Effects of Structural Order on Barrier Properties - American Chemical

Chapter 3

Effects of Structural Order on Barrier Properties

Downloaded by NORTH CAROLINA STATE UNIV on June 3, 2013 | http://pubs.acs.org Publication Date: May 9, 1990 | doi: 10.1021/bk-1990-0423.ch003

D. H. Weinkauf and D. R. Paul Department of Chemical Engineering and Center for Polymer Research, The University of Texas at Austin, Austin, TX 78712

The effects of molecular order on the gas transport mechanism in polymers are examined. Generally, orientation and crystallization of polymers improves the barrier properties of the material as a result of the increased packing efficiency of the polymer chains. Liquid crystal polymers (LCP) have a unique morphology with a high degree of molecular order. These relatively new materials have been found to exhibit excellent barrier properties. An overview of the solution and diffusion processes of small penetrants in oriented amorphous and semicrystalline polymers is followed by a closer examination of the transport properties of LCP's. The barrier properties of polymeric materials are determined by the chemical structure of the chain and the system morphology. The parameters derived from chemical structure, such as degree of polarity, inter-chain forces, a b i l i t y to crystallize, and chain stiffness, are essentially determined upon the selection of the particular polymer. Here, we w i l l focus on how molecular order influences the barrier properties of polymers, including molecular orientation and degree of c r y s t a l l i n i t y ; however, i t must be recognized that the range in which these quantitites can be manipulated w i l l depend on chemical structure. For many years, molecular orientation and c r y s t a l l i n i t y have been observed to improve the barrier properties of polymers (1-3). In extreme cases, drawing of semicrystalline polymers has been shown to reduce permeability by as much as two orders of magnitude. A crude understanding of the dependence of the transport parameters on penetrant size and chain packing can be 0097-6156/90/0423-0060$09.00/0 © 1990 American Chemical Society

In Barrier Polymers and Structures; Koros, W.; ACS Symposium Series; American Chemical Society: Washington, DC, 1990.


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o b t a i n e d t h r o u g h t h e c o n c e p t o f f r a c t i o n a l f r e e volume, s i n c e s o r p t i o n and d i f f u s i o n p r o c e s s e s depend upon t h e a v a i l a b i l i t y o f u n o c c u p i e d volume i n t h e p o l y m e r m a t r i x . In t h e l a m e l l a r c r y s t a l s o f s e m i c r y s t a l l i n e m a t e r i a l s and the extended chain s t r u c t u r e o f o r i e n t e d polymers, chain p a c k i n g i s u s u a l l y much more e f f i c i e n t t h a n i n t h e amorphous, i s o t r o p i c s t a t e . The e f f i c i e n c y o f c h a i n p a c k i n g i n t h e c r y s t a l l i n e phase r e d u c e s t h e f r e e volume a v a i l a b l e f o r t r a n s p o r t t o s u c h an e x t e n t t h a t , as a f i r s t a p p r o x i m a t i o n , t h e c r y s t a l l i n e phase may be r e g a r d e d as impermeable r e l a t i v e t o t h e amorphous p h a s e . The u n i q u e m o l e c u l a r p a c k i n g o f r o d - l i k e c h a i n s i n l i q u i d c r y s t a l l i n e p o l y m e r s (LCP) c l o s e l y r e s e m b l e s t h e extended chain s t r u c t u r e o f h i g h l y o r i e n t e d f l e x i b l e chain p o l y m e r s , s u g g e s t i n g t h a t t h e s e m a t e r i a l s a r e good candidates f o r b a r r i e r a p p l i c a t i o n s . T h e r m o t r o p i c LCP's, f i r s t d e v e l o p e d i n t h e e a r l y 1970's, have been t h e o b j e c t o f much i n t e r e s t b e c a u s e o f t h e i r e x c e l l e n t m e c h a n i c a l p r o p e r t i e s and ease o f product f a b r i c a t i o n . Preliminary o b s e r v a t i o n s have shown t h a t a c o m m e r c i a l l y a v a i l a b l e w h o l l y a r o m a t i c t h e r m o t r o p i c c o p o l y e s t e r has gas p e r m e a b i l i t y c o e f f i c i e n t s t h a t a r e lower than those o f p o l y a c r y l o n i t r i l e ( £ ) . These r e s u l t s r a i s e some f u n d a m e n t a l q u e s t i o n s as t o t h e n a t u r e o f t h e mechanism f o r t r a n s p o r t o f small molecules through a matrix o f ordered r i g i d r o d - l i k e chains. We f i r s t g i v e a c o n c i s e r e v i e w o f t h e e f f e c t s o f o r i e n t a t i o n and c r y s t a l l i n i t y on t h e b a r r i e r p r o p e r t i e s o f polymeric materials, paying p a r t i c u l a r attention t o t h e i r e f f e c t s on t h e s o l u b i l i t y and d i f f u s i o n c o e f f i c i e n t s . This w i l l p r o v i d e u s e f u l background f o r c o n s i d e r i n g t h e t r a n s p o r t p r o p e r t i e s o f l i q u i d c r y s t a l p o l y m e r s which, b e c a u s e o f t h e i r u n i q u e p r o p e r t i e s , may have some r o l e t o p l a y i n t h e quest f o r improved b a r r i e r polymers.

The Transport

Mechanism

The mechanism by which s m a l l gas m o l e c u l e s permeate t h r o u g h r u b b e r y o r g l a s s y amorphous p o l y m e r s has been d e s c r i b e d by many a u t h o r s ( 5 - 7 ) . I t w i l l be u s e f u l t o b r i e f l y r e v i e w t h e u n d e r l y i n g p a r a m e t e r s which a f f e c t p e r m e a t i o n . Because a s o l u t i o n - d i f f u s i o n p r o c e s s i s i n v o l v e d , t h e p e r m e a b i l i t y c o e f f i c i e n t o f amorphous p o l y m e r s i s t h e p r o d u c t o f t h e e f f e c t i v e d i f f u s i o n , D , and s o l u b i l i t y , S, coefficients.

