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Pergamon Chem ical Eno ineerin 0 Science Vol. 51 No. 15 pp. 3881-3885 1996Copyright © 1996 Elsevier Science Ltd

Printed in Great Britain. All rights reservedPII: S0009-2509 96)00233-3 0oo92509/96 SlS.0o+ 0.00

O n o ptim al temperature for dissolution of polymers in hydrogen bonding solvents*

(Fir s t r ece ived 21 N o v e m b e r 1995; rev ised ma n u scr ip t r ece ived 26 J a n u a r y 1996; a c c e p t e d 12 F e b r u a r y 1996)

INTRODUCTION

I n m i c r o l i th o g r a p h y , i t is i m p o r t a n t t o d e s i g n t h e p o l y m e r

d i s s o l u t i on c ond i t i ons i n a wa y t ha t w i ll e n s u r e t he d i s s o l u -t i o n o f t h e d e g r a d e d / u n c r o s s l i n k e d p o r t i o n s o f t h e p a t t e r n

w i t h m i n i m a l s w e l l i n g o f t h e u n e x p o s e d / c r o s s l i n k e d p o r -t i ons . H i ghe r d i s s o l u t i on r a t e a n d l e s s e r s we l l i ng a r e ge ne r -

a l l y c on f l i c t i ng de m a nds , s i nc e t he f a c t o r s t ha t f a v ou r t he

f o r m e r d o n o t f a v o u r t h e l a t t e r . A c h a n g e i n d i s s o l u t i o n

c o n d i t i o n s , s u c h a s i n c r e a s e i n t e m p e r a t u r e o r t h e t h e r m o -dyn a m i c qua l i t y o f t he s o l ve n t e tc ., i nc r e a s e s t he d i s s o l u t i on

r a t e . Howe ve r , i t a l s o i nc r e a s e s t he s w e l l ing o f t he po l ym e rf il m . Re c e n t l y , we s howe d De v o t t a a nd M a s he l ka r , 1995 )

t ha t t he s e c on f l i c t i ng r e qu i s i t e s c a n be a c c ompl i s he d byu s i n g a m i x e d s o l v e n t m e d i u m , w h e r e o n e o f th e c o m p o n e n t si s a t h e r m o d y n a m i c a l l y p o o r l o w m o l e c u l a r s iz e s o lv e n t. I n

t h i s w o r k , w e s h o w t h a t u n d e r c e r t a in c o n d i t i o n s , t e m p e r -a t u r e c a n p r oduc e s i mi l a r e f f e c t s i n hyd r oge n - bonde d s y s -

tems.D i s s o l u t io n o f p o l y m e r d e p e n d s b o t h o n t h e e x t e n t o f

s we l l i ng a s we l l a s t he d i f f u s i on r a t e o f t he s o l ve n t . I n t hea b s e n c e o f h y d r o g e n b o n d i n g i n t e r a c t i o n s , a n i n c r e a s e i nt e mpe r a t u r e i nc r e a s e s t he d i f f u s i on r a t e o f t he s o l ve n t a nd

t he e x t e n t o f swe ll ing . Th i s r e s u l t s in a c on t i nuo us e nha nc e -

m e n t o f t h e c h a i n m o b i l i t y w i t h in c r e a s e in t e m p e r a t u r e a n d

t h e r e fo r e i n fl u e n c es t h e o v e r a ll d i s s o lu t i o n r a t e M a n j k o w e tal., 1 98 7 ; P a p a n u et a t . , 1989a ) . Th i s c a n be s e e n f r om t he

d i s so l u ti o n d a t a o n t h e P M M A / M E K s y st e m P a p a n u et a t . ,

1989a) in Fig. 1 curv e a).I n c o n t r a s t , t h e d i s s o l u t i o n o f a p o l y m e r t h a t i n t e r a c t s

w i t h t h e s o lv e n t t h r o u g h h y d r o g e n b o n d i n g B l a c k a d d e r a n d

