A Kinetic Model for the Low Temperature Curing of an Unsaturated Polyester Resin with Single and Dual Initiators

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1 A Kineic Mdel fr he Lw Temperaure Curing f an Unsauraed Plyeser Resin wih Single and Dual Iniiars A Kineic Mdel fr he Lw Temperaure Curing f an Unsauraed Plyeser Resin wih Single and Dual Iniiars Mehdi Vafayan, Mhammad Hsain Beheshy* and Hasan Nasiri Deparmen f Cmpsie, Iran Plymer and Perchemical Insiue, P.O. Bx 4965/5, Tehran, I.R. Iran Received: 4 May 2006 Acceped: 4 Augus 2006 SUMMARY A kineic mdel has been develped fr he predicin f reacin and gel ime in he curing behaviur f an unsauraed plyeser resin iniiaed by mehyl ehyl kene perxide (MEKP, aceylacene perxide (AAP and he MEKP/AAP dual iniiar sysem. The curing behaviur was examined by gel ime and pseud-adiabaic exherm measuremens. We demnsraed ha a rm emperaure and fr a cnsan cncenrain f prmer, he lgarihm f he reacin ime ( fr each cnversin can be described as a linear funcin f he lgarihm f (I % R, namely ln = a - b ln (I % R, where I % is he iniial cnen (w% f ne f iniiars and R is a cnsan dependen n he sum f he iniial iniiar cnens, iniiar mlar masses and heir kineic parameers. I was als esablished ha here is a linear relainship f he ype ln((mekp %/(AAP %=AB gel beween he rai f he iniial iniiar cnens and he gel ime when MEKP and AAP mixures were used as dual iniiar sysems fr rm emperaure curing, wih a cnsan cncenrain f prmer. INTRODUCTION The curing reacin is a very impran sage in he prcessing f unsauraed plyeser resins prduce a cmpsie prduc. In rder achieve gd prduc qualiy, he curing reacin shuld ccur in a cnrllable manner. The curing prcess is a free radical chain grwh crss-linking cplymerisain beween he reacive diluens (e.g. syrene mnmer and he plyeser duble bnds riginaing frm he unsauraed dicarbxylic acid -3. The cplymerisain is iniiaed by perxides, az and azine cmpunds and is acivaed by cerain meal cmpunds, eriary amines and mercapans, r by hea. Several researchers 4-2 have invesigaed he kineics f he unsauraed plyeser resin-syrene cplymerisain sysem by differen echniques and have Rapra Technlgy, 2007 prpsed varius mdels predic he curing behaviur. Generally, he cmplexiy f he curing prcess hinders he esablishmen f universal kineic mdels ha describe he kineics in erms f he frmulain used, he iniiars, he prmers, r he inhibirs. The mehds emplyed sudy he curing behaviur have included differenial scanning calrimery (DSC -7, infrared specrscpy (IR, FTIR 0,4,6,8-9, gel ime sudies, dynamic mechanical hermal analysis (DMTA 5,20-24, pseudadiabaic exherm 25,26 and viscmeric measuremens 27. Sudies f he effec f a single iniiar n he gel ime and exherm behaviur are numerus 5,5,25, Rammis and Salla 0 fund ha fr each curing emperaure and degree f cnversin, here was a universal relainship f he ype ln = a-b ln [I] beween he *Crrespnding auhr: m.beheshy@ippi.ac.ir, Tel: reacin ime ( and he iniial iniiar cncenrain [I]. In [4], i was shwn ha a mixure f a high-emperaure iniiar (TBPB and a lw-emperaure ne (P6N can be much mre effecive han a single iniiar fr achieving a unifrm qualiy f cured cmpsies. This is because a judicius chice f mixures f w r mre iniiars can