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Stress Relaxation Behavior In The Primary Transition Region

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Stress Relaxation Behavior In The Primary Transition Region

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Content INFORMATION TO USERS This material was produced from a microfilm copy of the original document. While the most advanced technological means to photograph and reproduce this document have been used, the quality is heavily dependent upon the quality of the original submitted. The following explanation of techniques is provided to help you understand markings or patterns which may appear on this reproduction. 1.The sign or "target" for pages apparently lacking from the document photographed is "Missing Page(s)". If it was possible to obtain the missing page(s) or section, they are spliced into the film along with adjacent pages. This may have necessitated cutting thru an image and duplicating adjacent pages to insure you complete continuity. 2. When an image on the film is obliterated with a large round black mark, it is an indication that the photographer suspected th at the copy may have moved during exposure and thus cause a blurred image. You will find a good image of the page in the adjacent frame. 3. When a map, drawing or chart, etc., was part of the material being photographed the photographer followed a definite method in "sectioning" the material. It is customary to begin photoing at the upper left hand corner of a large sheet and to continue photoing from left to right in equal sections with a small overlap. If necessary, sectioning is continued again — beginning below the first row and continuing on until complete. 4. The majority of users indicate that the textual content is of greatest value, however, a somewhat higher quality/reproduction could be made from "photographs" if essential to the understanding of the dissertation. Silver prints of "photographs" may be ordered at additional charge by writing the Order Department, giving the catalog number, title, author and specific pages you wish reproduced. 5. PLEASE NOTE: Some pages may have indistinct print. Filmed as received. Xerox University Microfilms 300 North Z eeb Road Ann Arbor, Michigan 48106 /4-JL4,4/^ RELE, V ilas Balwant, 1943- STRESS R E L A X A T IO N B E H A V IO R IN T H E P R IM A R Y TRANSITION R E G IO N . U n iversity of Southern C alifornia, Ph.D., 1974 Chemistry, polymer I University Microfilms, A X E R O X Company, Ann Arbor, Michigan THIS DISSERTATION HAS BEEN MICROFILMED EXACTLY AS RECEIVED. STRESS RELA X A TIO N BEHAVIOR IN THE PRIM A RY TRANSITION REGION V ilas Balwant Rele A D isse rta tio n P resen ted to th e FA CU LTY O F TH E G R A D U A T E SC H O O L UNIVERSITY O F SO U TH ER N CALIFORNIA In P a r tia l F u lfillm e n t o f th e Requirements fo r th e Degree D O C T O R OF PHILOSOPHY (Chemistry) January 197^ UNIVERSITY OF SOUTHERN CALIFORNIA THE GRADUATE SCHOOL UNIVERSITY PARK LOS ANGELES, CALIFORNIA 0 0 0 0 7 This dissertation, written by ............ under the direction of A.i.S... Dissertation Com mittee, and approved by all its members, has been presented to and accepted by T h e Graduate School, in partial fulfillm ent o f requirements of the degree of D O C T O R O F P H IL O S O P H Y V Dean D ati DISSERTATION COMMITTEE Chairman Dedicated to M y Parents A C K N O W L E D G E M E N T S I would lik e to th an k Mr. R.F. K ratz of th e Koppers Company, j I n c ., M onroeville, P a ., f o r th e pure c h a ra c te riz e d polystyrene and Dr. J . Moacanin of th e J e t P ro p u lsio n L aboratory, Pasadena, C a lifo rn ia i fo r th e pure c h a ra c te riz e d p o ly v in y lb ip h e n y l. This p ro je c t was p a r tia lly supported by th e U .S. Army R esearch O ffice. I am g ra te fu l to P r o f. John J . A klonis fo r h is p ro fe ssio n a l advice during m y g rad u ate y e a rs . i i i T A B L E O F C O N T E N T S Page A C K N O W L E D G E M E N T S ............................................................................................ i i i LIST O F FIGURES .............................................................................................. v INTRODUCTION ..................................................................................................... 1 Chapter I . B A C K G R O U N D ...................................................................................... 3 A. V is c o e la s tic ity B. S tre s s R elax atio n Experiments C. G lass T ra n s itio n Temperature I I I STRESS RELAXATION BEHAVIOR IN TH E PR IM A R Y TRANSITION REGION............... 15 A. Maximum N egative Slopes B. T h e o re tic a l Background C. Experim ental D. R esu lts and D iscussion I I I . EFFECT OF PLASTICIZATION O N TH E DIMENSIONALITY OF POLYSTYRENE ............................................................................. 33 A. P la s tic iz a tio n B. E xperim ental C. R esu lts and D iscussion IV. CONCLUSIONS ..................................................................................... 76 REFERENCES ..................... 80 iv LIST O F FIG U R ES Figure Page 1. T e n sile E longation o f a Polymer Sample ........................... . . 4 2. D eform ation in Shear of a Polymer S a m p le............................... 5 3. S tre s s R elax atio n M aster Curve fo r P o ly sty ren e ................. 8 4. Tem perature Dependence of Modulus fo r P o ly sty ren e a t 10 seconds . . . . .................................................... - q 5. S p e c ific Volume as a Function of T e m p e ra tu re ...................... 13 6. S tre s s R elaxation M aster Curves fo r P o ly sty ren e and P o l y i s o b u t y l e n e ........................................................................... 16 7A. Maxwell Element . . . . ......................... 18 7B. R-B One Dimensional R e p re s e n ta tio n ........................................... 18 7C. T obolsky's Three Dimensional Model . t ................................... ^ 8i S tre s s R elaxation M aster Curve fo r PV B ................................... 30 9. P lo t of SI Versus G lass T ra n sitio n Temperature f o r PVB, PIB, P2VN, PS, and P«MS.......................................................... 31 10. The Prim ary T ra n sitio n region fo r PS P la s tic iz e d w ith 2.5 Weight P ercent D O P . . . . i . . .................................... 41 11. The Prim ary T ra n sitio n reg io n fo r PS P la s tic iz e d w ith 5 W eight' P ercent D O P........................................................................... 42 12. The Prim ary T ra n sitio n region fo r PS P la s tic iz e d w ith 10 Weight P ercent DOP........................................................................... 43 13. The Prim ary T ra n sitio n region fo r PS P la s tic iz e d w ith 20 Weight P ercent DOP...................................... 44 14. The Prim ary T ra n sitio n region fo r PS P la s tic iz e d w ith 25 Weight P ercent DOP.......................................................................... 45 15. The Prim ary T ra n sitio n region fo r PS P la s tic iz e d w ith 30 Weight P ercent DOP................................................................. 46 v Figure Page 16. SI Versus P la s tic iz e r C on cen tratio n fo r PS-DOP S y ste m ................................................................................................ 47 17. Versus P la s tic iz e r C oncentration fo r PS-DOP S y s te m ................................................................................................ 48 18. The Prim ary T ra n sitio n Region f o r PS P la s tic iz e d w ith 5 Weight Percent D EP * ........................ . .. . . . . . . 49 19. The Prim ary T ra n sitio n Region fo r PS P la s tic iz e d w ith 10 Weight Percent DEP.................................................................. 50 20. The Prim ary T ran sitio n Region f o r PS P la s tic iz e d w ith 20 Weight Percent DEP.................................................................. 51 21. The Prim ary T ra n sitio n Region fo r PS P la s tic iz e d w ith 25 Weight Percent DEP................................................................... 52 22. The Prim ary T ra n sitio n Region fo r PS P la s tic iz e d w ith 30 Weight Percent DEP. .......................................................... 53 23. DI Versus P la s tic iz e r C o n cen tratio n fo r PS-DEP System. 54 24. T^ Versus P la s tic iz e r C o n cen tratio n s fo r PS-DEP System. 55 25. The Prim ary T ra n sitio n Region f o r PS P la s tic iz e d w ith 5 Weight Percent D O S . .......................................................... 57 26. The Prim ary T ra n sitio n Region f o r PS P la s tic iz e d w ith 10 Weight Percent DOS................................................................... 58 27. The Primary T ra n sitio n Region f o r PS P la s tic iz e d w ith 20 Weight Percent DOS................................................................... 59 28. The Prim ary T ra n sitio n Region fo r PS P la s tic iz e d w ith 25 Weight Percent DOS........................................ 60 29. SI Versus P la s tic iz e r C o n cen tratio n fo r PS-DOS System. 61 30. T i Versus P la s tic iz e r C o n ce n tratio n fo r PS-DOS System. 62 31. The Prim ary T ra n sitio n Region f o r PS P la s tic iz e d w ith 5 Weight Percent PS (600).............................................................. 64 32. The Prim ary T ran sitio n Region f o r PS P la s tic iz e d w ith 10 Weight Percent PS (600) ..................................................... 65 33. The Prim ary T ra n sitio n Region f o r PS P la s tic iz e d w ith 15 Weight Percent PS ( 6 0 0 ) .......................................................... 66 ■ v i ....................................................... .. Figure Page 34. The Prim ary T ra n sitio n Region fo r PS P la s tic iz e d w ith 20 Weight P ercen t PS (600) ............................................ 