Kinetic Studies and Monte Carlo Simulations of radical Terand Tetrapolymerisations

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1 Kietic Studies ad Mote Calo Simulatios of adical Te- ad Tetapolymeisatios Poceedigs of Euopea Cogess of Chemical Egieeig (ECCE-6) Copehage, 6-0 Septembe 007 Kietic Studies ad Mote Calo Simulatios of adical Tead Tetapolymeisatios M. Dache, G. Schmidt-Naake Istitut fü Techische Chemie, Techische Uivesität Clausthal, D-8678 Clausthal-Zellefeld, Gemay Abstact Radical polymeisatio of thee ad moe moomes with diffeet eactivities ca lead to polymes with extemely diffeet copolyme compositios duig the polymeisatio pocess. A Mote Calo simulatio method will be peseted to descibe the copolyme compositio depedet o the covesio, the itegal ad diffeetial copolyme mixtue, the comoome covesios ad sequece distibutios of the comoomes. The simulatios wee used to develop semibatch moome additio policies. Usig the semibatch pocess chemically uifom polymes wee obtaied ove a wide covesio age. The esults wee veified by expeimetal ivestigatios of te- ad tetapolymeisatios of doo-, accepto-, ad eutal moomes i batch ad semibatch expeimets. Keywods: adical polymeizatio, tepolymeizatio, tetapolymeizatio, semibatch, mote calo simulatio. Theoy ad Computatioal methods Aalytical Model I the aalytical model, 9 popagatio eactios ae equied to descibe the polymeizatio pocess i case of tepolymeizatio (scheme ) ad 6 i case of tetapolymeizatio. ~M M k ~M M k ~M M k ~M v = k [~M [M v = k [~M [M v = k [~M [M ~M M k ~M M k ~M M k ~M v = k [~M [M v = k [~M [M v = k [~M [M

2 M. Dache et al. ~M M k ~M M k ~M M k ~M v = k [~M [M v = k [~M [M v = k [~M [M Scheme : tepolymeizatio popagatio eactios (~M i = macoadical, M i = moome, k = popagatio ate costat, v = popagatio ate ( =,, ) ) The -values of the coespodig biay systems ae defied as atio of the popagatio ate costats (Eq. ). =k ii /k ( =,, ) () This eactivity atios ca be detemied fom copolymeizatio expeimets usig lieaizatio [ o optimizatio methods [,, 4. Assumig steady-state coditios (v v ik = v ji v ki ), the Alfey-Goldfige equatio (Eq. ) was deived [5.The tepolymeizatio equatio ca be used fo calculatio of the tepolyme compositio (m, m, m ) fom the compositio feed (M, M, M ) at low covesio. By aalytical itegatio of this equatio, the istataeous ad global compositio of the tepolyme as a fuctio of the covesio is available. m : m : m = [ M : : () I special cases of the tepolymeizatio special equatios wee also developed: without homopolymeizatio of oe moome (k = 0, HAM-equatio) [6, without ay homopolymeizatio (k = k = k = 0, Bau's equatio) [7 ad tepolymeizatio with esticted eactio possibilities (k = k = k = 0, equatio fom ou goup) [0.The kietic equatios elated to the tetapolymeizatio wee deived by Che et al. [8. All this equatios descibe the polymeizatio i a cotiuous ad macoscopic mae.

3 Kietic Studies ad Mote Calo Simulatios of adical Te- ad Tetapolymeisatios Mote Calo Model Fo the covesio depedet simulatio of these te- ad tetapolymeizatios, the -values of the coespodig biay systems ad the iitial mola compositios of the eactio mixtue ae equied. The applied Mote Calo simulatio executes a defied total umbe of moome molecules of total = 0 8 that ae distibuted amog the give moome species accodig to the iitial mola compositio of the feed (Eq. ). i 0 i,0 = total with: i,0 = iitial umbe of moome molecules [M i 0 = moome cocetatio i the feed () The simulatio is stated with a adomly selected moome at the. Evey sigle step i this Mote Calo simulatio epesets the icopoatio of oe moome uit ito the polyme based upo the effective eactio pobabilities fo the give eactio coditios (Fig. ). The eactio pobabilities (Eq. 4, 5) deped oly o the cuet umbe of molecules ( i, j ) ad the give -values ( ). Oe moome is cosumed ad the chages i the case of a copolymeizatio step. P P = i = i i j i j j j i j homopolymeizatio step (i=j) (4) copolymeizatio step (i j) (5) --M P M ew P M --M ~M P M --M

4 M. Dache et al. --M P M ew ~M P M --M P M --M --M P M ew P M --M ~M P M --M Figue : Mote Calo step: eactio pathway fo icopoatio of oe moome uit ito the polyme The Mote Calo simulatio pocedue is executed by the mccopolyme pogam, pogammed i C with a Tcl-iteface, ad employig the Mesee Twiste highlevel 6-dimesioally equidistibuted uifom pseudo-adom umbe geeato [9. Oe eeds appoximately 5 s fo the calculatio of a tepolymeizatio up to 0.95 covesio o a AMD Opteo 86 CPU. The esults of the simulatio ae tacked at steps of 0.0 of total moome covesio ad ae aalyzed i espect to the itegal compositio of the polyme, compositio of the moome feed mixtue ad covesio of the give moomes. By compaiso with the esult of the pecedig aalysis step, the diffeetial polyme compositio is calculated. Moeove, aalysis of the sequece of moome uits povides ifomatio about the umbes fo each sequece legth of all ivolved moomes at evey aalysis step.