G h a v a m i k a , 1 9 79 ) s h o w s n o n - m o n o t o n i c b e h a v i o u r . F i g u r e1 c u r ve b ) s hows t yp i c a l da t a f o r t he d i s s o l u t i on o f po l y -

e t h e r s u l p h o n e i n c h l o ro f o r m . N o t e t h a t c h l o r o f o r m i s a p r o -

t o n d o n o r a n d t h e - O - a n d S = O g r o u p s in t h e p o l y m e rb a c k b o n e a r e p r o t o n a c c e p t o r s . T h i s r e s u l t s i n h y d r o g e n

b o n d i n g i n t e r a c t i o n s a n d t h e s w e ll in g o f th e p o l y m e r s h o w sa L C S T b e h a v i o u r B l h c k a d d e r a n d G h a v a m i k a , 1 9 79 ). I ns y s t e m s w h e r e s u c h h y d r o g e n b o n d i n g i n t e r a c t i o n s e x i s t ,

t h e r e is a n o p t i m u m t e m p e r a t u r e a t w h i c h t h e h i g h e r d i s so l u -t i on r a t e c a n b e a c h i e ve d wi t h l e a s t swe ll ing . No t he o r e t i c a l

mod e l p r e s e n t l y ex is ts , wh i c h c a n i n t e r p r e t t he da t a s how n i nF i g. l b) . W e b r i d g e t h i s i m p o r t a n t g a p i n t h i s c o m m u n i c a -

t ion .S i g n i fi c a n t w o r k h a s b e e n d o n e i n t h e p a s t t o s t u d y t h e

d i f f e r e n t a s pe c t s o f po l ym e r s we l l ing a nd d i s s o l u t i on He r -m a n a n d E d w a r d s , 1 99 0; T u a n d O u a n o , 1 9 77 ; L e e a n dP e p p a s , 1 9 8 7; P a p a n u et a l . , 1989b ; As t a r i t a a nd Sa r t i , 1978 ;P e p p a s et a l . , 1 9 9 4 ) . O u r s c h o o l h a s b e e n e x a m i n i n g t h e

i n t e r e st i n g a sp e c t s o f t h e d y n a m i c s o f d i s s o l u t io n o f p o l y m e rr e c en t ly . O u r s t u d ie s h a v e f o c u s e d o n t h e d e m o n s t r a t i o n o ft he p r e s e nc e o f a c r i t i c a l pa r t i c l e s i ze o f t he po l ym e r pa r t i c l e

* N C L C o m m u n i c a t i o n N o . 63 2 3.

b e l o w w h i c h t h e d i s s o l u t i o n t i m e b e c o m e s i n d e p e n d e n t o f

t he pa r t i c l e s iz e De vo t t a et a l . , 1994a ), c ompr e he ns i ve mo d-e l l i ng o f d i s s o l u t i on o f a po l ym e r pa r t i c l e i n a we l l - de f i ne d

c onve c t i ve f i el d Ra na de a n d M a s be l k a r , 1995 ), r o l e o f d i s e n -

ga ge m e n t dyna mi c s i n d i s s o l u t i on De v o t t a e t al ., 1994b ,1995 ) , d i s s o l u t i on o f po l ym e r in mi xe d s o l ve n t s De v o t t a a nd

M a s be l ka r , 1995 ), e t c . A ke y f e a tu r e o f ou r m ode l De vo t t a e tal., 1 99 5) h a s b e e n t h a t w e h a v e i n c o r p o r a t e d i n a k i n e t ic

m o d e l , t h e r e l a t io n s h i p o f t h e d i s e n g a g e m e n t r a t e t o t h es w e l li n g r at e , t h r o u g h t h e c h a n g i n g m o b i l i t y o f t h e d i s e n g a g -

i ng ma c r omol e c u l e a t t he ge l - l i qu i d i n t e r f a c e .

MODEL DEVELOPMENT

We c ons i de r t he s we l l i ng - d i s s o l u t i on p r ob l e m wi t h a s l a bge ome t r y . F o r s i mp l i ci t y , we wi l l a s s ume t h a t t he k i ne t i c s o f

d i s s o l u t i on i s c ompl e t e l y c on t r o l l e d by t h e p r oc e s s o f d i s e n -ga ge me n t o f c ha i n s f r om t he ge l - l i qu i d i n t e r f a c e . Howe ve r ,

w e c a n e a s i ly s h o w t h e f e a t u re o f t h e m a x i m u m e v e n i f t h e

p r o c e s s w a s p a r t i a l ly c o n t r o l l e d b y d i ff u s io n i n t h e b o u n d a r yl a ye r . Fu l l de t a i l s o f t he phys i c s be h i nd t he p r oc e s s o f d is -s o l u t i o n c a n b e s e e n i n o u r r e c e n t s tu d i e s D e v o t t a et a l . ,