67 35. SI Versus P la s tic iz e r C o n cen tratio n fo r PS-PS (600) System * 1 ...................................................................... 68 36. T^ Versus P la s tic iz e r C o n cen tratio n fo r PS-PR. (600) System ..................................................................... 69 . . » ' 37. The Prim ary T ra n s itio n REgion fo r PS P la s tic iz e d w ith 5 Weight P ercen t DMP......................................................... 70 38. The Prim ary T ra n s itio n REgion fo r PS P la s tic iz e d with 10 Weight P ercen t DMP'.................................................... 71 > • 39. SI Versus P la s tic iz e r C on cen tratio n fo r PS-DMP System. 72 40. Ti Versus P la s tic iz e r C o n cen tratio n fo r PS-DMP System. 73 41. SI Versus S o lu b ility P aram eter PS P la s tic iz e d with 10 Weight P ercen t P la s tic iz e r s ..................................................... 74 v i i A B STR A C T S tre s s R elax atio n Behavior in the Prim ary T ra n sitio n Region. Though th e s tr e s s re la x a tio n m aster curves fo r amorphous polym ers have th e same g en eral shape, they behave d iff e r e n tly in the: prim ary tr a n s itio n re g io n . Two in te r e s tin g cases are P o ly sty ren e (PS) and P o ly iso b u ty len e (PIB) w ith th e ab so lu te values o f maximum n e g a tiv e slop.® in th e prim ary tr a n s itio n re g io n , which we d efin e as stee p n ess in d ex (S I) of 1.6 and 0.6 re s p e c tiv e ly . PS decays one thousand tim es as ra p id ly as PIB. The Rouse-Bueche theory p re d ic ts the behavior of d i l u t e polymer s o lu tio n s and c o n sid e rs only the co-o rd in ated motion along th e m olecular backbone independent o f th e presence o f o ther neighboring ch a in s. The re la x a tio n b eh av io r o f th is one dim ensional l a t t i c e has a SI of 0 .5 . T obolsky's th re e dim ensional damped l a t t i c e re p re se n ta tio n makes th e m olecular m otion more c o -o p erativ e by coupling th e su b -u n it w ith a l l the neighboring su b -u n its around i t , and i t has a SI of 1 .5 . The varying d im en sio n ality of PIB and PS should be a ttr ib u te d to th e d iffe re n c e s in th e n atu re o f th e ir side-group s u b s titu e n ts as they have th e same carbon-carbon backbone. A c o rre la tio n between th e th e o - i r ie s and th e experim ental d ata i s hard to make sin c e th e mechanisms on th e m olecular le v e l re sp o n sib le fo r th e changes in d im e n sio n a lity a re not y e t co n c lu siv e ly ex p lain ed . T h erefo re, i t seems d e s ira b le to have : experim ental d a ta on some more polymers fo r comparison. With th is in mind, we stu d ie d th e s tr e s s re la x a tio n behavior of PVB. Our choice : of PV B was based on th e volume of i t s sid e group. The sid e-g ro u p in v i i l PV B i s tw ice as big asvih,.pS'.v P V B was found to have a SI of 1.4 and T o f 155°C. The previous s tr e s s re la x a tio n study i n th is la b o ra to ry © o f PVCH and P2VN gave S is of 1.31 and 1.32 re s p e c tiv e ly . The volume of sid e-g ro u p s u b s titu e n ts in PV C H and P2VN i s about 20 and 50 percent h ig h e r than th a t in PS. An appreciable in c re a se from 20% to 100% in volume and a ls o q u ite d iffe rn e t stereo ch em istry o f side-groups in PVCH, P2VN and PV B did not have any d r a s tic e f f e c t on th e re la x a tio n b eh av io r o f th e se polymers in the primary t r a n s i t i o n reg io n . The Sis o f th e se polym ers were not g ro ssly d iff e r e n t from PS!' though they have much h ig h e r Tgs. W e a lso s tu d ie d th e e ffe c t of p la s tic iz a tio n on the d im en sio n ality of PS. The p la s t i c i z e r m olecules sep arate th e c h a in s of p aren t polym er, th e re b y , low ering van der W aal's forces a c tin g between th e chains and have no e f fe c t on th e in te rn a l ro ta tio n s o f sm all segm ents. Since th e p l a s t i c i z e r m olecules do not f i t in to th e o r ig in a l l a t t i c e , . p la s tic iz a tio n should r e s u lt in a system o f lower d im e n sio n a lity . However, th e p l a s t i c i z e r m olecules are n o t e x a c tly in e r t and in te r a c t w ith th e ch ain s they se p a ra te . With th is in mind, we have stu d ied th e re la x a ito n behavior of PS p la s tic iz e d w ith d if f e r e n t high b o ilin g p o in t so lv e n ts th a t cover a sm all range on the s o l u b i l i t y param eter s c a le on e ith e r sid e of PS. W e have found th a t when the s o lu b ility param eters o f p la s tic iz e r ; i and PS a re th e same, th e SI is independent of p l a s t i c i z e r c o n te n ts, and th e d e v ia tio n in the value of s o lu b ility param eter o f th e p la s - , I t i c i z e r from th a t of PS re s u lts in lower SI and hence lower dim ension- j : j a l i t y . Our s tr e s s re la x a tio n experim ents on PS p la s tic iz e d w ith i ix I d if f e r e n t so lv en ts of v ario u s e n e rg e tic s e s ta b lis h th e c r e d ib ility of T obolsky's th ree dim ensional damped Debye l a t t i c e re p re s e n ta tio n and show th e im portant ro le played by van d er W aal's fo rces in d e te r mining shape of the prim ary tr a n s itio n re g io n . INTRODUCTION Of th e fiv e reg io n s of v is c o e la s tic behavior of polym eric m ateria ' a l s , the prim ary tr a n s itio n region (g la ss to rubber) is th e le a s t 'w ell understood a t th e m olecular le v e l. Many th e o re tic a l attem p ts have been made to p re d ic t the behavior in the primary tr a n s itio n reg io n from m olecular c o n s id e ra tio n s , but th e p re d ic tio n s of th e se th e o rie s seem to be lim ite d in th e ir a p p lic a tio n s to s p e c ific polym ers. A b a s ic c o n trib u tio n o f th ese th e o r ie s , however, i s th e ir emphasis on c e r ta in m olecular in te ra c tio n s in determ ining th e behavior in t h i s re g io n ; th ese in te ra c tio n s in clu d e in tr a as w ell as in te r m olecular co u p lin g s. One of th e th e o rie s was developed fo r d ilu te polymer s o lu tio n s and co n sid ers only th e in tra m o le c u la r in te ra c tio n s ; i t p re d ic ts a broad g la ss to rubber tra n s ito n compared to another theory which co n sid ers matching c o n trib u tio n s from in tr a and i n t e r m olecular in te r a c tio n s . These th e o rie s a re ex p lain ed in d e ta il in Chapter 2. W e have a lso Previewed p e rtin e n t background necessary fo r the understanding of our work in C hapter 1. The v a r ia tio n s in behavior in th e prim ary tr a n s itio n region fo r polymers w ith th e same carbon-carbon backbone have to be a ttr ib u te d I to the d iffe re n c e s in n a tu re of th e ir side-rgroup s u b s titu e n ts . For th is re a so n , we have stu d ie d th e s tr e s s re la x a tio n behavior o f poly— | :v in y lb ip h e n y l, C hapter 2, to gain in s ig h t in to the dependence o f th e g la ss to rubber tr a n s itio n on th e n a tu re of side-group s u b s titu e n ts . j P olyvinylbiphenyl was chosen because of th e bulkiness o f i t s s id e - i j group. W e assumed th a t th e bulky biphenyl group would a f f e c t in tra s R ^ h 2 chain in te ra c tio n s to a g re a te r ex ten t than the in te rc h a in in te ra c tio n s and th e d iffe re n c e s in in tr a and in te r chain couplings would be r e f le c te d in th e s tr e s s re la x a tio n behavior in the prim ary tr a n s itio n re g io n . W e have compared the behavior of polymers w ith d if f e r e n t sid e -g ro u p s and found th a t the behavior in th e prim ary tr a n s i t i o n re g io n i s not dependent on the siz e of the sid e-g ro u p s. W e have a lso In v e stig a te d the s tr e s s re la x a tio n b eh av io r of p la s tic iz e d amorphous poly sty ren e in order to e v a lu at th e dependence o f re la x a tio n in th is reg io n on m olecular fa c to rs such as i n t r a and i n t e r ch ain in te r a c tio n s . The in tro d u ctio n of p l a s t i c i z e r m olecules in p o ly sty re n e r e s u lts in sep aratio n of the p o ly sty ren e c h a in s; the ch ian se p a ra tio n should a f fe c t only in te rc h a in in te r a c tio n s and le a v e in tra c h a in in te ra c tio n s more or le s s unchanged. I t , acco rd in g to th e o r ie s , should make th e g lass to rubber tr a n s itio n broad compared to th a t of pure p o ly sty ren e which, we f e e l, would be tr u e i f th e p l a s t i c i z e r m olecules were in e r t. In p ra c tic e , p l a s t i c i z e r m olecules i n t e r a c t w ith th e p aren t polymer depending on th e ir e n e r g e tic s . For th is re a so n , we have stu d ied the s tre s s re la x a tio n b eh av io r o f p o ly sty ren e p la s tic iz e d with v ario u s high b o ilin g p o in t so lv e n ts t h a t in te r a c t d if f e r n e tly w ith the polystyrene c h a in s, C hapter 3. W e have made use of s o lu b ility param eter sc a le as a m easure o f i n t e r - m olecular in te ra c tio n s . Our s tre s s re la x a tio n experim ents on p la s tic iz e d p o ly sty ren e stro n g ly suggest an im portant r o le played by van d e r W aal's fo rce s in determ ining behavior in th e prim ary tr a n s itio n re g io n . CHA PTER 1 B A C K G R O U N D "' A. V is c o e la s tic ity S o lid s and liq u id s d if f e r g r e a tly in th e ir m echanical p ro p e rtie s . A p e rfe c tly e l a s ti c s o lid in te n sio n , Figure 1, is defined by Hooke’s law, a = Ey (1) where th e te n s ile s tr e s s a is th e fo rc e per u n it a re a , the s tr a i n y is th e deform ation p er u n it le n g th , and th e co n stan t E is Young’s modulus. One can a lso apply th e s tr e s s in sh e a r, F igure 2. The inform ation ob tain ed in sh ea r can e a s ily be converted to ten sio n by the use of a sim ple r e la tio n s h ip between the te n s ile modulus E and th e sh ear modulus G. The te n s ile modulus E » 3G (2) For m etals the modulus is found ex p erim en tally to be a fu n ctio n of tem perature. An e l a s ti c s o lid s to re s energy when th e e x te rn a l fo rces do work on i t , and th is energy is used to re s to r e i t s o rig in a l shape when th e e x te rn a l fo rces a re removed. An id e a l liq u id is defined by Newton’s law, a - nt (3) where f is th e r a te of s tr a i n and th e c o n sta n t ^,‘ ; i s 't h e Y v is c b s ity y . W e should n o tic e th a t th e s tr e s s on th e id e a l liq u id i s n o t depen dent on th e s tr a in but on th e r a te o f s t r a i n . The id e a l liq u id d is s ip a te s a l l i t s energy and rem ains in i t s deformed s ta t e F ig u re 1 TENSILE ELO N G A TION I 1 A = w idth of the sample B = th ick n ess o f the sample L0 = i n i t i a l len g th of the sample L = f in a l len g th of the sample F = fo rc e on the sample in dynes a F dynes/ 2 = — J cm A B _ L-Lft 5 F igure 2 D EFO RM A TIO N IN SH EA R 4 -A A -> ? = volume of the sample A A = displacem ent in the y d ire c tio n F = fo rce in the y d ire c tio n « = » angle of deform ation ■ y * = ta n 1 1 = F dynes. 