Ρ = DS

(1)

The s o l u b i l i t y c o e f f i c i e n t i s t h e r a t i o o f t h e e q u i l i b r i u m concentration of the d i s s o l v e d penetrant t o i t s p a r t i a l p r e s s u r e i n t h e t h e gas p h a s e . Investigations of sorption i s o t h e r m s f o r g a s e s i n g l a s s y p o l y m e r s have l e a d t o t h e hypothesis that the equilibrium concentration i s the r e s u l t


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BARRIER POLYMERS AND STRUCTURES

o f c o n t r i b u t i o n s from b o t h Henry's law and Langmuir ( h o l e f i l l i n g ) t y p e s o r p t i o n mechanisms, o r t h e s o - c a l l e d " d u a l s o r p t i o n " model. Thus, t h e s o l u b i l i t y i s dependent upon b o t h p o l y m e r - p e n e t r a n t i n t e r a c t i o n s and t h e volume a v a i l a b l e f o r "hole f i l l i n g . " Over a r e a s o n a b l e t e m p e r a t u r e range, t h e a p p a r e n t s o l u b i l i t y c o e f f i c i e n t , S, can be e x p r e s s e d i n terms o f a v a n ' t H o f f r e l a t i o n s h i p , and a preexponential factor, S. 0

S = S exp(-^) Downloaded by NORTH CAROLINA STATE UNIV on June 3, 2013 | http://pubs.acs.org Publication Date: May 9, 1990 | doi: 10.1021/bk-1990-0423.ch003

0

(2)

Here, t h e h e a t o f s o r p t i o n , ΔΗ§ , i s a c o m p o s i t e parameter i n v o l v i n g b o t h s o r p t i o n mechanisms. The H e n r y ' s law mode r e q u i r e s b o t h t h e f o r m a t i o n o f a s i t e and t h e d i s s o l u t i o n of the s p e c i e s i n t o t h a t s i t e . The f o r m a t i o n o f a s i t e i n v o l v e s an e n d o t h e r m i c c o n t r i b u t i o n t o t h i s p r o c e s s . In t h e c a s e o f t h e Langmuir mode, t h e s i t e a l r e a d y e x i s t s i n t h e p o l y m e r m a t r i x and, c o n s e q u e n t l y , s o r p t i o n by h o l e f i l l i n g y i e l d s more e x o t h e r m i c h e a t s o f s o r p t i o n . A form o f F i c k ' s law d e s c r i b e s t h e d i f f u s i o n o f g a s e s t h r o u g h t h e amorphous polymer m a t r i x . The d i f f u s i o n c o e f f i c i e n t has been o b s e r v e d t o f o l l o w an A r r h e n i u s r e l a t i o n s h i p , c h a r a c t e r i s t i c o f an a c t i v a t e d p r o c e s s .

D = D

exp(--^

0

(3)

In t h i s e q u a t i o n , E p i s t h e a c t i v a t i o n e n e r g y r e q u i r e d t o g e n e r a t e an o p e n i n g between polymer c h a i n s l a r g e enough t o a l l o w the penetrant molecule to pass. The a c t i v a t i o n e n e r g y i s a f u n c t i o n o f t h e i n t r a - and i n t e r - c h a i n f o r c e s t h a t must be overcome i n o r d e r t o c r e a t e t h e space f o r a u n i t d i f f u s i o n a l jump o f t h e p e n e t r a n t . The a c t i v a t i o n e n e r g y o f d i f f u s i o n w i l l be g r e a t e r t h e l a r g e r t h e p e n e t r a n t m o l e c u l e , t h e s t r o n g e r t h e polymer c o h e s i v e e n e r g y , and t h e more r i g i d t h e c h a i n s . By s u b s t i t u t i n g E q u a t i o n s 2 and 3 i n t o E q u a t i o n 1, t h e p e r m e a b i l i t y can a l s o be e x p r e s s e d i n terms o f an A r r h e n i u s type r e l a t i o n s h i p .

Ρ = P exp^^j

(4)

E =

(5)

0

where P

E

D

+ ΔΗ

5

A conceptual a l t e r n a t i v e to the formulation of t r a n s p o r t p a r a m e t e r s i n terms o f t h e a c t i v a t e d - s t a t e a p p r o a c h , p a r t i c u l a r l y when c o n c e r n e d w i t h polymer morphology, i s t h e use o f f r e e volume t h e o r y (8-10).


In

3.

WEINKAUF & PAUL


t h i s a p p r o a c h , t h e t r a n s p o r t p a r a m e t e r s a r e dependent on t h e s t a t i s t i c a l d i s t r i b u t i o n o f t h e f r e e volume i n t h e polymer matrix. The t r a n s p o r t p r o c e s s i s t h o u g h t t o be d i r e c t l y r e l a t e d t o the p r o b a b i l i t y of a p e n e t r a n t f i n d i n g a pathway l a r g e enough t o p e r f o r m a d i f f u s i o n a l " s t e p " from one s o r p t i o n s i t e t o a n o t h e r . Cohen and T u r n b u l l (£) and Fujita have d e r i v e d e x p r e s s i o n s f o r t h e e x p o n e n t i a l dependence o f t h e d i f f u s i o n c o e f f i c i e n t on t h e f r a c t i o n a l f r e e volume, /,


