A Mathematical Modeling of Temperature Rising Elution Fractionation (TREF) of Ethylene/1-Octene Copolymer

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1 Papr od: pp1 (Oral) IChE Intrnational Confrn 11 Novmbr 11, 11 at Hatyai, Songkhla HAILAND A Mathmatial Modling of mpratur Rising Elution Frationation (REF) of Ethyln/1-Otn Copolymr Ekaphol Siriwongsarn 1,2, Nuttawat Chokputtanawuttilrd 1, Siripon Anantawaraskul 1,2*, Abdulaziz A. Alghyamah 3, João B. P. Soars 3 1 Cntr of Exlln for Ptrolum, Ptrohmials and Advand Matrials (PPAM), Dpartmnt of Chmial Enginring, Faulty of Enginring, Kastsart Univrsity, Bangkok, 9, hailand 2 Cntr for Advand Studis in Nanothnology and Its Appliations in Chmial, Food and Agriultural Industris, Kastsart Univrsity, Bangkok 9, hailand 3 Dpartmnt of Chmial Enginring, Univrsity of Watrloo, Ontario, N2L 3G1, Canada * fngsia@ku.a.th Abstrat mpratur rising lution frationation (rf) is a polymr haratrization thniqu widly usd to stimat th hmial omposition distributions (CCDs) of smi-rystallin opolymrs. Howvr, a quantitativ dsription of rf frationation mhanism is still unlar baus all availabl modls ould not dsrib kinti rol in rf frationation pross. In this work, w dvlopd a nw mathmatial modl for rf, whih is basd on population balan onpt and taks th rystallization kinti and dissolution kinti during th analysis into aount. h proposd rf modl was found to dsrib th xprimntal rf profils of thyln/1-otn opolymrs wll at svral oprating onditions (i.., ooling rat, hating rat, and solvnt flow rat). Kyword: hmial omposition distribution, rystallization kinti, dissolution kinti, thyln/1-otn opolymr, modling, tmpratur rising lution frationation (rf) 1

2 1. Introdution mpratur rising lution frationation (rf) is a haratrization thniqu usd to stimat of hmial omposition distribution (CCD) of smi-rystallin opolymrs by frationating polymrs aording to thir hain rystallizabilitis in a dilut solution [1]. rf is a two-stp pross onsisting of rystallization and lution stps. In th first stp, polymr hains ar rystallizd and pripitatd from a dilut solution at a onstant ooling rat in a olumn loadd with an inrt support. In th sond stp, a solvnt flows through th olumn whil tmpratur is inrasd at a onstant hating rat, luting th polymr rystallizd in th first stp in th rvrs ordr. h onntration of polymr bing lutd at ah lution tmpratur is monitord with a mass-snsitiv dttor. As th lution tmpratur an b rlatd to omonomr ontnt. rf profils ould b usd to infr CCDs. Prviously, thr ar two approahs usd to modl rf rsults. h first usd a thrmodynami modl xtndd from th Flory-Huggins thory [2]. h othr uss th Stokmayr bivariat distribution, whih thortially dsrib hmial omposition distribution, to intrprt rf profil of binary opolymrs [3]. h sond approah has bn usd to dsrib polyolfins with broad molular wight and omposition distributions and th natur of multipl sit typ atalysts. Howvr, ths modling approahs wr basd on th onpt of thrmodynami quilibrium an thrfor, ould not dsrib th important kinti ffts on rf rsults that xprimntally obsrvd arlir [4]. In this work, a nw mathmatial rf modl basd on population balan onpt and rystallization and dissolution kintis was dvlopd. h modl was validatd with xprimntal rf profils of an thyln/1-otn opolymr at svral onditions. support and hld for stabilization at 9 o C for 4 min bfor rystallization stp. In rystallization stp, th polymr hains rystallizd and pripitatd onto th support by a slow rdution of th tmpratur to 3 o C undr a onstant ooling rat (.1-. o C/min). h olumn tmpratur was kpt at 3 o C for 4 min for stabilization bfor th lution stp. In lution stp, a pur solvnt (CB) flowd through th olumn at a onstant flow rat (.1-. ml/min) whil th tmpratur was slowly inrasd to o C at a onstant hating rat (.1-. o C/min). h onntration of th polymr bing lutd was monitord by an infrard dttor and was plottd as a funtion of th lution tmpratur. 