8/12/2019 Supercritical Fluid 2

1/13

ELSEVIER PI h S0032-3861(97)00593-4Polymer Vo l . 3 9 No . 1 3 , p p . 2 9 0 3 - 2 9 1 5 , 1 9 9 8 1 9 98 Elsev ie r Sc ien ce L tdPr in ted in Gr ea t B r i ta in . A l l r ig h ts r ese r v ed0 0 3 2 - 3 8 6 t / 9 8 / $ 1 9. 0 0 + 0 . 0 0

Kinetics o f p ressure - indu ced phase se para t ion(P IP S ) f ro m p o l y m e r s o l u ti o n s b y t im e - r e s o l v e dl igh t sca t te r ing . Po lye thy len e -F n -pe ntan eW e n h a o Z h u a n g a n d E r d o g a n K i r a n *De partm ent of Chemical Engineering, Un iversi ty of Maine, Orono, M E 04469-5737, USAReceived 2 March 1997; revised 8 Ju ly 1997; accepted 16 Ju ly 1997)Kinetics of pressure-induced phase separation (PIPS) in solutions of polyethylene + n-pentane at high pressureshave been investigated using a novel experimental s ystem which permits imposing controlled, multiple rapid (andrepetitive) pressure quenches of different penetration depths into the region of immiscibility of the system. Theevolution of new phase formation is monitored by time-resolved light scattering using a f ibre optic scattering cell as afunction of the depth of penetration into the two-phase regions. It is show n that the rate of change in the scatteredlight intensities increases with quench depth, becoming very fast and eventually reaches an apparent limiting valuefor quenches below a characteristic penetration depth. Determination of these quench pressures below which phaseseparation is extremely rapid identif ies a kinetic phase separation boundary below the binodal pressures w hich is ofpractical signif icance. This is because pressure-induced phase separation by rapid expansion is an important step inprocessing of materials such a s polymers w ith near- and supercritical f luids. The results are shown for liquid-liquidphase separation for polyethylene solutions of two different molecular w eights (108 000 and 16400) in n-pentanesubjected to pressure quenches as deep as 10 MPa. 1998 Elsevier Science L td. All rights reserved.(Keywords: pressure-induced phase separation; polyethylene + n - p e n t a n e ; t i m e - r e s o l v e d l i g h t scattering)

I N T R O D U C T I O NT h e l i t e ra t u r e o n p h a s e s e p a r a t i o n i n p o l y m e r s y s t e m s i s r i c ha n d i n c l u d e s a v a r i e t y o f e x p e r i m e n t a l t e c h n i q u e s t h a t tr y tos i m u l a t e t h e d i f f e r e n t c o n d i t i o n s e n c o u n t e r e d i n p r a c t i c e .I n d e e d , a h o m o g e n e o u s p o l y m e r s o l u t i o n m a y u n d e r g op h a se se~_ara t io n a s a r e su l t o f a ch an g e in t em p er a tu re ~ -5 ,p r e s s u re -1 3, c o m p o s i t i o n ( w h i c h m a y c o m e a b o u t f r o ma d d i t i o n o f a n o n - s o l v e n t 14 -1 7 o r r e m o v a l o f t h e s o l v e n t a s i ns o l v e n t e v a p o r a t i o n ) . P h a s e s e p a r a t i o n m a y a l s o a r i s e f r o mc h a n g e s d u e t o c h e m i c a l r e a c t i o n s a s i n p o l y m e r i s a t i o n 1s '1 9,o r f r o m c h a n g e s i n t h e e x t e r n a l f i e l d s o r t h e h y d r o d y n a m i c sm 2 0 2 1o f t h e s y s t e s u c h a s c h a n g e s i n a p p l i e d s h e a r ' .A m o n g t h e s e , s o l v e n t a n d t h e r m a l - i n d u c e d p h a s e s e p a r a -t i o n a r e b y f a r t h e m o s t c o m m o n t e c h n i q u e s t h a t a r ee m p l o y e d . H o w e v e r , d u e t o t h e g r o w i n g i n t e r e s t i n s u p e r -c r i t ic a l f l u id b a s e d p r o c e s s e s w h e r e p r e s s u r e r e d u c t i o n i s a ni n t e g r a l s t e p i n t h e r e c o v e r y o f t h e e n d - p r o d u c t ( o r t h es o l v e n t ) , t h e r e i s n o w m u c h i n t e r e s t i n p r e s s u r e a s ap a r a m e t e r i n p h a s e s e p a r a t i o n f r o m p o l y m e r s o l u t i o n s 6 -9 .P r e s s u r e - i n d u c e d p h a s e s e p a r a t i o n ( P I P S ) o f f e r s a s p e c i a la d v a n t a g e i n t h a t p r e s s u r e c a n b e c h a n g e d v e r y r a p i d l y i nt h e b u l k o f t h e s o l u t i o n a n d t h e t w o - p h a s e r e g i o n s c a n b ee n t e r e d f a s t e r t h a n w o u l d b e p o s s i b l e b y o t h e r t e c h n i q u e s .T h e e s s e n t i a l f e a t u r e s o f P I P S a r e d e s c r i b e d i n Figure 1.T h i s i s a p r e s s u r e -c o m p o s i t i o n p h a s e d i a g r a m s h o w i n g t h eb i n o d a l ( t h e c u r v e t h a t s e p a r a t e s t h e s t a b le o n e - p h a s e r e g i o nf r o m t h e r e g i o n i n w h i c h t w o p h a s e s c o e x i s t i n e q u i l i b r i u m )a n d t h e s p i n o d a l ( w h i c h d i v i d e s t h e t w o - p h a s e r e g i o ni n t o m e t a s t a b l e a n d u n s t a b l e p o r t i o n s ) b o u n d a r i e s , a n dt h e s t a b l e , m e t a s t a b l e a n d t h e u n s t a b l e r e g i o n s . T h i s i sa n i d e a l i s e d d i a g r a m i n t h a t i n r e a l s y s t e m s , d u e t o

* T o w h o m c o r r e s p o n d e n c e s h o u l d b e a d d r e s s e d

p o l y d i s p e r s i t y o f p o l y m e r s , t h e b i n o d a l a n d s p i n o d a lc u r v e s d o n o t n e c e s s a r i l y m e r g e a t t h e m a x i m u m o f t h eb i n o d a l - - t h e y m e r g e a t a h i g h e r c o n c e n t r a t i o n . T h ep r e s s u r e r e d u c t i o n p a t h s A B a n d A " B " r e p r e s e n t p h a s es e p a r a t i o n i n t h e m e t a s t a b l e r e g i o n b y n u c l e a t i o n a n dg r o w t h m e c h a n i s m . I n r e l a t i v e l y d i l u t e s o l u t i o n s ( p a t h A B )p o l y m e r - r i c h p h a s e n u c l e a t e s i n a s o l v e n t - r i c h c o n t i n u o u sp h a s e , w h e r e a s i n a c o n c e n t r a t e d s o l u t i o n ( p a t h A " B " ) ,p o l y m e r - l e a n p h a s e n u c l e a te s i n a p o l y m e r r i c h - p h a s ew h i c h i s c o n t i n u o u s . T h e s e a r e c h a r a c t e r i s e d b y t h ee x i s t e n c e o f c o n t i n u o u s - p h a s e , d i s p e r s e d - p h a s e m o r p h o l o g y .T h e p r e s s u r e r e d u c t io n p a t h A ' B ' r e p r e s e n t s p h a s e s e p a r a t i o nb y s p i n o d a l d e c o m p o s i t i o n . H e r e , t h e re i s n o th e r m o d y n a m i cb a r r i e r t o p h a s e g r o w t h a n d t h e s o l u t i o n w h i c h i s a t i t sc r i t i c a l c o n c e n t r a t i o n u n d e r g o e s s p o n t a n e o u s a n d c o n -t i n u o u s p h a s e s e p a r a t i o n w i t h t h e f o r m a t i o n o fc o - c o n t i n u o u s p h a s e s i n th e e a r l y s t a g e s o f p h a s e s e p a r a t i o n .I n t h e l a t e r s t a g e s o f p h a s e s e p a r a t i o n , t h e b i c o n t i n u i t y o f t h ep h a s e s m a y h o w e v e r b e l o s t t h r o u g h r i p e n i n g ( c o a r s e n i n g )a s t h e s y s t e m s e e k s t o m i n i m i s e i t s f r e e e n e r g y b ym i n i m i s i n g i n t e r f a c i a l a r e a u n l e s s t h e s t r u c t u r e i s f r o z e nd u e t o g e l a t i o n o r v i t r i f ic a t i o n d u r i n g p h a s e s e p a r a t i o n . T h ec o - c o n t i n u o u s d o m a i n s t r u c t u r e s m a y b r e a k i n t o d r o p l e t s . I ts h o u l d b e n o t e d t h a t f o r th e s e p r e s s u r e r e d u c t i o n p a t h s f r o man in i t i a l p re s s u re P ~ to a f i n a l p res su re o f P ~ ., t h e f i n a le q u i l i b r i u m c o m p o s i t i o n s o f t h e t w o p h a s e s t h a t a r e f o r m e da r e a l l t h e s a m e , ~ I b a n d ~ l I b - T h e r a t i o o f t h e e q u i l i b r i u mp h a s e f o r e a c h c a s e i s h o w e v e r d i f f e r e n t ( a n d c a n b ed e t e r m i n e d b y t h e l e v e r r u l e ) .

Figure 2 i l l u s t r a t e s t h e d i f f e r e n t m o r p h o l o g i e s t h a td e v e l o p d u r i n g p h a s e s e p a r a t i o n a n d w h e n t h e f i n a le q u i l i b r i u m s t a g e i s r e a c h e d . T h e k i n e t i c s o f p h a s es e p a r a t i o n p r o c e s s e s h o w e v e r m a y p r e v e n t r e a c h i n g t h ef i na l e q u i l i b r i u m s t a t e a n d t h e i n t e r m e d i a t e n o n - e q u i l i b r i u m

POLYMER Vol ume 39 Number 13 1998 2903

8/12/2019 Supercritical Fluid 2

2/13

Kineti cs o f P IPS from po lym er so lu t ions : W. Zhua ng and E. K iran

(/)13.

Pi

Pe

Pf

A I A 'One-Phase

A "

S p i n ~ o d a l B i n o d a l

U n s t a b l e

Two-Phases M e t a s t a b l e

I I s ~ I l bPolym er concentration

F i g u r e 1 S c he m a t i c r e p r e s e n t a t ion o f p r e s s u r e - i ndu c e d pha s e s e pa r at i oni n t he p r e s s u r e - c om pos i t i on pha s e d i a g r a m . T he b i noda l a nd t he s p i noda le nve l ope s s e pa r a t e t he s t a b l e one - pha s e , u ns t a b l e t wo- pha s e r e g i ons . T her e g i on b e t we e n t h e s p i noda l a nd t he b i no da l ( s ha de d a r e a i n t he f i gu r e ) ist he m e t a s t a b l e r e g i on . T h r e e d i f f e r e n t p r e s s u re r e du c t i on pa t h s ( A B , A ' B 'a nd A "B ") a r e s hown f o r s o l u t i ons a t t h r e e d i f f e r e n t po l y m e r c on -cent ra t ions , a l l s ta r t ing a t an ini t ia l pressure of P i in the one-phasehom oge ne ou s r e g i on a nd e nd i ng a t a f i na l p r e s s u r e o f P f . i n t he t wo- pha s er e g i ons . T he s e pa t h s , e ve n t hou gh d i f f e r e n t , a l l r e s u l t i n t he s a m ee q u i l i b r iu m pha s e c om po s i t i ons t b t b a nd q ~l Ib . N e w pha s e f o r m a t i onp r oc e e ds b y N u c l e a t i on a nd G r owt h m e c ha n i s m whe n m e t a s t a b l e r e g i onsa re ente red (pa ths AB, and A"B") , and b y S p i noda l De c om pos i t i onm e c ha n i s m whe n t he u ns t a b l e r e g i ons a r e e n t e r e d ( pa t h A ' B ' ) u ponr e du c t i on i n p r e s s u r e

s t a t e s m a y b e l o c k e d - i n a s i n v i t r i f i c a t i o n . F r o m F i g u r e 1a n d F i g u r e 2 , i t i s e a s y t o s e e h o w p r e s s u r e - i n d u c e d p h a s es e p a r a t io n m a y l e a d t o d i f f e r e n t m o r p h o l o g i e s , r a n g i n g f r o m