avid excessively large exhermic heas f reacin. Li e al. 30 develped a mechanisic kineic mdel predic he reacin kineics using dual iniiars. They fund ha he MEKP and TBPB dual iniiar sysem had a synergisic effec n he reacin rae. In he presen wrk we have develped a kineic mdel fr he predicin f reacin rae and gel ime fr dual iniiar sysems. We have sudied he influence f MEKP, AAP and heir mixures n he rm emperaure curing kineics f an unsauraed plyeser resin when he cure is acceleraed wih cbal naphhenae, and have cmpared he resuls wih hereical predicins. Plymers & Plymer Cmpsies, Vl. 5, N. 3,

2 Mehdi Vafayan, Mhammad Hsain Beheshy and Hasan Nasiri Thereical Predicin I has been assumed ha he dissciain f a dual hydr perxide iniiar sysem wih he aid f a meallic prmer invlves fur reacins: ROOH C k 3 d RO. OH- C ( 3 ROOH C k d 2 ROO. H C (2 ROOH C k - 3 d RO i OH C (3 3 ROOH C k d 2 ROO i H C (4 where ROOH, R OOH and C represen he MEKP, AAP and cbal species, respecively. k d, k, k and d d2 k represen he rae cnsans fr d2 he frmain f he alkxy (RO. and R O. and perxy (ROO. and R OO. radicals, respecively. In addiin, he iniiaing radicals may hemselves be cnsumed by side reacins such as alkxy reducin by C r perxy decmpsiin by hea, which furher cmplicae he kineics if hey have been cnsidered. Beaunez e al. 29 have ned ha he alkxy radical is much mre reacive ehylenic mnmers han he perxy radical. Therefre, equains ( and (3 deermine he rae f iniiain. Accrding equains (2 and (4, C is regeneraed, which resuls in a pseud seady sae fr he C cncenrain. By assuming a seady sae cndiin fr he frmain f C, he rae f iniiain can be given by 3 : R i = kf [ROOH][C ] k f [R OOH][C ] (5 where f and f dene he efficiency f MEKP and AAP respecively. (The efficiency is defined as he fracin f he radicals prduced by he decmpsiin f he iniiars ha iniiae a plymer chain. [C ] is he iniial cncenrain f cbal naphhenae. k and k are defined as: k = kdkd2 k k d d2, kdkd2 k = k k (6 d d2 Generally, he radicals cncenrain increases iniially and hen remains alms cnsan. Based n he seady-sae assumpin fr radical cncenrains, he rae f plymerisain (R p f a mnmer (M is given by 32 : Rp - dm [ ] Ri 2 = kp[ M]( / (7 d k k where k p, k and k are he rae cnsans c d fr chain prpagain, erminain by cmbinain and erminain by disprprinain respecively. Le us assume ha here is nly a bimlecular erminain beween he radicals and ha k c = k d = k (i.e.; k c k d = 2k. Subsiuing equain (5 in equain (7, he plymerizain rae will be equivalen : dm [ ] dα = kp( α [ M ] d d kf [ ROOH ] k f [ ROOH] [ C ] 2k c d (8 Where k is bimlecular erminain cnsan and α is he degree f cnversin (i.e.; α=-[m]/ [M]. The dissciain rae f ROOH (eq ( is given by: drooh [ ] = kd ROOH C d [ ][ 2 ] (9 By inegraing eq (9, we bain: [ ROOH ] = [ ROOH ] e -k d[c ] 0 (0 Anher equain can be wrien analgusly eq (0 fr R OOH: 2 / [ ROOH] = [ ROOH] e -k d [C ] 0 ( where [ROOH] and [R OOH] are he iniial cncenrains f he iniiars. By subsiuing [ROOH] and [R OOH] frm equains (0 and (, respecively in equain (8 and rearranging we bain he fllwing equain: dα C = kp( α( [ 2 ] d 2k -k d[ C ] 0 ( kf [ ROOH ] e kf[ ROOH] e 2 / -k d [C ] 0 / 2 (2 The rae cnsans fr he frmain f he alkxy radicals are