Chapter 2
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Assessment of Particle Size Distribution and Spatial Dispersion of Rubbery Phase in a Toughened Plastic Β. Z. Jang and Y. S. Chang Materials Science Program, Auburn University, AL 36849
A simplified statistical scheme for image analysis has been proposed to describe the spatial distribution of rubber particles in a plastic matrix. Based on this scheme, a software package compatible with a Hewlett-Packard personal computer has been developed which i s capable of analyzing the particle size distribution and spatial dispersion of rubber particles in a toughened plastic. With slight modification this package may be adapted to other computer systems for studying the second-phase morphology of any multiphase composite. The normalized dispersion index (NDI) calculated from the TEM micrographs by the image analysis method appears to be a very sensitive index for describing the spatial dispersion of rubber particles in high impact polystyrene (HIPS) samples. Materials with a small NDI (e.g., NDI < 0.142), signaling a good dispersion of rubber particles in the polystyrene matrix, appear to have the capability of quickly and uniformly developing thick crazes upon loading and thereby dissipating a great amount of strain energy. The morphological parameters obtained were correlated with the microscopic crazing behavior and the macroscopic mechanical properties. A stress f i e l d overlap concept was proposed to explain the effects of particle dispersion on the mechanical behavior of HIPS. A general rubber-toughening theory was also reviewed and discussed. The technical and commercial success of high impact polystyrene (HIPS) and (ABS) has led to a widespread research program on the use of rubbers as toughening agents for plastics. There is now an impressive l i s t of rubber-toughened polymers including both amorphous and 0097-6156/87/0332-0030$06.00/0 © 1987 American Chemical Society Provder; Particle Size Distribution ACS Symposium Series; American Chemical Society: Washington, DC, 1987.
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2.
JANG AND
CHANG
Spatial Dispersion of Rubbery Phase
s e m i c r y s t a l l i n e t h e r m o p l a s t i c s , and t h e r m o s e t t i n g r e s i n s . In a l l o f these m a t e r i a l s , the aim i s to i n c r e a s e f r a c t u r e r e s i s t a n c e w h i l e a t the same time p r e s e r v i n g the d e s i r a b l e p r o p e r t i e s o f the parent polymer (J.) . The r e l a t i o n s h i p s between s t r u c t u r e and p r o p e r t i e s o f r u b b e r - m o d i f i e d polymers are complex because o f the l a r g e number o f s t r u c t u r a l v a r i a b l e s i n v o l v e d ( 1 - 4 ) . The major s t r u c t u r a l parameters t h a t are important i n a polymer with a g i v e n chemical composition and m o l e c u l a r weight c h a r a c t e r i s t i c s are (a) rubber c o n t e n t , (b) volume f r a c t i o n o f the d i s p e r s e d phase, (c) r u b b e r p a r t i c l e s i z e d i s t r i b u t i o n , (d) degree o f c r o s s l i n k i n g o f the r u b b e r , and (e) degree o f i n t e r f a c i a l a d h e s i o n between the d i s p e r s e d and m a t r i x phases. One p o t e n t i a l l y important f a c t o r t h a t has been l a r g e l y overlooked i s the s t a t e o f rubber p a r t i c l e d i s p e r s i o n . P a r t i c l e d i s p e r s i o n w i l l a f f e c t the s t r e s s d i s t r i b u t i o n i n the p l a s t i c m a t r i x and t h e r e f o r e w i l l determine the mechanical behavior o f a toughened p l a s t i c . C r a z i n g and shear y i e l d i n g g e n e r a l l y are b e l i e v e d to be the two p r i m a r y sources o f energy a b s o r p t i o n when a toughened p l a s t i c i s m e c h a n i c a l l y loaded (1,3-4). The i n i t i a t i o n and growth o f both c r a z e s and shear bands are c r i t i c a l l y dependent upon the morphology o f the d i s p e r s e d r u b b e r y phase. T h e r e f o r e , the a b i l i t y t o adequately c h a r a c t e r i z e the complex morphology o f the rubbery phase i s o f g r e a t importance. The development o f s u i t a b l e techniques has i n f a c t p l a y e d an important p a r t i n the study o f s t r u c t u r e - p r o p e r t y r e l a t i o n s h i p s , and hence i n improving and extending the range o f toughened p r o d u c t s . The p r i n c i p a l methods a v a i l a b l e f o r t a c k l i n g the phase morphology c h a r a c t e r i z a t i o n problems are o p t i c a l and e l e c t r o n m i c r o s c o p y , l i g h t s c a t t e r i n g , and C o u l t e r Counter (_1). I f the rubber p a r t i c l e s are l a r g e enough t o be r e s o l v e d , o p t i c a l m i c r o s c o p y i s the s i m p l e s t and cheapest method f o r s t u d y i n g morphology. However, the most s u c c e s s f u l method f o r s t u d y i n g morphology i n rubber-toughened p l a s t i c s has been the osmium-staining method developed by Kato ( 5 - 7 ) ; the method being a p p l i c a b l e t o polymers c o n t a i n i n g u n s a t u r a t e d r u b b e r s . For t h o s e m a t e r i a l s c o n t a i n i n g rubbers t h a t cannot be s t a i n e d s u c c e s s f u l l y the