MODELING MOLECULAR WEIGHT DISTRIBUTION, VINYL CONTENT AND BRANCHING IN THE REACTIVE EXTRUSION OF HIGH DENSITY POLYETHYLENE

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1 Li Aei Applie eeh :4-49 ( ODELIN OLECULA WEIHT DISTIBUTION VINL CONTENT AND BANCHIN IN THE EACTIVE EXTUSION OF HIH DENSIT OLETHLENE. ASTEASUAIN.V. ÉEZ C. SAOIA A. BANDOLIN l iloo e Igeieí Quíi (UNS-CONICET CC 77 8 Bhí Bl Agei. oli@plpiqui.eu. A We uy eive oifiio of high eiy polyehylee y ogi peoxie. We ipove peviou oel ple of eiig vege oleul weigh viyl oe o iopoe he lulio of log-hi hig oplee oleul weigh iiuio. We lule vege oleul weigh log-hi hig iexe fo oleule wih give ue of viyl y pplyig oule oe ehique ove hoe vile. No oe ehique w pplie o he viyl oe o he oel h he piliy of lulig hoe vege quiie fo evey viyl oe. To lule oleul weigh iiuio we pply poiliy geeig fuio efiiio wih epe o he oleul ize o he le of il polye peie of give ue of viyl. We ue wo ii efiiio of poiliy geeig fuio eh oe iely pplile eihe o he ue o weigh iiuio. Thee poiliy geeig fuio e ueilly ivee o oi he oepoig lule oleul weigh iiuio. eul give eepe iigh io he evoluio of viyl goup hig poi foio. WD viyl oe peiio e ope wih quliive expeiel howig he oel piliie. Keywo WD heil oelig pgf Viyl oe Log-hi hig. I. INTODUCTION High eiy polyehylee (HDE i veile heopli fo whih pou e evelope oiue o ope ew ppliio. I i poue eihe lie polye o oe wih ho-hi he if o-ooe i ue. The peifi popeie of eh HDE ge eul fo he oiio of evel vile: eiy oleul weigh oleul weigh iiuio (WD viyl oe egee of hig (W Hley99. Cly ehology h e poile he ipovee of he pefoe of he iffee ge of HDE. Nevehele eive oifiio i elihe eooi po-eo opio o ilo oleul popeie of HDE i oe o oe i ge of ppliio. Ogi peoxie e ue o geee piy il h will he polye. I i geelly epe h piy il hyoge fo he polye oleule whih he uegoe ily oliig. Depeig o he opeig oiio ei egee of iio y e oeve. Viyl oe ply ipo ole i he eive oifiio. The oeio of eil oule o pee i polyehylee eee pily fo ieig iiil peoxie oeio iiig og eleiviy ow hei eio. I h lo ee oeve h he iee i oleul weigh i highe fo ei wih highe viyl oe (Seeg e l. 997; Suw Ble 99. A oifiio poee he iiilly lie polye eoe ieigly he he he hvig ize iil o h of he oigil polye oleule. The eio of hi ype of he le o i hge i heologil ehil popeie iue y éez e l. (. Few heil oel i he lieue eie he peifi poe of oifiio of polyehylee. Soe of he ue iil ppoh eviewe y loo e l. (994 he i iee eig he peiio of gel poi of vege oleul weigh WD of he ol fio. The iil ppoh oe o povie ifoio fuio of ie. Suw Ble (99 wee he fi o ue iei ppoh. They ie he peiio of oleul weigh iiuio llowig oleule wih eihe o viyl. They lule he iiuio y ieizig i i up o 5 egee of polyeizio poi. They oie goo peiio of oleul weigh fo low eiy polyehylee lie low eiy polyehylee u o fo HDE. Wih epe o viyl oe hey oul o pei op lge he oe oeve expeielly i ll e. I peviou wo we popoe iei oel (eee e l. 999 h eie he legh of he polye hi he oeio of viyl goup iuleouly. The eulig ifiie ye of le equio w olve uig oule oe ehique. The oel peie vege oleul weigh he vege oeio of viyl goup fuio of ie. Thi oel eule i ipove peiio of he expeiel ove he peviouly 4