very large, herefre expnenials f equain (2 can be develped as a pwer series: -k d[c ] 0 e kd[ C ], -k d[c ] 0 e k [ C ] d By subsiuing he abve apprximains in equain (2 we bain: dα C = kp( α( [ 2 ] 2 / ( kf [ ROOH ] d 2k kf[ ROOH] ( kkd f[ ROOH] k kd f [ R OOH ] [ C ] / 2 We define A, B and C as: A= k p C ( [ 2 ] / 2k 2 (3 (4 B = kf [ROOH] k f [R OOH] (5 C = (kk d f [ROOH] k k df [R OOH] [C ] (6 Subsiuing A, B and C in equain (3 and rearranging and inegraing a a given emperaure frm a curing ime =0 where he degree f cnversin α=0 a ime wih he degree f cnversin α, we bain: 84 Plymers & Plymer Cmpsies, Vl. 5, N. 3, 2007

3 A Kineic Mdel fr he Lw Temperaure Curing f an Unsauraed Plyeser Resin wih Single and Dual Iniiars = 2A 32 / 32 / ln( α [( ] 3C B C B (7 C is much larger han B, s (B-C 3/2 in equain (7 can be develped as a pwer series: = 2A 3 ln( α 3C B 2 CB B And finally: ( = ln α / B A 2 32 / 2 / 32 / (8 (9 Subsiuing A and B frm equains (4 and (5 in equain (9 and aking lgarihms, we bain: ln( ln = ln α k ( [ C ] 2 / p 2k ln( kf [ ROOH ] [ k f R OOH ] 2 (20 Iniial iniiar cnen ((ROOH % r (R OOH % can be relaed he iniial iniiar cncenrain ([ROOH] r [R OOH] fr hmgeneus sluins by he fllwing equain: [ROOH] = m (ROOH % r [R OOH] = m (R OOH % (2 where m and m are he iniiars mlar masses. Subsiuing [ROOH] and [R OOH] f equain (2 in equain (20 we bain: ln( α ln = ln( k( [C ] p 2k 2 ln(kfm (ROOH % kfm(r OOH % /2 (22 Nw suppse he sum f he iniial iniiar cnens (w% (i.e.; (ROOH % (R OOH % be cnsan. Cnsequenly, equain (22 can be ransfrmed in equain (23: ln = ln( k p ln( α kfm k f m ( [ ] 2 / C 0 2k ln(( ROOH % R 2 where R is defined as: (23 kfm R = kfm k f m (( ROOH % ( R OOH % = cnsan (24 Fr a given emperaure and a cnsan degree f cnversin, here is a linear relainship beween he ln and he ln ((ROOH %R f he ype: ln = a - b ln (I % R (25 The dependence f he gel ime n he rai f he iniial cncenrains f he iniiars (i.e.; [ROOH] /[R OOH] can be analysed by cnsidering he rai f he disappearance raes f ROOH and R OOH. Because he reacin medium is hmgeneus and he cbal species always exiss in any siuain a any ime we can suppse ha his rai is cnsan unil gelain fr a given emperaure: Or d[ ROOH ]/ d = d[ R OOH ]/ d kd[ ROOH ][ C ] = Cnsan k d[ R OOH ][ C ] [ ROOH ] = K [ R OOH ] K is an anher cnsan. (26 (27 Subsiuing [ROOH] and [R OOH] frm equains (0 and ( in equain (27 a he gel ime and rearranging resuls in he fllwing: [ ROOH ] [ ROOH] = Ke ( kd kd[ C ] 0 gel By aking lgarihms we bain: (28 ln [ ROOH ] [ R OOH ] = ln K ( kd kd[ C ] gel (29 Subsiuing [ROOH] and [R OOH] frm equain (2 in equain (29 and rearranging i resuls: ln ( ROOH % ( R OOH % ln( ( = K m kd kd [ C ] gel m (30 Fr a given emperaure and a cnsan cncenrain f prmer, here is a linear relainship beween ln ((ROOH %/(R OOH % and he gel ime. EXPERIMENTAL Maerials The unsauraed plyeser resin used in his sudy was a :.5:.4:.44 mlar mixure f maleic anhydride, isphehalic acid, prpylene glycl and diehylene glycl cnaining 40% by weigh syrene (BUSHEPOL 7529, Bushehr Chemical Indusry, wih an average f 5.88 ehylenic unsauraed grups per plyeser mlecules. The unsauraed plyeser resin was emplyed as received wihu remving he inhibir. The inhibir cnen f resin was % as indicaed by he supplier and i was he same amun fr all samples. We used varius amuns f MEKP and AAP and heir mixures ( w% as i shwn in Table. MEKP and AAP were supplied by Elf Achem wih he cmmercial names f Luperx K and Luperx K3, respecively. 0.5 w% cbal naphhenae (cmmercial grade was used as prmer. Plymers & Plymer Cmpsies, Vl. 5, N. 3,

