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18 Physical Aging of Glassy Polymers: Effects of Subsidiary

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Relaxation Processes A. S. MARSHALL and S. E. B. PETRIE Research Laboratories, Eastman Kodak Company, Rochester, NY 14650

As discussed previously (1-8), glassy, or partially glassy, polymers prepared under normal conditions have excess thermody namic properties because of the kinetic aspects of the glass transformation process. As a consequence of this thermodynamic potential, the physical properties of glassy polymers change with time and approach those of the corresponding equilibrium glassy state, the rate of change being commensurate with the level of segmental molecular mobility associated with the rigid matrix. In parallel with small changes in the thermodynamic state of glassy polymers on aging or annealing, rather profound changes have been observed in some of the mechanical properties (8-17). Especially noteworthy is the loss of general ductile behavior that has been documented for many polymers on aging or annealing at temperatures below their respective glass-transition temperatures (8-17). Of particular concern in studies of processes, especially diffusion-controlled processes (18), taking place in rigid envi ronments are matrix-viscosity effects attributable to changes in the thermodynamic state of glassy matrices (1). Consequently, the rates of these relaxation processes associated with the nonequilibrium nature of the glassy state, and the factors that in fluence them are of considerable technological importance as well as of academic interest. To gain information concerning the rates of relaxation pro cesses characteristic of the glassy state, and to project longterm aging effects, particularly for polymers, a general study was undertaken of relaxation rates and of the influential variables (2). The procedure adopted for following the progress of the relaxation processes at various temperatures for selected glassy materials was to monitor enthalpy relaxation. In earlier investigations involving both polymeric and non polymeric compounds (1,2), it was established that the primary rate-controlling factor is the temperature, more precisely the temperature interval, of the glass transformation process. With decreasing temperature below T , the time required for the enthalpy of either polymeric or nonpolyfieric glassy materials to decrease g

0-8412-0485-3/79/47-095-245$05.00/0 ©

1979 A m e r i c a n C h e m i c a l Society

In Durability of Macromolecular Materials; Eby, R.; ACS Symposium Series; American Chemical Society: Washington, DC, 1979.


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by a s p e c i f i c amount becomes exceedingly long. Of the secondary f a c t o r s t o be considered i n a study o f t h i s n a t u r e , a fundamental v a r i a b l e i s the molecular weight. D e t a i l e d s t u d i e s {2) of r e l a x a t i o n r a t e s f o r n e a r l y monodisperse a t a c t i c polystyrenes (PS) o f v a r i o u s molecular weights ranging from 2.0 x 10 t o 811 x 10 have shown t h a t the r e l a x a t i o n r a t e at comparable temperature i n t e r v a l s below T (T - T ^ ) , where T^ denotes the annealing temperature, increased somlwhaf with decreasing molecular weight below a c r i t i c a l r e g i o n corresponding t o the c r i t i c a l molecular-weight range observed i n the molecular-weight dependence o f T (19)> A s l i g h t dependence o f r e l a x a t i o n r a t e on molecular-weigtr? p o l y d i s p e r s i t y i n v o l v i n g low-molecular-weight polymer was a l s o observed. Consistent with these o b s e r v a t i o n s , the r e l a x a t i o n r a t e of a nonpolymeric g l a s s , A r o c l o r 5^60, was somewhat f a s t e r than t h a t o f n e a r l y monodisperse a t a c t i c PS having a s i m i l a r T but higher molecular weight. A l l of these r e s u l t s s u g g e s t t h a t molecular chain dimensions have a small e f f e c t , i n a d d i t i o n t o reducing T , on the l i m i t e d segmental m o b i l i t y o c c u r r i n g i n the g l a s s y f t a t e . g