p o w d e r s , t o p o r o u s s t r u c t u r e s o f d i f f e r e n t p o r e s i z e a n dd i s t r i b u t i o n s . C l e a r l y , n o t o n l y t h e f i n a l t h e r m o d y n a m i cs t a t e , bu t a l so t he k i ne t i c s o f phase s ep a ra t i on and t he t i mes c a l e i n v o l v e d i n n e w p h a s e f o r m a t i o n a r e o f g r e a tt echno l og i ca l i n t e r e s t .E x p e r i m e n t a l a n d t h e o r e t i c a l s t u d i e s o n t h e k i n e t i c so f p h a s e s e p a r a t i o n h a v e b e e n m o s t l y r e p o r t e d f o rpo l ym er b l ends sub jec t ed t o a t e mp era t u r e quen ch 2 '3 '21-24.I n p o l y m e r b l e n d s k i n e t i c s a r e e a s i e r t o f o l l o w b e c a u s e o ft h e h i g h v i s c o s i t y a n d l o w d i f f u s i v i t y , a n d t h u s t h e l o n g e rt i m e s c a l e s t h a t a r e i n v o l v e d . F o r p o l y m e r s o l u t i o n s ,t h e d y n a m i c s o f p h a s e s e p a r a t i o n a n d t h e e a r l y - s ta g es t r u c t u r e d e v e l o p m e n t a r e f a s t , a n d f o r d e e p q u e n c h e st i m e s c a l e s m a y b e e x t r e m e l y s h o r t , m a k i n g t h e s e s y s t e m se x p e r i m e n t a l l y m o r e d i f f ic u l t to s t u d y i f n o t i n a c c e s s ib l e .Tab le 1 i s a summary of a l l t he ava i l ab l e l i t e r a t u r e on t hek i n e t i c s o f p h a s e s e p a r a t i o n f r o m p o l y m e r s o l u t i o n si n v o l v i n g a p o l y m e r p l u s a s o l v e n t . M a n y o f t h e s e s t ud i e sr e p o r t t h e c o n s e q u e n c e s o f t e m p e r a t u r e - i n d u c e d p h a s es e p a r a t i o n ( T I P S ) . O u t s i d e o u r l a b o r a t o r y , o n l y t w o o t h e rs t u d i e s h a v e b e e n r e p o r t e d o n t h e k i n e t i c s o f p r e s s u r e -i n d u c e d p h a s e s e p a r a t i o n i n p o l y m e r s o l u t i o n s w i t hm e a s u r e m e n t s o n t h e t i m e s c a l e s o f p h a s e s e p a r a t i o n .K u w a h a r a e t a / . 38'39 h a v e r e p o r t e d o n t h e d y n a m i c s o fs p i n o d a l d e c o m p o s i t i o n i n p o l y d i m e t h y l s i l o x a n e - I- d i e t h y lc a r b o n a t e s u b j e c t e d t o a s h a l lo w p r e s s u r e q u e n c h o f 0 . 0 4 -0 . 0 7 4 M P a n e a r a t m o s p h e r i c p r e s s u r e . K o j i m a et a l . h a v er e p o r t e d o n t h e c o n s e q u e n c e s o f s h a l lo w p r e s s u r e - q u e n c h e s(ca. 0 . 0 3 - 0 . 0 5 M P a ) f r o m a n i n it i al p r e s s u r e o f a b o u t5 M P a f o r a 1 . 5% s o l u ti o n o f p o l y p r o p y l e n e ( M = 3 5 5 0 0 0 ,P D I = 6 . 5 ) in t r i c h l o rf l u o r o m e t h a n e . B a s e d o n t i m e -r e s o l v e d s c a t t e r e d l i g h t i n t e n s i t i e s , t h e a u t h o r s c o n c l u d e dt h a t p h a s e s e p a r a t i o n p r o c e e d e d b y s p i n o d a l d e c o m p o s i t i o nf o r 0 . 0 5 M P a q u e n c h b e l o w t h e p h a s e b o u n d a r y a t 4 5 2 K ,b u t b y n u c l e a t i o n a n d g r o w t h f o r a s h a l l o w e r q u e n c hdep t h o f 0 .03 M P a 37. I n ou r p r ev i ous pub l i ca t i ons 6"7w e r e p o r t e d o n t h e t i m e - e v o l u t i o n o f s c a t t e r e d l i g h ti n t e n s it i es i n s o l u t i o n s o f p o l y s t y r e n e + p e n t a n e f o r r ap i dd e e p q u e n c h e s i n t o t h e r e g i o n o f i m m i s c i b i l i t y f r o m h i g h

T a b l e 1 L i t e r a t u re on k i ne t i c s o f pha s e s e pa r a ti on i n po l y m e r s o l ut i onsS y s t e m Q u e nc h R e f e r e nc em o d e / m e a s u r e m e n tt e c hn i q u eP o l y ( 2 , 6 - d i m e t hy l - l , 4 - phe ny l e t he r ) ( P P O) + c a p r o l a c t a mP o l y s t y r e ne + d i i s ode c y l ph t ha l a t eS t y r e ne o l i gom e r s - t - e - c a p r o l a c t oneP o l y s t y r e ne + c y c l oh e x a neP o l y s t y r e ne + c y c l ohe x a neP o l y ( p - phe n y l e ne b e z ob i s ox a z o l e ) ( P B O) + m e t ha ne s u l f on i c a c idP o l y s t y r e ne + d i e t hy l m a l ona t eP o l y s t y r e ne + c y c l ohe x a ne ; P S + d i e t hy l m a l ona t eI s o t a c ti c po l y p r opy l e ne + d i phe ny l e t he rP o l y m e r + l i q u id c r y s ta lP o l y ( d i i s op r opy l f u m a r a t e ) + E8P o l y s t y r e ne + d i oc t y l ph t ha l a t eP o l y p r opy l e ne + t r i c h lo r o f l u o r om e t ha neP o l y d i m e t hy l s i l ox a ne - t- d i e t hy l c a r b ona t eP o l y s t y r e ne + pe n t a neP o l y e t hy l e ne + pe n t a neP o l y s t y r e ne + m e t hy l c y c l ohe x a n e

T I P S / O M S m o l d e r s e t a l . 25T I P S / O M N o j i m a e t a l . 26T I P S / OM T a na k a et al . 27 ,28T I P S / T R - LS La l a nd B a ns i l 29TIPS /SEM , BE T, Aube r t 30.31S I P S / T R - LS N e l s on a nd S oa ne 5TIPS /M Tanaka 32T I P S / S E M/ P O R S ong a nd T or k e l s on 33T I P S / O M M c G u i r e e t a l . 34S I P S / LS Ki k u c h i e t a l . 35T I P S / S A X S X i e e t a l . 36P I P S / LS Ko j i m a e t a l . 37P I P S Ku wa ha r a e t a l . 38,39P I P S / T R - LS Ki r a n 6 ; K i r a n a nd Zhu a ng 7 ; Zhu a ng 4 0P I P S / T R - LS Zhu a ng a nd Ki ra n8 '9 ; Zhu a ng 4 0PIPS/T R-L S Kiran ~3; Xio ng 62

T I P S = t e m pe r a t u r e - i ndu c e d pha s e s e pa r a ti on ; OM = op t i c a l m i c r os c opy ; T R - LS = t i m e - r e s o l ve d l igh t s c a tt e r ing ; S I P S = s o l ve n t indu c e d pha s e s e pa r a t ion ;S EM = s c a nn i ng e l e c t ron m i c r os c opy ; S A X S = s m a l l a ng l e X - r a y s c at t e r ing ; LS = l i gh t s c a t t er i ng ; P OR = po r os i m e t r y ; P I P S = p r e s s u r e - i ndu c e d pha s esepara t ion.

2 9 0 4 P O L Y M E R V o l u m e 39 N u m b e r 1 3 1 9 9 8

8/12/2019 Supercritical Fluid 2

3/13

Kineti cs o f P IPS f rom po lym er so lu t ions : W. Zhua ng and E. K i ran

y A B ~

1

l l

Ib

libF i gu r e 2 S c he m a t i c r e p r e s e n t a t i on o f t he d i f f e r e n t m or ph o l og i e s ( pa r ti c l e s , i n t e r c onne c t e d ne t wor k , po r ou s m a t r i x ) t hat a r e f o r m e d a nd t he i r e vo l u t i on( c oa r s e n i ng p r oc e s s ) w i t h t i m e u pon pha s e s e pa r a t i on de pe nd i n g u pon t he pha s e s e pa r a t i on pa t h f o l l owe d , a s de s c r i b e d in Figure 1. They a l l r each a f ina l two-pha s e e q u i l i b r i u m s t a t e w i t h i de n t i c a l pha s e c o m pos i t i ons , b u t d i f f e r e n t pha s e - vo l u m e r a t io s . Un de r c e r t a i n c i r c u m s t a nc e s , t he k i ne t ic s o f ph a s e s e pa r a t i on m a ypr e ve n t r e a c h i ng t he f i na l e q u i l i b ri u m s t a te , t he r e b y l oc k i ng - i n t he n on - e q u i l i b r i u m s t a t e s l e a d i ng t o d i f f e r e n t m or pho l og i e s

p r e s s u r e s . T h e s e s t u d i e s w e r e t h e v e r y f i r s t i n v e s t i g a t i o n s o ft h e i r k i n d i n w h i c h r a p i d d e e p - q u e n c h e s ( u p t o a b o u t1 0 M P a ) h a v e b e e n e m p l o y e d i n a r e p e t i t iv e m a n n e r a n dh a v e s h o w n t h a t t h e t i m e - s c a l e o f n e w p h a s e f o r m a t i o ni n d e e d b e c o m e s v e r y s h o r t f o r d e e p q u e n c h e s . R e c e n t l y , w ea l s o r e p o r t e d 8 '9 o n t h e t i m e s c a l e a n d r a t e o f p h a s es e p a r a t i o n f o r p o l y e t h y l e n e ( M w = 1 6 4 0 0 ) 4 - p e n t a n es y s t e m a t 1 50 C f o r c o n c e n t r a t i o n s i n t h e r a n g e o f 1 - 1 5 %b y m a s s s u b j e c t e d t o d i f f e r e n t p r e s s u r e q u e n c h e s r a n g i n gf r o m s h a l l o w t o d e e p q u e n c h e s .I n t h e p r e s e n t p a p e r , w e r e p o r t o n t h e d e t a i l s o f ar e l a t i v e l y n e w t e c h n i q u e b a s e d o n t i m e - r e s o l v e d l i g h ts c a t t e r i n g u s i n g a f i b r e - o p t i c c e l l w h i c h p e r m i t s c o n t r o l l e dp r e s s u re d r o p / j u m p e x p e r i m e n t s t o b e c o n d u c t e d o n a g i v e ns o l u t io n i n a r e p e t i t i v e m a n n e r . T h e r e s u l t s a r e p r e s e n t e d f o rp o l y e t h y l e n e 4 - n - p e n t a n e s o l u t i o n s . S p e c i f i c a l l y , t h ep r e s e n t a r t i c l e p r o v i d e s i n f o r m a t i o n o n t h e k i n e t i c s o fp r e s s u r e i n d u c e d p h a s e s e p a r a t i o n o f p o l y e t h y l e n e ( P E

1 08 0 0 0 ) f r o m n - p e n t a n e s o l u t io n s . I t i s s h o w n t h a t w h e n t h et w o - p h a s e r e g i o n s a r e e n t e r e d r a p i d l y , b e l o w a c h a r a c t e r -i s t i c q u e n c h d e p t h , t h e t i m e s c a l e f o r n e w p h a s e g r o w t hb e c o m e s e x t r e m e l y s h o r t . T h e s e c h a r a c t e r i s t i c p r e s s u r e sw h i c h d e p e n d o n t h e p o l y m e r c o n c e n t r a t i o n h e l p i d e n t i fy ak i n e t i c p h a s e s e p a r a t i o n b o u n d a r y w h i c h i s o f p r a c t i c a ls i g n i f i c a n c e . A n y r a p i d p r e s s u r e - q u e n c h b e l o w t h i sb o u n d a r y r e s u l t s i n e x t r e m e l y f a s t p h a s e s e p a r a t i o n .E X P E R I M E N T A LExperimental system

Figure 3 s h o w s t h e s c h e m a t i c s o f t h e o v e r a l l e x p e r i m e n t a ls y s t e m . I t c o n s i s ts o f t w o o p t i c a l c e l l s , a m a i n d i s s o l u t i o nc e l l ( M C ) a n d a s c a t t e r i n g c e l l ( S C ) w h i c h a r e i n t e r -c o n n e c t e d . O t h e r c o m p o n e n t s o f t h e s y s t e m a r e th e l a s e rs o u r c e ( L S ) , l i g h t d e t e c t o r s ( P M T , P D ) , p r e s s u r e a n dt e m p e r a t u r e s e n s o r s ( P T ) , a m a g n e t i c r e c i r c u l a t i o n p u m p

P O L Y M E R V o l u m e 3 9 N u m b e r 13 1 9 98 2 9 0 5

8/12/2019 Supercritical Fluid 2

4/13

Kinetics of PIPS from polymer solutions: W Zhuang and E KiranC P V

~ ~ - ~ D P M T_PTR E SS U R E L E X I T Q I ~ V L V DT 1 ~ _ i S C , - -~ " " " ~ ~ ~ ,i SP AL E X IT ? (SO LVENTL I N E ~ V [ L S ~ '~ ' C O M P U T E R

LF V C V RDFigure 3 Experimental system to study kinetics of pressure-induced phase separation by time-resolve d light scattering. (AP G = automated p ressuregenerator; A V = air-actuated valve; CP = circulation pump; CV = check valve; LF = line filter; LS = laser source; LVDT = linear variabledifferential transformer; M = motor; MC = main cell; PD = photo-detector; P G = pressure generator; PI = pressure indicator; PL : pressure generation line;PMT = photo -multiplier tube; PT = pressure transducer; RD = rupture disc; SC = scattering cell; SP = sample port; VVA = variable-vo lume assembly)( C P ) , a n a i r - a c t u a t e d v a l v e ( A V ) , a n d t h e m a n i f o l d s f o rs o l v e n t d e l i v e r y a n d d i s c h a r g e a n d p r e s s u r e c o n t r o l . I n t e r n a lv o l u m e o f th e m a i n c e l l i s c h a n g e d b y m o v i n g a p i s t o ni n s i d e th e v a r i a b l e - v o l u m e p a r t ( V V A ) o f t h e m a i n c e l l w i t ht h e a i d o f a n a u t o m a t e d p r e s s u r e g e n e r a t o r ( P G N ) . T h e m a i nc e l l a l o n g w i t h i ts m o t o r i s e d p r e s s u r e g e n e r a t o r a n d t h e r e a lt i m e p i s t o n p o s i t i o n ( a n d t h u s i n t e r n a l v o l u m e ) s e n s i n gc a p a b i l i t y ( L V D T ) f u n c t i o n s a l s o a s a n a u t o m a t e d P V Tap p a ra tu s 41.