4 Mehdi Vafayan, Mhammad Hsain Beheshy and Hasan Nasiri Table. The iniiars cnen (w% used in his sudy Sample (MEKP%AAP% =.5% w/w (MEKP%AAP% = 2.0% w/w Insrumenain and Prcedures The cure exherm was measured accrding ASTM D 247. The plyeser resin cnaining 0.5 w% cbal accelerar was mixed wih he apprpriae amun f iniiars a ambien emperaure and he mixure was vigrusly mixed fr ne minue. Apprximaely 70 g f his mixure was pured in a paper cup (50 ml a ambien emperaure. The heigh f he mixure in he paper cup was 50 mm. The ime-emperaure daa were bained by placing a hermcuple cnneced a digial hermmeer in he cenre f he islaed paper cup. The gel ime was deermined by measuring he resisance he min f a 3 mm diameer aluminium ube prbe using a gel ime meer (J. Gndenhve & Hubner. The effec f hea lss he envirnmen was crreced by using he hea balance mehd f Rjas and e al. 27. The cnversin values a each ime were calculaed by he fllwing equains: Tad = Texp U ( Texp T d 0 (3 ( Tad T α = ( Tad,max T (32 where T ad is he crreced emperaure fr adiabaic cndiins, T is he ambien emperaure, α is he degree f cnversin, and U is he rai f he glbal hea ransfer cefficien per uni mass he specific hea, and assumed be cnsan. A pl f ln (T exp -T vs ime gives a sraigh line frm a cerain ime afer he experimenal maximum emperaure. The U value is bained by calculaing he gradien f his line. RESULTS AND DISCUSSION Curing Behaviur f Single Iniiar Sysems We will firs presen he curing behaviur f he unsauraed plyeser resin wih w differen single iniiars. Figure illusraes he impran rle f MEKP in he curing behaviur f he plyeser resin a hree differen MEKP cnens (w%. The ded curves in Figure represen he adiabaic emperaures calculaed frm equain (3. Accrding his figure, a high MEKP cnens he inducin perid r gelain ime is shrer, bu he exherm is higher. I is bvius ha he greaer he amun f MEKP, he mre quickly he peak ime ccurs. This crrespnds a greaer decmpsiin rae f he iniiar as expressed in equain (9 during he curing prcess. On he her hand ΔT ad, max (i.e., T ad, max - T did n remain cnsan fr MEKP values ranging frm w%, s he iniiar may be depleed befre he cmplein f reacin, and he reacin had n gne cmplein. Figure 2 shws graphs f ln vs. ln (I %. Fr a single iniiar sysem R=0 because k is zer (see equain (24, s equain (25 changes in: ln = a-b ln (I % (33 Fr all he cnversins in Figure 2, he relainship beween ln and he lgarihm f he iniial iniiar cnen was linear, wih regressin cefficiens beween 0.99 r Therefre, equain (33 is valid fr describing he curing f unsauraed plyeser resins wih MEKP, when he iniial cncenrain f MEKP varies beween.0 and 2.0 w%. Figure. Temperaure rise curves fr he unsauraed plyeser resin cured wih.0,.5 and 2.0% MEKP. The ded curves are he adiabaic emperaures calculaed frm he experimenal curves accrding equain (3 86 Plymers & Plymer Cmpsies, Vl. 5, N. 3, 2007

