Cumulatve olyme comoston o BA n BA/A co-olymezaton T = and BA = x n(acc.) w(acc.) Cumulatve molecula weght vs conveson olecula weght w (g/mol) aveages (g/mol) Conveson Fgue. olecula weght aveages o BA/A co-olymezaton T =, AIBN =.5, and BA =

45 olecula weght aveages (g/mol) w (g/mol) 3 x n(acc.) w(acc.) Cumulatve molecula weght vs conveson Conveson Fgue 3. olecula weght aveages o BA/A co-olymezaton T =, AIBN =., and BA = Comoston dt o BA/A coolymezaton BA/A = /9 BA/A = 5/75 BA/A = 4/ BA/A = 5/5 BA/A = 75/5 F BA (nst.) Conveson Fgue 4. Smulaton o comoston dt o nstantaneous F BA n BA/A co-olymezaton T =, Butyl acetate (solvent) = 7 wt%, and AIBN = wt% o total mxtue 45

46 8 4 Deental comoston dstbutons o BA/A coolymezaton BA/A = /9 BA/A = 5/75 BA/A = 4/ BA/A = 5/5 BA/A = 75/5 dx/df BA (nst.) F BA (nst.) Fgue 5. Deental nstantaneous co-olyme comoston dstbutons o BA n BA/A co-olymezaton T =, Butyl acetate (solvent) = 7 wt%, and AIBN = wt% o total mxtue 4

47 3.7 Sty/AN Co-olymezaton Sty/AN co-olymes ae used as common themolastcs wth good mechancal and chemcal oetes, and easy to ocess as well. Sty and AN monomes ae also oten olymezed wth butadene to oduce ABS ubbe. In ste o the academc/ndustal nteest, ts ull conveson netcs has been lagely unstuded. Gaca-ubo et al. (4) eoted eactvty ato values (Sty-AN, AN-Sty) = (.3,.78) along wth elable coolymezaton exemental data. AN monome exhbts heteogeneous olymezaton. In bul, the olyme ectates n the eacton medum (monome) and oms a olyme-ch hase, whch maes cetan netc ate constants deent om those n a homogeneous eacton. The comlex mechansm o hase seaaton s not comletely undestood and ths may also aect coolymezaton chaactestcs. Gaca-ubo et al. (4) obseved that Sty/AN n bul s a homogeneous ocess thoughout most o the conveson ange when the Sty (monome ) ntal eed comoston s hghe than.5, hence t was ossble to test the multcomonent model wth exemental data om such an oeatng egon. Fgue eesents conveson oles o bul co-olymezatons wth Sty () om.5 to.9. Dsceances stat manestng themselves at Sty content o 7 %. In Fgue 7, model edctons o esdual Sty monome mole acton ollow exemental data accetably. It should be noted that the azeotoc ont (azeo.) o ths system s exected to exst between.5 and., ate whch the deceasng tend o esdual monome mole acton stats to evese n Fgue 7. Ths s an motant obsevaton, ndcatng whch monome s eeentally ncooated nto the olyme, detemned by eactvty atos. In ths system, Sty monome s moe eadly ncooated nto the olyme than AN when Sty s.5, a mole acton slghtly lowe than the azeotoc ont, and the ooste henomenon haens at mole actons hghe than the azeotoe. The oles ae exected to level o at the lmtng conveson, ate whch comoston wll stay constant. 47

48 Fgue 8 shows the accumulated numbe-aveage sequence length o Sty (edctons and exemental data). Ths lot hels to undestand how the Sty/AN mcostuctue wll change thoughout the ente conveson. When Sty and AN mola contents ae smla n the system, the Sty aveage sequence length s slghtly above one and the chan develos almost le an altenatng co-olyme (-ABABAB-). As Sty nceases, the sequence length also nceases, esecally at hgh conveson. Then the monome sequencng attens esemble those o a bloc co-olyme (-AAABBBAA-). odel tends agee well wth exemental data. Conveson vs tme Conveson =.5 =. =.7 =.8 = tme (mn.) Fgue. Smulaton o bul co-olymezatons o Sty/AN T = and AIBN =.5 ( = Sty) 48

49 esdual Sty mole acton vs tme.9 esdual Sty mole acton =.5 =. =.7 =.8 = tme (mn.) Fgue 7. Smulaton o esdual mole actons o Sty n Sty/AN co-olymezaton T = and AIBN =.5 ( = Sty) Sequence length(acc.) o Sty Cumulatve numbe aveage sequence length o Sty vs conveson =.5 =. =.7 =.8 = Conveson Fgue 8. Smulaton o accumulated numbe-aveage sequence lengths o Sty n Sty/AN co-olymezaton, T = and AIBN =.5 ( = Sty) 49

50 3.8 Sty/HEA Co-olymezaton Sty/HEA ull conveson ange exements wee conducted by Km (39). Knetc studes o any olymezaton nvolvng HEA ae extemely scace. HEA olymezaton exhbts hgh molecula weght oducts though cosslnng eactons by olymezaton o dvnyl mutes, whch ae sde oducts n the hydoxylalyl acylate olymezaton, and tanse to olyme. Ths leads to dcultes n the analyss o ts olyme chaactestcs. Some eseach gous have gven aoxmate estmates o the eactvty atos o Sty/HEA co-olymezaton, but the model uses Sty-HEA =.54 and HEA-Sty =.79 om Km (39), whose netc study was moe systematc. A 3 actoal desgn was conducted to nvestgate the eect o temeatue (4 and 5 ), ntato concentaton (AIBN =.5 and.5 mol/l), and ntal monome eed comoston ( = Sty =.55, and.84). eesentatve esults ae shown n Fgues 9 to. Some dsceances ae obseved at hgh conveson wthn othewse qute satsactoy model tends. canus et al. (47) conducted not only Sty/HEA co-olymezatons (T = 5, AIBN =.5, and = Sty =.) but also Sty/EA/HEA te-olymezaton exements. The co-olymezaton data ae lotted along wth the data om Km (39) n Fgue. Agan, the model ollows the exemental tends well. odel testng wth the te-olymezaton exemental data wll be dscussed late. 5

51 Conveson vs tme Conveson =. =.55 = tme (mn.) Fgue 9. Smulaton o Sty/HEA bul co-olymezatons T = 4, AIBN =.5 ( = Sty) Conveson vs tme Conveson =.55 = tme (mn.) Fgue. Smulaton o Sty/HEA bul co-olymezatons T = 5, AIBN =.5 ( = Sty) 5

52 Conveson vs tme Conveson =.55 =. = tme (mn.) Fgue. Smulaton o Sty/HEA bul co-olymezatons T = 5, AIBN =.5 ( = Sty) 5