2 Li Aei Applie eeh :4-49 ( eioe iei oel of Suw Ble. I hi wo we pee geelizio of ou peviou oel whih llow u o ou fo he eie oleul weigh iiuio well he log-hi hig. We evelop eepe iigh io he viyl goup iiuio og he oleule give he opeig oiio of he oifiio poe. We fou o he oifiio ig ple i pe o epeue ue oiio whee iio i o eule. II. ATHEATICAL ODEL We evelop e of le fo he eig peie whee he iffee legh ue of viyl ue of hig poi e e io ou. A iple oe ehique w ue o lule ue weigh vege oleul weigh well vege ue of hig poi fo peie hvig viyl To lule oleul weigh iiuio we pply ohe fo ehique h e ue of poiliy geeig fuio (pgf efiiio pplie o he ue weigh WD followig he geel ehique illue i Aeui e l. (. Equio e e fo he pgf of eh peie fo whih i piiple i woul e poile o lule WD fo peie hvig ii ue of viyl. The oe of he iiuio e eee ipu o hey u e lule fuio of eiee ie iuleouly wih he pgf. The pgf fo oiee i hi wo e efie fo iee iiuio hoe fou i polye iee hei foe vile i el oue. Thi e he ive o e ue i iulio ivolvig polyei peie uh he oe i hi wo. I he pee poe i u e oiee h we fo polye hee exi ozeo pgf uve fo he egiig. I oequee hi pgf u e eie fo he WD of he vigi ei. I hi wo we lule pgf fo he glol oleul weigh iiuio. The lule pgf e ueilly ivee uig wo iveio eho (pouli 956; Sehfe 97. Thi llow eovey of WD. The oifiio poe i poule o ou iohelly i pefely ie h poe he uul upio of qui-ey e of il i o eploye. We fou o he pegel egio oly. The oel ou fo he exiee of viyl goup i he polye oleule. No eiio i ipoe o he xiu ue of viyl goup pe oleule. oleule wih o viyl e lo llowe. We lo e io oieio he peee of log-hi he. il oil e ue o oi oly oe ive ie ie he oel h ee ipleee o pefo lulio i he pegel egio. The popoe ehi i how elow (Eq. 6. Thi ehi i exeio of he oe we peviouly epoe (eee e l I hi wo we oue o eep of he ue of he we o o ilue he iio eio ie he egee of iio ppe o e egligile he opeig oiio fo whih he expeiel ue fo opio wee oie. Iiiio Hyoge Aio I i 4 h h Teiio y Coiio ( Chi Tfe o olye ( ( (4 (5 (6 I hee equio I i he iiio i he iiiio il poue y hel eopoiio of he peoxie iiio (Eq. e polye oleule e oil whee he fi iex iie he ue of ooei ui he eo iex iie he ue of he he hi oe he ue of viyl. The fi eo iexe y vy ewee ifiiy he hi oe ewee zeo xiu ele o he ue of ooe. Evey ie hyoge io ou i he oe of he oleule (Eq. polye oleule i ovee o oil of he e ize ue of viyl log-hi hig poi. Equio epee hyoge io h oue viyl goup he i hi e he eulig oil h he e ize ue of hig poi u oe viyl le. A he iei o fo hee eio e give pe ui of eive ie whe pefoig le hey u e uliplie y he ue of eive ie ivolve. Teiio i ue o ou y oiio (Eq. 4 whee he eulig polye oleule h legh ue of viyl goup ue of hig poi equl o he u of he epeive quiie i he eig il. If oil hyoge ywhee o polye oleule hi fe o polye ou (Eq The iuio i iil o he hyoge io y iiiio il. le e elihe fo ll of he peie ivolve i he eio ehi follow (Eq. 7-. eoxie Iiio I i I (7 4