0 “ 12 6 a f t e r th e s tr e s s i s removed. There a re many m a te ria ls th a t have in te rm e d ia te m echanical p r o p e rtie s between th o se of the e l a s ti c s o lid and th e id e a l liq u id , and th e m a te ria ls a re known as v is c o e la s tic . P l a s t i c s , among o th e r th in g s , f a l l in th is c la ss o f m a te ria ls . V is c o e la s tic m a te ria ls elo n g ate w ith time under a co n stan t s t r e s s ; m oreover, t h e i r s tr e s s decays w ith time when they are under a c o n stan t s t r a i n . The m echanical p ro p e rtie s of v is c o e la s tic m a te ria ls depend on both tim e and tem p eratu re. A p a rt of th e energy of v is c o e la s tic m a te ria ls i s d is s ip a te d and a p a rt is s to re d . The r e l a t iv e amounts o f th e energy d is s ip a te d and th e energy s to r e d , however, depend on th e tem perature and the experim ental tim e s c a le under c o n s id e ra tio n . B. S tre s s re la x a tio n experim ent. T his ex perim ental technique is based on th e f a c t th a t th e s tr e s s on a v is c o e la s tic sample a t co n stan t s tr a i n decays w ith tim e. The s tr e s s re la x a tio n experim ent in te n s io n , F ig . 1 , i s c a rrie d out by su b je c tin g the sample to an in stan ta n e o u s c o n sta n t s tr a i n and then m easuring th e s tr e s s as a fu n c tio n o f tim e. Thus th e s tr e s s e (T ,t) - y E (T ,t) (4) The modulus (E) i s a fu n ctio n of both tim e (t) and tem perature(T ) . T h e re fo re , th e experim ents are c a rrie d out a t a co n sta n t tem p eratu re, and th e modulus i s observed as a fu n ctio n of tim e. A p lo t of log E (t) vs log t y ie ld s a m aster cu rve. The main reason fo r using the lo g -lo g sc ale i s th a t th e m aster curve covers the mod ulus and tim e over many o rd ers o f m agnitude, and a lin e a r p lo t would miss many s a lie n t fe a tu re s of v is c o e la s tic b eh av io r. The m aster curves fo r amorphous u n c ro ss-lin k e d polymers have th e same g en eral shape.^ The shape fo r th e c r y s ta llin e polymers i s de- pendent on the amount of c r y s t a l l i n i t y . The work in th is th e s is is m ainly concerned w ith th e b eh av io r of amorphous u n cro ss-lin k ed polym ers. The m aster curve fo r an amorphous u n cro ss-lin k ed p o ly sty - O rene sample o f high m olecular w eig h t, F igure 3, has four d is tin c t reg io n s. The g lassy p la te a u has a r e la tiv e ly tim e independent modulus o f about 10^® dynes/cm^. The tr a n s la tio n a l and r o ta tio n a l m olecular motions of th e carbon-carbon backbone a re e s s e n tia lly frozen in th e g lassy s ta t e , and the m a te ria ls a re hard and sometimes b r i t t l e . The lower p la te a u a t about 5 x 10^ dynes/cm^ i s ch arac t e r i s t i c of th e rubbery s ta t e . Rubbers a re a sso c ia te d w ith a long-range d iffu s io n a l m olecular m otion. The samples a re s o ft and can be deformed many tim es th e ir o r ig in a l len g th w ith ease. The len g th of th e rubbery p la te a u i s m olecular w eight dependent, and th e> p lateau vanishes below a c r i t i c a l m olecular w eig h t, where th e m olecules do not have s tre s s -s u p p o rtin g entaglem ents. The secondary tr a n s itio n (E < 5 x 106 d^ - f 8) is ch arac t e r i s t i c of liq u id lik e b e h a v io r, where th e m olecules move p a st one an o th er. C ross-linked polymers do n o t show the secondary L og t sec. 8 Figure 3 STRESS RELAXATION M ASTER C U R V E FO R POLYSTYRENE Log E(t) dynes/cm . 2 ^ CJI 0 9 * * « J OO CO ■ ro a* CJI 0 9 oa 0 9 t r a n s i t i o n , as the m olecules are prevented from flow by th e in te r-m o le c u la r c r o s s - lin k s , and they have rubbery p la te a u extending to i n f i n i t e tim e. The shape of th e flow re g io n , however, i s sen s i t i v e to th e m olecular w eight d is tr ib u tio n of th e sam ple, and p o ly d isp e rse m a te ria ls have a broad secondary tr a n s itio n . The g la ss to ru b b er tr a n s i t i o n , whibh is also known as th e prim ary t r a n s i t i o n , occurs w ith a d ecrease in modulus o f th re e o rd ers 10 2 7 2 of m agnitude form 10 dynes/cm to 10 dynes/cm ; a m ajor p a rt of th e s to re d energy is d is s ip a te d as th e sample goes through th e prim ary t r a n s itio n . The behavior in th e prim ary t r a n s itio n reg io n w ill be d iscu ssed in d e t a i l in Chapter 2. The e n tir e m aster curve is u su a lly covered in about tw elve decades of tim e s c a le . The experim ental lim ita tio n s , however, 3 allow one to m easure s tr e s s e s in the time range of 10 to 2 X 10 seconds. T h e re fo re , the complete m aster curve is co n stru cted 4 by u sin g th e tim e-tem p eratu re su p e rp o sitio n p r in c ip le . The su p e rp o s itio n p r in c ip le s ta te th a t th e e f fe c t of tem perature on a v is c o e la s tic p ro p e rty i s to s h i f t i t along th e tim e s c a le . Thus, E [T ,t] = E [Tx, a(T )tJ (5) where a(T) i s a c o n sta n t and i t depends only on the d iffe re n c e in te m p e ra tu re s, T -T j. The m aster curve a t a tem perature T^ can be reduced to a new tem p eratu re T by m erely applying a s h i f t f a c to r a(T) along th e tim e s c a le . So th e experim ents are c a r rie d out a t d if f e r e n t c o n sta n t tem peratures to give v ario u s p o rtio n s of th e m aster curve. They a re reduced to a common tem perature by 1° keeping the p o rtio n of th e m aster curve a t th a t tem perature fix e d and,-moving the r e s t o f the p o rtio n s along the tim e a x is u n t i l they a re superposed to g iv e one curve. M oreover, C £ a v e r t ic a l s h i f t is suggested » to tak e in to account th e changes in d e n sity w ith tem p eratu re, but a t about room tem perature? the v e r t ic a l s h if t s a re w ith in the experim ental e r ro r . The a p p lic a tio n of s tr a in always re q u ire s a f i n i t e time and is never in sta n ta n e o u s. The f a c to r - o f - te n ru le h e lp s to m inim ize th e e f f e c ts of f i n i t e s tr a i n tim e on th e sh o rt-tim e modulus. This ru le allow s one to m easure th e s tr e s s e s a t tim es g r e a te r than th e s tr a i n tim e by a f a c to r of' te n . The f a s t a p p lic a tio n o f s tr a i n to a sample w ith modulus c lo se to th e g la ssy p la te a u sometimes r e s u lts in a fra c tu re or slip p a g e from th e clamps. So in th is d i f f i c u l t reg io n a slow co n sta n t s t r a i n - r a t e , suggested by K elchner? e t a l . , could be follow ed by a co n sta n t s tr a i n p e rio d . C. G lass tr a n s itio n tem perature Tg. W e have seen in the previous se c tio n s th a t th e modulus o f a v is c o e la s tic m a te ria l is a fu n c tio n of both tim e and tem p e ra tu re . T h erefo re, th e dependence o f th e modulus on tem perature., can be measured by keeping th e tim e c o n sta n t, say a t 10 seconds. The dependence o f modulus on tem perature,® F igure 4 , has the same g en eral shape as the p lo t of log E (t) vs log t a t co n stan t tem p eratu re. I t has th e glassy re g io n a t th e modulus of about 11 Figure 4 TEM PER A TU R E DEPENDENCE OF A M O R P H O U S PO LY STY REN E AT 10 SECO N D S Log E(t) dynes/cm ? CO cn 09 ro — H O n cn ISI 12 10 2 6 2 10 dynes/cm and th e ru bbery p lateau a t about 5 x 10 dynes/cm . The g lass to rubber t r a n s i t i o n occurs over a tem perature range. The g lass tr a n s itio n re g io n in log E(T) vs T measurem ents, however, 9 depends on th e tim e s c a le o f th e experim ent, and a change in the experim ental tim e r e s u lts in a s h if tin g of the e n tir e curve along the tem perature a x is . A good way to m easure th e Tg of a m a te ria l is to study i t s s p e c ific volume as a fu n c tio n of te m p e ra tu re ^ , Figure 5, and observe the tem p eratu re where a bend in th e p lo t occu rs. The tem perature a t th e bend i s th e Tg of th e m a te ria l. The Tg is found to be dependent on th e r a te of cooling o r h e a t i n g .^ The bend is in d ic a tiv e o f th e f a c t th a t th e therm al expansion c o e ffic ie n t of the sample has d if f e r e n t v alu es below and above. the g la ss tra n s itio n tem perature. In th e high tem perature range th e therm al expansion c o e f fic ie n ts a re c h a r a c te r is tic of rubbers and below Tg th a t of g la s s e s . The d iffe re n c e s in th e therm al expansion c o e ffic ie n t are a s s o c ia te d w ith th e v a rio u s amounts of fre e volume present in the g la ssy and rubbery s ta t e s . The amount of fre e volume in a polymer sample i s th e d iffe re n c e between i t s a c tu a l 12 volume and the volume of th e s o lid ly packed polymer m olecules. 