1994a , b , 1995 ; Ra na de a nd Ma s he l ka r , 1995 ; De vo t t a a nd

M a s he l k a r , 1995 ).T h e d i f f u s i o n o f s o l v e n t i n t o t h e p o l y m e r f i l m c a n b e

de s c r i be d by t he f o l l owi ng c ons e r va t i on e qua t i on :

c3----~=O---~ Or, O x. ] O < ~x < ~ L . 1)

He r e , ~b, i s t he vo l um e f r a c t i on o f t he s o l ve n t a n d D , , is t hemu t ua l d i f f u s i on c oef fi ci en t, wh i c h i s e va l ua t e d u s i ng t he

f r e e- v o l um e m o d e l o f V r e n t a s a n d D u d a Z i e li n s k i a n d

Duda, 1992) .

T h e i n i t i a l a n d t h e b o u n d a r y c o n d i t i o n s f o r e q. 1 ) a r e a sfollows:

~ b , = 0 a t t = 0 , O < ~ x < ~ L o 2)

D m O C k S = O a t x = 0 , t > 0 3)O x

4~s=~b] at x = l , t > 0 . 4 )

He r e , ~b] i s t he i n t e r f a c e c on c e n t r a t i on o f t he s o l ve n t , wh i c hw i ll d e p e n d o n t h e t e m p e r a t u r e o f t h e s o l v e n t i n t h e d i s s o lu -

t i o n m e d i u m .As t h e s o l ve n t d i ff u s e s i n t o t h e po l yme r f il m , i ts t h i c kne s s

i nc r e a s e s , a nd a s t he po l y me r c h a i n l e a ve s t he i n te r f a c e , t he

t h i c k n e s s re d u c es . A s s u m i n g c o m p l e t el y d i s e n g a g e m e n t c o n -t r o l le d d i s s o l u t i o n k i ne t ic s , t h e n e t r a t e o f m o v e m e n t o f t h ege l - l i qu i d i n t e r f a c e c a n be de s c r i be d a s f o ll ows :

l

dt = D, , x=t -- ka, 5)

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F i g . 1 . Expe r i me n t a l da t a on t he va r i a t i on o f d i s s o l u t i on r a t e w i t h t e mpe r a t u r e : ( a ) w i t hou t hyd r oge nb o n di n g: P M M A / M E K s ys te m ( P ap a n u e t a l . , 1989a ) ; a nd ( b ) w i t h hyd r oge n bond i ng : po l ye t he r s u l -

p h o n e /C H C 1 3 s y s te m ( B l a c k a d d e r a n d G h a v a m i k a , 1 97 9) .

He r e , kd i s t he t i me - de pe nde n t d i s e nga ge me n t r a t e o f t hepo l ym e r c ha i n s f r om t he ge l - l i qu i d i n t e r f ac e . The phys i c s o f

t h i s d i s e n g a g e m e n t p r o c es s h a s b e e n e l a b o r a t e d b y u s i n o u r

p r e v i o u s w o r k ( D e v o t t a e t a l . , 1994a, b , 1995) . As a p olym erc ha i n r e qu i r e s a c e r t a i n t i me t o d i s e nga ge f r om t he ge l - l i qu i d

i n t e rf a c e , t he d i s e n ga ge m e n t r a t e i s in i t i a l l y z e r o . Th i s m i n -i mu m t i me r e qu i r e d f o r t he f i r s t f ew c ha i n s t o d i s e nga ge i se qu i va l e n t t o t h e r e p t a t i on t i me , wh i c h i s r e l a t e d t o ~b~ a s

t ,ev = t0(~b/p) s (Bro cha rd a nd de G enn es , 1983). The refore ,

we a s s ume t h a t t he f o l l owi ng c ond i t i on e x i s ts a t t hege l - l i qu i d i n t e rf a c e :

k d = 0 t < tr e p . (6)

I n a n e a r l i e r a na l y s i s ( De v o t t a e t a l . , 1995), we re la ted th e

d i s e n g a g e m e n t r a t e t o t h e i n s t a n t a n e o u s m o b i l i t y o f t h e

d i s e nga g i ng c ha i n s . As t he s o l ve n t pe ne t r a t e s , t he c ha i n swi t h i n t he ge l pha s e d i s e n t a ng l e t he ms e l ve s a nd be c omemo r e m ob i l e . I f t he s o l ve n t d i f fu s i v it y i s h i gh , t he n i t p e n -