(6) where, D and Β a r e c o n s t a n t s c h a r a c t e r i s t i c o f p a r t i c u l a r polymer-penetrant systems. The c o n c e p t o f f r e e volume has been o f more l i m i t e d use i n t h e p r e d i c t i o n o f s o l u b i l i t y c o e f f i c i e n t s ; a l t h o u g h , P e t e r l i n (JJJ has s u g g e s t e d t h a t t h e s o l u b i l i t y c o e f f i c i e n t i s d i r e c t l y p r o p o r t i o n a l t o t h e f r e e volume a v a i l a b l e i n t h e p o l y m e r m a t r i x . In many r e s p e c t s , t h e f r e e volume e x p r e s s i o n s c l o s e l y resemble the r e l a t i o n s h i p s developed i n the a c t i v a t e d s t a t e approach. In f a c t f o r t h e c a s e o f d i f f u s i v i t y , t h e two models can be shown t o be m a t h e m a t i c a l l y e q u i v a l e n t by i n c o r p o r a t i n g t h e r m a l e x p a n s i o n models s u c h as t h e one p r o p o s e d by Fox and F l o r y {12.) . The u s e f u l n e s s o f t h e f r e e volume model; however, l i e s i n t h e a c c e s s i b i l i t y o f t h e f r a c t i o n a l f r e e volume, t h r o u g h t h e use o f group c o n t r i b u t i o n methods d e v e l o p e d by B o n d i (12.) and Sugden (14.) , f o r c o r r e l a t i o n o f b a r r i e r p r o p e r t i e s o f p o l y m e r s o f d i f f e r e n t s t r u c t u r e as d e m o n s t r a t e d by Lee (15.) . 0

The

E f f e c t s of

Crystallinity

The p o t e n t i a l a d v a n t a g e o f c r y s t a l l i n e p o l y m e r s f o r b a r r i e r a p p l i c a t i o n s was r e c o g n i z e d by Morgan ( 1 ) ; although, p r e v i o u s i n v e s t i g a t o r s had r e p o r t e d r e d u c e d p e r m e a b i l i t i e s i n s e m i - c r y s t a l l i n e p o l y m e r s (2,1) . As w i l l be discussed, t h e e q u i l i b r i u m c o n c e n t r a t i o n o f s o r b e d p e n e t r a n t and t h e d i f f u s i o n p r o c e s s a r e a f f e c t e d by c r y s t a l l i n i t y i n u n i q u e l y d i f f e r e n t ways. S o r p t i o n i n S e m i c r y s t a l l i n e P o l y m e r s . The work o f s e v e r a l i n v e s t i g a t o r s has c o n c l u d e d t h a t t h e c h a i n p a c k i n g i n polymer c r y s t a l l i t e s i s such t h a t i t p r e c l u d e s the d i s s o l u t i o n o f even s m a l l gas m o l e c u l e s (16-23). T r a n s p o r t i n s e m i - c r y s t a l l i n e p o l y m e r s can, t h u s , be t r e a t e d on t h e b a s i s o f a s i m p l e two phase model, c o n s i s t i n g o f a d i s p e r s e d impermeable c r y s t a l l i n e phase i n a p e r m e a b l e amorphous m a t r i x . L a s o s k i and Cobbs (17) attempted t o c o r r e l a t e the s o l u b i l i t y o f water vapor i n unoriented poly(ethylene terephthalate) and n y l o n 610 w i t h


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the degree o f c r y s t a l l i n i t y . Over a c r y s t a l l i n e range 0 t o 40 %, t h e y f o u n d t h e s o l u b i l i t y t o be a l i n e a r f u n c t i o n o f t h e amorphous volume f r a c t i o n , Φ,

S = SO a

(7)

where S i s t h e s o l u b i l i t y c o e f f i c i e n t f o r t h e c o m p l e t e l y amorphous m a t e r i a l . M i c h a e l s (UD confirmed the v a l i d i t y o f t h e s i m p l e two phase model ( f o r a r u b b e r y amorphous phase) o v e r a wide range o f c r y s t a l l i n i t y from measurements of the s o l u b i l i t y o f s m a l l probe gases i n p o l y e t h y l e n e (Figure 1). S u r p r i s i n g l y , the heats of s o l u t i o n of the amorphous phase remained i n d e p e n d e n t o f d e g r e e o r method o f crystallization. W h i l e t h i s i s a s i m p l e and a p p e a l i n g model, one might e x p e c t t h a t t h e s i g n i f i c a n t amount o f s t r e s s imposed by c r y s t a l l i z a t i o n on t h e n o n - c r y s t a l l i n e phase would a l t e r i t s s o r p t i o n p r o p e r t i e s . In 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 ) , however, M i c h a e l s e t a l ( Z i ) f o u n d t h e d e c r e a s e i n s o l u b i l i t y accompanying c r y s t a l l i z a t i o n was s m a l l e r t h a n t h a t p r e d i c t e d by E q u a t i o n 7. They p r o p o s e d t h a t c r y s t a l l i z a t i o n t e n d e d t o o c c u r i n t h e d e n s e r r e g i o n s o f t h e amorphous m a t r i x , t h e r e b y e f f e c t i v e l y c o n c e n t r a t i n g t h e volume o f m i c r o v o i d s i n t h e r e m a i n i n g amorphous r e g i o n s . E x p e r i m e n t a l s o r p t i o n i s o t h e r m s showed t h a t t h e s o r p t i o n c a p a c i t y o f t h e Langmuir o r " h o l e f i l l i n g " mechanism p e r u n i t volume o f amorphous phase i n c r e a s e d by 40% on c r y s t a l l i z a t i o n . More r e c e n t work by P u l e o and P a u l (ZA.) has c o n c l u d e d t h a t c e r t a i n c r y s t a l s t r u c t u r e s w i l l p e r m i t s o r p t i o n and s u b s e q u e n t d i f f u s i o n o f s m a l l gas m o l e c u l e s . In t h i s i n v e s t i g a t i o n , gas s o r p t i o n and t r a n s p o r t measurements were made u s i n g p o l y ( 4 - m e t h y l - l - p e n t e n e ) (PMP) samples h a v i n g a wide r a n g e o f c r y s t a l l i n i t y . In c o n t r a s t t o E q u a t i o n 7, e x t r a p o l a t i o n t o 100% c r y s t a l l i n i t y s u g g e s t s t h a t t h e c r y s t a l l i n e phase has a f i n i t e s o l u b i l i t y coefficient, r o u g h l y 30% o f t h a t f o r t h e amorphous phase, f o r gases s u c h as CO2 and C H 4 . S i n c e s o r p t i o n i n t h e PMP samples s t r i c t l y obeys H e n r y ' s law, t h e " h o l e f i l l i n g " argument a p p l i e d by M i c h a e l s f o r PET i s not j u s t i f i a b l e . The d e p a r t u r e from c o n v e n t i o n a l c r y s t a l l i n e b e h a v i o r i s a t t r i b u t e d t o t h e open s t r u c t u r e o f t h e PMP c r y s t a l l a t t i c e where t h e r e a r e gaps o f s u f f i c i e n t s i z e t o accommodate s m a l l gas m o l e c u l e s which, o f c o u r s e , i s n o t t h e c a s e f o r p o l y e t h y l e n e . V i e t h and Wuerth (25.) f o u n d n e g a t i v e d e v i a t i o n s from t h e s i m p l e two phase model f o r s e m i c r y s t a l l i n e p o l y p r o p y l e n e suggesting that the presence of c r y s t a l l i t e s i n some way r e d u c e s t h e s o r p t i v e c a p a c i t y o f t h e amorphous phase. However, a n a l y s i s o f samples u s i n g x - r a y d i f f r a c t i o n r e v e a l e d the presence of a l e s s s t a b l e c r y s t a l l i n e phase h a v i n g a lower d e n s i t y . S i n c e t h e c r y s t a l l i n e volume f r a c t i o n i s commonly d e t e r m i n e d f r o m d e n s i t y measurements, t h e p r e s e n c e o f a second, l e s s dense (however, s t i l l impermeable) c r y s t a l l i n e phase would seem a