U s i n g t h i s s y s t e m p r e s s u r e c h a n g e s i n t h e s c a t t e r i n g c e l la r e b r o u g h t a b o u t r e p e t i t i v e l y w i t h o u t c h a n g i n g t h es o l u t i o n , a n d t h e t i m e d e p e n d e n t c h a n g e s i n t h e s o l u t i o na r e f o l l o w e d b y t h e t i m e - e v o l u t i o n o f t h e s c a t t e r e d l i g h ti n t e n s it i e s t h a t a r e m o n i t o r e d a t d i ff e r e n t a n g l e s . T h e s y s t e mp e r m i t s c h a n g i n g t h e p r e s s u r e e i t h e r s l o w l y o r f a s t . A f t e rl o a d in g t h e s y s t e m w i t h t h e p o l y m e r a n d t h e s o l v e n tc o r r e s p o n d i n g t o a t a r g e t c o n c e n t r a t i o n , f u l l y h o m o g e n e o u sc o n d i t i o n s a r e a c h i e v e d b y m a n i p u l a t i o n o f th e p r e s s u r e a n dt e m p e r a t u r e w h i l e k e e p i n g t h e v a l v e s b e t w e e n t h e t w o c e l l so p e n a n d m a i n t a i n i n g r e c i r c u l a t i o n b e t w e e n t h e c e l l s . T h e na t a g i v e n t e m p e r a t u r e , m o v i n g t h e p i s t o n a t c o n t r o l l e d r a t e sb r i n g s a b o u t s l o w p r e s s u r e c h a n g e s . A f t e r p h a s e s e p a r a t i o nc o n d i t i o n s a r e r e a c h e d a n d t h e p r o g r e s s o f n e w p h a s ef o r m a t i o n i s m o n i t o r e d , t h e s y s t e m i s b r o u g h t b a c k t o i n i ti a lp r e s s u r e f o r a n o t h e r e x p e r i m e n t t o b e c o n d u c t e d s t a r t i n ga g a i n f r o m t h e o n e - p h a s e h o m o g e n e o u s c o n d i t i o n s . F o rr a p i d p r e s s u r e r e d u c t i o n s , t h e v a l v e s i n t h e c o n n e c t i n g l i n e sa r e f i r st c l o s e d t o i s o l a t e t h e m a i n - c e l l a n d t h e s c a t t e r i n g - c e l lf r o m e a c h o t h e r . T h e n t h e p r e s s u r e i n t h e m a i n c e l l i sr e d u c e d t o a l o w v a l u e c r e a t i n g a p r e s s u r e d i f f e r e n t i a lb e t w e e n t h e m a i n c e l l a n d t h e s c a t t e r i n g c e l l ( w h i c h i sm a i n t a i n e d a t t h e i n i t i a l h i g h p r e s s u r e ) . T h e n , t h e a i r -a c t u a t e d v a l v e i s q u i c k l y o p e n e d . T h e v e r y r a p i d c h a n g e s i nt h e p r e s s u r e a n d t h e s c a t t e r e d l i g h t i n t e n s i t i e s i n t h es c a t t e r i n g c e l l a r e m o n i t o r e d a s a f u n c t i o n o f ti m e . F o r t h en e x t e x p e r i m e n t w i t h a d i ff e r e n t q u e n c h d e p t h , t h e s y s t e m i sa g a i n b r o u g h t b a c k t o t h e i n i t i a l p r e s s u r e . A f t e r h o m o -g e n i s a t i o n , t h e c e l l s a r e o n c e a g a i n i s o l a t e d , t h e p r e s s u r e i nt h e m a i n c e l l i s r e d u c e d t o a n e w l o w e r v a l u e , a n d t h e v a l v ei s t h e n o p e n e d t o i n d u c e r a p i d p h a s e s e p a r a t i o n i n t h es o l u t i o n i n s i d e t h e s c a t t e r i n g c e l l. T h e s y s t e m i s th u s r a t h e ru n i q u e i n p e r m i t t i n g t h e s t u d y o f i m p o s i n g d i f f e r e n tp r e s s u r e q u e n c h d e p t h s o n a g i v e n s o l u t i o n w i t h o u t h a v i n gt o r e l o a d t h e c e l l s a f t e r e a c h e x p e r i m e n t . W e r e f e r t o t h i s

t e c h n i q u e a s M R P D - - M u l t i p l e R a p i d ( R e p e t i t i v e )P r e s s u r e - D r o p t e c h n i q u e 7 .O p t i c a l c e l l s w i t h d i f f e r e n t g e o m e t r i e s c a n b e u s e d a s t h es c a t t e r i n g c e l l. I n o u r p r e v i o u s p u b l i c a t i o n s w e r e p o r t e d d a t ao b ta in ed w i th a f l a t -w in d o w c e l l 6 "7 . Th e r e su l t s p rese n ted int h i s p a p e r w e r e o b t a i n e d w i t h a f i b r e - o p t i c s c a t t e r i n g c e l lw i t h a v e r y s m a l l i n t e r n a l v o l u m e t h a t w a s d e s i g n e d t os h o r t e n t h e p a t h l e n g th s a n d r e d u c e m u l t i p l e s c a t t e r in g . T h ed e t a i l s o f t hi s n e w c e l l a r e s h o w n i n Figure 4. T h e c e l l ,m a d e o f s t a i n l e s s s t e e l , h a s s e v e n p o r t s f o r f i b r e - o p t i cc o n n e c t i o n s a n d a p o r t f o r p r e s s u r e / t e m p e r a t u r e s e n s o r .T r a n s m i t t e d ( 0 ) a n d s c a t t e r e d l i g h t f r o m d i f f e r e n t a n g l e sw i t h r e s p e c t t o t h e i n c i d e n t l i g h t c a n b e m e a s u r e d w i t hs e n s o r s a t t a c h e d t o t h e f i b re - o p t i c s . T h e d y n a m i c c h a n g e s i np r e s s u r e i n t h e s c a t t e r i n g c e l l i s m o n i t o r e d b y a p i e z o e l e c t r i cp r e s s u r e t r a n s d u c e r ( P C B P i e z o t r o n i c s ) w h i c h h a s ar e s p o n s e t i m e o f 2 # s .O p t i ca l f ib res u sed in t h i s s e t -up a re g l a s s f ib re w i th a co red i a m e t e r o f 1 0 5 / z m c o a t e d w i t h p o l y i m i d e f o r h i g h -t e m p e r a t u r e u s e ( o b t a i n e d f r o m S p e c T r a n C o ) . T o p r o t e c tt h e t h in o p t i c a l f i b r e f r o m p h y s i c a l d a m a g e a n d h e l p s e a l i nt h e c o n n e c t i o n s , t h e f i b r e s w e r e s h i e l d e d w i t h P E E K t u b i n go f 1 /1 6 " o . d . an d 0 . 0 0 7" i . d . Th e tub in g i s t h en m o un ted o n tot h e s c a t t e r i n g c e l l a n d s e a l e d . T h e l e n g t h o f t h e f ib r ee x t e n d i n g i n t h e c e ll d e t e r m i n e s t h e e f f e c t i v e p a t h l e n g th o ft h e c e l l. F o r t h e p r e s e n t s e t - u p , t h i s e f f e c t i v e l e n g t h i s a b o u t2 . 5 m m .I n t h e p r e s e n t s t u d y , t h e g r e e n l i g h t o f a n A r g o n - i o n l a s e r( L e x e l M o d e l 9 5 - A R 2 ) w i th a w a v e l e n g th o f 5 1 4 n m h a sb e e n u s e d . I t s p o w e r i s a d j u s t a b l e a n d c a n b e c o n t i n u a l l yc h a n g e d f r o m 1 0 m W t o 2 W . F o r t h e m e a s u r e m e n t s i n th ep r e s e n t s t u d y a r a n g e o f 1 0 m W h a s b e e n u s e d . S c a t t e r e dl i g h t i n t e n s i t i e s w e r e m o n i t o r e d u s i n g s e n s i t i v e p h o t o -m u l t i p l i e r t u b e s ( P M T ) o r r e s i s t i v e p h o t o - d e t e c t o r s ( P D ) .T h e s i g n a l f r o m t h e P M T i s p r o c e s s e d u s i n g a f a s t m u l t i p l e -c h a n n e l s c a l e r ( S t a n f o r d I n s t r u m e n t s ) w i t h a m e m o r ys t o r a g e c a p a b i l i t y o f 1 6 0 0 0 d a t a p o i n t s . T h e s i g n a l s f r o ma l l d e t e c t o r s a r e t r a n s f e r r e d t o t h e c o m p u t e r f o r r e a l - t i m ed i s p l a y a l o n g w i t h s y s t e m p r e s s u r e a n d t e m p e r a t u r e .System controls and calibrations

T h e o v e r a l l s y s t e m c o n t r o l s a n d t h e d a t a a c q u i s i t i o np r o t o c o l s a r e b u i l t a r o u n d a n I B M c o m p a t i b l e p e r s o n a lc o m p u t e r w i t h a p l u g- i n A / D b o a r d . T h i s I S A b u s A / D b o a r d

2 9 0 6 P O L Y M E R V o l u m e 3 9 N u m b e r 1 3 1 99 8

8/12/2019 Supercritical Fluid 2

5/13

Kinetics of PIPS from polymer solutions: W Zhuang and E Kiran

In ciden t laser beam ~ ~ " A ' "

Pressure i.' j / . . . . ' ~ "t ransducer

Transmitted-light ~ '\/ I \ \ l90 Scattered-light

Pressuret ransducer

Outlet JF i g u r e 4 S c h e m a t i c s d i a g r a m o f t h e f i br e - op t i c s c a t t e ri n g c e ll . T h e c y l i n d r i c al s t a i n l e s s - s t e e l c e l l b o d y h o s t s s e v e n p o r t s f o r f ib r e -o p t i c c o n n e c t i o n s ( i n c id e n tl a s e r b e a m , t r a n sm i t t e d , ( 0 ) a n d t h e s c a t t e r e d l i g h t f r o m a n g l e s 3 0 , 6 0 , 9 0 , 1 2 0 a n d 1 5 0 w i th r e sp e c t t o t h e i n c id e n t l i g h t ) a n d a p o r t f o r p r e s su r e /t e m p e r a t u r e s e n s o r

has e i gh t 12-b i t d i f fe r en t i a l ana l og i npu t channe l s , t wo12-bit a n a l o g o u t p u t s a n d o n e i n d i v i d u a l l y a d d r e s s a b l e 8 - b i tI / O p o r t . T h e a n a l o g i n p u t c h a n n e l s t a k e i n t h e s i g n a l s o f t h et e m p e r a t u r e s f r o m t h e t h e r m o c o u p l e s ( J - t y p e ) o n t h e c e l l sa n d t h e R T D ( P t - t y p e ) in t h e o v e n , t h e c e l l p r e s s u r e f r o m t h eo n - l i n e s t r a i n - g a u g e p r e s s u r e t r a n s d u c e r a n d t h e v o l u m ef r o m t h e L V D T .T h e t e m p e r a t u r e s e n s o r s ( i. e . T C a n d R T D ) a r e c a l i b r a t e da g a i n s t a s t a n d a r d p r o b e o r a f a c t o r y c a l i b r a te d o n e b ya d j u s ti n g t h e p r e - a m p l i f i e r o f t h e s e n s o r s ( h a r d w a r ec a l i b r a t i o n ) o r b y f i n e t u n i n g t h e s c a l i n g p a r a m e t e r i n t h ec o n t r o l p r o g r a m ( s o f t w a r e c a l ib r a t io n ) . A n o v e r a l l a c c u r a c yo f 0 . 5 K a n d a r e s o l u t i o n o f 0 . 1 K i s m a i n t a i n e d . P r e s s u r ec a l i b r a t i o n s a r e c a r r i e d o u t a g a i n s t a H e i s e g a u g e a n dc o r r e c t i o n s a r e m a d e t h r o u g h a d j u s t i n g t h e s c a l i n g p a r a -m e t e r i n t h e c o n t r o l p r o g r a m . I n p r e s s u r e r e a d i n g s u p t o7 0 M P a , a n o v e r a l l a c c u r a c y o f 0 . 1 4 M P a a n d a r e s o l u t i o n o f0 . 0 1 7 M P a i s m a i n t a in e d .C a l i b r a ti o n s o f l i g h t d e t e c t o r s a re a c h i e v e d b y a d j u s ti n gt h e s c a l i n g f a c t o r i n t h e c o n t r o l p r o g r a m w h i l e t h e s e n s o r i s

e x p o s e d t o a k n o w n l i g h t s o u r c e ( a t l o w p o w e r s e t t i n g s o fthe laser) .C o r r e c t i o n s t o sc a t t e r e d l i g h t i n t e n s i t i e s