13 F erry , Landel, and W illiam s have shown th a t the fn a c tio n a l fre e volume a t the Tg f o r a l l amorphous polymers i s 0.025. T herefore, the Tg fo r amorphous polym ers is a s ta t e o f is o - f r e e volume. The tra n s la tio n a l and r o ta ti o n a l motion o f th e carbon-carbon backbone in the glassy s t a t e i s e s s e n tia lly fro z e n , because the p o te n tia l 13 Figure 5 SPECIFIC V O L U M E A S A FUNCTION OF TEM PER A TU R E 106 105 1 0 4 “ a co 103 102 101 100 20 0 40 60 80 120 b a r r ie r s fo r th e motion are high compared to th e therm al energy. The g en eratio n o f fre e volume a t th e Tg allow s th e m olecules to have long-range d iffu s io n a l m otion. The Tg i s dependent on th e s tr u c tu r e , e n e rg e tic s , and m olecular w eight of th e m a te ria l. ^ Pdlymers w ith s t i f f bulky sid e -g ro u p s, as opposed to long f le x ib le s id e -c h a in s , tend to have high v alu es of Tg. The p o lar polymers have high g la s s tr a n s itio n tem p eratu res. High b a r r ie r s to in te rn a l r o ta tio n make th e chains s t i f f , and th e s t i f f chains have high valu es o f Tg. The Tg in c re a se s w ith th e m olecular w eight u n t i l i t reach es some c r i t i c a l m olecular w eight, and above th is m olecular w eight th e Tg rem ains f a i r l y c o n sta n t. C H A PTE'R -2 STRESS RELAXATION BEHAVIOR IN TH E PRIM A RY TRANSITION REGION A. Maximum negative s lo p e s . Though th e s tr e s s re la x a tio n m aster curves f o r amorphous polym ers have th e same g en eral shape, they behave d if f e r e n tly in th e prim ary tr a n s itio n reg io n . The measurements of maximum n e g a tiv e s lo p e s in the tra n s ito n reg io n a ffo rd a way to compare the r a p id ity o f th e ir re la x a tio n b eh av io r. For t h i s re a so n , we have d efin ed S teepness Index (SI) as th e a b so lu te v alu e of th e maximum n e g ativ e slo p e in the prim ary tr a n s itio n re g io n . Two in te r e s tin g cases are p o ly s ty re n e ^ (ps) and polyisbbutyl'erie^C PIB ) w ith th e S is o f 1.6 and 0.6 re s p e c tiv e ly , F igure 6. The two m aster curves a re a r b i t r a r i l y s h ifte d along th e tim e ax is f o r com parison., PS decays alm ost one thousand tim es as ra p id ly as PIB. Many th e o r e tic a l attem p ts have been made to p re d ic t th e s t r e s s re la x a tio n b ehavior of polymers from m olecular co n sid eratio n s and w ill be d iscu ssed in th e next se c tio n . In th is ch ap ter we w i l l an aly se th e e f fe c t o f volume and s tru c tu re o f th e rin g sid e -g ro u p s on th e SI. B. T h e o retic a l background. The v is c o e la s tic behavior so f a r seen i s p u rely phenomenologi c a l, and i t would be in te re s tin g to know some m echanical model whose b eh av io r resem bles v is c o e la s tic p u o cessesi The Maxwell 16 Figure 6 M A STER C U R V ES FOR POLYSTYRENE A N D POLYISOBUTELENE Log E ft) dynes cm? r “ e <a OB ro w 17 17 18 elem ent, * fig u r e 7 , d e sc rib e s th e s tr e s s re la x a tio n b eh av io r of v is c o e la s tic m a te ria ls . I t c o n s is ta of an id e a l sp rin g w ith a sp rin g c o n sta n t Eo connected to a dashpot which has a p is to n immersed in a v isco u s f lu id of v is c o s ity p. The Maxwell body under a co n stan t s tr a in y s to re s a l l th e energy in th e sp rin g a t sh o rt tim es and then d is s ip a te s i t as th e m otion o f th e dashpot r e le a s e s th e sp rin g . The s tr e s s a t tim e t f o r a Maxwell body -tE n a ( t) = aQ e (6) where aQ is th e s tr e s s a t zero tim e and term is defined as th e re la x a tio n tim e T. D ividing both sid e s of eq u atio n 6 by th e s tr a i n y and re w ritin g we have -fc_ E ( t) = E0 e T (7) The m aster curve fo r th e Maxwell elem ent shows only one tr a n s itio n re g io n a t tim e T, and i t can be made to have two tr a n s itio n s lik e any h ig h m olecular w eight v is c o e la s tic m a te ria l by coupling two Maxwell elem ents in p a r a lle l w ith T^ « T2 and E^ « 1 & 2 ' This s e t o f elem ents has two p la te a u s a t m oduli! E^ and E2 and two tr a n s itio n s a t tim es T^ and T2 * So th e modulus a t tim e t - t E ( t) - Ex d T l + E2 e T2 ( For ji Maxwell elem ents in p a r a l l e l , we have -t_ n Ti E (t) - E Ei e (9) i - 1 18 Figure 7 a. Maxwell Element b. R-B One Dim ensional R epresentation c. T ob o lsk y 's Three Dimensional Model 19 The slo p e of th e m aster curve fo r a Maxwell elem ent - 41-g g M t) = . - t (1 0 ) d lo g t T - ' The slo p e , th e re fo re , Is dependent on tim e and goes to i n f i n i t y a t i n f i n i t e tim e. M oreover, th e Maxwell elem ent does no t ex p lian v is c o e la s tic behavior on the m olecular le v e l. Rouse-^ and Bueche^® independently in tro d u ced a m olecular th eo ry to e x p la in th e behavior of d ilu te polymer s o lu tio n s . In R-B th eo ry , a lin e a r polymer m olecule i s d iv id ed in to 2 su b -u n its long enough to have th e ir end-end d ista n c e s G au ssian .21 The sub-m olecules a c t as Hookean sp rin g s w ith th e fo rce f«': - k0x ( i i ) where K0 is th e sp rin g co n stan t and, from th e th eo ry of rubber 3KT & e l a s t i c i t y ,22 i s equal to ~ 2 . & 2 is th e ro o t mean square end-end d is ta n c e ^ of the sub-m olecule. X is th e displacem ent from th e e q u ilib riu m end-end d istan ce; k i s th e Boltzman c o n sta n t. The th e o r e tic a l approach is f u rth e r s im p lifie d by re p re se n tin g th e sub-m olecules in the form o f beads, and th e e n tir e m olecule i s d e sc rib e d , F igure 7, by th e Z beads jo in e d - to g e th e r in a lin e a r fa sh io n by Z -l e n tro p ic s p rin g s. The e n tir e a rra y o f beads and sp rin g s is immersed in a v isco u s f lu id . Only th e response along th e m olecular a x is i s co n sid ered , and th e s tr e s s e s a c tin g perpen d ic u la r to th is a x is are assumed to have no e f f e c t on th e m otion of th e m olecule. T h erefo re, th e non-viscous fo rc e on th e i t h bead 20 f i = -3KT0 + 2X± - X± -]) (12) R2 til where X .^ is the displacem ent o f th e i bend from i t s eq u ilib riu m th p o s itio n . The v isco u s drag on th e i bead. f i = p *1 (13) where p is the f r i c t i o n f a c to r of th e bead moving through th e so lu tio n w ith v e lo c ity x ^. When th e a c c e le ra tio n o f thebead i s n e g lig ib le , the v isc o u s and e l a s t i c fo rces must b alan ce. Thus, -3KT p Xi = ft2 (~Xi+ l + 2Xi " Xi+1) (14) Every m olecule has i t s c h a r a c te r is tic normal modes o f m otion, which are a sso c ia te d w ith corresponding re la x a tio n tim es. til The so lu tio n of eq u atio n 14 gives the re la x a tio n tim e of P normal mode p a2 Z2 P 6 1 1 Z K T P2 (15) where P = 1 ,2 ,3 ,-------- , Z. T h erefo re, the s tr e s s r e la x a tio n modulus a t tim e t - t Z T E ( t) = E 3NKT e P (16) P=1 and fo r continous d is tr ib u tio n o f re la x a tio n tim es, we have z ' I E ( t) = / 3N K T e p dP. (17) 1 S u b stitu tio n of Tp from eq u atio n 15 and on in te g r a tio n , we find E ( t ) = - ~ | - l / 2 [n T ^ ] / (18) where Tmax is th e maximum re la x a tio n tim e corresponding to p= l. The slo p e of th e R-B m aster curve fr S fr ^ - -i < 1 9 > d log t Thus th e R-B theory d e sc rib e s th e behavior of p o ly iso b u t- y ieh i» h u t i t does n o t ex p lain th e d iffe re n c e s in slo p e fo r o th e r polym ers. High polymers have two tr a n s itio n regions where as R-B th eo ry p re d ic ts only one tr a n s ito n . Since th e R-B theory is d erived fo r d ilu te polymer s o lu tio n s , i t com pletely n e g le c ts the e f f e c t of m olecular entanglements on v is c o e la s tic b ehavior. F e rry , L andel, and W i l l i a m s ^ have m odified th e R-B th eo ry f o r a p p lic a tio n to u n d ilu ted high polym ers, where a polymer m olecule i s surrounded by o th e r m olecules o f i t s own kind. The R-B th eo ry is e s s e n tia lly unm odified fo r low m olecular w eight polym ers, and an o th er h ig h e r f r i c t i o n fa c to r is in tro d u ced , fo r polymers w ith m olecular w eight s u f f ic ie n tly high to have in term o lecu lar en tan g lem en ts, to d e sc rib e th e re la x a tio n tim es in th e flow re g io n . The index jP i s s a id to have a c r i t i c a l value Pe , and th e m olecular motion i s assumed to in v o lv e entanglem ents below Pe and be u n a ffec te d by the entanglem ents above Pe. Thus th e re la x a tio n tim es tp - s y f c l - ■ p > pe (2o) tp - (21) where th e f r i c t i o n fa c to r >> P. 22 In summary, th e F L W m o d ificatio n d e sc rib e s in g e n e ra l th e v is c o e la s tic b eh av io r of u n d ilu ted high polym ers. The R-B tr a n s itio n becomes g la ss to rubber tr a n s itio n in F L W m o d ific a tio n . I t p re d ic ts th e slo p e of - | in th e prim ary tra n s itio n re g io n , but i t does not e x p la in th e d iffe re n c e s in slo p e fo r o th er polym ers. The R-B th eo ry re p re s e n ts a polymer m olecule by a one dimen- 25 s io n a l a rra y of beads and sp rin g s. Tobolsky used a th re e dimen s io n a l a rra y of beads and sp rin g s immersed in a v isco u s f l u i d , F ig u re 7, and found a ste e p e r d is tr ib u tio n of re la x a tio n tim es. The tim e dependent modulus T E (t) - / E(T) e T dT (22) ^min and can be w r itte n as Tmax = i T E(T) e T din T (23) •M nin T — t ■ tmax — T 1 H(T) e T dlnT (24) min H(T) = T E(T) (25) where H(T) is th e d is tr ib u tio n of re la x a tio n tim es. The R-B th eo ry p re d ic ts 1 H(T) - a i T " 2 (26) where a^ is a c o n sta n t. 23 With every normal mode of motion is a s so c ia te d a c h a ra c te ris t i c frequency of v ib ra tio n and corresponding re la x a tio n tim e. The n a tu re o f d is tr ib u tio n o f freq u en cies is th e same as th a t of re la x a tio n tim es. Tobolsky has used the c la s s ic a l d is tr ib u tio n of freq u en cies fo r a th re e dim ensional Debye l a t t i c e ^ and found th e d is tr ib u tio n o f re la x a tio n tim es H(T) - a2 T (27) where a£ is a co n sta n t. Thus th e d is tr ib u tio n o f re la x a tio n tim es fo r a th re e dim ensional damped