3. rf Modl 3.1. Population balan onpt rf olumn was omputationally disrtizd into 4 intronnting, wll-mixd ontrol volums (v i ) as shown in Fig. 1. In th rystallization stp, polymr hains rystallizd aording thir rystallization kintis uniformly in ah ontrol volum. In th lution stp, th dissolution kintis quation was usd to dsrib polymr moluls dissolvd bak and thn th population balan onpt was usd for mass traking of polymr lutd in, flowing into, and flowing out of ah ontrol volum as shown in Fig. 1., j Mass lutd at, C,vi(, j) C(, j), 1 C,v4(, 1) C(, 1), 2 C,v39(, 1) + C,v4(, 2) C(, 2) 2.1. Matrial 2. Exprimntal, 3 C,v38(, 1) + C,v39(, 2) + C,v4(, 3) C(, 3), 4 C,v37(, 1) + C,v38(, 2) + C,v39(, 3) + C,v4(, 4) C(, 4). An thyln/1-otn opolymr sampl produd with a singl-sit typ atalyst was usd for paramtr stimation and modl validation. his opolymr sampl has a numbr avrag molular wight (M N ) of 4,7 g/mol and avrag 1-otn ontnt of 2.19 mol% [4]. 2.2 rf analysis rf analysis was arrid out by with a Crystaf-rf- V-LS manufaturd by PolymrChar S.A. (Valnia, Spain). In dissolution stp, th polymr sampl was dissolvd in 1, 2, 4 trihlorobnzn (CB) in a rystallization vssl at a onntration of 1 mg/ml at 16 o C for 1 h. h polymr solution was thn introdud into a rf olumn pakd with an inrt, j C,v1(, j-39) + C,v2(, j-38) + + C,v39(, j-1) + C,v4(, j) C(, j)., n C,v1(, n-39) + C,v2(, n-38) + + C,v39(, n-1) + C,v4(, n) Fig. 1. Mass traking of lutd polymr 3.2. Wight distribution of LES C(, n) In this work, th longst thyln squn (LES) of polymr hain whih is inflund by both molular wight and 1-olfin fration was onsidrd to b th ky fator affting hain rystallizability. h wight distribution of LES, W(LES), was drivd in th prvious publiation [6]. 2

3 3.3. h modifid Gibbs-homson quation h modifid Gibbs-homson quation was proposd to dsrib th fft of hain lngth (r) on th dissolution tmpratur ( d ) []: d r r d s r whr d is th quilibrium dissolution tmpratur of hains with infinit lngths, s is a suprooling tmpratur for rf, and α is a onstant that is invrsly proportional to th nthalpy of fusion. For opolymrs, th LES is onsidrd to b th main paramtr ontrolling th hain rystallizability. hrfor, th LES is usd instad of hain lngth (r), as in quation (2): whr, d (1) B ( LES ) A (2) LES 3.4. Crystallization kintis quation A d s (3) B (4) d Rntly, S. Anantawaraskul t al. proposd a mathmatial modling of Crystallization analysis frationation (Crystaf) for thyln opolymrs [7]. h kinti of rystallization of polymr hain whih had bn dvlopd from an Avrami quation was applid for rf. A modifid rystallization kintis quation for rystallinity (X ) of th LES whn th tmpratur rahs an b xprssd with th following quation: X LES,, 1 xp k CR n, d, d, whr CR is a onstant ooling rat during rystallization stp, n is th Avrami xponnt, k is th apparnt Avrami prfator avraging ovr a rang of rystallization tmpratur and, is a dissolution tmpratur of LES in rystallization stp (subsript ). h onntration of rystallin of ah LES and, C (LES, ), in rf olumn during rystallization stp () an b alulatd by inorporation with disrtizd W(LES) and X, as in (6). LES, W LES X LES C, (6) 3.4. Dissolution kintis quation In prvious works, Avrami quation had bn applid for dissolution of rystals