C or rec t i ons a r e made t o t he s ca t t e r ed l i gh t i n t ens i t i e s i no r d e r t o i n c o r p o r a t e t h e e f f e c t o f b a c k g r o u n d s c a t t e r i n g(a r i s i ng f rom so l u t i on dens i t y f l uc t ua t i ons , r e f l ec t i ons f romt he ce l l wa l l s , o r dus t pa r t i c l e s ) . F or t h i s pu rpose , s ca t t e r edand t r ansmi t t ed l i gh t in t ens it ie s a r e de t e rmi ned a t ho mog enousone-phase cond i t i ons ( fa r r emoved f rom t he t wo-phasereg i ons ) where concen t r a t i on f l uc t ua t i ons can be a s sumed t oaccount fo r on l y a neg l i g ib l e p ropor t i on o f t he s ca t t e r ed l igh t.A s s u m i n g t h a t t h e b a c k g r o u n d l e v e l s a r e p r o p o r t i o n a l t o t h eamount o f l i gh t en t e r i ng t he s ca t t e r i ng vo l ume , l fo l l owi ngt h e p r o c e d u r e s d e s c r i b e d i n th e l i t e ra t u r e , t h e c o r r e c t e dv a l u e o f t h e s c a t t e r e d l i g h t i n te n s i t y is o b t a i n e d b ys u b t r a c t i n g t h e b a c k g r o u n d s c a t t e r i n g lob f r o m t h ee x p e r i m e n t a l l y o b s e r v e d v a l u e Io, that i s ,

P O L Y M E R V o l u m e 3 9 N u m b e r 1 3 19 98 2 9 0 7

8/12/2019 Supercritical Fluid 2

6/13

Kineti cs o f P IPS f rom po lym er so lu t ions : W. Zhua ng a nd E. K i ranw h e r e

r o [ 1 o i l , r ] h ~a n d [ I 0/ It r] * c o r r e s p o n d s t o t h e r e a d i n g s i n t h e h o m o g e n e o u sr e g i o n , a n d I t r i s t h e t r a n s m i t t e d l i g h t i n t e n s i t y .

T o d o c u m e n t t h e c h a n g e s i n t h e s c a t t e r e d l i g h t i n t e n s i t ya f t e r a q u e n c h , t h e s c a t t e r e d l i g h t i n t e n s i t ie s a r e r e p o r t e d a sn o r m a l i s e d i n t e n s i t i e s I /Io. Th e s c a t t e r e d l i g h t i n t e n s i t y I i sn o r m a l i s e d w i t h r e s p e c t t o t h e i n i ti a l s c a t t e r e d l i g h t i n t e n s i tyo f t h e s o l u t i o n I o p r i o r t o t h e q u e n c h .Materials

T h e p o l y e t h y l e n e s t a n d a r d s (M w = 1 0 8 0 0 0 , Mw/Mo =1 . 3 2 a n d M w = 1 6 4 0 0 , M w / M , = 1 . 1 6 ), h y d r o g e n a t e dp o l y b u t a d i e n e s a m p l e s , u s e d i n t h e p r e s e n t w o r k w e r eo b t a i n e d f r o m S c i e n t i f i c P o l y m e r P r o d u c t s , I n c . T h es o l v e n t , n - p e n t a n e ( p u r i t y > 9 9 % ) , w a s p u r c h a s e d f r o mA l d r i c h C h e m i c a l C o .

R E S U L T S A N D D I S C U S S IO NP r e s s u re q u e n c h e x p e r i m e n t s w e r e c o n d u c t e d i n p u re c a r b o nd i o x i d e , p u r e n - p e n t a n e a n d i n s o l u ti o n s o f p o l y e t h y l e n e i nn - p e n t a n e . T h e r e s u l t s a r e d i s c u s s e d b e l o w .Pressure - induced phase separa t ion (PIP S)- -ba s icmethodology

T h e b a s i c m e t h o d o l o g y i n P I P S i s d e m o n s t r a t e d i nFigure 5a a n d b. Figure 5a s h o w s t h e d e m i x i n g p r e s s u r e s a sa f u n c t i o n o f t e m p e r a t u r e f o r a p o l y m e r s o l u t i o n ( a t a g i v e nc o n c e n t r a t i o n ) d i s p l a y i n g L C S T t y p e b e h a v i o u r s u c h a sp o l y e t h y l e n e + n - p e n t a n e s y s t e m . T h e p r e s su r e r a n g ea b o v e t h e d e m i x i n g p r e s s u r e s i d e n t i f i e s t h e o n e - p h a s eh o m o g e n e o u s r e g i o n . T h e t w o - p h a s e r e g i o n s ( t h e m e t a -s t a b l e a n d u n s t a b l e r e g i o n s ) f o r th e s y s t e m i s e n t e r e d e i t h e rb y r e d u c i n g t h e p r e s s u re o r b y i n c r e a s i n g t h e t e m p e r a t u r e .Figure 5b s h o w s t h e d e m i x i n g p r e s s u r e s a s a f u n c t i o n o fp o l y m e r c o n c e n t r a t io n a t a g i v e n t e m p e r a tu r e w h i c h i np r a c t i c e i s g e n e r a t e d f r o m a c o n s t a n t t e m p e r a t u r e c u t o f t h ed e m i x i n g d a t a ( a s i n Figure 5a) o b t a i n e d a t d i f f e r e n tc o n c e n t r a t i o n s . A l s o s h o w n i n t h e s e f i g u r e s a r e t h e s p i n o d a lc u r v e s ( d o t t e d c u r v e s ) w h i c h f o r m t h e b o u n d a r i e s f o r t h em e t a s t a b l e a n d u n s t a b l e r e g i o n s f o r t h e s y s t e m , a n d t y p i c a lp r e s s u r e - q u e n c h p a t h s ( A - E ) t h a t m a y b e f o l l o w e d .

I n p r e s s u r e - i n d u c e d p h a s e s e p a r a t i o n , t h e o b j e c t i v e i s t oe n t e r t h e t w o - p h a s e r e g i o n b y r e d u c i n g t h e p r e s s u r e .D e p e n d i n g u p o n t h e d e p t h o f t h e p r e s s u re q u e n c h i m p o s e d ,t h e s y s t e m m a y e n t e r i t s m e t a s t a b l e o r u n s t a b l e r e g i o n . I n ar e c e n t m e t h o d o l o g y t h a t w e d e v e l o p e d 7 , w e s y s t e m a t i c a l lym a p o u t t h e p h a s e s e p a r a t i o n p r o c e s s i n a s e ri e s o f p r e s s u r ed r o p e x p e r i m e n t s e a c h s t a r t i n g f r o m t h e s a m e i n i ti a lp r e s s u r e i n t h e o n e - p h a s e r e g i o n , b u t e n d i n g a t ap r o g r e s s i v e l y l o w e r p r e s s u r e s i n t h e t w o - p h a s e r e g i o n .M o r e s p e c i f i c a l l y , s t a rt i n g f r o m a p o i n t A i n t h e o n e - p h a s er e g i o n , f i r st a r a p i d p r e s s u r e d r o p i s i m p o s e d t o r e a c h a p o i n tB w h i l e m o n i t o r i n g t h e t i m e - e v o l u t i o n o f th e s c a t t e r e d l ig h ti n t e n si t ie s . T h e p r e s s u r e o f t h e s y s t e m i s t h e n b r o u g h t b a c kt o p o in t A a n d n o w a n e w p r e s s u re q u e n c h i s i m p o s e d t or e a c h a p o i n t C w h i c h i s a t a l o w e r f i n a l p r e s s u r e . O n c ea g a i n t h e p r e s s u r e i s b r o u g h t b a c k t o t h e in i t ia l p r e s s u r e a n dt h e p r e s s u r e q u e n c h i s c a r r i e d o u t w i t h e v e n l o w e r e n d -p r e s s u r e s t o a p o i n t D a n d f i n a l l y E , w h i l e r e c o r d i n g t h es c a t t e r e d l i g h t i n t e n s i t i e s d u r i n g e a c h q u e n c h .

I t s h o u l d b e n o t e d t h a t r a p i d p r e s s u r e q u e n c h e s a r ed i f f i c u l t t o a c h i e v e i s o t h e r m a l l y . T h e s y s t e m f o l l o w s a n o n -i s o t h e r m a l , n e a r l y a d i a b a t i c e x p a n s i o n p a t h w i t h a d r o p i n

(a)

. - , I

1 1 .

one-phase ~ i ;A j l /

r ~ ~

B' stab le

, ~ E ' ~ two-phase

T e m p e r a t u r e

(b) O n e P h a s eA o Binodal//B ~ Spinodal

P o l y m e r c o n c e n t r a t i o nFigure 5 (a) Schema tic representation of the dem ixing pressures (thebinodal) and the spinodal phase bounda ry as a function of temperature for apolym er solution displaying LC ST (low er critical solution temperature)type behavior. The so lid line represents the dem ixing pressure and thedashed line represents the spinodal phase bound ary. Abov e the dem ixingpressure is the one-phase homogeneous egion and below is the two-phaseregion. Between the d e-mixing pressure and the spinodal boundary is themetastable region. Two-phase regions are entered by decreasing thepressure or by increa sing the tempe rature. The path AF represents the idealisothermal pressure-quench path w hich in prac tice cannot be achieved. Dueto adiabatic cooling, the actual path (A 'F') d uring pressure quench will bedifferent and will be accomp anied with a decrease in temperature. (b)Schematic representations of multiple repetitive/rapid pressure drop(MRPD) technique to study kinetics of pressure-induced phase separation(PIPS) fro m the polym er solution. The method ology involves severalpressure quenc h experiments, all starting from the same initial one-phaseconditions (point A), but each w ith different penetration depth into the two-phase (metastable and unstable) regions w ith progressively low er finalpressures, i.e. the quench paths that are followed are A B, AC , AD, AE andAF. T im e evolution of scattered light intensities during each quench ismonitored as an imprint of the progress of phase separation

t e m p e r a t u r e . B e c a u s e t h e c e l l s a r e i n a h e a t e d o v e n , a n db e c a u s e t h e y h a v e a l a r g e t h e r m a l m a s s , t h e a c t u a lt e m p e r a t u r e o f th e s o l u t i o n s u n d e r g o i n g p r e s s u r e d r o p i si n f a c t h i g h e r t h a n w o u l d b e a n t i c i p a t e d f r o m a t r u ea d i a b a t i c e x p a n s i o n p r o c e s s . T h e a c t u a l p a t h s d u r i n gp r e s s u r e d r o p e x p e r i m e n t s a r e s c h e m a t i c a l l y d e m o n s t r a t e din Figure 5a. F o r t h e p r e s e n t s y s t e m , Figure 6 s h o w s t h ee x p e r i m e n t a l l y o b s e r v e d t e m p e r a t u r e d r o p i n t h e sc a t t e r i n gc e l l d u r i n g a r a p i d p r e s s u r e - q u e n c h f r o m a b o u t 1 6 M P a t o6 M P a f o r a s y s t e m w h i c h i s in i t i a ll y m a i n t a i n e d a t a b o u t1 4 7 C . W i t h a 1 0 - M P a p r e s s u r e d r o p , w h i c h i s a c h i e v e d i n a