of



3. WEINKAUF & PAUL

£

Effects ofStructural Order on Barrier Properties

0.10 ο • Time-lag Method

0.08

ϋ

· •

Static Method

0.06

.9? 0.04

0.02

0.00 0.0

0.2

0.4

0.6

0.8

1.0

Amorphous Volume Fraction, Φ. Figure 1. Effect of amorphous phase content on the solubility coefficients of various gases in semi-crystalline polyethylene. (Data taken from Ref. 19.)


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t o o f f e r an e x p l a n a t i o n f o r t h e s e o b s e r v a t i o n s . Results l i k e t h e s e s u g g e s t t h a t we r e c o n s i d e r t h e p o t e n t i a l o f gas s o r p t i o n e x p e r i m e n t s as an a n a l y t i c a l t o o l f o r p r o b i n g t h e m i c r o s t r u c t u r e of polymers. D i f f u s i o n i n S e m i c r y s t a l l i n e Polymers. The e x t e n s i o n o f t h e s i m p l e two phase model t o i n c l u d e t h e d i f f u s i o n c o e f f i c i e n t i n s e m i c r y s t a l l i n e p o l y m e r s r e q u i r e s some refinements. Given the t e n s o r i a l c h a r a c t e r of the d i f f u s i o n p r o c e s s e s , one must f i r s t c o n s i d e r t h e s p a t i a l o r g a n i z a t i o n o f t h e d i s p e r s e d impermeable p h a s e . Second, one m i g h t , a l s o , e x p e c t t h a t t h e " c r o s s l i n k i n g " e f f e c t from t i e m o l e c u l e s between c r y s t a l l i t e s and o t h e r c h a i n s m e r e l y a n c h o r e d t o t h e c r y s t a l would r e d u c e t h e m o b i l i t y o f t h e amorphous p h a s e . B o t h i s s u e s have been t h e f o c u s o f numerous i n v e s t i g a t i o n s (19-29). The most w i d e l y a c c e p t e d v i e w o f d i f f u s i o n i n s e m i c r y s t a l l i n e p o l y m e r s stems from t h e e x t e n s i v e s e r i e s o f s t u d i e s c o n d u c t e d by M i c h a e l s and c o w o r k e r s (18-23). Using an e l e c t r i c a l a n a l o g o f a p o r o u s medium c o n s i s t i n g o f conducting channels, the f l u x of a penetrant through a s e m i c r y s t a l l i n e p o l y m e r can be e x p r e s s e d as f o l l o w s

(8)

where D i s t h e d i f f u s i v i t y o f t h e gas i n t h e c o m p l e t e l y amorphous p o l y m e r . The t e r m α i s t h e c r o s s - s e c t i o n a l a r e a f r a c t i o n of the regions a v a i l a b l e f o r t r a n s p o r t . The q u a n t i t y τ i s t h e " t o r t u o s i t y f a c t o r " accounting f o r the impedance o f f l o w o f f e r e d by t h e i n c r e a s e d e f f e c t i v e p a t h l e n g t h as w e l l as v a r i a t i o n s i n t h e c r o s s s e c t i o n a l a r e a o f the conducting regions. I f t h e s y s t e m o f impermeable c r y s t a l l i t e s i s randomly d i s p e r s e d , t h e a r e a f r a c t i o n , a, and t h e amorphous volume f r a c t i o n , Φ , can be e q u a t e d . From t h i s model, t h e e f f e c t i v e d i f f u s i o n c o e f f i c i e n t becomes a

(9)

U s i n g a n o t h e r e l e c t r i c a l a n a l o g approach, K l u t e (23.,21) a r r i v e d a t a s i m i l a r e x p r e s s i o n i n which t h e impedance f a c t o r was t e r m e d t h e " t r a n s m i s s i o n f u n c t i o n . " In b o t h c a s e s , however, t h e p r o p e r t i e s o f t h e c o n d u c t i n g phase a r e c o n s i d e r e d n o t t o be i n f l u e n c e d by t h e c r y s t a l l i n e p h a s e . A l t h o u g h t h i s was found t o be t r u e f o r s o r p t i o n , M i c h a e l s e t a l a s s e r t e d t h a t t h e c r y s t a l l i t e s would r e d u c e t h e m o b i l i t y o f t h e c h a i n s i n t h e amorphous phase and, t h u s , f u r t h e r reduce penetrant d i f f u s i o n r a t e s . The " c h a i n