3 . ASTEASUAIN. V. ÉEZ C. SAOIA A. BANDOLIN iy il ( 4 h h i i I f (8 olye oleule wih ooe ui hig poi viyl ( ( ( (.5 h h (9 il oleule wih ooe ui hig poi viyl ( ( ( ( ( ( h h ( The le equio e ifiie i ue. I hi wo we eploy wo fo ehique o e le o lule polye popeie he pgf he oe ehique. A oule oe ehique i eque o lule vege oleul popeie uh oleul weigh log-hi hig poi pe ooei ui viyl oe. The pgf fo e well uie fo he eovey of he oplee WD fe ppopie iveio. By pplyig he oe efiiio o he legh ue of he we oi oule oe fo eh populio of oleule wih give ue of viyl goup. Thi llow u o lule vege popeie fo oleule wih iffee ue of viyl goup: h h oe oe fo polye wih viyl (......;...; h h oe oe fo il wih viyl (......;...; To fo le Eq. 9 u e uliplie y he e up fo ll polye legh he. The eulig oe le e how i Eq. ( (4. I houl e oe h whe olvig he h oe he (h oe oe ppe i hee equio. Thee e eie uig log-ol ppoxiio i eee e l. (999. Equio u e olve iuleouly. I oe o iplee he opue pog he u i Eq. 8 u e eple y he oe hey epee. The ye of 6 (J x iff oiy iffeeil equio y e olve ueilly (e 97. J x i hoe o h eul e epouile. ( ( (.5 h h ( 4

4 Li Aei Applie eeh :4-49 ( h h ( ( ( ( ( (4 The followig ueful polye popeie e lule fo oe eul: Nue-vege oleul weigh fo oleule wih viyl ( 8 (5 Weigh-vege oleul weigh fo oleule wih viyl w( 8 (6 Nue of hig poi pe ooei ui X( (7 Weigh pee of oleule wih viyl Wvi( 8 (8 lol popeie ( l w l X l e oie y uig eh e i he equio hough ll poile vlue of. Fo exple fo he glol ue vege oleul weigh he followig expeio i ue: l 8 ( ( (9 To eie oleul weigh iiuio we ue iffee efiiio of pgf fo fo ue o weigh iiuio. Fo eil o he ppliio of he ehique he ee i efee o Aeui e l. (. Biefly hoe wo iiuio hve oie poiliie ele o he ue weigh fio epeively. I eh e he poiliy h ei fio of il o polye oleule wih viyl hve legh i yolize y ( N J whee iie ue iiuio iie weigh iiuio. The poiliy geeig fuio e efie (ille oo 988: Φ ( z z ( N J ( α Tle : Ble e hei oepoig pgf fo fo WD Ble e gf fo T α α α ( U z Φ ( T U Φ ( z T T α. α U Φ (. z αz ( U Φ ( z T T l α( l α ( U Φ ( z ( U Φ l ( z z 44