2 9 08 P O L Y M E R V o l u m e 3 9 N u m b e r 1 3 1 9 98

8/12/2019 Supercritical Fluid 2

7/13

1 4 9 2.00

e'~E( )j -

1 4 81 4 71 4 6

1 4 51 4 41 4 3

~ o o~ o ~ o

o o

co o o c ~ o o o ~ o

~ c m ~ o c o o o c O o o ~ o c ~( to o o ~ n r ~ o o o 0 oo oo o ~ o ~ o % . . . .o o o co m c~ oo o oo ooo 0 o o o C c o 0 O oo

1 2t~~ 8n

0 1 0 0 2 0 0 3 0 0 4 0 0 5 0 0T i m e , m s

Figur e 6 Experimental observation of temperature drop in the scatteringcell during a rapid pressure-quench (at a rate of about 200 MPa/s) from 16to 6 MPa. The initial temperature of the solution in the scattering cell isabout 147C

t i m e i n t e r v a l o f a b o u t 5 0 m s , t h e t e m p e r a t u r e d r o p i so b s e r v e d t o b e a b o u t 2 C . T h e t e m p e r a t u r e o f th e c e l l w a sm o n i t o r e d u s i n g a s p e c i a l u n s h i e l d e d t h e r m o c o u p l e( O m e g a , m o d e l I R C O - 0 0 5 ) t o m i n i m i s e t h e r m a l l a g a n df o l l o w t h e t e m p e r a t u r e c h a n g e s t o t h e g r e a t e s t e x t e n tp o s s i b l e i n t h e t i m e s c a l e o f t h e p r e s s u r e c h a n g e s . I n a l le x p e r i m e n t s c o n d u c t e d t h e t o t a l p r e s s u r e q u e n c h w a s n og r e a t e r t h a n 1 0 M P a a n d t h e r e f o r e t h e m a g n i t u d e o f th ea c t u a l te m p e r a t u r e c h a n g e d u r i n g q u e n c h c a n b e r e g a r d e d t obe l e s s t h an 2 C .T h e t e m p e r a t u r e e f f e c t a s s o c i a t e d w i t h p r e s s u r e - q u e n c he x p e r i m e n t s h a v e b e e n w e l l r e c o g n i s e d i n t h e l i t e r a t u r e i nc o n n e c t i o n w i t h p h a s e s e p a r a t i o n i n o l i g o s t y r e n e + p e n t a n em i x t u r e s ~, b u t m o s t e x t e n s i v e l y i n c o n n e c t i o n w i t hs p i n o d a l d e c o m p o s i t i o n i n b i n a r y f l ui d m i x t u r e s 4 2- 51 .T e m p e r a t u r e e f f e c t d e p e n d s o n t h e q u e n c h d e p t h , a n d i n ar e c e n t s t u d y w i t h i s o - b u t o x y e t h a n o l + w a t e r s y s t e m , fo r aq u e n c h o f 1 - 1 . 5 M P a , a t e m p e r a t u r e c h a n g e o f 0 . 2 - 0 . 4 Cw a s r e p o r t e d 46. A n o t h e r f a c t o r t h a t i n f lu e n c e s t h e a c t u a lt e m p e r a t u r e i n a g i v e n s y s t e m u n d e r g o i n g p h a s e s e p a r a t i o ni s t h e c o n t r i b u t i o n f r o m t h e h e a t o f s o l u t i o n t h a t s h o u l d b et a k e n i n t o ac co unt 43'47. C a l o r i m e t r i c d a t a f o r p o l y m e rs o l u t i o n s a t h i g h p r e s s u r e s a r e r a r e . E v e n t h o u g h h e a t o ff u s i o n a n d f u s i o n t e m p e r a t u r e s h a v e b e e n r e c e n t l y r e p o r t e df o r h i g h e r a l k a n e s ( C 2 4 - C 6 0 ) a n d f o r p o l y e t h y l e n e s a tp r e s s u r e s u p t o 5 0 0 M P a 52, h e a t o f s o l u t i o n d a t a f o rp o l y e t h y l e n e + n - p e n t a n e m i x t u r e s a r e n o t a v a i l a b l e .T h u s , a p r i o r y c a l c u l a t i o n o f t h e t e m p e r a t u r e p a t h a s s o c i a t e dw i t h a p r e s s u r e q u e n c h p a t h i s n o t e a s y , a n d d i r e c tm e a s u r e m e n t o f t e m p e r a t u r e i s t h e b e s t r e l i a b l e o p t i o n .Figure 7 s h o w s t h e e v o l u t i o n o f s c a t t e r e d l i g h t i n t e n s i ti e sa t 9 0 f o r p u r e c a r b o n d i o x i d e w h e n s u b j e c t e d t o d i f f e r e n tp r e s s u r e q u e n c h e s f r o m a n i n i t ia l p r e s s u r e o f 1 4 M P aa t 2 5 C . T h e p r e s s u r e q u e n c h e s a r e a c c o m p l i s h e d w i t h i n5 - 2 0 m s , a n d t h e s c a t t e r e d l ig h t i n te n s i t i e s a r e m o n i t o r e do v e r a t i m e i n t e r v a l o f 2 0 0 m s . I t i s s h o w n t h a t w h e np ressu re i s r ed uce d f ro m 1 4 M P a to : 1 2 .6 , 1 0 .8 , 8 . 8 o r6 . 8 M P a , t h e r e l a t i v e c h a n g e i n t h e s c a t t e r e d l i g h t i n t e n s i tyi s i n s ig n i f i can t , w h i l e f o r t h e quen ch to 6 . 1 MP a , a r ap idd r a m a t i c i n c r e a s e i s n o t e d . T h e c r i t i c a l p r e s s u r e a n d

2 . 0

1 .8

. . . . . . P e = 1 2 . 6 M P aP e = l O . 6 M P a

1 . 8 P e = 8 . 8 M P a ~ /P e = 6 .8 i P a , N r vP e = 6

1 o~_ 1.4

1.2

1 . 0 ~ L ;O.E , I , I , I , I ,4 0 8 0 1 2 0 1 6 0 2 0 0

T i m e , m sFig ure 7 Evolution of scattered light intensities at 90 with time for purecarbon dioxide when subjected to different pressure quenches from an

............. Pe =1 3 .0 M P aP e = 1 0 . 2 M P aP e = 7 . 9 M P a

- , - - - P e = 4 . 4 M P a. T . .

1 .6

-~ . 1 .4

1 .2

1 .0

Kinet ics of PIPS f rom po lym er solu t ions: VV. Zh uan g a nd E. Ki ran

1 0 0 2 0 0 3 0 0 4 0 0 5 0 0T i m e , m s

Fig ure 8 Evolution of scattered light intensities at 90 with time for puren-pentane when subjected to different pressure quenches from an initialpressure of 14 MPa at 150C. Final (quench) pres sures are as indicated

t e m p e r a t u r e f o r c a r b o n d i o x i d e a r e 7 . 3 8 M P a a n d 3 1 . 2 C .A t 2 5 C a n d 1 4 M P a , c a r b o n d i o x i d e i s in t h e l i q u i d s t a te .V a p o u r p r e s s u r e o f c a r b o n d i o x i d e a t 2 5 C i s 6. 4 1 M P a ( a n da t 2 3 C i t i s 6 . 2 M P a) 5 3. F o r t h e quen c h to 6 . 1 MP a , t h ev a p o u r - l i q u i d p h a s e b o u n d a r y h a s b e e n c r o s s e d , a n d t h i sp h a s e s e p a r a t i o n p r o c e s s i s r e c o r d e d b y t h e c h a n g e i n t h esca t t e r ed l i g h t i n t en s i t i e s . In o th e r quen ch es , t h e f lu idr e m a i n s i n t h e l i q u i d s t a t e . T h e c h a n g e i n d e n s i t y d u e t ov o l u m e e x p a n s i o n s h o w s i t s e l f o n l y a s s m a l l c h a n g e s i n t h er e l a t i v e s c a t t e r e d l i g h t i n t e n s i t y .Figure 8 s h o w s t h e e v o l u t i o n o f s c a t t e r e d l i g h t i n t e n s it i e sa t 9 0 f o r p u r e n - p e n t a n e w h e n s u b j e c t e d t o s e v e r a l p r e s s u r eq u e n c h e s t o d i f f e r e n t e n d - p r e s s u r e s s t a r t i n g f r o m a n i n i t i a ll i qu id s t a t e a t 1 4 MP a an d 1 5 0 C . ( Th e c r i t i ca l p re s su re an d

P O L Y M E R V o l u m e 3 9 N u m b e r 1 3 1 9 9 8 2 9 0 9

8/12/2019 Supercritical Fluid 2

8/13

Kinetics of PIPS from polymer solutions: W Zhuang and2 . 0

1 . 8

1 .6.,..o- - . . 1 . 4m

1.2

1 . 0

1 % P E 1 0 8 , 0 0 0 , 1 4 - 8 . 2 M P a- - p u r e n - p e n t an e , 1 4 - 7 . 9 M P a

0.E ~ I , I , I , I h1O0 200 300 400 500T i m e , m s

Fig ure 9 Compar ison of the evolution of scattered light intensities at 90of a polyethylene -I- n-pentane solution with that of pure n-pentane whensubjected to a similar pressure quench to an end-pressure above thevapour-li quid phase boundary for n-pentane

t e m p e r a t u r e f o r n -p e n t a n e a r e 3 . 3 7 M P a a n d 1 9 6. 6 C ,r e s p e c t i v e l y . ) T h e d a t a s h o w s t h a t t h e l i q u i d - v a p o u rp h a s e b o u n d a r y i s c r o s s e d f o r t h e q u e n c h t o 1 .9 M P a . I ts h o u l d b e n o t e d h o w e v e r t h a t t h e v a p o u r p r e s s u r e o f p e n t a neat 150C is 1 .58 MP a 54.Figure 9 c o m p a r e s t h e b e h a v i o u r o f a p o l y e t h y l e n e +n - p e n t a n e s o l u t i o n w i t h th a t o f p u r e n - p e n t a n e w h e ns u b j e c t e d t o a s i m i l a r p r e s s u r e q u e n c h t o a n e n d - p r e s s u r ea b o v e t h e v a p o u r - l i q u i d p h a s e s e p a r a t i o n b o u n d a r y f o rn - p e n t a n e . I t i s t h e l i q u i d - l i q u i d p h a s e s e p a r a t i o n i n th ep o l y m e r s o l u t i o n t h a t l e a d s t o t h e i n c r e a s e i n t h e s c a t t e r e dl i g h t i n t e n s i t y . I t w a s i m p o r t a n t t o i n s u r e t h a t t h e p h a s e -s e p a r a t i o n i n t h e p o l y m e r s o l u t io n s w e r e b e i n g c o n d u c t e d i na r a n g e a w a y f r o m t h e l i q u i d - v a p o u r p h a s e s e p a r a ti o n f o rt h e s o l v e nt . T h e b e h a v i o u r o f p o l y e t h y le n e + n - p e n t a n es o l u t i o n s i s d e s c r i b e d i n d e t a i l i n t h e f o l l o w i n g s e c t i o n s .Pressure-induced phase separation in polyethylenesolutions

P h a s e s e p a r a t i o n s t u d i e s w e r e c o n d u c t e d u s i n g p o l y -e t h y l e n e s a m p l e s w i t h n a r r o w m o l e c u l a r w e i g h t d i s t r i b u -t i o n s . T w o p o l y m e r s a m p l e s w e r e e v a l u a t e d : o n e w i t h am o l e c u l a r w e i g h t o f 1 0 8 0 0 0 a n d t h e o t h e r 1 6 4 0 0 .Polyethylene Mw = 108000; M~IVI, = 1.32) + n-pentane

T h e q u e n c h p a t h s f o r th i s s y s t e m a r e s h o w n i n Figure 10.I n t h i s f i g u r e , t h e s o l i d c u r v e r e p r e s e n t s t h e d e m i x i n gp r e s s u r e s a s a f u n c t i o n o f p o l y m e r c o n c e n t r a t i o n ,d e t e r m i n e d a s c l o u d p o i n t s f r o m s l o w p r e s s u r e r e d u c t i o no 40 55e x p e r i m e n t s a t 1 5 0 C ' . T h e r e g i o n a b o v e t h e c u r v er e p r e s e n ts t h e o n e - p h a s e h o m o g e n e o u s r e g io n .F o l l o w i n g t h e m e t h o d o l o g y d e s c r i b e d a b o v e , a t e a c hc o n c e n t r a t i o n ( u p t o 5 % b y m a s s ) , t h e s o l u t i o n ( i n i ti a l l y a t ah i g h p r e s s u r e c o r r e s p o n d i n g t o a p o i n t i n t h e o n e - p h a s er e g i o n , i . e . p o i n t A ) w a s s u b j e c t e d t o p r o g r e s s i v e l y d e e p e rp r e s s u r e q u e n c h e s ( i. e . c o r r e s p o n d i n g t o p r e s s u r e s a t p o i n t sB , C , D an d E ) .Figures 11 a n d 12 s h o w t h e p r e s s u r e p r o f i l e s a n d t h ee v o l u t i o n o f t h e s c a t t e r e d l i g h t i n t e n s i t i e s a t 9 0 a s a