Debye l a t t i c e , e q u atio n 27, is much s te e p e r than th a t fo r a one dim ensional damped l a t t i c e , eq u atio n 26. Combining eq u atio n 27 and 24, we fin d th a t th e modulus E( t ) = _ _ 2_ _ . (28) ^ Train where EQ is th e modulus a t zero tim e, and Tm £n is th e minimum re la x a tio n tim e corresponding to a value o f P eq u al to Z. The slo p e of the m aster curve from e q u atio n 28 d lo g E (t) _ ^ foo\ d log t " 2 K Thus th e th re e dim ensional damped Debye l a t t i c e gives a SI of 1 .5 , which has been found fo r amorphous p o ly sty re n e . A com parision of R-B and Tobolsky models should give us in s ig h t as to th e n a tu re of m olecular mechansims re sp o n sib le fo r th e v a r ia tio n o f slo p e. What we u n d erstan d 'fro m th e se models i s th a t th e r a p id ity o f re la x a tio n depends on th e d im en sio n ality of th e l a t t i c e . The h ig h er th e d im e n sio n a lity , th e f a s te r is the re la x a - | tio n , which means th a t th e re la x a tio n p ro cesses become more and more c o -o p erativ e w ith in c re a sin g d im e n sio n a lity . The su b -u n its are not only coupled w ith th e ir n e a re s t neighbors on th e same chain but also w ith th e o th e r neighboring s u b -u n its . The in term o lecu lar fo rc e s provide the coupling between the s u b -u n its . The re la x a tio n behavior o f PIB and PS in th e prim ary tr a n s itio n ' reg io n are d escrib ed by th e R-B th eo ry and motion of th ree dim ensional : damped Debye l a t t i c e o f Tobolsky re s p e c tiv e ly . The d iffe re n c e s in th e : behavior o f PS and PIB, one could say , r e s u l t from the d is s im ila r itie s in n atu re o f t h e i r sid e-g ro u p s as they have th e same carbon-carbon : f backbone. The in te ra c tio n s o f th e sid e-g ro u p s w ith in the chain and w ith o ther chains provide i n t r a and i n t e r m olecular couplings resp ec tiv e ly . When th e in tr a and i n t e r sp rin g co n sta n ts are matched as in Tobolskyfs model, the m a te ria l behaves lik e a th re e dim ensional l a t t i c e . PS may be a case where th e i n t r a and in te r sp rin g co n stan ts a re m atched; g iv in g i t s re la x a tio n b eh av io r a th re e dim ensional ch a ra c te r. PIB, on th e o th er hand, may have h ig h e r i n t r a sp rin g co n stan ts than in te r i sp rin g c o n s ta n ts , and in t h i s case what we see may be the response due j to in tra m o lec u lar in te r a c tio n s . i W e have in v e s tig a te d th e re la x a tio n behavior of polyvinylbiphenyl j w ith th e assum ption th a t th e bulky b ip h en y l goup would make i n t r a - i m olecular sp rin g s s t i f f e r , th u s somehow d istu rb in g the balance between j i :th e in tr a and i n t e r sp rin g c o n s ta n ts . The unmatched springs would g ive j | i t a V - lower d im e n sio n ality and in tu rn broader primary tr a n s itio n j region than observed fo r PS . W e a re a lso going to compare o u r o b ser v a tio n s w ith th e d a ta a v a ila b le in l i t e r a t u r e on o th e r polym ers. C. E xperim ental The s tr e s s re la x a tio n experim ents are c a rrie d out on a ta b le model In s tro n w ith a fix e d upper cross-beam and a movable low er beam. Two clamps are extended from th e se beams by means of Invar ro d s , and a sample o f approxim ate s iz e 6 cm x 0 .5 cm x 0.3 cm is secu red between th e clam ps and elo n g ated in a s tr e s s re la x a tio n experim ent by moving down th e lower beam. The upper clamp is connected to a load c e l l su p p o rted on th e fix ed beam. The load c e l l , in tu r n , tra n sm its th e fo rc e on th e sample to a s t r i p ch art pen re c o rd e r, and the fo rc e i s recorded as a fu n ctio n of tim e fo r h a lf an h o u r. The re c o rd e r has .a range o f one gram to ten kilogram s. The w idth and b read th o f th e sample are measured a c c u ra te ly up to a thousandth of a c en tim e te r w ith a m icrom eter, an d :th e len g th between th e clamps is measured w ith a cathotom eter w ith an accuracy of + 0.0005 cm. A sh o rt w orking d ista n c e cathom eter w ith an accuracy of + 0.001 cm is used to m easure th e change in len g th of the sample upon d efo rm atio n , which is u s u a lly clo se to one p ercen t o f th e i n i t i a l le n g th . E xtensions of about 3 % of th e i n i t i a l len g th in the reg io n c lo s e to rubbery p la te a u (E clo se to 10^ dynes/cm^) enable a c c u ra te measurements o f fo rc e on th e sam ples. The modulus, p a r tic u la r ly in th e prim ary tr a n s itio n re g io n , i s stro n g ly tem perature dependent and, th e r e fo r e , a double-chamber f o rc e d - a ir asbestos oven i s used to keep th e exp erim en tal tem perature co n stan t w ith in + 0.02° K. The o u te r chamber i s m aintained a t a fix e d tem perature about 70°K below th e ex p erim en tal tem perature by means of a co n stan t tem perature w ater b a th , and i t elim in ates th e e f f e c t of flu c tu a tio n s in the room tem p eratu re. The oven is h eated by using two riichrome w ire p o rc e la in cones made by Eagle E le c tr ic . One of the cones i s c o n tro lle d by a v a ria c and a c ts as a co n sta n t h eat so u rce, and the o th e r cone i s a c tiv a te d by an Aminco s u p e rs e n sitiv e re la y and is used as a fin e tem p eratu re c o n tro l. The flu c tu a tio n s in tem perature in s id e th e oven a re minimized by using a fan to c ir c u la te the a ir . A fte r th e sample is secured between th e clam ps, th e oven i s heated to a tem perature about 20°K above th e g la s s tr a n s itio n tem perature of th e sample. The therm al expansion of the sample w h ile h e a tin g is compensated by slow ly moving down th e lower beam to avoid buckling of th e sample. Then th e sample is allow ed to re la x fo r about h a lf an hour a t t h i s co n sta n t e le v a te d tem perature and slow ly cooled to a d e sire d tem perature in about th re e hours. The sample is m aintained a t th is tem p eratu re f o r one hour to allow i t to have an e q u ilib riu m volume and then elo n g ated about a p ercen t of th e i n i t i a l len g th by moving th e low er beam downward a t a high speed. The te n s ib le s tr e s s r e la x a tio n experim ent i s c a rrie d out as d escrib ed in ch ap ter 1. 27 D. R esu lts and d is c u s s io n . The R-B th eo ry p re d ic ts th e b eh av io r of d ilu te d polymers and, th e re fo re , i t co n sid e rs only th e c o -o rd in ated m otion along th e m olecular backbone independent o f the presence of o th er neighboring ch ain s. The re la x a tio n b eh av io r o f th is one dim ensional l a t t i c e has a steepness index o f 0 .5 , which has been observed fo r p o ly iso bu ty len e (PIB ). T obolsky's th re e dim ensional damped l a t t i c e r e p re se n ta tio n makes th e m olecular motion more co -o p erativ e by coupling a su b -u n it w ith a l l th e neighboring u n its around i t , and i t has a steep n ess index o f 1 .5 which corresponds to th e re la x a tio n behavior of p o ly sty ren e (PS) in th e prim ary tr a n s itio n reg io n . The varying d im e n sio n a litie s o f PIB and PS should be a ttrib u te d to th e d iffe re n c e s in th e n a tu re of th e ir sid e groups as they have the same carbon-carbon backbone. K e l c h n e r ^ ? stu d ie d the re la x a tio n behavior of hydrogenated PS and observed a SI of 1.31 fo r polyvinylcyclohexane (PVCH), which is not g ro ssly d if f e r e n t from th e SI of 1.6 fo r PS. I t was concluded th a t the re la x a tio n behavior of PS through th e prim ary tr a n s itio n was not stro n g ly O Q dependent on any II— II in te ra c tio n s th a t might e x is t. Fugimoto, e t a l . , observed th e SI o f 0.9 fo r poly -« -m eth y lsty ren e (P*MS). An I n te re s tin g f a c t to n o tic e h e re " is th a t th e re la x a tio n behavior in the prim ary tr a n s itio n re g io n is changed d r a s tic a lly by sub s ti t u t i o n of a m ethyl group in an alpha p o s itio n w ith th e phenyl rin g . A c o rre la tio n between th e th e o rie s and experim ental d a ta is hard to make sin c e th e mechanisms on the m olecular le v e l re sp o n sib le fo r th e changes in th e d im en sio n ality are n o t y e t c o n c lu siv e ly ex p lain ed . T h erefo re, i t seems d e s ira b le to have ex p erim en tal d a ta on some more polymers fo r comparison. With th is in mind, we have s tu d ie d th e re la x a tio n behavior of p o ly v in y lb ip h en y l (PVB) and p o ly -2 -v in y ln a p h th alen e (P2VN). Our choice o f th e se polymers is based on th e ir volume and s tr u c tu r a l' d iffe re n c e s from th a t of PS. The m o lecu lar volume o f th e s id e groups is obtained from liq u id 29 d e n sity m easurem ents. Approx. r e la tiv e volume compared to benzene Benzene 1 Cyclohexane 1 .2 N aphthalene 1 .5 Biphenyl 2 .0 A sample of PVB (m olecular weight M n = 3.0 x 10^, M w = 4.9 x 105) was made a v a ila b le by Dr. J . Moacanin of th e J e t P ro p u lsio n L aboratory in Pasadena, C a lifo rn ia . The s tr e s s r e la x a tio n m aster curve fo r PVB, F igure 8, has a SI of 1 .4 , and PV B has a g la s s t r a n s i t i o n tem p eratu re of about 155°C. Kelchner^® s tu d ie d th e re la x a tio n behavior of P2VN and observed a SI o f 1 .3 2 . In Figure 9 , th e SI i s p lo tte d a g a in s t the g lass tra n s ito n tem p eratu re fo r PIB, PS, P=MS, PVCH, P2VN, and PVB. An a p p re c ia b le in c re a se from 20% to 100% in volume and a ls o q u ite d if f e r e n t stereo ch em istry of sid e groups in PVCH, P2VN, CH- C — C H i- C H < PIB n A — C H — CH2- PS CH CHz ch2 I — CH — CH. PVCH —>n P 2VN —>n Logt min. 30 Figure 8 STRESS RELAXATION M A STER C U R V E FO R PV B Log E|t| dynes cm? CO C O C O C O C O CO H CO 1-5 10 C/3 o\ < U n a 0 0 • H P C 4 0*5 x PIB - 5 0 PVB PVCHx x K¥un P2VN x PeCMS L and PVB do n o t have any d r a s tic e f f e c t on th e re la x a tio n behavior o f th e se