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67

i m m o b i l i z a t i o n " f a c t o r , β, was i n t r o d u c e d t o a c c o u n t f o r t h e change i n p e n e t r a n t m o b i l i t y c a u s e d b y t h e " c r o s s l i n k i n g " or "anchoring" e f f e c t of the c r y s t a l l i t e s . The e f f e c t i v e d i f f u s i v i t y c a n t h e n be e x p r e s s e d as


(10)

The c h a i n i m m o b i l i z a t i o n t e r m i n d i r e c t l y r e f l e c t s t h e amount o f i n c r e a s e i n a c t i v a t i o n e n e r g y o f d i f f u s i o n t h a t i s o b s e r v e d i n t h e amorphous phase upon c r y s t a l l i z a t i o n . It i s probably a f u n c t i o n o f both e f f e c t i v e c r y s t a l surface a r e a and p e n e t r a n t s i z e . I t was n o t e d , however, t h a t t h e c o n c e p t o f c h a i n i m m o b i l i z a t i o n l o s e s i t s s i g n i f i c a n c e as t h e r i g i d i t y o f t h e p o l y m e r backbone i n c r e a s e s (22.) . F i g u r e 2 summarizes t h e r e s u l t s o f L o w e l l and McCrum (2&) f o r t h e a p p a r e n t d i f f u s i o n and s o l u b i l i t y c o e f f i c i e n t s as a f u n c t i o n o f t e m p e r a t u r e f o r c y c l o p r o p a n e i n l i n e a r polyethylene through the melting point region o f the material. The a c t i v a t i o n e n e r g y f o r d i f f u s i o n i s h i g h e r i n the s e m i c r y s t a l l i n e m a t e r i a l than a f t e r melting, while t h e d e r i v e d h e a t o f s o l u t i o n i s n e a r l y t h e same above and below t h e m e l t i n g p o i n t . T h i s s u g g e s t s , as p r o p o s e d by M i c h a e l s e t a l (iâ), t h a t t h e presence o f t h e c r y s t a l l i t e s i m p a i r s t h e d i f f u s i o n a l m o b i l i t y i n t h e amorphous r u b b e r y phase, t h e e x t e n t t o w h i c h i n c r e a s e s as t h e t e m p e r a t u r e i s l o w e r e d , b u t does n o t a f f e c t t h e s o l u b i l i t y c h a r a c t e r i s t i c s o f t h e amorphous r e g i o n s . D i s t i n c t i o n s between t h e e f f e c t o f t o r t u o s i t y and c h a i n i m m o b i l i z a t i o n c a n be a p p r o x i m a t e d by a s s u m i n g t h a t the r e d u c t i o n i n d i f f u s i v i t y f o r chain i m m o b i l i z a t i o n f o r a s m a l l p e n e t r a n t gas s u c h as h e l i u m i s n e g l i g i b l e , i . e . , β ~ 1 . Then, t h e e f f e c t i v e t o r t u o s i t y c a n be a s s e s s e d by c o m p a r i n g t h e d i f f u s i v i t i e s o f h e l i u m i n t h e c o m p l e t e l y amorphous and the s e m i c r y s t a l l i n e m a t e r i a l s . Assuming t h a t t o r t u o s i t y i s independent o f penetrant diameter, the chain i m m o b i l i z a t i o n f a c t o r c a n t h e n be e s t i m a t e d f o r o t h e r l a r g e r p e n e t r a n t s u s i n g E q u a t i o n 10. A t h i g h l e v e l s o f c r y s t a l l i n i t y , though, t h e reduced c r o s s - s e c t i o n a l area o f t h e permeable, amorphous p a s s a g e s t e n d s t o e x c l u d e some l a r g e r d i f f u s i n g s p e c i e s , a t t r i b u t i n g s i g n i f i c a n t l y l a r g e r apparent reductions i n d i f f u s i v i t y t o the chain immobilization parameter. U n d e r s t a n d i n g t h e l i m i t a t i o n s o f s u c h an a p p r o a c h , M i c h a e l s e t a l have d i s c u s s e d t h e c o r r e l a t i o n t h e c h a i n i m m o b i l i z a t i o n p a r a m e t e r as a f u n c t i o n o f p e n e t r a n t d i a m e t e r and t h e amorphous volume f r a c t i o n (2Ώ.) . A t t e m p t s have a l s o been made t o r e l a t e t h e t o r t u o s i t y f a c t o r t o t h e amorphous volume f r a c t i o n . A power law r e l a t i o n s h i p has been s u g g e s t e d

τ =φ-η

(11)



68


Figure 2. Temperature dependence of transport coefficients for cyclopropane in linear polyethylene above and below the melting point. (Data taken from Ref 28.)


3.

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Effects ofStructural Order on Barrier Properties

where t h e exponent, n, f o r u n o r i e n t e d p o l y m e r s commonly r a n g e s from 1 t o 2. The t o r t u o s i t y i s dependent upon t h e s i z e , shape, and a n i s o t r o p i c n a t u r e o f t h e c r y s t a l l i n e phase. B a r r i n g any m e c h a n i c a l s t r e s s , most o f t h e s e p a r a m e t e r s a r e d e t e r m i n e d by t h e k i n e t i c s o f crystallization. F o r s e v e r a l p o l y m e r systems, ' η ' has been f o u n d t o be c o n s t a n t o v e r a wide range o f c r y s t a l l i n i t y


