Modelling of Vinylidene Fluoride Emulsion Polymerization

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1 Euroan Syosu on outr Add rocss Engnrng 5 L. uganr and A. Esuña (Edtors) 25 Elsvr Scnc B.. All rghts rsrvd. Modllng of nyldn Fluord Eulson olyrzaton. lads b, A.H. Alxooulos b, J. Bousqut c,. Karssds a,b a Dartnt of hcal Engnrng, Arstotl Unvrsty of Thssalon and b hcal rocss Engnrng sarch Insttut, Thssalon, Grc. c TotalFnaElf, Drcton Scntfqu, ES-DTE, Solaz, Franc Abstract In th rsnt study, a corhnsv athatcal odl for th ulson olyrzaton of vnyldn fluord (DF) n a s-batch ractor s dvlod. Th rdctv caablts of th odl ar donstratd by a drct coarson of odl rdctons th xrntal data on th onor fd rat, onor convrson, olcular ght avrags and olcular ght dstrbuton, an artcl sz and artcl sz dstrbuton, for a batch DF ulson olyrzaton ractor. It s shon that thr s a good agrnt btn odl rdctons and xrntal data. Kyords: olyrzaton, ulson, vnyldn fluord, odl, SD. Introducton oly(vnyldn fluord) (DF) s an ortant fluoroolyr hch xhbts a unqu cobnaton of rorts ncludng xcllnt chcal rsstanc, hgh thral stablty, and good chancal as ll as zolctrc rorts. Du to ts suror rorts, DF s dly usd as r and cabl nsulaton atral, as sht and lt-cast fls for lctroncs, n fttngs, valvs and us, tc. DF s roducd corcally by ulson and susnson olyrzaton rocsss. In ths ar, a corhnsv athatcal odl of th DF ulson olyrzaton rocss s dvlod. Th odl can rdct th olcular (.g., olcular ght dstrbuton, coolyr cooston, tc.) and orhologcal (.g., artcl sz dstrbuton) rorts of th latx n trs of rocss oratng condtons. Th athatcal odl ncluds: a) full dscrton of th ntcs and th atral balancs, b) calculaton of th gl ffct basd on th gnralzd fr-volu thory (Kraooulos and Karssds, 22), c) throdynac dtrnaton of onor arttonng and rssur calculaton, d) hyscal dscrton of th crystalln has and th aount of crystallnty, and ) calculaton of th artcl sz dstrbuton. Dtald xrntal asurnts on th olyrzaton rat, th onor fd rat, th olcular ght dstrbuton and th artcl sz dstrbuton r rovdd by ATOFINA. Th xrnts r carrd out n a 3 lt s-batch ractor. Th olyrzaton rssur as t constant throughout th racton by ntroducng addtonal onor nto th ractor. Intator and chan transfr agnt r addd at th bgnnng and at varous nstancs.

2 2. Modllng of DF Eulson olyrzaton Th athatcal odllng of ulson olyrzaton ractors has bn th subct of a grat nubr of ublcatons (Glbrt, 995). Nvrthlss, th dvlont of a corhnsv athatcal odl, caabl of rdctng th olcular (.g., olcular ght dstrbuton, coolyr cooston, tc.) and orhologcal (.g., artcl sz dstrbuton) rorts of th latx s not a trval tas, for thr s a nubr of hyscal and chcal hnona, hch cannot b xrntally assssd and, thus, odld. Th rsnt athatcal odl of th DF ulson olyrzaton ncluds: a) all th dffrntal/algbrac quatons dscrbng th ntcs of olyrzaton as ll as th voluton of th artcl sz dstrbuton, b) th calculaton of th gl ffct basd on th gnralzd fr-volu thory, c) th throdynac art (onor arttonng and rssur calculaton) and d) th hyscs of th crystalln has (aount of crystallnty, tc.). DF artcls Monor n atr Olgors rcursors Fgur. Eulson olyrzaton of DF 2. Kntc Mchans of Eulson olyrzaton Th ntcs chans of DF ulson olyrzaton can b dscrbd by th follong lntary ractons: actons n th aquous has Dcooston of ntator: roagaton n th aquous has: Trnaton n th aquous has: han transfr to onor n th has: I 2I + t Q t xx han transfr to TA n th aquous has: + X X + Q + Q

3 actons n th olyr has roagaton n th olyr has: han transfr to onor n th olyr has: han transfr to agnt n th olyr has: Trnaton n th olyr has: In th abov lntary ractons th sybols, t + Q xx + X X + Q, + Q, Q t Q dnot th lv and dad olyr chans that ar rsnt n th aquous () and olyr () has, rsctvly. Th subscrt dnots th ty of lv olyr chan n ultcoonnt systs (.., actv olyr chans ndng n onor of ty ). Follong th orgnal dvlonts of chards t al. (989), th consuton rat of th varous racton scs can b rttn. Tabl. olyrzaton rat xrssons at of Intator consuton at of onor consuton at of onor consuton n th artculat has at of onor consuton n th aquous has at of chan transfr agnt consuton at of gnraton of n stu gnratd surfactant Total rat of radcal ntry n th ulson has at of dad coolyr roducton I I + x ( ( f x + + f f ) x ( f )( + g I q x + I / ) d f ) / / / / / It should b notd that although th olyr artcl has s th an locus of olyrzaton, onor consuton n th aquous has s also ncludd. Thus, th total onor consuton rat n th ulson has,, s gvn by th su of th onor consuton rats n th olyr,, and th aquous has,. 3. Th oulaton Balanc Equaton In ordr to dscrb th dvlont of th SD n an ulson olyrzaton ractor a oulaton balanc aroach s loyd (. Karssds t al, 24). Th dstrbuton of artcls s consdrd to b contnuous ovr volu and s dscrbd by