in aquous solution [8-9]. For lution stp of rf, assuming polymr rystals ar dissolvd undr isothrmal stat, th kintis of dissolution of polymr rystals follows an mpirial Avrami quation whih is th rlationship btwn onvrsion fration (X ) and tim (t): X n t xp k t 1 (7) whr n and k ar adjustabl paramtrs; n is onstant for a givn polymr, whil k is a funtion of tmpratur. Although th rf frationation dos not oprat undr isothrmal ondition, th lution tmpratur rang ould b onsidrd to b small for a narrow rystallinity distribution of polymr hains having similar mirostruturs. A rlationship btwn th lution tmpratur,, and lution tim, t, is rquird with a onstant hating rat,, usd during lution stp to b writtn as: d dt (8) At th initial ondition (t = ), th lution tmpratur should b qual to th quilibrium dissolution tmpratur,. his quilibrium dissolution tmpratur that is a funtion of both molular wight and omonomr ontnt an b alulatd by quation (2). Intgrating quation (8) using th initial ondition, w an obtain a rlationship btwn lution tmpratur and lution tim: d, LES t (9) Finally, w an obtain a rlationship btwn onvrsion fration and lution tmpratur by ombining (7) and (9): X ( LES, ), 1 xp k n LES, () 3

4 X (LES,) is th onvrsion fration of LES sgmnt whn th tmpratur rahs. Consquntly, th onntrations of polymr lutd at in ah ontrol volum, C,vi ( ), an b alulatd by following quation: final C LES, X LES C (11), vi, LES1 initial W(LES) h prditd polymr lutd at ah, C( ), an b trakd as an atual mass-snsitiv dttor by doing population balan of whol ontrol volums as shown in Fig. 1. Hn, w an obtain th simulatd rf profil by diffrntiating C( ) and thn plotting dc( )/d against. Paramtrs involvd in this modl (A, B, n, k, A, B, n, and k ) wr stimatd by minimizing th sums of th squar of th diffrns btwn th simulatd and xprimntal rf profils: final C Cxp initial 2 modl (12) 4. Rsults and Disussion Fig. 2. shows th longst thyln squn distribution (LESD) for thyln/1-otn opolymr invstigatd in this work whih is obtaind from quation (1). h fft of ooling rat during th rystallization stp on rf profils ar shown in Fig. 3. h hating rat and solvnt flow rat wr kpt onstant at.2 o C/min and.2 ml/min, rsptivly. It was found that rf profils bom broadr and shift to a highr lution tmpratur rang whn ooling rat drass. It is probably du to th fat that polymr moluls hav mor tim to rarrang and rystalliz prftly losing to thir quilibrium rystallization tmpratur in as of slow ooling rat. Fig. 3. also ompars xprimntal and simulatd rf profils of thyln/1- otn opolymr at svral ooling rats. h simulatd rf rsults agr wll with th xprimntal rf rsults. Fig. 4. shows th fft of hating rat during th lution stp on rf profils. h ooling rat of.2 o C/min and solvnt flow rat of.2 ml/min wr usd in this invstigation. Fig. 4 also shows that th rf lution tmpraturs of both xprimntal and simulatd rsults bom broadr and shift to highr lution tmpratur with an inras in hating rat baus, at th sam solvnt flow rat, th polymr moluls will b lutd in a widr rang of rystallinitis with inrasing hating rats. h proposd modl is adquatly to dsrib th fft of hating rat on rf profils baus of th dissolution kinti fft LES Fig. 2. h LESD of thyln/1-otn opolymr h fft of solvnt flow rat on rf profils was invstigatd at a ooling rat of.2 o C/min and hating rat of.2 o C/min. rf pak tmpraturs is highr and th distributions bom narrowr whn a solvnt flow rat inrass. It is likly du to, at slow solvnt flow rats, solvnt taks longr rsidn tim in th olumn for luting polymr in a widr rang of rystallinitis so it an imply that polymr solution