5 A Kineic Mdel fr he Lw Temperaure Curing f an Unsauraed Plyeser Resin wih Single and Dual Iniiars Figure 2. Lgarihm f curing ime agains he lgarihm f he iniial cnen f MEKP fr he fllwing degrees f cnversin: 8, 20, 40, 52, 60 and 80% The daa in Table 2 fr he AAP sysem shw ha b scillaed beween 0.52 and I was apprximaely cnsan, suggesing ha here was n change in he reacin mechanism. The equain derived by Ck and e al. 26 predics he crrelain f he gel ime wih he cncenrain f he hree main species (inhibir, iniiar and accelerar. Ck e al. s equain is wrien as: / gel = k d [ROOH] [C ]/[X] (34 Table 2. The values f b a differen degrees f cnversin were calculaed using he equain ln = a-b ln (I % R fr an unsauraed plyeser resin cured wih MEKP, AAP and heir mixures Cnversin (% b MEKP AAP MEKP% AAP% =.5% MEKP% AAP% = 2.0% where [X] is he iniial cncenrain f inhibir. Accrding equain (34 he reciprcal gel ime is a linear funcin f he iniiar cncenrain. Figure 3 shws ha he relainship beween he reciprcal gel ime and he iniial MEKP and AAP cnens was linear. In his figure, he linear regressin shws an excellen fi. Curing Behaviur f Dual Iniiar Sysems Nw we cnsider he dual iniiar sysems which are very useful fr he curing f unsauraed plyeser resins. Dual sysems are emplyed because hey prvide rapid bu cnrlled cplymerisain. They can als give an addiinal degree f freedm cmpsie prduc manufacurers. The kineic parameer b a differen degrees f cnversin fr MEKP is shwn in Table 2. Daa in his able shw hw b increased frm as he degree f cnversin increased frm 8 80%. We wuld expec he b parameer be cnsan if here were n changes in he reacin mechanism. Our mdel assumes ha he erminain f he radicals ccurs in pairs, because accrding equain (7, he plymerisain rae increases a an rder f (2 /2 when he iniiain rae dubles. S b wuld assume a value f 0.5. Bu ur resuls shw ha i scillaes beween 0.84 and.00. As he degree f cnversin increases he cnsan b als increases, hereby suggesing ha as reacin prgresses he number f radicals ha are rapped wihu heir being effecive increases. Our resuls shwed ha he exherm behaviur f he AAP sysem was similar ha f he MEKP sysem fr curing an unsauraed plyeser resin a ambien emperaure. Bu he frmer has he shrer inducin ime. The curve ln vs. ln (I % fr he AAP sysems was linear fr all cnversins and he regressin cefficiens lay beween and We again bserved ha he relainship esablished in equain (33 was valid. Figure 4 gives he exherm behaviur f he unsauraed plyeser resin cured wih he varius prprins f MEKP and AAP. Alhugh he rais f he iniial iniiar cnens were variable he sum f heir iniial cncenrains was cnsan and equivalen.5 r 2.0 w%. Figures 5 and 6 shw he curves ln vs. ln (MEKP% R a differen degrees f cnversin fr dual iniiar sysems wih.5 and 2.0 w% (MEKPAAP, respecively. I can be seen ha he relainship esablished in equain (25 is valid fr describing he curing behaviur f his unsauraed plyeser resin wih bh.5 and 2.0 w% (MEKP AAP. Plymers & Plymer Cmpsies, Vl. 5, N. 3,