14

a . 1C

if)~ 8

A ~

co l tVE i

IIII

v v v iD e m i x i n g p r e s s u r e

I t I , I3 4 5

4 I , I , I0 1 2 6P o l y m e r c o n c en t ra t io n , m a s s %

Fig ure 10 Quench paths for polyethylene (M . = 108 000) + n-pentanepolymer solutions at different polymer concentrations. The solid curverepresents the actual de-mixing pressures (cloud points) at 150C for thissolution as a function of polymer concentration. The dashed lines representmultiple quenches experimentally carried out at each selected polymerconcentration

1 3

/ - - - 9 . 2 M P a1 2 / I 8 . 6 M P a| ~ 8 .0 M P a

11 / ~ 7 .4 M P a_lO

PE 108,000/n-pentane 0.5 % 150 C6 0 5 0 1 0 0 1 5 0 2 0 0T i m e , m s

Figure I t Pressure profiles of the multiple pressure quenches as afunction of time for the 0.5 polyethylene (Mw = 108000) + n-pentanesolution from an initial pressure of 12.5 MPa at 150C

f u n c t i o n o f t i m e f o r a s e t o f p r e s s u r e - q u e n c h e x p e r i m e n t sf o r t h e 0 . 5 w t % s o l u t i o n f r o m a n i n i ti a l p r e s s u r e o f1 2 . 5 M P a . Figure 11 s h o w s t h a t t h e p r e s s u r e q u e n c h e s a r ea c c o m p l i s h e d w i t h i n a b o u t 1 0 m s . A s s h o w n i n Figure 12,t h e s c a t t e r e d l i g h t i n t e n s i t i e s i n c r e a s e a n d t h e r a t e o fi n c r e a s e b e c o m e s g r e a t e r w i t h i n c r e a s e d q u e n c h d e p t h , i . e .w i t h l o w e r e d e n d - p r e s s u r e s . I n Figure 12, s c a t t e r e d l i g h ti n t e n s i ti e s a r e s h o w n o v e r a t o ta l o b s e r v a t i o n t i m e o f 2 0 s .Figure 13 s h o w s t h e r e s u l t s o f a r e p e a t s e t o f q u e n c he x p e r i m e n t s w i t h s i m i l a r e n d p r e s s u r e s , w i t h a s h o r t e r to t a lo b s e r v a t i o n t i m e o f 2 s . I n t h e s e f i gu r e s , th e s o l i d c u r v e s a r et h e s m o o t h e d c u r v e s .

2 9 1 0 P O L Y M E R V o l u m e 3 9 N u m b e r 1 3 1 9 98

8/12/2019 Supercritical Fluid 2

9/13

Kinetics of PIPS from polymer solutions: W Zhuang and E Kiran

PE 108,000/n-pentane 0.5 % 150 C

D

0 ~9 .8 MPa9.2 MPa8.6 MPa8.0 MPa7.4 MPa

, I , , , I , , = I , , , I , , , I , , , I ,0 4 0 0 0 8 0 0 0 1 2 0 0 0 1 6 0 0 0 2 0 0 0 0T i m e , m s

Figu re 12 Evolution of the scattered light intensities at 90 for a set ofmultip le pressu re quench es in 0.5 poly ethyl ene (Mw ---- 108000) +n-pent ane solut ion from an initi al pressu re of 12.5 MPa at 150C. Finalpressures are as indicated (see Figure 11). Observation time is 20 s. Thesolid curves are the smoothed curves

E 0 . 2 0

~ 0.16e-.~ 0.12

. : 0 . 0 8r-t~ ~ 0.04

t~ 0 . 0 0n~

'\\ \

\\

\\

\\\

\\

\\\

\\\

\ \\ \\ \

\\\

\\

6.0 7 .0 TP 8 .0 9 .0 10 .0E n d p re s s u r e , M P a

Fig ure 14 Rate of change of scattered light intensities with time (theslopes of the initial relative scattered intensity profiles) as a function of theend-pressure of pressure quenches which defines a characteristic endpressure, i.e. the transition pressure, TP. At pressures below this transitionpressure, phase separation proceeds extremely rapidly

._.o

PE 108,000/n-pentane 0.5 % 150 C

I m

g n D o

U ~. ~ ~ ~ . _ . - 2 ~o o o o

8.6 MPa0 ~ 8.3 MPa

B-.. l 8.0 MPa7.4 MPa-1 , i . , , i , , , i , , , i , , , i , , , i ,0 4 0 0 8 0 0 1 2 0 0 1 6 0 0 2 0 0 0

T i m e , m sFig ure 13 Evolution of the scattered light intensities at 90 for a set ofmultiple pressure quenches in 0.5 polyethylene (Mw = 108000) +n-pent ane solut ion from an initial pressure of 12.5 MPa at 150C. Finalpressures are as indicated. Observation time is 2 s. The solid curves are thesmoothed curves

A s c a n b e s e e n f r o m Figure 10, t h e p h a s e b o u n d a r y f o rt h i s s o l u t io n i s a b o u t 9 . 6 M P a . Figures 12 a n d 13 s h o w t h a tt h e c h a n g e s i n t h e s c a t t e r e d l i g h t i n t e n s i t y a r e i n d e e di n s i g n if i c a n t f o r a q u e n c h t o 9 . 8 M P a w h i c h i s a b o v e t h ec l o u d p o i n t p r e s s u r e , b u t b e c o m e s l a r g e f o r q u e n c h e s t o9 . 2 M P a a n d l o w e r p r e s s u r e s .A r e l a t i v e l y s i m p l e a p p r o a c h t o e v a l u a t e a n d c o m p a r e t h ed e p e n d e n c e o f t he p h a s e s e p a r a t io n p r o c e s s o n t h e q u e n c hd e p t h i s t o c o m p a r e t h e r a t e o f c h a n g e o f s c a t te r e d l i g h tin t en s i t i e s w i th t im e . Th e s lo p es o f t h e i n i t ia l ( sh o r t - t im e)re l a t i v e sca t t e r ed in t en s i ty p ro f i l e s f o r t h i s so lu t io n h av e b een

1412

108.._o

- - 6

PE 108,000/n-pentane 1.0 % 150 C

, .

9.8 MPa9.2 MPa

~ 8.6 MPa8.0 MPa7.4 MPa6.8 MPa

I a I ~ L I I I0 4 0 0 0 8 0 0 0 1 2 0 0 0 1 6 0 0 0 2 0 0 0 0T i m e , m s

Fig ure 15 Evolution of the scattered light intensities at 90 for a set ofmultiple pressure quenches in 1 polyethylene (Mw = 108000) +n-pent ane soluti on from an initia l pressur e of 12.5 MPa at 150C. Finalpressures are as indicated

e v a l u a t e d . I n Figure 14, t h e y a r e s h o w n a s a f u n c t i o n o f t h ee n d - p r e s s u r e r e a c h e d . F r o m s u c h a p l o t , a c h a r a c te r i s ti c e n dp r e s s u r e b e l o w w h i c h t h e r e i s a d r a m a t i c i n c r e a s e i n t h e r a teo f c h a n g e o f s c a t t e r e d l i g h t i n t e n s i t y i n p r e s s u r e - i n d u c e dp h ase sep a ra t io n can be id en t i f i ed . Th i s t r an s i t i o n p res su rew h e r e t h e t i m e s c a l e o f p h a s e s e p a r a t i o n s h o w s a r e m a r k a b l ec h a n g e i s n o t e d a s T P i n Figure 14. A t p r e s s u r e s b e l o w t h is' t r a n s i t i o n ' p r e s s u r e , p h a s e s e p a r a t i o n i s e x t r e m e l y r a p i d .F o r t h i s p o l y m e r - t - s o l v e n t s y s t e m , t h e p r e s s u r e - q u e n c he x p e r i m e n t s w e r e c o n d u c t e d a l s o a t h i g h e r p o l y m e rc o n c e n t r a t i o n s a n d t h e s c a t t e r e d l i g h t i n t e n s i t i e s w e r em o n i t o r e d a n d a n a l y s e d b y s i m i l a r p r o c e d u r e s . Figure 15

POLYMER Vo lu me 39 Nu mb er 13 1998 2911

8/12/2019 Supercritical Fluid 2

10/13

Kinetics of PIPS from polymer solutions: W Zhuang and E Kiran1 4

1 2 -

10i

PE 108,000/n-pentane 4.0 % 150 C

8 -

6 -

4 -

2 -

0-

t- - - - - - 9 .2 MPa

8 . 6 M Pa8 . 0 M Pa7.4 MPa6. 8 M Pa6. 2 M Pa

0 4000 8000 12000 16000 20000T i m e , m s

Fig ure 16 Evolution of the scattered light intensities at 90 for a set ofmultiple pressure quenches in 4 polyethylene (Mw = 108000) +n-pentane solution from an initial pressure of 12.5 MPa at 150C. Finalpressures are as indicated

0 . 4

" ~ 0 . 3E=: ~ 0 . 2

(.-0.156 o.o

11

Q .

--InnEl.

10

1

d em ix ing p res s u re a t 150 Cd e m i x i n g p r e s s u r e at 148 C

t r a n s i t i o n p r e s s u e at 150 C

i L , I L I , I ~ I1 2 3 4 5Polymer c o n c e n t r a t i o n , m a s s %

Figur e 18 Comparisons of de-mixing pressure and dynamic transitionpressure as obtained by the multiple pressure quench approach forpolyethylene (M~ = 108000) + n-pentane solution at different polymerconcentrations. The de-mixing pressures at 148C are included to accountfor the cooling effect (which is -2 C, shown in Figure 6) in the course ofrapid pressure reduction

o ( 3 0 . 5 3(3[ ] 1 . 0 %

3 . 0 %

20

1(3

7 . 0 8 . 0 9 . 0End pressure, MPaFig ure 17 Rate of change in relative scattered light intensities as afunction of the depth (end-pressure) of pressure quenches for polyethylene(Mw = 108 000) + n-pentane solutions at 150C. Solution concentrationsare as indicated

and Figure 16 show the smoothed scattered light intensityprofiles for the 1 and 4 . For shallow quenches, the datacollect ion interval was 20 s, but for deeper quenches, inorder to collect more data points to capture the fast changes,total observation times were reduced to 2 s or less. The rateof change of scattered light intensities are shown inFigure 17 as a function of the quench pressure for solutionsat 0.5, 1 and 3 concentrations. The transition pressures forextremely rapid phase separation were determined at eachconcentration. These pressures identify a kinetic boundaryinside the two-phase region below which the systemundergoes very rapid phase separation. The cloud pointpressures and the inner transition pressures obtained from

PE 16,400/n-pentane 3% 150 C

6 . 4 M Pa4. 6 M Pa

~ - 4 .3 M P a3. 6 M Pa2 . 9 M Pa

f ~ i - -i I i I i I i I i I0 100 200 300 400 500T i m e , m s

Fig ure 19 Evolution of the scattered light intensities at 90 for a set ofmultiple pressure quenches in 3 polyethylene (Mw = 16 400) + n-pentanesolution from an initial p ressure of 6.9 MPa at 150C. Final pressures are asindicated

pressure quench experiments are shown in Figure 18. Thisinner boundary is a kinetic phase boundary of practicalsignificance.Polyethylene Mw = 16400; M~VI, = 1.16) + n-pentane

Figures 19 and 20 are representative plots of the changein relative scattered light intensity at 90 with time for thissystem upon pressure quench to different end-pressures.The results are shown for 3 and 5 solutions at 150C.Similar experiments were conducted at several otherconcentrations. The transition pressures for each system

2912 POLYMER Vol ume 39 Number 13 1998

8/12/2019 Supercritical Fluid 2

11/13

Kineti cs o f P IPS f rom po lym er so lu t ions : W. Zhua ng a nd E. K i ran

m

3C

2 0

1 0

PE 16,400/n-pentane 5% 150 C

5 . 9 M P ar w ~ 5 . 4 M P a

5 . 0 M P a4 . 7 M P a

wW ~ 4. 4 M P a

, I i I i I i I I I0 2 0 0 4 0 0 60 0 8 0 0 1 0 0 0T i m e , m s

F i g ure 20 Evolutionof the scattered light intensities at 90 for a set o fmultiple pressure quenches in 5% polyethylene Mw = 16 400) + n-pentanesolution from an initial pressure of 6.9 M Pa at 150C. Final pressure s are asindicated