5 . ASTEASUAIN. V. ÉEZ C. SAOIA A. BANDOLIN whee Φ ( z ψ ( z oleule whe elig wih polye Φ ( z φ ( z i he e of il oleule. ( N J i lule follow ( N J T U T fo T ( whee T epee polye o il oleule wih ooei ui hig poi viyl goup U i he hh glol oe fo il o polye. I oe o fo he le equio (Eq. 9 u e uliplie y z e fo ll poile vlue of. Tle how he eul of he foio fo viou e i he le equio. The eulig pgf le e how i Eq.. pgf le fo polye oleule ( ψ ( z h h z z ( ψ ( z ( ψ ( z ( ψ ( z ( ψ ( z z ( ψ ( z ( φ ( z z ( φ ( z ( ( ψ ( z ( ( pgf le fo il oleule ( ψ ( z ( φ ( z z h z ( ψ ( z h ( ( ψ ( z ( ψ ( z z z ( ψ ( z ( φ ( z ( ( ψ ( z ( φ ( z ( φ ( z ( ( The fil ye o e olve i opoe of 6 (J x 4 (J x Nz le. Nz i he ue of vlue of z whee eh pgf u e evlue. Thi vlue i ou 5 epeig o he elee iveio eho he ue of poi o e eovee o eh WD. A ipu he oel equie he of polye o e oifie oleul weigh of ooe WD of he vigi ei ogehe wih i ue vege ( weigh vege (w oleul weigh viyl oe peoxie oeio peoxie oleul weigh opeig epeue eiee ie. The wo pgf of he vigi ei e lo eee; i y e eey o lule he fo he expeiel WD eile elewhee (Boli e l.. We ue he iei pee epoe elewhee (eee e l The oplee ye of equio i olve y e of he e lgoih fo iff ye ue fo he oe oel (e 97. Ulie wh w oe wih he oe equio we o o olve he pgf equio fo evey poile vlue of. Ie we lule he pgf fo he glol polye y lupig ll vlue. The oupu of he pgf oel oi of he wo ype of pgf fuio of eiee ie z. Thee quiie e he fe o he iveio lgoih. To ive he pgf we ue pio of he eho oigilly evelope y pouli (956 Sehfe (97 fo Lple fo. Sehfe eho elog o goup of eho h opue ple while pouli eho ue eie expio of he oigil fuio explie i exeive eview (Dvie i 979. I ief oh of he e ue of weighe u of vlue of he - 45

6 Li Aei Applie eeh :4-49 ( foe fuio ei poi of he fo vile o eove he oigil fuio give poi of i iepee vile. Eh eho equie he ue o fix he vlue of oe o wo pee whoe opiu vlue epe o he ype of fuio eig ivee. I he oigil wo oh eho wee ee uig fuio vey iffee fo he WD o e oie hee. Fo ou pupoe he we u o oly p he eho o e ue wih pgf fo (ie of Lple fo u we u lo fi he opiu vlue of he pee oie o eh eho whe eoveig fuio h ehve lie WD o. We hve peviouly how (Boli e l. h he Lple fo he pgf fo e equivle peifi vlue of hei iepe- e vile fou e z. ig ue of hi equivlee we hve pe evel ueil iveio eho popoe fo Lple fo fo he iveio of pgf fo (Aeui e l. ; Boli e l. evelope iei fo hooig he eho pee. We ue h equivlee hoe iei fo he iveio eho uie i he pee wo. The opuiol effo equie y eh eho y e eie y he ue of ie he pgf u e lule fo give ue of oleul weigh poi explie i ou peviou wo (Aeui e l. ; Boli e l. Thee quiie epe lo o he vlue of eho pee. III. ESULTS AND DISCUSSION To vlie he oel expeiel wee oie i ou looy (Co e l A oeil lie high eiy polyehylee povie y Oxy eoheil ( 7; w 5 w heilly oifie wih 5-Diehyl-5-Bi(Te-Buyl- eoxi-hexe. A powe of he vigi ei w ipege wih peoxie oluio o oi five iffee peoxie oeio: w%. Eh ixue w ee 7 C i pe fo wey iue o eue oplee eio. Sple wee lyze fo viyl oe y Fouie Tfo Ife Speoopy. WD of pou ple wee lyze y ize exluio hoogphy (SEC i We-5-C ALC-C wih e of olye Looie gel olu wih oil poe ize of Å efive iex eeo. 4- ihlooezee 4 C w ue olve flow e of l/i w eploye. Sie of oifie ei wee lyze igoig he peee of he hey houl e oiee quliive. Figue pee he WD of he vigi oifie ei. Tle. Avege popeie fo iffee iiil peoxie oeio Vigi ei ( ( ( ( l exp w ( w ( w ( w ( w l w exp Wvi ( Wvi ( Wvi ( Wvi ( %Vi exp /Vi exp vig X ( 5. 65x 7.x x -4. x.7x -4 Xi ( 78x 5 8.7x -5.9x -4.95x -4.69x -4 X (.5x -.58X -4.x -.66x - 4.x - X (.x -.44x x x x - X l x x -5.4x -4.89x x