Other secondary f a c t o r s t h a t could i n f l u e n c e the enthalpyr e l a x a t i o n process are s u b s t a n t i a l s u b s i d i a r y modes o f motion and structure-forming c a p a b i l i t y . E n t h a l p y - r e l a x a t i o n r a t e s f o r bisphenol-A polycarbonate (PC), which has s u b s t a n t i a l main-chain motion i n the g l a s s y s t a t e s ( 8 1 0 - 1 7 ) , and f o r p o l y ( e t h y l e n e t e r e p h t h a l a t e ) (PET), which i n a d d i t i o n t o having s u b s i d i a r y modes of motion has s i g n i f i c a n t c r y s t a l - o r d e r i n g tendency ( 8 , 9 ) , were studied i n d e t a i l , and the r e s u l t s are r e p o r t e d here. f

Experimental Enthalpy Relaxation. I t was e s t a b l i s h e d p r e v i o u s l y (1,20) through l i m i t e d e n t h a l p y - r e l a x a t i o n s t u d i e s o f a number of o r ganic g l a s s e s , some having widely d i f f e r i n g structure-forming c h a r a c t e r i s t i c s , that i t i s p o s s i b l e t o f o l l o w r e a d i l y by d i f f e r e n t i a l scanning c a l o r i m e t r y (dsc) the enthalpy changes t h a t occur i n g l a s s y m a t e r i a l s as a consequence of the nonequilibrium nature of the g l a s s y s t a t e . The procedure i n v o l v e s monitoring the abs o r p t i o n of thermal energy t h a t i s superposed on the s p e c i f i c - h e a t change a s s o c i a t e d w i t h the g l a s s t r a n s i t i o n observed during p r o grammed heating c y c l e s of aged o r annealed g l a s s e s . T y p i c a l dsc t r a c e s are i l l u s t r a t e d i n Figure 1. For both PC and PET, s i g n i f i cant increases were observed i n T , as determined by the procedure adopted here, with i n c r e a s i n g a n n i a l i n g time. For samples prepared and programmed under the same c o n d i t i o n s except f o r the annealing or aging step, the energy absorbed i n the T r e g i o n i s r e l a t e d t o the decrease i n excess enthalpy t h a t occurs during the annealing or aging process ( l , 2 0 ) . I f the s t a b i l i t y and r e p r o d u c i b i l i t y of the b a s e l i n e s i n the dsc t r a c e s are adequate, the amount o f energy absorbed i n the T i n t e r v a l o f a g l a s s y m a t e r i a l as a r e s u l t of annealing processed


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can be determined merely by superposing the dsc curves, obtained under i d e n t i c a l programming c o n d i t i o n s , f o r the sample i n the unannealed (quenched) and annealed s t a t e s and e v a l u a t i n g the net energy a b s o r p t i o n , (^(AH^ , T^, r ) , where AE^ i s the i n i t i a l excess enthalpy a t the annealing temperature and r i s the p r o gramming r a t e . Otherwise, a l e s s d i r e c t , but e q u i v a l e n t , procedure i s r e q u i r e d that i n v o l v e s e v a l u a t i n g the magnitude o f the endothermic peak and c o r r e c t i n g i t f o r enthalpy c o n t r i b u t i o n s a s s o c i a t e d with the i n c r e a s e s i n the T t h a t occur as the r e l a x a t i o n process p r o ceeds ( 1 . 2 ) . G e n e r a l l y , i t i s convenient t o express the enthalpy changes that occur during i s o t h e r m a l annealing o f a g l a s s i n terms o f a l t e r a t i o n s i n the enthalpy displacement from the e q u i l i b r i u m g l a s s y s t a t e , i . e . , a l t e r a t i o n s i n the excess enthalpy (H^ - H ) . Thus, a determination o f the energy absorption i n the T r e g i o n f o r a corresponding sample i n i t s e q u i l i b r i u m g l a s s y s t i t e under the same programming c o n d i t i o n s i s necessary. From s p e c i f i c - h e a t data and a knowledge o f the annealing and programming c o n d i t i o n s , i t i s p o s s i b l e t o estimate the maximum energy absorption Q ( 4 H , T , r ) i f d i r e c t measurement i s not r e a d i l y a t t a i n a b l e j A that i s , g

£

E

T

A

. T

,)