(2Q,2S) . A n n e a l i n g s e m i c r y s t a l l i n e samples has been f o u n d t o r e s u l t i n r e d u c t i o n s i n t h e t o r t u o s i t y p a r a m e t e r as much as 50% d e s p i t e l a r g e i n c r e a s e s i n c r y s t a l s i z e (22.,2JL) . Some w o r k e r s (2JL) have s u g g e s t e d , b a s e d on t h e k i n e t i c s o f c r y s t a l growth, t h a t t h i s i s t h e r e s u l t o f t h e f o r m a t i o n o f p e r m e a b l e gaps i n t h e c r y s t a l l i t e . In b r i e f , u n l i k e s o l u b i l i t y , t h e e f f e c t s o f c r y s t a l l i n i t y on t h e e f f e c t i v e d i f f u s i v i t y i n t i m a t e l y i n v o l v e t h e d e t a i l s o f t h e p o l y m e r morphology. Because o f t h e c h a i n i m m o b i l i z a t i o n e f f e c t , c r y s t a l l i n i t y may c a u s e an i n c r e a s e i n t h e a c t i v a t i o n energy o f d i f f u s i o n . However, observed decreases f o r the a c t i v a t i o n energy o f d i f f u s i o n f o r h e l i u m i n s e m i c r y s t a l l i n e m a t e r i a l s have been a t t r i b u t e d t o " g r a i n b o u n d a r y " e f f e c t s (2_â) . F o r a f i r s t a p p r o x i m a t i o n , some a u t h o r s have f o u n d i t s u f f i c i e n t t o use t h e f o l l o w i n g r e l a t i o n s h i p f o r t h e c o r r e l a t i o n o f amorphous volume f r a c t i o n and e f f e c t i v e d i f f u s i v i t y ,

D = DO

(12)

a

and t h u s , by s u b s t i t u t i n g P = S D 0 a

a

i n t o Eqn. 1, (13)

2

T h i s amounts t o s e t t i n g β = 1 and n=l i n E q u a t i o n s 10 and 11. U n d e r s t a n d a b l y , t h e s e a p p r o x i m a t i o n s a r e somewhat l i m i t e d in their predictive ability. More d e t a i l e d a s p e c t s o f t r a n s p o r t i n h e t e r o g e n e o u s media have been g i v e n i n t h e e x c e l l e n t r e v i e w s o f t h e s u b j e c t by B a r r e r (2&) and P e t r o p o l u s (21) . The models d e s c r i b e d by t h e s e a u t h o r s and o t h e r s i n c l u d e t h e e f f e c t s o f s i z e , shape, and a n i s o t r o p y o f t h e c r y s t a l l i n e phase on the t o r t u o s i t y . Models o f h i g h l y o r d e r e d a n i s o t r o p i c media have been d e m o n s t r a t e d t o have t o r t u o s i t i e s i n t h e range o f 30, w h i c h r e f l e c t s t h e r a t h e r d r a m a t i c r o l e t h a t o r i e n t a t i o n can have on t h e b a r r i e r p r o p e r t i e s o f s e m i c r y s t a l l i n e polymers. The E f f e c t s

of

Orientation

S t r e t c h i n g o r d r a w i n g o f p o l y m e r f i l m s i s u s e d t o improve m e c h a n i c a l b e h a v i o r , and under c e r t a i n c o n d i t i o n s c a n l e a d t o improved b a r r i e r p r o p e r t i e s . The d e g r e e o f o r i e n t a t i o n a c h i e v e d i s p r i m a r i l y dependent upon t h e draw r a t i o and


69


70


other process conditions. D e p e n d i n g on t h e mode o f d e f o r m a t i o n , t h e p e r m e a b i l i t y o f a p o l y m e r may i n c r e a s e o r decrease. Much o f t h e v a r i a n c e i n t r a n s p o r t d a t a f o r a g i v e n p o l y m e r t h a t has been r e p o r t e d can be a t t r i b u t e d t o t h e c o n d i t i o n s t h a t have been employed d u r i n g o r i e n t a t i o n o f the m a t e r i a l . The t r a n s p o r t p r o p e r t i e s o f amorphous and s e m i c r y s t a l l i n e p o l y m e r s a r e a f f e c t e d by o r i e n t a t i o n i n d i f f e r e n t ways, and, t h u s w i l l be c o n s i d e r e d separately. The e f f e c t s o f u n i a x i a l and b i a x i a l o r i e n t a t i o n can be q u i t e d i f f e r e n t . A l t h o u g h many c o m m e r c i a l p r o c e s s i n g t e c h n i q u e s impose a b i a x i a l s t r a i n on t h e p o l y m e r m e l t , we w i l l d e a l h e r e p r i m a r i l y w i t h u n i a x i a l l y deformed materials. O r i e n t a t i o n o f Amorphous P o l y m e r s . Since o p t i c a l c l a r i t y i s frequently a d e s i r e d property of packaging f i l m s , t h e s e m a t e r i a l s a r e o f t e n e s s e n t i a l l y amorphous, e.g. p o l y v i n y l c h l o r i d e (PVC) and p o l y s t y r e n e , and o r i e n t a t i o n i s one o f t h e few a p p r o a c h e s a v a i l a b l e f o r f i n e tuning b a r r i e r properties. To f u l l y u n d e r s t a n d t h e g r o w i n g data base of t r a n s p o r t p r o p e r t i e s o f o r i e n t e d f i l m s , i t w i l l f i r s t be n e c e s s a r y t o d i s c u s s t h e mechanism by which t h e s e p o l y m e r s o r i e n t (See F i g u r e 3). I n i t i a l l y , the u n o r i e n t e d p o l y m e r can be e n v i s i o n e d as an e n t a n g l e d network o f randomly c o i l e d c h a i n s . At t h e r m a l c o n d i t i o n s w h i c h a l l o w some d e g r e e s o f freedom, an a p p l i e d s t r e s s w i l l c a u s e c h a i n s t o u n c o i l and t h e axes o f t h e segments t o p r o g r e s s i v e l y become o r i e n t e d i n t h e d i r e c t i o n o f t h e deformation. Some d i s e n t a n g l e m e n t o f t h e c h a i n s may accompany t h i s p r o c e s s . I f the temperature i s reduced to a p o i n t where t h e p o t e n t i a l e n e r g y o f t h e e x t e n d e d c h a i n s i s l e s s t h a n t h e m e c h a n i c a l c o n s t r a i n t s imposed by neighboring c h a i n s , t h e o r i e n t e d c h a i n s w i l l be f r o z e n i n t o p l a c e and w i l l not r e t r a c t upon r e m o v a l o f t h e s t r e s s . Subsequent h e a t i n g , however, w i l l i n c r e a s e m o b i l i t y s u c h t h a t t h e p o l y m e r c h a i n s can c o n t r a c t and l o s e t h e p r e f e r r e d orientation. P o l y m e r s p l a s t i c a l l y deformed i n t h i s way commonly show d e c r e a s e s i n p e r m e a b i l i t y as a r e s u l t o f a r e d u c t i o n i n the e f f e c t i v e d i f f u s i o n c o e f f i c i e n t . For the c a s e o f r u b b e r y networks e x t e r n a l l y c o n s t r a i n e d i n a d e f o r m e d s t a t e , t h e e f f e c t o f o r i e n t a t i o n a p p e a r s t o have l i t t l e e f f e c t on e i t h e r s o l u b i l i t y o r m o b i l i t y (22.) . G e n e r a l l y , m a t e r i a l s t h a t a r e e l a s t i c a l l y deformed i n t h e s o l i d s t a t e a r e more p e r m e a b l e w h i c h may be a t t r i b u t e d t o an i n c r e a s e i n f r e e volume accompanying d e f o r m a t i o n (22.) . P r e s e n t l y , t h e amount o f d a t a on t r a n s p o r t i n u n i a x i a l l y o r i e n t e d amorphous p o l y m e r s i s s m a l l i n comparison with t h a t of s e m i c r y s t a l l i n e m a t e r i a l s . The t r a n s p o r t p r o p e r t i e s o f o r i e n t e d n a t u r a l r u b b e r (22.) , polystyrene (22,21) , p o l y c a r b o n a t e (25.) , and p o l y v i n y l c h l o r i d e (23,21) among o t h e r s have been r e p o r t e d . One o f t h e more c o m p l e t e d e s c r i p t i o n s o f t h e e f f e c t s o f u n i a x i a l o r i e n t a t i o n on gas t r a n s p o r t p r o p e r t i e s o f an amorphous p o l y m e r i s t h a t by Wang and P o r t e r (2A) f o r p o l y s t y r e n e .