4E~=->~ 3c=r -

,D> 2

c--c-OOt~rv,

F i g ure 21

A 1 . 0 %O 3 . 0 %[ ] 5 . 0 %

on I n7 83 4 5 6T P E n d p re s s u re , M P a

R a t e o f c h a n g e i n r e l a t i v e s c a t t e r e d l i g h t i n t e n s i t i e s a s afunction of the depth (end-pressure)of pressure quenches for polyethylene(Mw = 16400) + n-pentane solutions for different polym erconcentrationsat 150C

w e r e t h e n d e t e r m i n e d f r o m p l o t s o f t he r a t e o f c h a n g e i nr e l a t i v e s c a t t e r e d l i g h t i n t e n s i t y versus e n d - p r e s s u r e o f t h eq u e n c h a s s h o w n i n Figure 21. Figure 22 c o m p a r e s t h ec l o u d p o i n t p r e s s u r e s f o r t h i s s y s t e m w i t h t h e i n n e r ,d y n a m i c p h a s e - s e p a r a t i o n b o u n d a r y .Further discussion

T h e p r e s e n t o b s e r v a t i o n s s h o w t h e t r a n s i t i o n i n t h ek i n e t i c s o f p h a s e s e p a r a t i o n w i t h t h e q u e n c h d e p t h i m p o s e d .A d i s t i n c t c h a n g e i n t h e s c a t t e r e d l i g h t i n te n s i t y w i t h q u e n c hd e p t h h a s a l s o b e e n r e p o r t e d i n a s e r i e s o f t e m p e r a t u r eq u e n c h e x p e r i m e n t s c o n d u c t e d i n m i x t u r e s o f s t y r e n e

P E 1 6 , 4 0 0 / n - p e n t a n e

5Q _

g 4fflffl0- 3

/ d e m ix in g p r e s s u r e a t 15 0 C2 / ~ d e m ix in g p r e s s u r e a t 148 C

=. / t ransition pressure a t 15 0 C

0 1 2 3 4 5 6 7Polymer c o n c e n t r a t i o n , m a s s %

F i g u r e 2 2 C o m p a r i s o n s o f d e - m i x i n g p re s s u r e a n d th e d y n a m i c tr a n s it i o np r e s s u r e a s o b t a i n e d b y t h e m u l t i p l e p r e s s u r e q u e n c h a p p r o a c h f o rp o l y e t h y l e n e ( M ~ = 1 6 4 0 0 ) + n - p e n t a n e s o l u t i o n a t d i f f e r e n t p o l y m e rc o n c e n t r a t i o n s . T h e d e - m i x i n g p r e s s u r e s a t 1 4 8 C a r e a l s o i n c l u d e d top e r m i t c o m p a r i s o n s o n a c c o u n t o f t h e c o o l i n g e f f e c t i n t h e c o u r s e o f r a p i dp r e s s u r e r e d u c t i o n

o l i g o m e r s a n d e c a p r o l a c t o n e 27. T h e s c a t t e r e d l i g h t i n te n s i t yi n th a t s y s t e m i s r e p o r t e d t o b e m u c h l o w e r i n t h e n u c l e a t i o na n d g r o w t h r e g i m e t h a n t h e s p in o d a l d e c o m p o s i t i o n r e g i m ei f c o m p a r e d a t t h e s a m e p h a s e - s e p a r a t i o n t im e . T h e s p e e d o fp h a s e s e p a r a t i o n i n c r e a s e s w i t h a n i n c r e a s e i n q u e n c h d e p t ha n d s h o w s a s h a r p d e m a r c a t i o n a r o u n d t h e t r a n s i t i o n f r o mm e t a s t a b i l i t y t o u n s t a b i l i t y . O n e i s t h e r e f o r e t e m p t e d t om a k e t h e s u g g e s t i o n t h a t t h e k i n e t i c p h a s e b o u n d a r yr e p o r t e d i n t h e p r e s e n t s t u d y m a y b e i n d i c a t i v e o f ac h a n g e i n t h e m e c h a n i s m o f p ha s e s e p a r a t i o n f r o mn u c l e a t i o n a n d g r o w t h t o s p i n o d a l d e c o m p o s i t i o n . H o w e v e r ,a s d e m o n s t r a t e d i n Figure 5b, t h e t h e r m o d y n a m i c s p i n o d a lb o u n d a r y s h o u l d i n p r i n c i p l e m e r g e w i t h t h e b i n o d a l c u r v ea t t h e c r i ti c a l p o l y m e r c o n c e n t r a t i o n . T h e c r i t i c a l p o l y m e rc o n c e n t r a t i o n f o r th i s p o l y m e r + s o l v e n t s y s t e m w a s n o te x p e r i m e n t a l l y d e t e r m i n e d . P r e d i c t i o n s b y S a n c h e z -L a c o m b e a n d S A F T m o d e l s a f t e r f i t t i n g t h e e x p e r i m e n t a ld e m i x i n g p r e s s u r e s s u g g e s t s a c r i t i c a l c o n c e n t r a t i o n o fa b o u t 2 % b y m a s s f o r th e p o l y m e r w i t h M w = 1 0 8 0 0 0an d a t abo u t 5 % f o r t h e p o l ym er w i th Mw = 1 6 400 5 6 '5 7 .F o r p o l y m e r s w i t h p o l y d i s p e r s i t y , t h e a c t u a l c r i t i c a lc o n c e n t r a t i o n i s o f te n s h i f t e d t o h i g h e r c o n c e n t r a t i o n s .Figures 18 a n d 22 s h o w t h a t th e d y n a m i c i n n e r b o u n d a r y ,a s d e t e r m i n e d i n t h e p r e s e n t s t u d y , d o e s n o t m e r g e w i t h t h eb i n o d a l i n t h e c o n c e n t r a t i o n r a n g e e v a l u a t e d a n d t h u s d o e sn o t m e e t t h e c r i t e r i a f o r t h e r m o d y n a m i c s p i n o d a l b o u n d a r y .H o w e v e r , r e c e n t s t u d i e s b y T a n a k a 58"59 i n d i c a t e t h a t i n d e e pq u e n c h e x p e r i m e n t s i n v o l v i n g a s y m m e t r i c s y s t e m s s u c h a sp o l y m e r s o l u t i o n s , t h e p h a s e s e p a r a t i o n p r o c e s s m a y b es t r o n g l y a f f e c t e d b y e l a s t i c e f f e c t s , a n d s u c h s y s t e m s m a ys h o w a d y n a m i c s y m m e t r y l in e a n d u n d e r g o v i s c o e la s t ics p i n o d a l d e c o m p o s i t i o n . T a n a k a s u g g e s t s t h a t w h e n t h ec h a r a c t e r i s t i c d e f o r m a t i o n t i m e i s s h o r t e r ( a s w o u l d b e t h ec a s e i n r a p i d d e e p q u e n c h e s ) t h a n t h e c h a r a c t e r i s t i cr h e o l o g i c a l t i m e , p o l y m e r s o l u t i o n s b e h a v e l i k e e l a s t i cg e l s ( d u e t o e n t a n g l e m e n t s ) . I n c o n t r a s t , t h e y b e h a v e l i k ev i s c o u s f l u i ds f o r s l o w e r d e f o r m a t i o n s . F o r a d e e p q u e n c h , al a r g e d i f f e r e n c e i s e x p e c t e d i n t h e d y n a m i c s b e t w e e n t h e

P O L Y M E R V o l u m e 3 9 N u m b e r 1 3 1 9 9 8 2 9 1 3

8/12/2019 Supercritical Fluid 2

12/13

Kineti cs o f P IPS f rom po lym er so lu t ions : W. Zhua ng a nd E. K i rant w o c o - e x i s t i n g p h a s e s ( a n e l a s t i c o r t r a n s i e n t n e t w o r kc h a r a c t e r i s e d b y s l o w d y n a m i c s a n d a f l u i d c h a r a c t e r i s e d b yf a s t d y n a m i c s ) a n d v i s c o - e l a s t i c e f f e c t s m a y p l a y ad o m i n a n t r o l e i n t h e p r o g r e s s o f p h a s e s e p a r a t i o n . T h ee l a s t ic e f f e c t s a r e p r e s u m e d t o s u p p r e s s th e e n h a n c e m e n t o fc o n c e n t r a t i o n f l u c t u a t i o n s w h i c h i s c h a r a c t e r i s t i c o f t h ei n i ti a l s t a g e o f s p i n o d a l d e c o m p o s i t i o n . I n s y s t e m si n f l u en c e d b y e l a s t ic e f f e c t , th e e l a s ti c e n e r g y b a r r i e r m u s tb e o v e r c o m e f o r t h e p h a s e s e p a r a t i o n to p r o c e e d . T a n a k af u r t h e r a r g u e s t h a t i n s u c h s y s t e m s , p h a s e s e p a r a t i o nm a y p r o c e e d b y n u c l e a t i o n a n d g r o w t h i n t h e l e s s e l a s t i cp h a s e e v e n f o r a n u n s t a b l e s t a t e a n d m o v e t h e s p i n o d a lb o u n d a r y . T h e p r e s e n t o b s e r v a t i o n s c o u l d p e r h a p s b ep e r c e i v e d a s b e in g i n l i n e w i t h t h e s e a r g u m e n t s c o n s i d e r i n gt h e v e r y r a p i d q u e n c h r a t e s a n d d e e p q u e n c h e s t h a t a r ei m p o s e d .A n o t h e r f a c t o r t h a t n e e d s t o b e c o n s i d e r e d i s t h e s h i f t i nt h e l o c a t i o n o f t h e b i n o d a l w i t h t e m p e r a t u r e . A s p o i n t e d o u te a r l ie r , t h e s e ra p i d p r e s s u r e q u e n c h e s a r e a c c o m p a n i e d w i t ha c h a n g e i n t h e t e m p e r a t u r e o f t h e s o l u t i o n a n d i n t h e p r e s e n ts t u d y e x p e r i m e n t a l l y o b s e r v e d c h a n g e i s a b o u t 2 C o rl o w e r . S i n c e t h e p o l y e t h y l e n e 4- n - p e n t a n e s y s t e m s h o w sL C S T t y p e b e h a v i o u r , l o w e r i n g t h e t e m p e r a t u r e w i l l l o w e rt h e d e m i x i n g p r e s s u r e s a n d m o v e t h e b i n o d a l t o a l o w e rb o u n d a r y . I n Figure 18, t h e c l o u d p o i n t c u r v e f o r a s o l u t io na t 1 4 8 C i s a l s o i n c lu d e d . C o m p a r e d t o t h e c l o u d p o i n t c u r v ea t 150C , t h i s cu rv e r epresen t s t he l oca t i on o f t heb o u n d a r y f o r t h e c a s e w i t h t h e 2 C c o o l i n g a s a c t u a l l ym o n i t o r e d . T h e k i n e t i c p h a s e b o u n d a r y i s c l e a r l y a t m u c hl o w e r p r e s s u r e s t h a n c a n b e a t t r i b u t e d t o a s i m p l et e m p e r a t u r e d e p e n d e n t s h i f t i n t h e b i n o d a l , u n l e s s t h et e m p e r a t u r e s h i f t i s m u c h g r e a t e r a n d o c c u r s a t a r a t e f a s t e rt h a n c a n b e r e c o r d e d . T h e i n n e r b o u n d a r y m a y b e r e f l e c t in ga c h a n g e i n m e c h a n i s m o f p h a s e s e p a r a t io n . I f th i s b o u n d a r yw e r e r e p r e s e n t a t i v e o f t h e s p i n o d a l b o u n d a r y , i t w o u l d b et h e b o u n d a r y c o r r e s p o n d i n g t o a l o w e r t e m p e r a t u r e t h a n t h ei n i t i a l t em pera t u r e o f t he so l u t ion . As such , i t wou l d bem o r e a p p r o p r i a t e t o c o m p a r e i t w i t h t h e b i n o d a l b o u n d a r yc o r r e s p o n d i n g t o t h e l o w e r t e m p e r a t u r e . T h e d o w n s h i f tm o v e m e n t o f t h e b i n o d a l w i t h c o o l i n g i s i n th e r i g h td i r e c t i o n t o w a r d s i m p r o v i n g t h e p o s s i b i l i t y f o r m e r g i n g o ft h e s p i n o d a l a n d t h e b i n o d a l a t t h e c r i t i c a l p o l y m e rc o n c e n t r a t i o n .F o r s y s t e m s u n d e r g o i n g s p i n o d a l d e c o m p o s i t i o n ,t y p i c a l l y c o n d u c t e d a t t h e c r i t i c a l p o l y m e r c o n c e n t r a t i o ni m p o s e d t o s h a l l o w p r e s s u r e q u e n c h e s , s c a t t e r e d l i g h ti n t e n s i t y i s k n o w n t o i n c r e a s e w i t h t i m e a n d g o t h r o u g h am a x i m u m w i t h s c a t t e r in g a n g l e . I f i t f o ll o w s t h e l i n e a r i s e d2 2 2 4 3 8 6 0 6 1C a h n - H i l l i a r d T h e o r y - ' , t h e a n g l e a t w h i c h t h em a x i m u m i n t h e s c a t t e r e d l i g h t i n t e n s i t y i s o b s e r v e d i s at i m e i n v a r i a n t a n d t h e s c a t t e r e d l i g h t i n t e n s i t y g r o w se x p o n e n t i a l l y i n t i m e a c c o r d i n g t o