A

(1)

= (c - c ) [T (, ) *r *g °

where r . i s the programming r a t e , and c

and c are the s p e c i f i c f g heats of the f l u i d and g l a s s y s t a t e s , r e s p e c t i v e l y . The excess enthalpy at the annealing tern temperature T^ a f t e r an annealing p e r i o d t i s r e l a t e d t o Q and by P

P

£

(H

t

- H)

= CO^)

E

A

- Qjr

,J

(2) A

provided Q_ and Q, are measured at the same programming r a t e r_ (1). ^ ^ The instrument employed was the Perkin-Elmer d i f f e r e n t i a l scanning c a l o r i m e t e r , Model DSC-2. The temperature scale was c a l i b r a t e d w i t h the melting t r a n s i t i o n s o f indium, t i n , l e a d , and z i n c . The energy input was c a l i b r a t e d with the heat of f u s i o n of indium. Jhe scanning r a t e used throughout t h i s i n v e s t i g a t i o n was 5 C min" . In order t o achieve the h i g h e s t p r e c i s i o n p o s s i b l e , the c a l i b r a t i o n s were checked f r e q u e n t l y . Since the s t a b i l i t y o f the b a s e l i n e s and the r e p r o d u c i b i l i t y of the dsc curves were adequate, the s u p e r p o s i t i o n procedure f o r e v a l u a t i n g the energy a b s o r p t i o n at T o f an annealed g l a s s was adopted i n these s t u d i e s . ^ 1


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E r r o r s i n the determination o f ^ ( A H ^

, T^, r ) were observed A i f the annealing temperature was not maintained p r e c i s e l y , and i f the pans were not r e l o c a t e d e x a c t l y i n the same p o s i t i o n i n the dsc h o l d e r . To minimize these e r r o r s , the samples were annealed d i r e c t l y i n the h o l d e r . Under these c o n d i t i o n s , the unc e r t a i n t y i n the enthalpy measurements was l e s s than +0.02 c a l g" . S p e c i f i c heat was measured according t o the procedures given i n the instrument i n s t r u c t i o n manual. Data were r e p r o d u c i b l e t o +0.001 c a l g C . M a t e r i a l s . The bisphenol-A polycarbonate used i n t h i s i n v e s t igation% was Lexan lU5 as r e c e i v e d from General E l e c t r i c Co. (M ^3 x 1 0 * ) . The amorphous p o l y ( e t h y l e n e t e r e p h t h a l a t e ) was prepared by quenching melt-cast polymer o f molecular weight 2 x 10 t o the amorphous s t a t e . In order t o e l i m i n a t e the e f f e c t s o f previous thermal h i s t o r y , the approximately 10-mg, amorphous samples were heated t o temperatures about 30 C above the corresponding T 's observed f o r the unannealed m a t e r i a l s at the s e l e c t e d heating f a t e o f 5 C min" . Then, the samples were cooled t o the annealing temperature at the f a s t e s t r a t e permitted by the instrument. In these s t u d i e s , T was taken as t h e temperature at which the s p e c i f i c heat reacheS a value t h a t was midway between those corresponding t o t h e f l u i d and g l a s s y s t a t e s . w