technique o f l i g h t s c a t t e r i n g might be u s e f u l (8-10). For polymers t h a t can be d i s s o l v e d i n an e l e c t r o l y t e , C o u l t e r Counter may be used t o measure p a r t i c l e s i z e s ( i n the range 0.5 t o 400 jum) ( J ! ) . The method i s w e l l s u i t e d t o measuring the r e l a t i v e l y l a r g e p a r t i c l e s i n HIPS. S m a l l e r p a r t i c l e s tend to escape the d e t e c t i o n o f C o u l t e r Counter. F u r t h e r , the s p a t i a l d i s p e r s i o n o f rubber p a r t i c l e s cannot be r e v e a l e d by t h i s method. However, t h i s method has the advantages o f r e a d i l y p e r m i t t i n g a l a r g e sampling space as well as i n d i c a t i n g both p a r t i c l e s i z e and d i s p e r s i t y o f the d i s t r i b u t i o n . Presented i n t h i s paper are the r e s u l t s o f an i n v e s t i g a t i o n c o n c e r n i n g the l i n k between s t r u c t u r e and p r o p e r t i e s o f rubber-toughened p l a s t i c s . An attempt has been made t o a s s e s s the importance o f the s p a t i a l d i s t r i b u t i o n o f rubber p a r t i c l e s i n terms o f t h e i r e f f e c t i v e n e s s i n c o n t r o l l i n g c r a z e i n i t i a t i o n and growth. A l s o s t u d i e d i n p a r t i c u l a r were the e f f e c t s o f rubber p a r t i c l e s i z e on the mechanical p r o p e r t i e s o f HIPS m a t e r i a l s . A
Provder; Particle Size Distribution ACS Symposium Series; American Chemical Society: Washington, DC, 1987.
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PARTICLE SIZE DISTRIBUTION
computerized image a n a l y s i s and TEM t e c h n i q u e s were u t i l i z e d t o c h a r a c t e r i z e the r u b b e r y phase morphology. A s o f t w a r e package based on BASIC language has been developed t h a t i s c a p a b l e o f a n a l y z i n g the average p a r t i c l e s i z e , s i z e d i s t r i b u t i o n , volume f r a c t i o n o f p a r t i c l e s , and the degree o f p a r t i c l e d i s p e r s i o n i n a m a t r i x . A l t h o u g h s p e c i f i c a l l y d e s i g n e d f o r the Hewlett Packard Model 9836 p e r s o n a l computer, t h i s package may be r e a d i l y m o d i f i e d to be used i n o t h e r computer systems.
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Degree o f D i s p e r s i o n o f Rubber P a r t i c l e s Gurland (12) has developed a q u a n t i t a t i v e m i c r o s c o p y scheme f o r measuring the degree o f d i s p e r s i o n o f a g g r e g a t e s . The s t a t e o f a g g r e g a t i o n o f a c o n s t i t u e n t o f a heterogeneous m u l t i p h a s e m a t e r i a l may be d e s c r i b e d a s b e i n g d i s p e r s e d , agglomerated, o r c o n t i n u o u s . Such terms r e f e r t o the degree o f d i s p e r s i o n , which i s q u a n t i t a t i v e l y r e l a t e d t o t h r e e measurable parameters - the i n t e r f a c e o f s e p a r a t i o n , the f i n e n e s s , and the d i s t r i b u t i o n o f the p a r t i c l e s w i t h i n the m a t r i x (JL2). S u r f a c e o f s e p a r a t i o n . Where volume f r a c t i o n o f the d i s p e r s e d phase i s h i g h so t h a t the a r e a o f c o n t a c t between c o n t i g u o u s p a r t i c l e s o f the second phase i s u n n e g l i g i b l e the e x t e n t o f the s u r f a c e o f s e p a r a t i o n between the second phase and the m a t r i x has to be c o n s i d e r e d i n measuring the degree o f d i s p e r s i o n . For a two-phase composite the degree o f s e p a r a t i o n dp i s d e f i n e d a s : Sv(ab) dp =
Sv(ab) =
Sv(aa) + Sv(ab)
(1) Sv(total)
where Sv(ab) i s the a r e a o f the i n t e r f a c e between p a r t i c l e s o f the p a r t i c u l a t e phase and the m a t r i x , and Sv(aa) i s the a r e a o f c o n t a c t between c o n t i g u o u s p a r t i c l e s o f the p a r t i c u l a t e phase i n a volume. The v a l u e o f dp may be determined from i n t e r c e p t s o f random l i n e s and i n t e r n a l s u r f a c e s ( 1 2 ) : NL(ab) dp =
(2) NL(ab) + 2NL(aa)
where NL(ab) = average number o f i n t e r s e c t i o n w i t h p a r t i c u l a t e m a t r i x i n t e r f a c e per u n i t l e n g t h o f a random t e s t l i n e , and NL(aa) = t h a t w i t h p a r t i c l e - p a r t i c l e i n t e r f a c e . The d e t e r m i n a t i o n o f c o n t i g u i t y o r degree o f d i s p e r s i o n does not r e q u i r e any assumptions r e g a r d i n g volume f r a c t i o n , p a r t i c l e s i z e , o r p a r t i c l e shape. However, due t o the g e n e r a l l y d i s c r e t e n a t u r e o f the rubbery phase i n a t y p i c a l toughened p l a s t i c such as HIPS t h e r e e x i s t s e s s e n t i a l l y no c o n t i g u i t y between r u b b e r p a r t i c l e s , i . e . , dp ~ 1. F i n e n e s s . The a r e a o f the i n t e r f a c e between a p a r t i c u l a t e phase and the m a t r i x i s a f u n c t i o n o f the p a r t i c l e s i z e , s i n c e p a r t i c l e s i z e and s p e c i f i c s u r f a c e a r e i n v e r s e l y r e l a t e d . The u l t i m a t e
Provder; Particle Size Distribution ACS Symposium Series; American Chemical Society: Washington, DC, 1987.