polymers in th e prim ary tr a n s itio n re g io n . The SI o f th e se polymers a re not g ro ssly d iff e r e n t from p o ly sty ren e ' though they have much hig h er g la ss tr a n s itio n tem p eratu res than PS. The m ajor d e v ia tio n in the re la x a tio n b eh av io r o f P«M S from PS can n o t be explained a t th is sta g e . CHAPTER 3 EFFECT OF PLASTICIZATION O N T H E DIMENSIONALITY OF PO LY STY REN E A. P lasticization^-*- The p la s tic s in d u stry uses enormous amounts of p la s tic iz e r s to make s o f t and p lia b le p roducts from hard and b r i t t l e r e s in s . A p l a s t i c i z e r reduces the m elt v is c o s ity of th e r e s in and, th e re fo re , makes m olding p o s s ib le a t lower tem p eratu res. The p la s tic iz e d re s in s have high impact stre n g th down to low tem p eratu res. P la s tic iz a tio n can be achieved in te r n a lly or e x te rn a lly . A r e s in is in te r n a lly p la s tic iz e d by randomly co-polym erizing i t w ith another r e s in w ith lower Tg. The co-polym er has an in te rm e d ia te Tg between th a t of th e r e s in and th e p la s tic iz e r re s in . Polym eric m a te ria ls are e x te rn a lly p la s tic iz e d by blending them w ith high b o ilin g p o in t so lv e n ts . Low v is c o s ity of the so lv en t lowers th e Tg of the b len d . W e w i l l be concerned only w ith th e e x te rn a l p la s tic iz a tio n . The p la s t i c i z e r m olecules when blended w ith a polymer se p a ra te th e polymer chains and, th e re fo re , low er th e van der W aal's a t t r a c t iv e fo rc e s actin g 'b etw e en th e ch ain s. This is m an ifested in in crea se d m o b ility of th e ch ain , which is r e f le c te d in lower g la ss tr a n s itio n tem perature o f th e b len d . When th e in te r-m o le c u la r fo rc es between solv en t m olecules and.polymer chains a re com parable, a homogeneous blend i s formed; g re a t d iffe re n c e s in th e se fo rc e s r e s u lt in two phase system s. There are many ways to measure 33 34 th e degree of co m p atib ility , of s o lv e n ts w ith a polymer. The compa t i b i l i t y s c a le of in te r e s t to us i s known as th e s o lu b ility param eter index. The concept o f a s o lu b ility param eter was f i r s t introduced by H ild e b ra n d .^ He s ta te s th a t A H m = V m 0X 02 [ ( ) 1/2 - ( ) 1/2 3 (30) where A H m is th e o v e ra ll h eat o f m ixing, V m i s th e t o t a l volume of th e m ix tu re, A E i s th e m olar energy o f v a p o riz a tio n o f component 1 or 2 , V is the molar volume o f 1 o r 2 , and 0 is the volume fra c tio n AE o f 1 or 2 in the-'m ixture. The q u a n tity — ^ is th e energy of v ap o rir z a tio n per u n it volume and is d e scrib ed as th e cohesive energy d en sity A E 1/2 The ex p ressio n ( — ) i s d efin ed as th e s o lu b ility param eter 57 0 Equation 30, th e re fo re , can be r e w ritte n as A H m = Vm u0jL02 (S i-1^ ) 2 Since the process of m ixing of th e polymer w ith a solvent always r e s u lts in an in creased en tro p y , th e m agnitude and sign o f th e A H term are the decid in g f a c to rs in determ ining the q u a lity of th e s o lv e n t. In the d e riv a tio n of e q u atio n 31, no account was > 'K taken of any s p e c ific in te ra c tio n s .. -It was assumed to approximate th e mixing behavior of amorphous polym ers. T h erefo re, th e Hildebrand eq u atio n only accounts fo r zero o r p o s itiv e h e a t o f mixing fo r a polym er-solvent system . When th e s o lu b i l i t y param eters of the polymer and so lv en t have the same v a lu e s , th e h e a t of mixing i s z e ro , and th e mixing is assured by th e e n tro p ic f a c to r . The 35 d iffe re n c e s in the v alu es of s o lu b ility param eter, however, r e s u l t in a p o s itiv e h e a t of mixing and hence poor q u a lity o f th e so lv e n t. So tha s e le c tio n of a so lv e n t fo r an amorphous polymer should be based on s im ila r ity o f t h e ir s o lu b ility param eters. The s o lu b i l i t y p ara m eter of a poor so lv e n t u su a lly d if f e r s in m agnitude from th a t of the polymer by two u n its o r more. The s o lu b i l i t y param eter of a so lv en t may be ob tain ed 33 by one o f th e fo llo w in g methods : . 1) h eat of v a p o riz a tio n ; 2) c o e f f ic ie n t of therm al expansion and c o m p re s s ib ility ; 3) r e l a tio n sh ip betw een p re ssu re and tem perature; 4) van d er W aal’s gas c o n sta n t; 5) c r i t i c a l p re ssu re ; 6) su rfac e te n s io n . The s o lu b ility param eter fo r a polymer is determ ined by sw ellin g l ig h tly c ro ss-lin k e d polymer sam ples in v ario u s so lv en ts w ith d if f e r e n t s o lu b ility p aram eters. The so lv e n t which gives maximum sw e llin g i s assumed to have th e same s o lu b ility param eter as th e polym er. The s o lu b ility param eters fo r many polymers and so lv en ts are l i s t e d in th e 33,34,35 l i t e r a t u r e . PS has a SI of 1.6 c lo se to 1.5 p re d ic te d fo r th e m otion o f a th re e dim ensional damped Debye l a t t i c e o f Tobolsky, Some of th e sp rin g s in th e th re e dim ensional re p re s e n ta tio n are ijl^ ra ia n d .'th e .re s t i n t e r m o lecu lar in te r a c tio n s . The in tr a m olecular coupling i s provided by th e b a r r i e r to r o ta tio n of a few segments o f th e b a c k b o n e ^ '* ^ w hile th e in te rm o le c u la r coupling is van der Waal’s in n a tu re . Tobolsky and Chapoy assumed th a t th e in tro d u c tio n o f a p la s t i c i z e r in PS would only a f f e c t th e in term o lecu lar in te ra c tio n s le a v ih g 36 in tra m o le cu la r in te ra c tio n s unchanged. They p la s tic iz e d PS w ith d io - c ty lp h th a la te (DOP) and d im eth y lp h th alate (DM P) and found th a t the SI decreased w ith in c re a sin g c o n c e n tra tio n of D O P and DM P. T heir con clu sio n of PS as an example o f a th re e dim ensional l a t t i c e was based on the f a c t th a t p l a s tic iz e r m olecules sep arated the PS chains making i t a le s s coupled system . The s e p a ra tio n o f ch a in s, th e argued, lowered th e d im en sio n ality o f th e system and hence th e S I. This would be tru e i f th e p la s tic iz e r m olecules were i n e r t. The p la s t i c i z e r m olecules in r e a l i t y in te r a c t w ith th e chains they sep arate and th e ir degree of in te r a c tio n , we f e e l , should be seen in the ex ten t th e p la s tic iz e r s low er th e S I. For th is reaso n , we have stu d ied the re la x a tio n b ehavior of PS p la s tic iz e d w ith so lv en ts o f d iff e r e n t e n e rg e tic s . W e have used th e s o lu b ility param eter s c a le as a measure o f in term o lecu lar in te ra c tio n s . W e r e a liz e th a t the s o lu b ility param eter i s not an exact measurement o f m olecular in te ra c tio n s and our use of i t as a r e la tiv e s c a le has been q u ite ^ s a tis fa c to r y . B. Experim ental P la s tic iz e d p o ly sty ren e sam ples were prepared using d iff e r e n t p l a s tic iz e r s as obtained from th e s u p p lie r: d ie th y lp h th a la te , U.S. I n d u s tr ia l Chem icals, I n c ., N .Y ., N .Y .: d io c ty l p h th a la te , M atheson, Coleman and B e ll, E ast R u th erfo rd , N .J .; diphenyl methane, Matheson, Coleman and B e ll, E ast Rufcherford, N .J .; d io c ty l se b a c a te , |C ity Chemical C o rp ., N .Y ., N.Y. Also a sample of p o ly sty ren e (m. w t. 600, Mw/M n = 1 .1 ) from the P ressu re Chemical C o rp ., P i t t s b u rg , P a ., was used as a p la s tic iz e r . A p o ly sty re n e sample (M n * * l-.l x 10^, M w * » 2.74 x 10-*) was obtained from th e Koppers Company, I n c ., M onroeville, Pa. I t was f i r s t p r e c ip ita te d from a 2 % by weight p o ly sty ren e s o lu tio n in : chloroform in a te n -fo ld excess o f methanSl and was then d rie d a t 160°C fo r a day in a vacuum oven. The p la s tic iz e d p o ly sty re n e samples were prepared by mixing v ario u s amounts of p l a s t i c i z e r (u su a lly 5%, 10%, 15% and 20% by weight) w ith p o ly sty re n e in powder form. Thin film s were prepared by p ressin g th e blend a t tem p eratu res 50-60 d eg rees above th e g la ss tra n s itio n tem perature of th e m ix tu re. The film s w ere then c u t and repressed to ensure thorough m ixing; 5 cm x 0.5 cm x 0.3 cm samples were molded from th e cu t film s and annealed f o r two hours a t th is tem perature in a p re s s . The h ig h ly v isco u s sample o f low m olecular weight p o ly sty re n e , however, was found n o t to mix w ell th is way. T herefore, th e blen d of low m olecular w eight PS w ith high m olecular w eight PS was p rep ared by p r e c ip ita tin g i t from an acetone-chloroform s o lu tio n in a 50%-50% by volume m ixture of w ater and m ethanol. The a c e to n e - chloroform s o lu tio n o f PS blend was made by f i r s t sw e llin g th e blend i in 3% by w eight acetone so lu tio n and then adding j u s t enough chloroform to d iss o lv e th e b lend. The p r e c ip ita te was d rie d o v ern ig h t a t 160°C in a vacuum oven and pressed in to a sample as p re v io u sly d e sc tib e d . E lectro n micrographs of 20% by w eight d io c ty l p h th a la te sample and pure PS a t 40K m ag n ific a tio n were found to be id e n tic a l, and i t was assumed th a t a reaso n ab le mixing had been achieved by use of th e above p ro ced u re. The experim ental s e t up was same as d escrib ed in Chapter 2. The s tr e s s re la x a tio n experim ents were c a rrie d out in th e usual way, Chapter 1. A v e sse l f i l l e d w ith p u re p l a s t i c i z e r was kept in s id e th e relaxom eter in an attem p t to m inim ize th e lo ss of p l a s t i c i z e r from th e sample su rfa c e . D u p lic a te runs on a l l samples in d ic a te d no evidence of any p l a s t i c i z e r lo s s . A p p licatio n of the tim e-tem perature su p e rp o sitio n p r in c ip le to th e re la x a tio n d ata was q u ite s a tis fa c to ry . C. R esu lts and D iscussions W e have seen in C hapter 2 th a t PS has a slo p e of 1.6 charac- 25 t e r i s t i c o f the th re e dim ensional damped Debye l a t t i c e of Tobolsky. Some of th e sp rin g s in the th re e d im en sio n al re p re s e n ta tio n are in tra -m o le c u la r and th e r e s t in te r.