will rah to dttor at latr tims and highr lution tmpraturs. h simulatd rf profils an dsrib this trnd wll as shown in Fig.. h funtion in quation (12) was minimizd to stimat th optimum modl paramtrs (A, B, n, k, A, B, n, and k ) for ah ondition. All valus of paramtrs of thyln/1-otn opolymr at svral onditions ar shown in abl 1. For paramtrs stimation, th xprimntal rf profils ould b aptabl for rpatability with th standard dviation of thir pak tmpratur is.33. From th paramtr stimations, th ooling rat affts paramtr k signifiantly [7], and quit affts paramtr B, and k baus th rat of ooling rlats to th prftion of rystal whil rystallization. Paramtr B, and k ar also inflund by th hating rat. Wight prnt 2 Cooling rat =.1 C/min Cooling rat =.2 C/min Cooling rat =. C/min Modl Elution tmpratur ( o C) Fig. 3. Comparison btwn xprimntal and simulatd rf profils at svral ooling rats 4

5 Wight prnt Elution tmpratur ( o C) Hating rat =.1 C/min Hating rat =.2 C/min Hating rat =. C/min Modl Fig. 4. Comparison btwn xprimntal and simulatd rf profils at svral hating rats Wight prnt Flow rat =.1 C/min Flow rat =.2 C/min Flow rat =. C/min Modl Elution tmpratur ( o C) Fig.. Comparison btwn xprimntal and simulatd rf profils at svral solvnt flow rats. Conlusions A nw rf modl was dvlopd basd on th onpt of population balan that taks th kintis of rystallization and dissolution into aount to dsrib th fft of oprating onditions (ooling rat, hating rat, and solvnt flow rat) on rf profils. h modl ould dsrib th xprimntal rf profils of an thyln/1-otn opolymr masurd at svral oprating onditions. Aknowldgmnts h authors would lik to thank th Dow Chmial Company for donating th opolymr sampls for this study and th hailand Rsarh Fund (RF), Cntr of Exlln for Ptrolum, Ptrohmials and Advand Matrials of hailand (PPAM), Graduat Shool and Kastsart Univrsity for thir kind finanial supports. Rfrns [1] S. Anantawaraskul, J. B. P. Soars, P. M. Wood-adams, Frationation of smirystallin polymrs by rystallization analysis frationation and tmpratur rising lution frationation, Adv Polym Si 182 () 1-4. [2] J. Borrajo, C. Cordon, J. M. Carlla, S. oso, G. Goizuta, Modlling th frationation pross in REF systms: hrmodynami simpl approah, J Polym Si: Part B: Polym Phys 33 (199) [3] J. B. P. Soars, A. E. Hamil, Analyzing REF data by Stokmayr s bivariat distribution, Maromol hory Simul 4 (199) [4] S. Anantawaraskul, J. B. P. Soars, P. M. Wood-adams, Efft of opration paramtrs on tmpratur rising lution frationation and rystallization analysis frationation, J Polym Si: Part B: Polym Phys 41 (3) [] D. Bigzadh, J. B. P. Soars,. A. Duvr, Modling of frationation in CRYSAF using mont arlo simulation of rystallizabl squn lngth: thyln/1-otn opolymrs synthsizd with singl-sit-typ atalysts, J Appl Polym Si 8 (1) [6] S. Costux, S. Anantawaraskul, P. M. Wood-adams, J. B. P. Soars, Distribution of longst thyln squn in thyln/αolfin opolymrs synthsizd with singl-sit-typ atalysts, Maromol hory Simul 11 (2) [7] S. Anantawaraskul, P. Jirahaithorn, J. B. P. Soars, J. Limtrakul, Mathmatial modling of rystallization analysis frationation of thyln/1-hxn opolymrs, J Polym Si: Part B: Polym Phys 4 (7) -17. [8] N. Dmirkiran, A. Künkül, Dissolution kintis of ulxit in prhlori aid solutions, Int. J. Minr. Pross. 83 (7) [9] Y. Sun, X. Song, J. Wang, Y. Luo, J. Yu, On-lin monitoring of lithium arbonat dissolution, Cryst Rs hnol 44 (9) abl 1. Estimatd valu of paramtrs of thyln/1-otn opolymr at svral onditions CR SFR Rat ( o C/min Paramtrs for rystallization stp Paramtrs for lution stp and ml/min) A B n k A B n k