3.

WEINKAUF & PAUL


As seen i n T a b l e 1, t h e d e c r e a s e i n p e r m e a b i l i t y can be d i r e c t l y a t t r i b u t e d t o a dramatic r e d u c t i o n i n the e f f e c t i v e d i f f u s i o n c o e f f i c i e n t , w h i l e t h e r e i s a much s m a l l e r e f f e c t on t h e a p p a r e n t s o l u b i l i t y . A similar dependence o f t h e s o l u b i l i t y and d i f f u s i o n c o e f f i c i e n t s on t h e draw r a t i o has been o b s e r v e d i n o t h e r u n i a x i a l l y o r i e n t e d polymers ( 3 5 - 3 7 ) . Because t h e g l a s s t r a n s i t i o n and d e n s i t y o f t h e p o l y s t y r e n e samples were f o u n d i n d e p e n d e n t o f t h e draw r a t i o , t h e y c o n c l u d e d t h a t t h e r e d u c t i o n i n d i f f u s i v i t y was due t o a n i s o t r o p i c r e d i s t r i b u t i o n o f t h e f r e e volume d u r i n g d r a w i n g . U s i n g an e x p a n s i o n c o e f f i c i e n t r e l a t e d t o draw r a t i o , t h e p o l y s t y r e n e d a t a were s u c c e s s f u l l y c o r r e l a t e d u s i n g t h e C o h e n - T u r n b u l l f r e e volume t h e o r y . However, t h e s i t u a t i o n was f o u n d t o be more complex f o r PVC (23). T h e r m a l and m e c h a n i c a l h i s t o r y i n f l u e n c e m i c r o s t r u c t u r e o f p o l y m e r s and t h e s e e f f e c t s s h o u l d be c o n s i d e r e d when i n t e r p r e t i n g t r a n s p o r t d a t a . Work by E l H i b r i (23) and Brady e t . a l . (22) on u n i a x i a l l y and b i a x i a l l y o r i e n t e d PVC d e m o n s t r a t e s t h e complex dependence o f t h e t r a n s p o r t p a r a m e t e r s on t h e v a r i o u s t h e r m a l and m e c h a n i c a l h i s t o r i e s employed. At c o n s t a n t draw r a t i o s o v e r a wide range o f d r a w i n g t e m p e r a t u r e s , t h e e f f e c t i v e d i f f u s i o n c o e f f i c i e n t i n c r e a s e d and d e c r e a s e d i n t e m p e r a t u r e ranges b o t h above and below t h e g l a s s transition. The e f f e c t o f b i a x i a l o r i e n t a t i o n was f o u n d t o decrease the p e r m e a b i l i t y , again, through a r e d u c t i o n i n the e f f e c t i v e d i f f u s i v i t y . As t h e b i a x i a l s t r e t c h i n g became more " u n b a l a n c e d " ( i . e . , l a r g e r draw r a t i o a l o n g a p a r t i c u l a r a x i s ) , the p e r m e a b i l i t i e s decreased f u r t h e r . G e n e r a l l y , as t h e mode o f d e f o r m a t i o n becomes more u n i a x i a l , t h e b e n e f i t s i n terms o f improved b a r r i e r p r o p e r t i e s become l a r g e r (21) . O r i e n t a t i o n of S e m i c r y s t a l l i n e Polymers. The a n i s o t r o p i c arrangement o f impermeable p o l y m e r c r y s t a l l i t e s c a u s e d by d e f o r m a t i o n g e n e r a l l y d e c r e a s e s t h e e f f e c t i v e d i f f u s i v i t y by i n c r e a s i n g t h e t o r t u o s i t y . In a d d i t i o n , d r a w i n g o f s e m i c r y s t a l l i n e p o l y m e r s has been f o u n d t o improve t h e b a r r i e r p r o p e r t i e s t h r o u g h s t r e s s - i n d u c e d c r y s t a l l i z a t i o n and o r i e n t a t i o n o f t h e r e m a i n i n g amorphous phase. Consequently, the r e d u c t i o n i n p e r m e a b i l i t y caused by o r i e n t a t i o n o f a c r y s t a l l i z a b l e polymer a r e o f t e n s u b s t a n t i a l l y l a r g e r t h a n t h o s e o b s e r v e d i n nonc r y s t a l l i z a b l e polymers. As w i t h amorphous p o l y m e r s , t h e t r a n s p o r t p r o p e r t i e s of o r i e n t e d s e m i c r y s t a l l i n e polymers depend on t h e draw r a t i o and t h e d e f o r m a t i o n mechanism. S t r e t c h i n g above t h e m e l t i n g p o i n t w i t h subsequent c r y s t a l l i z a t i o n o f t h e m a t e r i a l can l e a d t o q u i t e d i f f e r e n t r e s u l t s than the s t r e t c h i n g of a l r e a d y c r y s t a l l i n e materials. C r y s t a l l i z a t i o n from an o r i e n t e d m e l t may o c c u r d u r i n g e x t r u s i o n and i n j e c t i o n m o l d i n g p r o c e s s e s o f c r y s t a l l i z a b l e polymers. The c r y s t a l l i n e m i c r o s t r u c t u r e which r e s u l t s i s