7 . ASTEASUAIN. V. ÉEZ C. SAOIA A. BANDOLIN w i 5.5E-4 5.E-4 4.5E-4 4.E-4.5E-4.E-4.5E-4.E-4.5E-4.E-4 5.E-5.E vigi ei.5%.5 %.75 %. %. % oleul Weigh Fig.. eue weigh WD fo vigi ei oifie pou (ee: Iiil peoxie oeio w% of polye wih "" viyl eiee Tie ( Tle how oe of he oel eul wih epe o vege oleul pee. eul e iiie y ue of viyl (. lee oe h hee e oleule wih gee ue of viyl h hoe how; we hve oly peee he o elev oe. ( w( geelly iee wih ieig peoxie oeio fo ll vlue. The vege vlue fo he eie ple e vey loe o hoe of oleule wih zeo oe viyl goup whih epee he highe popoio i he ple. oleule wih he lge viyl oe hve highe oleul weigh lowe polyipeiie oie wih ll ue of lge oleule poue y he oliig eio. The iffeee ewee expeiel lule vlue e oe evie he highe iiil peoxie oeio whee he polye i geig loe o he gel poi expeiel eul e oe eo-poe. Weigh iiuio of polye wih give ue of viyl goup e how i Tle Fig.. The le how he evoluio of he iiuio fuio of eiee ie fo iiil peoxie oe of.% w/w. Beue of he piul yhei poe ue o poue ou HDE i i eole o ue h he uee polye oi oly oleule wih oe viyl goup. A he eio poee o viyl goup e oue pouig oleule wih o viyl. Thee lo ppe oleule wih oe h oe viyl ue o he oliig eio. The iiuio of viyl oe of he polye ee wih ll he iiil peoxie oeio e how i Tle. I y e oeve h fo ll peoxie oeio ou hlf he oi of oleule wihou viyl. A peoxie oeio iee he fio of h oi high-viyl oleule e o iee expee. The expeiel o viyl oe e loe o he lule vlue fo oleule wih oe viyl. w% of polye wih "" viyl eiee Tie ( Fig.. opoiio of oleule wih give ue of viyl goup (. Wih epe o oliig he oleule wih highe viyl oe e he o he oe. The vege ue of hig poi iee wih ieig peoxie oeio eul oie wih he e of ou fiig. The lule weigh iiuio oie uig he lgoih y pouli he e of he poe fo iffee iiil peoxie oeio i how i Fig.. The oepoig vigi ei WD i lo how fo opio. A oeig i peie he iiil peoxie oeio iee. Thi i ue o he highe iiiio il oeio h eul whih fvo oliig eio. WD uve o he oe fo he vigi ei high oleul weigh. A houle ppe. w% filly iol e i evie fo. w%. The peie WD fo ll peoxie oeio e vey iil o he ex- 47