Results and D i s c u s s i o n E n t h a l p y - r e l a x a t i o n data obtained f o r g l a s s y PC and PET duri n g isothermal annealing at s e v e r a l temperatures below t h e i r r e s p e c t i v e T 's are given i n Figures 2 and 3 , i n which the excess enthalpy £ 0 ^ - QjJ i s p l o t t e d as a f u n c t i o n o f l o g t . The c a l c u l a t i o n s o r Q_(6H_ , T , r ) were based on (c - c ) o f 0.0778 A f K c a l g" C~ and 0.0855 c a l g~ C" f o r PC and PET, r e s p e c t i v e l y , as deduced from the s p e c i f i c - h e a t data obtained with the dsc. For a l l o f the polymers, the time r e q u i r e d f o r r e l a x a t i o n of the enthalpy t o that o f the e q u i l i b r i u m g l a s s y s t a t e at the various temperatures i s extremely l o n g , even at temperatures o f the order o f 15°C below the corresponding g l a s s - t r a n s i t i o n temperat u r e s . The p r i n c i p a l rate-determining f a c t o r i s the g l a s s t r a n s i t i o n temperature, as a n t i c i p a t e d from previous studies (!#). Enthalpy r e l a x a t i o n f o r PC and PET proceeded almost comp a r a b l y at corresponding temperature i n t e r v a l s below t h e i r r e s p e c t i v e T *s (T - T . ) . Furthermore, a comparison o f these d a t a w i t h th§ PS r i s u l t s obtained p r e v i o u s l y (2) r e v e a l s no notable d i f f e r e n c e s . The r e l a x a t i o n r a t e s a t comparable temperat u r e i n t e r v a l s below T f a l l i n the order PET> PS> PC — an order A

p

P


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1 1 1 III

Polycarbonate Lexan 145 (Tq = I46°C)

1.5


I22°C

-

T 1.0 o

I29°C

0 cf 1

O 0.5

1—i—i -

I0 '

Figure 2.

i i 111.1

I0

i , U

i

i

i

11111

i

i

i

i

11111

1

1 1 1 M i

10' Annealing time, hr

Enthalpy-relaxation data for PC at various temperatures


3

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reverse t o t h a t f o r T . I f i t i s assumed that the molecular weights of both PC and PET were above the c r i t i c a l molecular-weight r e g i o n , as was the case f o r PS (2), and t h a t the c o n t r i b u t i o n s o f any low-molecularweight f r a c t i o n s t o the r e l a x a t i o n processes were not s i g n i f i c a n t , the e n t h a l p y - r e l a x a t i o n data suggest t h a t molecular s t r u c t u r e does not have a s t r o n g i n f l u e n c e on r e l a x a t i o n processes assoc i a t e d with t h e n o n e q u i l i b r i u m nature o f the g l a s s y s t a t e . F u r t h e r , the d a t a i n d i c a t e t h a t n e i t h e r s u b s i d i a r y modes o f motion i n v o l v i n g groups i n the main c h a i n nor the c r y s t a l - f o r m i n g tendency of polymers has a s i g n i f i c a n t e f f e c t on these r e l a x a t i o n processes. The e f f e c t o f molecular s t r u c t u r e on the e n t h a l p y - r e l a x a t i o n processes can be explored i n g r e a t e r d e t a i l by c o n s i d e r i n g , as p o i n t e d out i n previous s t u d i e s o f r e l a x a t i o n processes f o r g l a s s e s ( 1 - 6 ) , t h a t the r a t e o f enthalpy r e l a x a t i o n i s a f u n c t i o n o f the extent o f the displacement of the system from i t s c o r r e s ponding e q u i l i b r i u m s t a t e (Qg - 9^.)^ as w e l l as a f u n c t i o n o f


g

A

temperature, T^. f At At constant constant tempe temperature, the r e l a x a t i o n time f o r each of the samples s t u d i e d was {-dCmtcL - Q.O/dtjf m fx>und t o be an e x p o n e n t i a l f u n c t i o n o f CQg - Q ^ • The T

data f o r PC and PET are p l o t t e d i n Figures h and ^ , r e s p e c t i v e l y . A l s o , at constant enthalpy displacement from the e q u i l i b r i u m g l a s s y s t a t e , ( Q - Q^), an Arrhenius temperature dependence was observed f o r the r e l a x a t i o n time f o r each polymer, as i l l u s t r a t e d i n F i g u r e s 6 and 7 f o r PC and PET, r e s p e c t i v e l y . Some o f the data p l o t t e d i n Figures 6 and 7 correspond t o e x t r a p o l a t e d values o f the enthalpy d a t a i n Figure 2, because o f the exceedingly l o n g r e l a x a t i o n times r e q u i r e d t o achieve a constant enthalpy d i s p l a c e ment f o r the lower a n n e a l i n g temperatures. Thus, t h e r a t e o f enthalpy r e l a x a t i o n f o r each polymer can be expressed i n terms o f temperature and excess enthalpy according t o a r e l a t i o n s h i p o f the form d e s c r i b e d p r e v i o u s l y ( l ) , i . e . , £