In l(q, t) = In l(q, O) + 2Rq t (1)w h e r e R q i s t he r a t e cons t an t and , q i s t he s ca t t e r i ng vec t o ra n d d e f i n e d a s

q = (4a-/X) s in (0/2) (2)w h e r e X i s th e w a v e l e n g t h o f t h e l i g h t a n d 0 i s t h e s c a t t e r in ga n g l e . F o r p o l y m e r s o l u t i o n s t h e i n t e n s i t y m a x i m u m i so b s e r v e d a t l o w a n g l e s , t y p i c a l l y b e l o w 1 5 In t he p r esen t sys t em, t he s ca t t e r ed l i gh t i n t ens i t i e s cou l dn o t b e m e a s u r e d a t s u c h l o w a n g l e s a n d t h e p r e s e n c e o ra b s e n c e o f a m a x i m u m o f s c a t t e r e d i n te n s i t y w i th s c a t t e r i n ga n g l e , a n d w h e t h e r o r n o t q m i s t im e i n v a r i e n t a s w o u l d b e

p r e d i c t e d b y t h e l i n e a r i s e d C a h n - H i l l i a r d f o r m a l i s m c o u l dn o t b e d i s c e r n e d f o r t h e ra p i d d e e p - q u e n c h e x p e r i m e n t s .C u r r e n t r e s e a r c h i n o u r l a b o r a t o r y i s f o c u s e d o n t h e l o wa n g l e m e a s u r e m e n t s f o r f u r t h e r e l u c i d a t i o n o f t h e c h a n g ei n m e c h a n i s m a n d t h e s p i n o d a l p r o c e s s u n d e r s h a l l o wa n d d e e p - q u e n c h e x p e r i m e n t s . S h a l l o w p r e s s u r e - q u e n c he x p e r i m e n t s c o n d u c t e d i n p o l y s ty r e n e + m e t h y l c y c l o h e x a n ea t t he c r i t i ca l po l ymer concen t r a t i on i n a f i a t -w i ndows c a t t e r i n g c e l l w h i c h p e r m i t s m o n i t o r i n g t h e s c a t t e r i n gi n t ens i t i e s a t l ow ang l es d i sp l ay a l l t he we l l -known aspec t so f s p i n o d a l d e c o m p o s i t i o n w i t h r e s p e c t t o a n g u l a r v a r i a t io nof s ca t t e r ed l i gh t i n t ens i t i e s 13'62. Ho we ver , fo r r ap i d andd e e p q u e n c h e s s i m i l a r t o t h o s e d e s c r i b e d i n t h e p r e s e n ts t u d y , th e d y n a m i c s t o b e m o n i t o r e d b y t h e s a m p l i n g r a t e sa c c e s s i b l e w i t h c o m m e r c i a l l i n e a r i m a g e s e n s o r s b e c o m ev e r y f a s t a n d t h e s c a t t e r i n g m a x i m u m c a n n o t b e c a p t u r e de v e n a t c r it i c a l p o l y m e r c o n c e n t r a t i o n s . T h e s e o b s e r v a t i o n sf u r t h e r t h e n o t i o n t h a t i n r a p i d q u e n c h e x p e r i m e n t s t h ed y n a m i c s o f p h a s e s e p a r a t i o n m a y d i s p l a y d i f f e r e n tc h a r a c t e r is t i c s. W e a r e e x p l o r i n g a l t e r n a t iv e a p p r o a c h e s t od o c u m e n t t h e e x t r e m e l y s h o r t t i m e ( i . e . m i c r o s e c o n d )proces ses .Conclusions

P r e s s u r e - i n d u c e d p h a s e s e p a r a t i o n i n p o l y m e r s o l u t i o n sc a n b e c o n v e n i e n t l y f o l l o w e d u s i n g a d u a l c e l l o p t i c a ls y s t e m . R a p i d p r e s s u r e - q u e n c h e x p e r i m e n t s i n p o l y m e rs o l u t i o n s i d e n t i f y a k i n e t i c p h a s e b o u n d a r y b e l o w t h ed e - m i x i n g p r e s s u r e s . T h i s b o u n d a r y i s a d y n a m i c p h a s eb o u n d a r y b e l o w w h i c h p h a s e s e p a r a t i o n p r o c e s s e s a r ee x t r e m e l y r a p i d .

R E F E R E N C E S1 . N i sh i , T . , W a n g , T . T . a n d K w e i , T . K . , Macromolecules, 1975, 8,2 2 7 .2 . S n y d e r , H . L . a n d M e a k in , P . J . , Polym. Sci. , Polymer Symp., 1985,7 3 , 2 1 7 .3 . I n o u e , T . a n d O u g iz a w a , T . J . , Macromol . Sci . -Ch em. , 1989,A2 6( 1 , 147 .4 . L lo y d , D . R . , K in z e r , K . E . a n d T se n g , H . S . , J . Membrane Sci. ,1990, 52, 239.5 . N e l so n , D . S . a n d S o a n e , D . S . , Polym. E ng. Sci. , 1993, 33, 1619.6 . Kiran, E. , in Supercrit ical Fluids--Fundamen tals for Application,e d . E . K i r a n a n d J . M . H . L e v e l t S e n g e r s . K l u w e r A c a d e m i cP u b l i sh e r s , D o r d r e c h t , T h e N e th e r l a n d s , 1 9 9 4 .7 . K i r a n , E . a n d Z h u a n g , W . , J . Supercrit . Fluids, 1994, 7, 1.8 . Z h u a n g , W . a n d K i r a n , E . , Proceedings of the 1st Joint TopicalConference on Proces sing, Structure and Properties of Polymeric

Materials, A I C h E , N e w Y o r k , 1 9 9 6 .9 . K i r a n , E . a n d Z h u a n g , W . , i n Supercrit ical Extraction, e d . M .A b r a h a m a n d A . K . S u n o l. A C S S y m p o s i u m S e ri e s 6 70 , W a s h i n g -ton, DC, 1997 .1 0 . K ie p e n , F . a n d B o r c h a r d , W . , Macromolecules, 1988, 21, 1784 .1 1 . W e l l s , P . A . , d e L o o s , T h . W . a n d K le in t j e n s , L . A . , Fluid PhaseEquilibria, 1993, 83, 383.12. Goel, S . K . an d B eckman , E . J . , P o lymerE n g . Sc i . , 1994 , 34 , 1137.13. Kiran , E. , in Proc. the 4th International Symposium on Supercrit icalFluids, V o l . C , S en d a i , J a p a n , 1 1 - 1 4 M a y 1 9 9 7 , p p . 7 7 7 - 7 8 4 .1 4 . L in , F . - C . , W a n g , D . - M . a n d L a i , L - Y . , J . Membrane Sci. , 1996,1 0 9 , 9 3 .1 5 . K o r o s , W . J. a n d P in n a u , 1. , i n Polymeric Gas SeparationMembranes, e d . D . P a u l a n d Y . P . Y a m p o l ' s k i i . C R C P r e s s , B o c aRaton, 1994 , p . 209.16. Dixon, D.J. andJohnston, K.P.,J. Appl. Poly. Sci. , 1 9 9 3 , 5 0 , 1 9 2 9 .1 7 . D ix o n , D . J . , J o h n s to n , K . P . a n d B o d m e ie r , R . A . , A I C h E J., 1993,39, 127 .1 8 . R y a n , A . J . , Polymer, 1990, 31, 707 .1 9 . O k a d a , M . , F u j im o to , K . a n d N o s e , T . , Macromolecules, 1995, 28,1795.2 0 . C h a n , C . K . , P e r r o t , F . a n d B e y s e n s , D . , P h ys . Rev . A , 1991, 43,1826.

2914 POLYMER Vol ume 39 Number 13 1998

8/12/2019 Supercritical Fluid 2

13/13

Kinet ics of PIPS f rom po lym er so lut ions: 14/. Zhu ang and E. Ki ran21. Hashimoto, T., Takeba, T. and Fujioka, K., in D y na m i cs a ndPatterns in Complex Fluids , ed. A. Onuki and K. Kawasaki.Springer, Berlin, 1990.22. Hashimoto, T., Phase Transitions, 1988, 12, 47.23. Han, C. C. and Akcasu, A. Z., Annu. Rev. Phys. Chem., 1992,43, 61.24. Perrault, F. and Prud'homme, R. E., Polm. Eng. Sci., 1995, 35, 34.25. Smolders, C. A., von Aartsen, J. J. and Steenbergen, A., Kolloid-Z.Polm., 1971, 243, 14.26. Nojima, S., Tsutsumi, K. and Nose, T., Po l y m e rJ . , 1982, 14, 225.27. Tanaka,H., Yokokawa, T., Abe, H., Hayashi, T. and Nishi, T., Phys.Rev. Lett., 1990, 65, 3136.28. Tanaka,H. and Sigehuzi, T., Phys. Rev. Lett., 1995, 75, 874.29. Lal, J. and Bansil, R., Macromolecules, 1991, 4, 290.30. Aubert, J. H. and Clough, R. L., Polymer, 1985, 26, 2047.31. Aubert, J. H., Macromolecules, 1988, 21, 3469.32. Tanaka, H., Phys. Rev. Lett., 1993, 71, 3158.33. Song, S.-W. and Torkelson, J. M., Macromolecules, 1994, 27, 6389.34. McGuire, K. S., Laxminarayan, A. and Lloyd, D. R., Polymer, 1995,36, 4951.35. Kikuchi, H., Usui, F. and Kajimaya, T., Po l y m e r J., 1996, 28, 35.36. Xie, Y., Ludwig, K. F., Bansil, R., Gallagher, P. D., Konak, C. andMorales, G., Macromolecules, 1996, 29, 6150.37. Kojima, J., Nakayama, Y., Takenaka, M. and Hashimoto, T., Rev.Sci. lnstrum., 1995, 66, 4066.38. Kuwahara, N. K. and Kubota, K., Phys. Rev. A, 1992, 45, 7385.39. Kuwahara, N., Hamano, K., Aoyama, N. and Nomura, T., Phys.Rev. A., 1983, 27, 1724.40. Zhuang, W., Ph.D. thesis, University of Maine, Orono, ME, 1995.41. Zhuang, W. and Kiran, E., Rev. Sci. lnstrum., 1996, 67, 244.42. Wong, N.-C. and Knobler, C. M., J. Chem. Phys., 1978, 69(2), 725.

43. Metz, U. and Schneider, G. M., Ber. Bunsenges. Phys. Chem., 1990,94, 447; 1990, 94, 452.44. Clerke, E. A. and Sengers, J. V., Physica, 1983, I18A, 360.45. Sieber, M. and Woermann, D., Ber. Bunsenges. Phys. Chem., 1991,95, 15.46. Bailey, A. E. and Cannell, D. S., Phys. Rev. Lett., 1993, 70, 2110.47. Donley, J. P. and Langer, J. S., Phy s i ca A, 1994, 204, 202.48. Steinhoff, B. and Woermann, D., J. Chem. Phys., 1995, 103, 8985.49. Schneider, G. M., Pure AppL Chem., 1991, 63, 1313.50. Schneider, G. M., Dittman, M., Metz, U. and Wenzel, J., PureAppl. Chem., 1987, 59, 79.51. Yamamura, O., Takahara, S. and Suga , H., J. Non-Cryst. Solids',1995, 183, 144.52. Hohne, G. W. H. and Blankhorn, K., Thermochimica Acm, 1994,238, 351.53. Angus, S., Armstrong, B. and deReuck, K. M. (ed.), InternationalThermodynamic Tables of the Fluid State. C arbon Dioxide.Pergamon, New York, 1976.54. Vargaftic, N. B., Tables on the Thermophysical Properties ofLiquids and Gases , 2nd edn. Wiley, New York, 1975.55. Kiran, E. and Zhuang, W.. Polymer, 1992, 33, 5259.56. Kiran, E., Xiong, Y. and Zhuang, W., J. Supercrit. Fluids, 1993, 6,193.57. Xiong, Y. and Kiran, E., J. Appl. Polym. Sci., 1995, 55, t805.58. Tanaka,H., J. Chem. Phys., 1994, 100(7), 5323.59. Tanaka,H., Int. J. Thermophys., 1995, 16, 371.60. Cahn, J. W., Acta Metal., 1961, 9, 795.61. Cahn, J. W., J. Chem. Phys., 1965, 42, 93.62. Xiong, Y., Ph.D. thesis, University of Maine, Orono, ME, inpreparation.

P O L Y M E R V o l u m e 3 9 N u m b e r 13 1 9 9 8 2 9 1 5