6 Mehdi Vafayan, Mhammad Hsain Beheshy and Hasan Nasiri Figure 3. Reciprcal gel ime pled agains he iniial cncenrains (w% f AAP (< and MEKP (5 Wih regarding f equain (24, R (he value f R when he sum f he iniial cnen f iniiars is.5%, R 2 (he value f R when he sum f he iniial cnen f iniiars is 2.0% and R /R 2 can be wrien: R = k f m (.5%/ [kfm-k f m ] (35 R 2 = k f m (2.0%/ [kfm-k f m ] (36 R /R 2 =0.75 (37 Figure 4. Temperaure rise curves fr he unsauraed plyeser resin cured wih he mixures f MEKP and AAP. The ded curves are he adiabaic emperaure calculaed frm he experimenal curves accrding equain (3. a MEKP% AAP % =.5%; b MEKP % AAP % = 2.0% (a T find R and R 2, i is necessary deermine he values f k, k, f, f, m and m firs. Bu we bained R by rial and errr and hen subsiued is value in equain (37, s ha he calculain f R 2 became pssible. As shwn in Table 2 he value f b fr.5 and 2.0 w% (MEKP AAP was apprximaely cnsan, s i can be assumed ha here was n change in he reacin mechanism. The dependence f he gel ime n he lgarihm f he iniial iniiar cncenrain rai fr.5 and 2.0 w% (MEK AAP is shwn in Figure 7. Frm equain (30 a linear relainship exised beween ln (MEKP%/AAP% and he gel ime. Therefre, we cnsider ha he rai f he iniiar disappearance rae was cnsan up gelain fr a given emperaure. CONCLUSIONS (b I has been demnsraed ha, here is a general relainship f he ype ln = a-b ln (I %R beween he reacin ime and he iniial iniiar cnen fr he curing f unsauraed plyeser resins wih dual iniiar sysems prviding ha he sum f he iniial iniiar cnens is cnsan. Fr a single iniiar sysem his general frmula cnvers a special frm in which R vanishes (i.e., ln = a b ln (I %. I was already knwn ha in a single iniiar sysem he gel ime is 88 Plymers & Plymer Cmpsies, Vl. 5, N. 3, 2007

7 A Kineic Mdel fr he Lw Temperaure Curing f an Unsauraed Plyeser Resin wih Single and Dual Iniiars Figure 5. Lgarihm f curing ime pled agains he lgarihm f (MEKP% R fr he fllwing degrees f cnversin: 8, 20, 40, 52, 60 and 80% (MEKP% AAP% =.5% inversely relaed he iniial iniiar cncenrain. Our experimens als shw ha here is a linear relainship beween he reciprcal gel ime and he mehyl ehyl kene perxide and aceylacene perxide cncenrains. Fr mehyl ehyl kene perxide and aceylacene perxide mixures (dual iniiar sysems he gel ime was fund be prprinal he lgarihm f he iniial iniiar rai, as prediced by hery. REFERENCES Figure 6. Lgarihm f curing ime agains he lgarihm f (MEKP% R 2 fr degrees f cnversins 8, 20, 40, 52, 60 and 80% (MEKP% AAP% = 2.0% Figure 7. Gel ime pled agains he lgarihm f iniial iniiar cncenrain rai. Hrie K., Mia I. and Kambe H., J. Plym. Sci. (A-, 8 ( Yang Y.S. and Lee L.J., Macrmlecules, 20 ( Yang Y.S. and Lee L.J., Plymer, 29 ( Han C.D. and Lee D.S., J. Appl. Plym. Sci., 34 ( Muzumdar S.V. and Lee L.J., Plym. Eng. Sci., 3 ( Bach G.L. and Macsk C.W., J. Appl. Plym. Sci., 44 ( Ramis X. and Salla J.M., Plymer, 36 ( Yun Y.M., Lee S.J., Lee K.J., Lee Y.K. and Nam J.D., J. Plym. Sci. Phys., 35 ( Marin J.L., Plymer, 40 ( Ramis X. and Salla J.M., J. Plym. Sci. Phys., 37 ( Vilas J.L., Laza J.M., Garay M.T., Rdriguez M. and Len L.M., J. Appl. Plym. Sci., 79 ( Ruisn D., Sain M. and Cuurier M., J. Appl. Plym. Sci., 89( Lin C.M. and Weng C.I., Plym. Eng. Sci., 40 ( Yang H. and Lee L.J., J. Appl. Plym. Sci., 84 ( Sp K.J., US Paen; N. 5,973, Huang Y.J. and Leu J.S., Plymer, 34 ( Plymers & Plymer Cmpsies, Vl. 5, N. 3,

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