1

=

-dClnC^ - C ^ Q ,

A

e

x

p

_

(

jyjg,)

e

x

p

jc

(

Q

E

. Q^J

(3)

dt where Eg i s the apparent a c t i v a t i o n energy o f enthalpy r e l a x a t i o n , and A and C are constants. With the appropriate values f o r E^, A, and C, f o r each polymer, equation (3) represents w e l l the experimental data obtained. There i s e x c e l l e n t agreement between InT c a l c u l a t e d from equation (3) as a f u n c t i o n o f (Q_, - Q ) and the experimental data obtained f o r PC and PET, as i l l u s t r a t e d i n Figures k and 5. The values o f EL, A, and C o f equation (3) f o r PC and PET v a r i e d l i t t l e (Table I ) . The constant C, which r e f l e c t s the dependence of the r e l a x a t i o n r a t e on the magnitude of the excess enthalpy, was l a r g e r f o r PC than f o r PET (the value f o r PS was



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Figure 4. Relationship between the relaxation time, r, and the enthalpy displacement from the equilibrium glassy state, (Q — Qt), for PC at various temperatures E

Figure 5. Relationship between the relaxation time, r, and the enthalpy displacement from the equilibrium glassy state, (Q — Qt), from PET at various temperatures E



MARSHALL

Figure 6.

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Arrhenius temperature plots for enthalpy-relaxation times at a constant excess enthalpy of 0.5 cal g' for PC 1



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3

Figure 7.

Arrhenius temperature plots for enthalpy-relaxation times at a constant excess enthalpy of 0.5 cal g' for FET 1

ENTHALPY-RELAXATION

DATA FOR VARIOUS GLASSY POLYMERS

k cal mole"'

C, g cal"

PC (Lexan 145)

317

13.1

PS (Koppers 8 X )

292

12.2

PET

263

11.2

EH-

Polymer



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intermediate between those f o r PC and PET) • The apparent a c t i v a t i o n energy E„ i n the temperature-dependent term a l s o was s l i g h t l y l a r g e r f o r PC than f o r PET (again t h e value f o r PS was intermediate between those f o r PC and PET). These data concerning the m o l e c u l a r - s t r u c t u r e dependency o f the e n t h a l p y - r e l a x a t i o n process suggest t h a t the f a c t o r s t h a t i n fluence the onset o f segmental m o b i l i t y i n f l u e n c e enthalpy r e l a x a t i o n , but t h a t t h e presence o f mobile groups i n t h e main chain or the c r y s t a l - o r d e r i n g tendency o f polymers does not seem t o have a s i g n i f i c a n t e f f e c t on t h e r a t e o f enthalpy r e l a x a t i o n . These f a c t o r s , however, are b e l i e v e d t o i n f l u e n c e the f l e x u r a l p r o p e r t i e s o f these polymers (8-17)* To summarize t h e e f f e c t s o f the molecular s t r u c t u r a l charact e r i s t i c s considered i n t h i s and t h e previous ( l ) i n v e s t i g a t i o n on t h e temperature dependence o f the e n t h a l p y - r e l a x a t i o n r a t e , the r e l a x a t i o n times a t a constant excess enthalpy (Q_, - Q^) « 0.5 c a l g " are p l o t t e d i n F i g u r e 8 as a f u n c t i o n o f the c o r r e s ponding temperature i n t e r v a l below T , i . e . , at t h e same (T - T ^ ) , f o r t h e various organic g l a s s e s , Aro§lor 5**60 ( i s t h e r e l a x a t i o n t i m e , iL. i s t h e apparent a c t i v a t i o n energy o f enthalpyr e l a x a t i o n , ( Q - Q ) i s the excess enthalpy, and A and C are constants. Tne values o f EL, A, and C o f these r e l a t i o n s h i p s have been found t o vary s l i g n t l y w i t h molecular s t r u c t u r e i n a manner s i m i l a r t o t h a t observed f o r t h e m o l e c u l a r - s t r u c t u r e dependence o f the g l a s s - t r a n s i t i o n temperature. Neither the presence o f mobile groups i n t h e main chain nor the c r y s t a l - o r d e r i n g tendency o f polymers seems t o have a s i g n i f i c a n t e f f e c t , i f any, on the r a t e o f enthalpy r e l a x a t i o n o f these polymers. Thus, one could conclude that the molecular s t r u c t u r e o f g l a s s y polymers has only a small e f f e c t on t h e r e l a x a t i o n p r o cesses a s s o c i a t e d with t h e nonequilibrium thermodynamic s t a t e o f the g l a s s e s .