5 Kietic Studies ad Mote Calo Simulatios of adical Te- ad Tetapolymeisatios The Mote Calo method eables the compehesive simulatio of te- ad tetapolymeizatios i a extemely staightfowad mae. I ou simulatios moome molecules ad ot the moome cocetatios ae icluded i cotast to the aalytical model. Theefoe the developmet of semi-batch moome additio policies is moe easily to implemet. The umbe of moome molecules was iceased at defied total moome covesio. The Polymeizatio pocess is descibed as a fuctio of the polymeizatio ate ad ot as a fuctio of time.. Expeimetal sectio Mateials Methyl methacylate/mma (Fluka) ad styee/s (BASF) wee distilled ude educed pessue. Acyloitile/AN was distilled at ambiet pessue. N- pheylmaleimide was ecystallized fom methaol. All othe chemicals wee used without futhe puificatio. Polymeizatio All eactios wee caied out ude N -atmosphee ude a itoge atmosphee at 60 C with AIBN (0.04 mol/l) as iitiato i,4-dioxae. The oveall moome cocetatio was 6.6 mol/l. To stop the eactio, the samples wee cooled apidly. The polyme was obtaied by pecipitatio i a tefold volume excess of methaol. Afte dyig the poduct i a vacuum ove at 50 C, the covesio was detemied gavimetically. Fo elemetal aalysis the poduct was dissolved i THF, epecipitated i methaol ad died agai. Elemetal Aalysis The detemiatio of copolyme compositio was caied out by meas of a elemetal aalysis system vaio-el fom Elemeta Aalysesysteme. This istumet woks i the idepedet opeatio modes CHN ad O. Fo detemiatio of the elemetal compositio thee measuemets wee caied out fo each sample.. Results ad Discussio Tepolymeizatio Accodig to the polaity of thei double bods, give by thei e-value, moomes ca be divided ito doo (D), accepto (A) ad eutal (N) moomes. The tepolyme MMA/S/NPI is a N/D/A-system, cotaiig styee as a stog doo ad NPI as a stog accepto moome. Diffeet moome compositios wee polymeized fo 6 hous. The time depedet tepolyme compositio has bee detemied fom the elemetal aalysis data. Fo the covesio depedet simulatio of this polymeizatio expeimets the - values of the coespodig biay systems ae equied. All values ae published fom ou goup [0 ad ae summaized i table.

6 M. Dache et al. moomes MMA S NPI AN MMA S NPI AN Table : copolymeizatio atios mola compositio MMA NPI S mola compositio S NPI MMA A covesio B covesio Figue : Tepolymeizatio of MMA/S/NPI (0./0.6/0.), symbols: expeimetal polyme compositio fom elemetal aalysis boad lies: simulated polyme compositio thi lies: esidual moome compositio A: batch expeimet B: semibatch expeimet Figue -A pesets the compaiso of covesio depedet expeimetal ad simulated polyme compositios. The ageemet betwee the expeimetal polyme compositios ad the esults fom the Mote Calo simulatio is vey good. The calculated esidual NPI cotet shows, that the used NPI is cosumed completely at 45 % oveall moome covesio. At highe covesios, oly a copolymeizatio of styee ad MMA occus. Chemically uifom poducts fomed by adical multicompoet polymeizatio ca oly be obtaied ude semi-batch coditios. The Mote Calo method ca be used to develop semi-batch moome additio policies fo the sythesis of chemically uifom polymes. The stepwise moome additio (4 steps, moome NPI) was calculated ad expeimetally veified fo the tepolymeizatio of MMA/S/NPI. Chemically uifom polymes wee obtaied ove a wide covesio age.

7 Kietic Studies ad Mote Calo Simulatios of adical Te- ad Tetapolymeisatios Tetapolymeizatio Fo the examiatio of the tetapolymeizatio we exteded the tepolyme system of MMA/S/NPI by acyloitile (AN) that acts as additioal accepto moome. Usig he eactivity atios fom table, the covesio depedet esidual moome ad copolyme compositio of this system wee calculated with the Mote Calo simulatio. The esults of the simulatio ad the expeimetally detemied tetapolyme compositio ae show i Fig. -A. The semibatch expeimet (Fig. - B) also leads to chemically uifom polymes. The good ageemet of expeimet ad simulatio shows the uivesal applicability of ou simulatio method. mola compositio A MMA 0. AN covesio NPI S Figue : Tetapolymeizatio of MMA/S/NPI/AN (0./0.5/0./0), symbols: expeimetal polyme compositio fom elemetal aalysis boad lies: simulated polyme compositio thi lies: esidual moome compositio A: batch expeimet B: semibatch expeimet ( expeimets, test of the epoducibility) mola compositio B MMA AN NPI covesio S 4. Coclusio Compaiso betwee the expeimetal esults ad the Mote Calo simulatio fo adical polymeisatios of doo, accepto ad eutal moomes with highly diffeet eactivities, demostates the pecisio of the peseted Mote Calo model fo tepolymeizatios ad tetapolymeizatios. If the -values of the biay subsystems ae coectly kow, copolyme compositios, comoome compositios ad moome covesios ca be descibed i good ageemet with expeimetal data up to high covesios. The calculated, diffeetial copolyme compositios ad sequece distibutios lead to a bette udestadig of the coelatios betwee polyme stuctue ad feed compositio fo multicompoet polymeizatios. Futhemoe, these Mote Calo simulatios ae a poweful tool fo the developmet of semi-batch moome additio policies fo the sythesis of chemically uifom polymes.

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