71

72

BARRIER P O L Y M E R S AND STRUCTURES

h— O—H

h—


L

L

Draw Ratio = λ = ~Γ~~ Figure 3. Orientation of randomly coiled chains in an amorphous polymer.

Table 1. Effect of Molecular Orientation on C O - Transport Behavior in Polystyrene at25 - C t

Draw Ratio

Orientation Factor, f

Permeability (Barrers)

Diffusivity, D 2

(cm/sec) χ 10

10

Solubility, S (cm (STPycm atm) 3

3

1.0

0.0

8.0

24.0

25.1

1.8

0.016

5.8

19.0

23.4

3.1

0.048

2.9

7.5

29.6

4.4

0.122

1.5

-

-

5.0

0.170

1.0

4.6

16.0

t (Data taken from Ref. 34.)



3.

WEINKAUF & PAUL


h i g h l y dependent upon t h e d e g r e e o f s t r a i n imposed (38-40). In t h e r e g i o n o f low o r z e r o s t r e s s , a s p h e r u l i t i c m o r p h o l o g y i s formed ( F i g u r e 4a), where t h e l a m e l l a r c r y s t a l s t r u c t u r e s propagate r a d i a l l y from the n u c l e a t i o n site. At h i g h e r l e v e l s o f s t r e s s i n t h e m e l t , t h e n u c l e a t i o n s i t e s o r i e n t a l o n g t h i n f i b r i l l a r axes p r o m o t i n g the growth o f l a m e l l a r c r y s t a l s p e r p e n d i c u l a r t o the d i r e c t i o n of s t r a i n (Figure 4b). With exceedingly high l e v e l s o f s t r a i n imposed by t h e p r o c e s s i n g c o n d i t i o n s , t h e c r y s t a l l i z a t i o n p r o c e s s r e s u l t s i n complete replacement of t h e s p h e r u l i t c s t r u c t u r e by a u n i d i r e c t i o n a l c r y s t a l l i n e m o r p h o l o g y , o f t e n r e f e r r e d t o as a " s h i s h kebab" s t r u c t u r e (Figure 4c). In t h i s morphology, t h e l a m e l l a r c r y s t a l l i t e s a r e s e p a r a t e d by amorphous r e g i o n s o f l o o s e l o o p s , t i e m o l e c u l e s , and f r e e c h a i n ends ( F i g u r e 4 d ) . O r i e n t a t i o n of s e m i c r y s t a l l i n e polymers below the m e l t i n g p o i n t i s o f t e n r e f e r r e d t o as " c o l d d r a w i n g . " A l t h o u g h some s t r e s s c r y s t a l l i z a t i o n does o c c u r , t h e p r o c e s s p r i m a r i l y i n v o l v e s the t r a n s f o r m a t i o n of e x i s t i n g crystalline structures. A w i d e l y a c c e p t e d model o f t h e d e f o r m a t i o n mechanism i s t h a t p r o v i d e d by P e t e r l i n ( F i g u r e 5) ( 4 1 ) . P r i o r t o n e c k i n g , the c r y s t a l l a m e l l a e which c o n s t i t u t e t h e s p h e r u l i t i c s t r u c t u r e become a r r a n g e d i n a t i l t e d stack f o r m a t i o n (5b). N e c k i n g marks t h e transformation from s p h e r u l i t i c t o a m i c r o f i b r i l l a r s t r u c t u r e . In t h i s p r o c e s s , s m a l l b l o c k s o f l a m e l l a r c r y s t a l s a r e t o r n away f r o m t h e o r i g i n a l l a m e l l a e t o form a f i b r i l l a r s t r u c t u r e o f c r y s t a l l i t e s and t a u t t i e m o l e c u l e s (5c). O f t e n , b u n d l e s o f f i b r i l s a r e formed f r o m i n t e r f i b r i l t i e m o l e c u l e s (5d). Under moderate draw r a t i o s , t h e s p h e r u l i t i c s t r u c t u r e and t h e b u n d l e s o f f i b r i l s c o e x i s t

Effects of Structural Order on Barrier Properties - American Chemical

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