-ra o le c u la r. The in te r-m o lec u lar coupling r e s u lts from van d er W aal's fo rc e s a c tin g between the c h ain s. T obolsky,38,3^ e t a l . , have proposed a damped to rs io n a l o s c illa to r (DTO) as a b a s ic m otional u n it extending over about th re e carbon-carbon atoms. So th e in tra -m o le c u la r sp rin g s are provided by the hindered r o ta tio n o f th e s e segments of the chain. Tobolsky and Chapoy38 have s tu d ie d th e re la x a tio n behavior of PS p la s tic iz e d w ith d io c ty l p h th a la te (DOP) and dim ethyl p h th alate (DM P) w ith the assum ption th a t th e in tro d u c tio n of any p la s tic iz e r should only a f fe c t the in te r-c h a in in te r a c tio n s le a v in g in tra -c h a in 39 in te ra c tio n s more or le s s unperturbed. The p l a s tic iz e r m olecules s e p a ra te th e ch ain s o f p aren t polym er, thereby, low ering van der Waal’s fo rc e s a c tin g between the ch ain s and have no e f f e c t on th e in te rn a l r o ta tio n s of sm all segm ents. Since th e p l a s t i c i z e r m olecules do n o t f i t in to the o r ig in a l l a t t i c e , according to Tobolsky, p la s tic iz a tio n should r e s u l t in a system o f low er dimen s io n a lity . They found th a t th e steep n ess index decreased w ith in c re a sin g p l a s t i c i z e r c o n c e n tra tio n . T h erefo re, they concluded th a t p o ly sty ren e indeed was an example of the th re e dim ensional damped Debye l a t t i c e . The in c o rp o ra tio n of p l a s t i c i z e r m olecules in p o ly sty ren e p a r tly destroyed th e o rig in a l l a t t i c e and thus p ro g re ssiv e ly reduced i t to a l a t t i c e of lower d im e n sio n ality w ith in c re a sin g p la s t i c i z e r co n te n ts. However, th e p la s tic iz e r m olecules are n o t e x a c tly in e r t and in te r a c t w ith th e chains they s e p a ra te . The n a tu re o f th e ir in te ra c tio n s should be r e fle c te d in th e ir a b ility in low ering th e d im e n sio n a lity o f th e o r ig in a l l a t t i c e . W e a lso know th a t th e s o lu b ility param eter is a good measure of in te r-m o le c u la r in te ra c tio n s With th is in m ind, we have stu d ied th e re la x a tio n b eh av io r of p o ly sty ren e p la s tic iz e d w ith d if f e r e n t high b o ilin g p o in t so lv e n ts th a t cover a sm all range on th e s o lu b ility param eter s c a le on e ith e r s id e of p o ly sty re n e. P la s tic iz e r S o lu b ility Param eter D O P 7.9 D M P 8.3534 PS 8.5636 D O S 8.6 DEP 10.0 D M P 10.7 W e have rep eated Chapoy's measurements on polystyrene p la s tic iz e d w ith DOP, F igures 10 - 15. Our o b serv atio n s are in agreement w ith h is work, although th e re a re sm all d iffe re n c e s a t th e h ig h er p la s tic iz e r c o n c e n tra tio n s. As we in creased the co n cen tratio n of D O P from 0 - 30% by w eig h t, th e steepness index went down from 1.6 to 1 .0 , F igure 16. M oreover, the c h a r a c te r is tic tem perature T i,^9 which is d e fin e d as the tem perature where the ten-second modulus is o f th e o rd e r o f 10^ dynes/cm^, was lowered from 100°C to 28°C, F ig u re 17. S im ilar experim ents were c a rrie d out on p o ly sty ren e p la s tic iz e d w ith d ie th y l p h th a la te , and th e steep n ess index and T i were low ered in a s im ila r fa sh io n , Figures 18 - 24. The most in te r e s tin g s tr e s s re la x a tio n behavior was shown by p o ly sty ren e p la s tic iz e d w ith d io c ty l seb acate (DOS), Figures 25-30. The steep n ess index rem ained f a i r l y co n stan t over the D O S co n cen tratio n range o f 0 - 25% by w eight w h ile th e T i d r a s tic a lly changed from 100°C to 23°C. On th e s u rfa c e , th is observation seems to c o n tra d ic t Chapoy's claim about th e v a lid ity of polystyrene L o g t min. Figure 10 Log E (t) dynes/ cm. 41 C O o O C O L o g t min. Figure 11 42 - | 2 Log E (t) dynes/cm CO CO I CO CJ1 o ° N co 'V I- C M 0 ) 9 - 1 3 60 C M S o 0 9 ( U C •d w w 60 o 8 — 1 I-------------- 10?. OOP SI =1*36 T = 8 0 °C Log t min. Figure 13 2 Log E (t) dynes/cm ea co r t PL 3 C/ S N O . V CJI O Figure 14 Log E (t) dynes/cm L o g t J min Figure 15 Log E (t) dynes/cm N o Figure 16 47 SI C J1 X ro b ) oe dOO oz OL 1 1 0 T oz o t 09 T i M - (TO e n ( D t- > -v j 0 0 1 00L 0 0 L o g € Figure 18 Log E (t) dynes/cm & 3 C/I C J I IMa M o " o m Q J U P 6 0 •H F p 6 u ■ — C O a) £ T d /■N 4J W b C O h 3 8 0 1 0 ^ DEP S I = 1*2 T =B 7°C Log t min. m C M o C M C D 3 b o *rl p H B a c o c u £ T 3 W t > C - O •J 8 7 20/.DEP SI = M 5 T = 42°C Log t min. L o g t min. 52 Figure 21 2 Log E (t) dynes/cm C O O S N C O n N c / > u n d30%|M Figure 23 54 j i C J 1 N U Figure 24 56 as a th re e dim ensional damped Debye l a t t i c e , but c lo s e r c o n sid e ra tio n s a t th e m olecular le v e l in d ic a te th a t th e re la x a tio n b eh av io r o f D O S p la s tic iz e d p o ly sty ren e should support Chapoy’s c o n clu sio n s. W e know th a t th e p la s tic iz e r m olecules should only a f f e c t th e i n t e r - m olecular s p rin g c o n sta n ts leav in g in tra -m o le c u la r in te r a c tio n s unchanged, which a re b a r r ie r s to in te rn a l ro ta tio n s o f a few carbon-carbon bonds. The in te r-m o le c u la r in te ra c tio n s a re van der Waal*s in nature.W hen polymer-polymer in te ra c tio n s a re n o t th e same as p l a s t i c i z e r - p l a s t i c i z e r in te ra c tio n s , th e in te r-m o le c u la r sp rin g c o n sta n ts of the p a re n t polymer are changed on p la s tic iz a tio n . Thus th e p la s tic iz e d polymer should have lower d im e n sio n a lity than, th e p a re n t polym er, which should in tu rn be r e fle c te d in p ro g re ssiv e ly d e c re asin g ste e p n ess index w ith in c re a sin g p l a s t i c i z e r c o n c e n tra tio n . This i s tru e in case of p o ly sty ren e p la s tic iz e d w ith DOP, DEP, and D M P . The s o lu b ility param eter, as we have seen b e fo re , m easures th e in te r-m o le c u la r in te ra c tio n s and has v alu es o f 7 .9 , 1 0 .0 , and 10.7 fo r DOP, DEP, and D M P re s p e c tiv e ly , which a re d iff e r e n t from th e v alu e o f 8.56 fo r PS. When the polym er-polym er i n t e r a c tio n s a re th e same as p l a s t i c i z e r - p l a s t i c i z e r in te r a c tio n s , th e in te r-m o le c u la r sp rin g c o n sta n ts of p aren t polymer a re unchanged on p l a s tic iz a tio n . This should m aintain th e o r ig in a l d im e n sio n ality of th e p a re n t polymer in p la s tic iz e d system and keep th e stee p n ess index independent of p l a s t i c i z e r c o n te n ts. In o th e r w ords, s im ila r e n e rg e tic s of th e p la s t i c i z e r and polymer enable p la s tic iz e d sy stem tto tra n sm it s tr e s s e s e l a s ti c a ll y in a fash io n analogous L o g t min. Figure 25 I 57 I 2 Log E (t) dynes/cm . C J 1 60 o» Figure 26 2 Log E (t) dynes/cm. CO o O Q n & 3 II . s * u i c/s o L o g t Figure 27 2 Log E (t) dynes/cm. s i CO ' CO II 3 C /I M 71 “ • CJ 1 r > Figure 28 2 Log E (t) dynes/cm. e o m rt & 3 to rv SOO 7 ' W Figure 29 61 SI cn is> s o n ' l l * * 62 Figure 30 o C J 1 a CX I 63 to th e p a re n t polym er. This is what we observe in th e case o f poly s ty re n e p la s tic iz e d w ith DOS. The s o lu b ility param eter fo r D O S i s about 8.6 which is clo se to the s o lu b ility param eter o f 8.56 fo r p o ly sty re n e . Thus the s im ila rity in s o lu b ility param eters o f PS and D O S leav es th e prim ary tr a n s itio n reg io n unchanged. This b eh av io r c le a r ly in d ic a te s th a t the in te r-m o le c u la r fo rc e s , in a d d itio n to in tra -m o le c u la r fo rc e s, play a m ajor r o le in de term in in g d im e n sio n a litie s of polymer. To t e s t the v a lid ity of th is argument r we used low m olecular w eight PS (m. wt. 600) as a p la s tic iz e r , because n o th in g could be c lo s e r to PS sample in. s o lu b ility param eter than i t s own low m olecular w eight f r a c tio n . The SI remained ap p reciab ly c o n s ta n t, F igures 31 - 35, and had a value of about 1.4 a t 20% w eight of PS (600). The T i changed from 100°C to 70°C. S im ilar r e s u lts were o b tain ed f o r diphenylm ethane (DM P) , Figures 38 - 41, which has a s o lu b ility param eter of 8.35. The v a r ia tio n of SI o f p la s tic iz e d p o ly sty ren e w ith th e so lu b i l i t y param eter of p la s tic iz e r s is shown in F igure 42, where the c o n c e n tra tio n of a l l p la s tic iz e r s is kept a t 10% by w eig h t. I t has a peak a t the s o lu b ility param eter o f PS c le a r ly in d ic a tin g th a t th e d e v ia tio n in th e s o lu b ility param eter o f th e p la s t i c i z e r from th a t o f PS re s u lte s in lower SI and hence low er d im e n sio n a lity . The unique b eh av io r o f D O S p la s tic iz e d PS e s ta b lis h e d th e e x iste n c e o f in te r-m o le c u la r couplings in polymers and t h e i r im portance in determ ing re la x a tio n behavior of polym ers. I t su p p o rts Tobolsky’s L o g t min. Figure 31 64 Log E (t) dynes/cm. CO CO CJI — . v c / > CJ L o g t min. Figure 32 65 2 Log E (t) dynes/cm. s i OO CO o OS C J1 C J 1 C O L o g t Figure 33 66 2 Log E (t) dynes/cm. OS (O CJ 1 0> O r ~ - . vO C M n a ) n 3 0 0 • H P 4 S u c o a ) R T 3 4 J w W 0 0 o ► 4 8 7 T T 20% PS SI =1-37 T=69°C Log t min. wt^PS Figure 35 SI CJ 1 Sd Figure 36 69 C O 0 9 Figure 37 o r - > . C S 8 a a a ) a >, 4 - 1 W 6 0 O ► J 8 0 T 5 $ ONIP SI =1*47 T=83C Log t min. L o g t min. Figure 38 71 ! i Log E (t) dynes/cm. CO CO c / > 09 09 O ' dWO^lM Figure 39 SI C J1 C J 1 difllO ^lM Figure 40 73 O Tj C. C O CJ 1 SOLUBILITY PA R A M ETER 75 th re e dim ensional damped Debye l a t t i c e model in re p re se n tin g re^* la x a tio n behavior o f polymers in th e prim ary t r a n s i t i o n reg io n . I t is c le a r now th a t when th e in te r-m o le c u la r and i n t r a m olecular sp rin g co n stan ts a re m atched, th e polymer behaves as a th re e dim ensional damped Debye l a t t i c e w ith th e SI of 1 .5 , which i s th e case fo r PS. Since no o th e r polymer i s known to have the SI of 1 .5 , i t i s reasonable to assume PS to be an unique case where th e sp rin g co n sta n ts match g iv in g i t s re la x a tio n b eh av io r a th re e dim ensional c h a ra c te r. The d iffe re n c e s in th e sp rin g co n sta n ts r e s u lt in lower d im e n sio n a lity , and the SI has a v a lu e between 0.5 and 1.5 depending on th e extend of th e se d iffe re n c e s . Though th e s o lu b ility param eter i s a crude measure of in te r-m o le c u la r in te ra c tio n s , i t has proved u s e fu l in ev alu atin g im portance of in te r-c h a in in te ra c tio n s in re la x a tio n b ehavior of amorphous polymers in th e prim ary tr a n s itio n re g io n . Our s tr e s s re la x a tio n experim ents on p o ly sty re n e p la s tic iz e d w ith d iff e r e n t so lv e n ts of v ario u s e n e rg e tic s p o s itiv e ly e s ta b lis h th e c r e d ib ility o f Tobolsky’s th re e dim ensional damped Debye l a t t i c e re p re s e n ta tio n and show th e im portant ro le played by van der W aal's fo rc e s in determ ining shape of the prim ary tr a n s itio n re g io n . W e fe e l assured to say th a t p o ly sty ren e i s indeed an example o f th re e dim ensional damped Debye l a t t i c e . CHAPTER 4 CONCLUSIONS W e have stu d ied the s tr e s s r e la x a tio n b ehavior in th e prim ary tr a n s itio n region of PS p la s tic iz e d w ith v ario u s high b o ilin g p o in t s o lv e n ts . Our choice of PS as a t e s t m a te ria l was based on the f a c t th a t i t is th e only polymer so f a r known to have th e SI of 1.6 c lo se to the SI of 1.5 p re d ic te d by Tobolsky fo r th e re la x a tio n behavior of the th re e dim ensional damped Debye l a t t i c e . Some of th e sp rin g s in th e th re e dim ensional l a t t i c e are in term o lecu lar and th e r e s t in tram o lecu lar. The in te rm o le c u la r coupling r e s u lts from van der W aal's fo rc e s a c tin g between th e c h a in s, and th e in tr a m olecular springs are provided by th e h in d ered r o ta tio n of a few segments of the chain. The in tro d u c tio n of any p l a s t i c i z e r should only a f f e c t th e in te r-c h a in in te ra c tio n s leav in g in tra - c h a in in te ra c tio n s more o r le s s unperturbed. The p l a s tic iz e r m olecules se p a ra te th e chains of p aren t polymer, th ereb y , low ering van der W aal's fo rc e s a c tin g between th e chains and have no e f f e c t on th e in te r n a l r o ta tio n s of sm all segments. Since p l a s tic iz e r m olecules do not f i t in to the o r ig in a l l a t t i c e , p la s tic iz a tio n should r e s u l t in a system of lower d im en sio n ality . Our work on PS p la s tic iz e d w ith DEP and D O P revealed j th e dependence of the SI on th e p l a s t i c i z e r c o n c e n tra tio n ; th e SI decreased w ith in crea sin g p la s t i c i z e r c o n c e n tra tio n . The in co rp o ra- I ! tio n o f p la s tic iz e r m olecules in p o ly sty re n e p a r tly destro y ed th e j 76 S o rig in a l l a t t i c e and p ro g re s siv e ly reduced i t to a l a t t i c e o f lower d im en sio n ality w ith in c re a sin g p l a s t i c i z e r co n ten ts as p rev io u sly rep o rted by Tobolsky, e t al.®® The most in te r e s tin g s tr e s s re la x a tio n behavior was shown by PS p la s tic iz e d w ith DOS. The SI rem ained f a i r l y co n sta n t over th e D O S co n cen tratio n range o f 0 - 25% by w eight w hile th e Tf d ra s t i c a l l y changed from 100°C to 23°C. On th e s u rfa c e , th is o b serv atio n seems to c o n tra d ic t Chapoy's claim s about th e v a lid ity of po ly sty ren e as a th re e dim ensional damped Debye l a t t i c e , but th e c lo se considera tio n s a t the m olecular le v e l in d ic a te th a t th e re la x a tio n behavior o f D O S p la s tic iz e d p o ly sty ren e should support Chapoy's work. However, th e p la s tic iz e r m olecules a re n o t e x a c tly in e r t and in te r a c t w ith th e chains they s e p a ra te . The n a tu re of th e ir in te ra c tio n s should be re fle c te d in th e ir a b i l i t y in- low ering th e d im en sio n ality of the o rig in a l l a t t i c e . The in te rm o le c u la r in te ra c tio n s a re van der W aal's in n atu re . When polym er-polym er in te ra c tio n s are n o t th e same as p la s tic iz e r - p la s tic iz e r in te r a c tio n s , the in te rm o le cu la r spring co n sta n ts of th e p aren t polymer a re changed on p la s tic iz a tio n . Thus th e p la s tic iz e d polymer should have lower d im en sio n ality than th e p aren t polymer. This i s what happens in case o f PS p la s tic iz e d w ith D O P and DEP. W e expect th e SI to decrease w ith in creasin g p la s tic iz e r co n te n ts. When th e polym er-polym er in te ra c tio n s a re th e same as th e ’ ,p la s t i c i z e r - p l a s t ic iz e r in te r a c tio n s , th e in te r m olecular sp rin g co n sta n ts of p a re n t polymer a re unchanged on p la s tic iz a tio n . This should m ain tain th e o r ig in a l d im en sio n ality 78 of the p aren t polymer In p la s tic iz e d system and SI should be indepen dent o f th e p l a s t i c i z e r c o n c e n tra tio n , which i s observed in case of PS p la s tic iz e d w ith DOS. PS and D O S have the same values o f so lu b i l i t y param eters. The s o lu b ility param eter i s a good measure of the in te rm o le c u la r in te r a c tio n s . A p lo t of th e SI v ersu s the s o lu b ility param eter a t 10% by w eight of a l l p la s tic iz e r s in d ic a te s th a t th e d e v ia tio n in s o lu b ility param eter of p la s tic iz e r from th a t of PS r e s u lts in low ereing of SI and, in tu rn , d im en sio n ality . I t i s c le a r now th a t when th e .in term o lecu lar and in tram o le cu la r sp rin g c o n sta n ts are matched th e polymer behaves as a th re e dimen sio n a l damped Debye l a t t i c e w ith th e SI of 1 .5 . The d iffe re n c e s in th e sp rin g c o n sta n ts r e s u l t in lower d im en sio n a lity , and th e SI has a value between 0 .5 and 1.5 depending on th e se d iffe re n c e s . Our s tr e s s r e la x a tio n experim ents on PS p la s tic iz e d w ith so lv e n ts of d iff e r e n t e n e rg e tic s show th e im portant r o le played by van der Waal’s fo rces in determ ing shape o f th e prim ary tr a n s itio n reg io n . W e have a lso s tu d ie d th e s tr e s s re la x a tio n behavior o f PVB. I t has a s u b s titu e n t tw ice as b ig as th a t in PS. PV B has a SI of 1.4 which i s n o t g ro s s ly d if f e r e n t from SI of 1.6 fo r PS. One could explain t h i s independence of SI on th e s iz e of the side-group j s u b s titu e n t from th e p o in t of view o f three*dim ensional re p re s e n ts - j tio n . The phenyl rin g s in PS s tic k out lik e sp ik es and in te r a c t ! with the phenyl rin g s on th e o th e r c h a in s, making i t a highlyccoupled ; system. The b a r r i e r to r o ta tio n of a few segments of th e chain j provides th e in tra m o le c u la r coupling. PS may be a unique case where th e se sp rin g c o n sta n ts are matched g iv in g i t th re e dim ensional c h a ra c te r. The tw ice as long s u b s titu te n t in PV B could more e f f e c - 1 tiv e ly couple one chain w ith a n o th e r, and a t the same tim e, th is bulky biphenyl could pro v id e h ig h er b a r r ie r to ro ta tio n . Thus m aintains the b alan ce between th e in tr a and th e in te r spring c o n sta n ts. T h erefo re, i t s s tr e s s r e la x a tio n behavior is not g ro ssly d iffe re n t from th a t o f PS. Fugimoto,^®et a l . , have re p o rte d a SI of 0.9 fo r poly « methyl s ty re n e . At f i r s t , th is v alu e of SI seems abnormal, but th e c o n sid e ratio n s in th re e dim ensional p e rsp e c tiv e make i t look reaso n a b le . A sm all nbnpplar; m ethyl group in = p o sitio n should not change in te rm o le c u la r in te ra c tio n s a p p re c ia b ly . I t should make lin in g o f phenyl rin g s from neighboring chains ra th e r d i f f i c u l t . Thus making i t a le s s coupled system . The m ethyl group might a lso have in creased th e b a r r ie r to r o ta tio n . This should r e s u lt in d i f f erences in the in t r a and in te r sp rin g co n sta n ts giving i t a lower d im en sio n ality and hence lower slo p e . REFERENCES 1. Tobolsky, A .V ., P ro p e rtie s and S tru c tu re of Polym ers, John Wiley & Sons, I n c ., New York, 1967, p . 73. 2. 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Stress Relaxation Behavior In The Primary Transition Region

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Asset Metadata

Creator Rele, Vilas Balwant (author)

Core Title Stress Relaxation Behavior In The Primary Transition Region

Degree Doctor of Philosophy

Degree Program Chemistry

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag chemistry, polymer,OAI-PMH Harvest

Language English

Contributor Digitized by ProQuest (provenance)

Advisor Aklonis, John J. (committee chair), Beaudet, Robert A. (committee member), Partridge, Edward (committee member)

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c18-679443

Unique identifier UC11356033

Identifier 7414472.pdf (filename),usctheses-c18-679443 (legacy record id)

Legacy Identifier 7414472.pdf

Dmrecord 679443

Document Type Dissertation

Rights Rele, Vilas Balwant

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the au...

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus, Los Angeles, California 90089, USA