2.
Spatial Dispersion of Rubbery Phase
JANG AND CHANG
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l e v e l o f d i s p e r s i o n i s determined by the f i n e n e s s which i s u s u a l l y s p e c i f i e d by the average p a r t i c l e s i z e and the s i z e d i s t r i b u t i o n f u n c t i o n . The data on f i n e n e s s may, t h e r e f o r e , be o b t a i n e d from C o u l t e r Counter measurements o r image a n a l y s i s i n the case o f toughened p l a s t i c s . The computer programs developed i n our l a b p r o v i d e a c o n v e n i e n t t o o l t o a n a l y z e the p a r t i c l e f i n e n e s s i n terms o f p a r t i c l e r a d i u s , a r e a , and p e r i m e t e r .
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S p a t i a l D i s t r i b u t i o n . As suggested by Gurland ( 2 ) , a q u a n t i t a t i v e measure o f the degree o f homogeneity o f p a r t i c l e placement i n the m a t r i x i s the s t a n d a r d d e v i a t i o n o f the d i s t r i b u t i o n o f p a r t i c l e s i n small volumes o r areas o f the m i x t u r e : (3) Where Nvi i s the observed number o f p a r t i c l e s per u n i t volume i n the i t h sample and Tfv i s the a r i t h m e t i c mean number o f p a r t i c l e s i n η samples. (The index i r e f e r s t o the i t h sample i n a s e t o f η samples, and not t o the p a r t i c l e s i z e c l a s s ) . Maximum homogeneity i s c h a r a c t e r i z e d by a minimum s t a n d a r d d e v i a t i o n δ . If» on the o t h e r hand, s p e c i a l s e p a r a t i n g o r a g g l o m e r a t i n g t e n d e n c i e s e x i s t among the p a r t i c l e s , the v a l u e o f δ w i l l be l a r g e . In p r a c t i c e , the s t a n d a r d d e v i a t i o n v a l u e s are determined from the observed p a r t i c l e d i s t r i b u t i o n i n small areas o f m e t a l l o g r a p h i c a l l y prepared random s e c t i o n s through the m u l t i p h a s e sample. In s t u d y i n g HIPS morphology, t h i n s e c t i o n s were u l t r a m i c r o t o m e d from 0 s 0 - s t a i n e d samples a t random l o c a t i o n s and o r i e n t a t i o n s . A minimum o f 20 t r a n s m i s s i o n e l e c t r o n micrographs were taken from each sample and a n a l y z e d . Because the u n d e r s t a n d i n g o f the l i n k between the p a r t i c l e d i s p e r s i o n s t a t e and c r a z i n g i s i m p o r t a n t , the use o f the rubber p a r t i c l e volume f r a c t i o n VFi per u n i t volume o f the i t h sample, i n s t e a d o f N v i , as an index seems t o be more a p p r o p r i a t e . T h e r e f o r e , E q u a t i o n 3 may be r e p l a c e d by: η
η
4
(4) where VF i s the a r i t h m e t i c mean volume f r a c t i o n o f rubber p a r t i c l e s i n η samples. In two dimensions (such as i n TEM p h o t o g r a p h s ) , a c o n v e n i e n t d i s p e r s i o n index (DI) may be d e f i n e d as: (5) where A F i i s the area f r a c t i o n o f rubber p a r t i c l e s i n the i t h micrograph and AF i s the average area f r a c t i o n i n η micrographs. A small v a l u e o f 6 w i l l r e p r e s e n t a u n i f o r m d i s p e r s i o n o f rubber p a r t i c l e s and i s g e n e r a l l y a p r e f e r r e d m o r p h o l o g i c a l f e a t u r e . In o r d e r t o a l l o w f o r comparison between two m a t e r i a l s t h a t may have d i f f e r e n t average p a r t i c l e s i z e s and p a r t i c l e volume f r a c t i o n s , the experimental s t a n d a r d d e v i a t i o n