4 a artcl nubr dnsty functon, n (,t), hch rrsnts th nubr of artcls thn a dffrntal volu sz rang, to +d, r unt volu of latx. Th rat of chang of th nubr dnsty functon s dscrbd by th follong nonlnar ntgro-dffrntal oulaton balanc quaton: ϑn (,t ) ϑ[ G n (,t )] + ϑt ϑ 2 β(,u )n ( )n (U,t )du n β( U,U )n ( U )n (U,t )du d dt + δ( )r ( t ) hr β(u,) s th coagulaton rat rnl btn artcls of volus U and, G (,t) s th groth rat of a artcl of volu at t t and r (t) s th artcl nuclaton rat. Th scond tr on th LHS rrsnts th artcl groth du to racton n th latx artcl (olyr has) and th to ntgral trs on th HS rrsnt changs n artcl sz du to aggrgaton. Th thrd tr on th HS dscrbs th ffct of dluton du to th s-batch fdng of th onor. Th boundary condton for th gnral condton s gvn by: n (,). For an unsdd ulson olyrzaton, th ntal condton s gvn by: n (, t). It should b notd that th rsnt ulson olyrsaton odl dtrns th avrag nubr of radcals r artcl for ach artcl-sz of th SD. Th gnral dynac BE s solvd sultanously th th ntcs quatons usng th orthogonal collocaton on fnt lnts thod (Alxooulos t al., 24). 4. Sulaton sults Th rdctng caablts of th rsnt odl r donstratd by a drct coarson of odl rdctons th xrntal data on th onor fd rat, onor convrson, an artcl sz and artcl sz dstrbuton, as ll as th olcular ght dstrbuton for a DF ulson olyrzaton ractor. All olyrzatons r rford at T83 n a 3lt s-batch ractor. In th frst xrnt, th ntator (otassu rsulfat) and th chan transfr agnt r addd n th ntal r-ulson. As th racton rocds, th ractor rssur as t constant by contnuous addton of DF onor. In Fgs. 2a and 2b, th total aount of DF onor fd nto th ractor as ll as th fd rat ar coard to odl rdctons. As can b sn, th xrntal data and th odl rdctons ar n xcllnt agrnt. In Fg. 3a, th calculatd rssur dro rofl s coard to th xrntal data on th ractor rssur. Th rdctd nubr and ghtavragd olcular ght dstrbutons ar dctd n Fg 3b. Exrntal data fro a nubr of dffrnt xrntal rcs r coard to th odl rdctons. In artcular, th ffct of ultl ntator and TA shots durng th cours of th racton as studd n dtal. In Fg. 4, th xrntal DF fd rats ar coard to odl rdctons for to dffrnt rcs. ()

5 (DF Fd (g)) DF Fd at (g/hr) T (n) T (n) Fgur 2. DF ulson olyrzaton (a) Total DF fd and (b) DF Fd at 8 3x 6 MWN MWW rssur (bar) Molcular Wght 2x 6 x T (n) T (n) Fgur 3. DF ulson olyrzaton (a) actor rssur (b) Avrag olcular ght DFFdat(g/hr) DF Fd at (g/hr) T (n) T (n) Fgur 4. DF ulson olyrzaton (a) To ntator shots (b) Multl ntator and TA shots In Fg. 4a, an addtonal aount of ntator s fd nto th ractor at 45 and 275n. As can b sn, th xrntal data agr vry ll th th nurcal rdctons. It s clar that n th lat stags of olyrzaton, th addton of ntator rsults n a

6 substantal ncras n th racton rat. Frquntly, a TA s addd durng th cours of th racton to odfy th MWD. Hovr, th addton of TA can dcras th rat of racton du to an ncras n th roducton of TA-trnatd radcals hch ar lss ractv. onsquntly, ntator s frquntly addd togthr th th TA. In Fg. 4b, th rdctd DF fd rat s coard to xrntal data for a cas of ultl TA and ntator shots durng th cours of th racton. Dst th ncrasd scattr n xrntal data t s clar that th odl rdctons agr vry ll th th xrntal data Datr (n) 5 5 Noralzd SD % Solds artcl Datr (n) Fgur 5. DF ulson olyrzaton (a) Man datr (b) Fnal SD In Fg. 5a, th voluton of th an artcl datr corrsondng to th rsults of Fg. 4a s dctd. In Fg. 5b, th fnal SD s shon for th cas corrsondng to th rsults of Fg. 2a. As can b sn, th rdctd dstrbuton s n farly good agrnt th th xrntal SD. Th rdctd SD s slghtly narror but th a oston s accuratly rdctd to thn 5-2n. 5. onclusons A corhnsv athatcal odl of th DF ulson olyrzaton rocss has bn dvlod. Th rdctvs caablts of th odl ar donstratd by a drct coarson of odl rdctons th xrntal data on th rat of onor consuton, rorts of th fnal latx such as olcular ght dstrbuton and artcl sz dstrbuton for a DF ulson olyrzaton ractor. It s shon that thr s a good agrnt btn odl rdctons and xrntal data. Th rat of onor convrson dnds on both ntator and TA addton rats durng th cours of th racton. Th addton of TA tnds to dcras th racton rat but s countr-balancd by th sultanous addton to th ractor of an arorat aount of ntator. frncs Alxooulos A.H., A.I. oussos and. Karssds, 24, h. Eng. Sc. 59, 575. Glbrt,.G., Eulson olyrzaton, 995, Acadc rss, London. Kraooulos, A. and. Karssds, 22, Macroolculs 35, 455. Karssds., A.H. Alxooulos, A.I. oussos, G. Doazs and. Kotoulas, 24, Ind. & Eng. h. s. 43, 729. chards J.., J.. ongalds and.g. Glbrt, 989, J. Al. oly. Sc. 37, 2727.