F

Acknowledgment s The authors are indebted t o J . E. Fogg and W. W. Jacobe o f the Manufacturing Technology D i v i s i o n , Kodak Park, Eastman Kodak Company, f o r the p r e p a r a t i o n o f t h e amorphous PET f i l m used i n these s t u d i e s . Summary In l i f e t i m e considerations f o r g l a s s y or p a r t i a l l y g l a s s y polymeric m a t e r i a l s , an important f a c t o r i s t h e p h y s i c a l aging process a s s o c i a t e d with the nonequilibrium thermodynamic s t a t e o f g l a s s e s . Because o f t h e k i n e t i c aspects a s s o c i a t e d w i t h t h e transformation o f a melt t o a glass i n the g l a s s - t r a n s i t i o n temperature i n t e r v a l , t h e g l a s s y s t a t e s o f m a t e r i a l s prepared under normal c o o l i n g c o n d i t i o n s have excess enthalpy and volume r e l a t i v e t o those o f t h e corresponding e q u i l i b r i u m s t a t e s t h a t can be achieved through slow c o o l i n g o r annealing regimes. F o r glasses with excess thermodynamic p r o p e r t i e s , there i s a thermodynamic p o t e n t i a l f o r t h e p r o p e r t i e s t o approach those o f t h e e q u i l i b r i u m s t a t e , i . e . , t o decrease with t i m e , t h e r a t e o f decrease being commensurate w i t h t h e l e v e l o f molecular or segmental molecular m o b i l i t y i n t h e g l a s s y s t a t e . Preliminary s t u d i e s suggest t h a t the r a t h e r s u b s t a n t i a l changes observed i n some o f t h e p h y s i c a l p r o p e r t i e s , p a r t i c u l a r l y the f l e x u r a l p r o p e r t i e s , o f g l a s s y o r p a r t i a l l y g l a s s y polymers subjected t o various annealing regimes at temperatures below t h e i r r e s p e c t i v e g l a s s - t r a n s i t i o n temperatures a r e a s s o c i a t e d w i t h t h e l o s s o f excess thermodynamic propert i e s t h a t take p l a c e as a r e s u l t o f t h e annealing processes. To a s c e r t a i n the e f f e c t s o f modes o f motion i n v o l v i n g groups i n t h e polymer chain on t h e r e l a x a t i o n processes a s s o c i a t e d w i t h t h i s p h y s i c a l aging phenomenon, enthalpy r e l a x a t i o n s t u d i e s were undertaken o f two polymers having s u b s t a n t i a l main-chain motion i n the glassy s t a t e — p o l y (ethylene t e r e p h t h a l a t e ) and bisphenol-A p o l y -


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MATERIALS

carbonate. The enthalpy r e l a x a t i o n data f o r t h e g l a s s y polymers suggest that n e i t h e r the presence o f mobile groups i n t h e main chain nor the c r y s t a l - f o r m i n g tendency o f polymers has a s i g n i f i cant e f f e c t on the r a t e o f enthalpy r e l a x a t i o n .

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RECEIVED

December 8, 1978.


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