8 Li Aei Applie eeh :4-49 ( peiel oe how i Fig.. I u e oe h o pee ue w oe uig of oplee WD. Siil eul wee fou whe uig eihe Sehfe o pouli eho whe uig he oepoig opiu pee he opuiol effo eig iil i oh eho. I houl e oe h pgf le e olve fo e of z vlue eeie y he expee ge of he WD. Boh iveio eho y pei ll egive o poiive vlue fo give oleul weigh if hee e vey few oleule of h ize. I he e of Fig. he ge i wie h he ul WD eulig i he oeve ll egive vlue. w i 5.5E-4 5.E-4 4.5E-4 4.E-4.5E-4.E-4.5E-4.E-4.5E-4.E-4 5.E-5.E vigi ei.5%.5 %.75 %. %. % oleul Weigh Fig.. Clule weigh WD fo iffee iiil peoxie oeio y pouli eho eue WD fo he vigi ei. IV. CONCLUSIONS I hi ppe we popoe ehe oel fo he eive oifiio of high-eiy polyehylee. We hve olve ye of foe le equio fo he h poe oieig he ize ue of he ue of viyl goup of ll he oleule. I i pee fo he oel i vli up o he gel poi. We hve pplie pgf fo o he le equio hu llowig he eipio of he ue weigh WD of he oifie polye. Nueil iveio of he foe vile h llowe vey goo eovey of he eie oleul weigh iiuio ope o he expeiel iiuio eue y SEC. The wo ueil iveio eho ue gve eul of ople quliy iil opuiol o. The oel h lo povie peiio of viyl oe hig poi h y help i he ueig of he oifiio poe. Ovell ou oel i pee ge of evelope oiue vile leive o pilo pl o iuil le il--eo expeie wih eooi fey vge. I i ool h h poeil i opiizio uie of iuil eo i he evelope of ew polye ge. Aowlegee Thi eeh wo w uppoe y CONICET Uivei Niol el Su. EFEENCES Aeui. A. Boli C. Soi eovey of oleul weigh iiuio fo foe Doi. II: Appliio of ueil iveio eho olye (. Aeui. C. Soi A. Boli eovey of oleul weigh iiuio fo foe oi. I: Appliio of pgf o le eiig eio ivolvig fee il olye (. Boli A.. Aeui C. Soi A. López- oíguez K.S. Whieley B. el Ao Feáez Nueil iveio ehique i he eovey of oleul weigh iiuio expee i iffee foe oi. Expeiel vliio oly. Eg. Si (. Co.A. J. iñ L.. Quizi.D. Fill E.. Vllé oifiió e poliolefi eie poeo po-eo A el Sipoio Ageio e olíeo (SA 97 Sie e L Ve Agei 69-7 (997. Dvie B. B. i Nueil iveio of he Lple fo: uvey opio of eho J. Cop. hy. - (979. e C.W. Nueil Iiil Vlue ole i Oiy Diffeeil Equio eie-hll Eglewoo Cliff New Jeey (97. loo.e.. Tg E. Ko A.E. Hiele Cheil oifiio of polyolefi y fee il ehi: oelig expeiel uy of iuleou o iio hig oliig olye 5 - (994. ille D.. C.W. oo Newo pee fo oliig of hi wih legh ie iiuio J. oly. Si. B 6-54 (988. pouli A. A New eho fo he Iveio of Lple Tfo Qu. Appl. h (956. eee.e. C. Soi E.. Vllé A. Boli A ipove iei oel fo he peoxie iiie oifiio of polyehylee oly. Eg. Si (999. éez C.J. E.. Vllé L. Quizi. Fill Copive lyi of he heologil ehvio of polyehylee oifie uig iffee eho o. Epoe Vol II (. 48

9 . ASTEASUAIN. V. ÉEZ C. SAOIA A. BANDOLIN Seeg A. T. Heeg B. ufo Coliig eio i uue low eiy polyehylee olye (997. Sehfe H. Algoih 68. Nueil iveio of Lple fo D5 Co. AC (97. Suw D. S.T. Ble The eive oifiio of polyehylee. I. The effe of low iiio oeio o oleul popeie oly. Eg. Si (99. Suw D. S.T. Ble The eive oifiio of olyehylee. II: heil oelig oly. Eg. Si (99. W I.. D.W. Hley A iouio o he ehil popeie of oli olye J. Wiley & So Chihee (99. eeive: Sepee 6. Aepe fo puliio: Deee 4. eoee y ue Eio: J. Ceá S. Diz A. Boi. 49