e t r a t e s i n t o t he po l yme r r a p i d l y . The r e f o r e , t he mob i l i t y o ft he c ha i n s w i t h i n t he ge l pha s e i nc r e a s e s f a s t e r a nd s uc hh i gh l y mob i l e c ha i n s , whe n t he y ha ve t o d i s e nga ge a t t hege l - l i qu i d i n t e r f a c e , d i s e nga ge a t a f a s t e r r a t e . The r e f o r e ,a c c o r d i n g t o o u r e a r li e r p o s t u l a te s ( D e v o t t a e t a l . , 1995), wec a n r e l a t e t he d i s e nga ge m e n t r a t e d i r e c t l y t o mob i l i t y o f t he

d i s e nga g i ng l a ye r o f c ha i n s a s f o ll ows :

k a o z m p t > t r e p .

(7)He r e , mp i s t he t i me - de p e nde n t mob i l i t y o f t he d i s e nga g i ng

po l ym e r c ha i n s . The m ob i l i t y o f t he po l ym e r mo l e c u l e s w i t h -i n t he l a ye r o f ge l pha s e c ha nge s t he e x t e n t o f d i s e n t a ng l e -m e n t . A s e x p l a in e d i n o u r e a r l i e r w o r k ( D e v o t t a e t a l . , 1995),t he m ob i l i t y o f t he c ha i n s a t d i f f er e n t po i n t s w i t h i n t he ge l

pha s e i s a s s ume d t o v a r y a s f o ll ows :

O m- ---e = K ( m p ® - r ) . 8 )O t

He r e , K i s a k i ne t i c c ons t a n t a nd mp . ~ i s t he ma x i mumm o b i l i t y t h a t t h e p o l y m e r c h a i n c a n a t t a i n a t t h a t c o n c e n t r a -

t i o n, w h e n a s t a t e o f m a x i m u m d i s e n t a n g l e m e n t is a t t a i n e da t l a r ge t i me . Th i s mob i l i t y o f t he po l yme r mo l e c u l e s w i l lde pe nd on t he f r e e vo l ume . The r e f o r e , i t i s g i ve n by t he

f o l l owi ng r e l a t i on ( Ku l ka r n i a nd Ma s he l a r , 1983 ) :

m , , o ~ = A d p exp \ fa ,} (9)

He r e , f 0 is t he f re e vo l ume o f t he ge l pha s e a n d i s ob t a i ne d bya s s um i ng a dd i t i v i t y o f f re e vo l ume s a s f o l l ows ( Ku l ka r n i a n dM a s he l ka r , 1983 ):

fo = fp~bp + L q ~ (10)

w h e r e f p a n d f s a r e t h e f r e e v o l u m e s o f t h e p u r e p o l y m e r a n dpur e so lvent , respect ive ly . ~bp an d tk , a re the v olum e f rac t io nso f t he po l ym e r a nd t he s o l ve n t a t d i f f e r e n t po i n t s w i t h i n t hegel phase, respectively.

T h e f r e e v o l u m e s o f th e p u r e c o m p o n e n t s a t a n y t e m p e r -a t u r e c a n be e va l ua t e d u s i ng t he f o l l owi ng r e l a t i on i n t e r ms

o f t he g l a s s t r a n s i t i on t e mpe r a t u r e ( To ) a nd t he t he r ma lexp ans ion coeff ic ient of f ree volum e (cO:

f = f T g ) + ~ T - - T a ) . (11)



Optimal temperature for dissolution of polymers

The next question to be addressed is the variation of theinterface concentration of the solvent with the temper atureof the dissolution medium. This can be evaluated by assum-ing a thermodynamic equilibrium at the interface. Recently,

Lele e t a l . (1995) developed a lattice fluid hydrogen bonding Componen t(LFHB) mode l for isotropic swelling of cross linked gels bymodifying the LFHB model of Panayiotou and Sanchez Polymer(1991). In the present case, swelling of the polymer film is Solventconsidered to be only in one direction and the polymer is

physically entangled. Therefore, we modify the model fora case of non-i sotropic swelling of the physically crosslinkedpolymer by incorporating the appropriate changes in theelastic free energy contribution to the chemical potential.Thus, the chemical potential of the solvent at the gel-liquid i - j pair

interface is given by i = 1, j = 1

AP---Z1= 1n( 1/~1) + (1 - r l / r 2 ) ~ 2 + rlp~ 2X12 i = 1,j = 2R T

[ ]i e + ( g _ 1 ) i n (1 _ ~ ) + _ i n ~

+ r l - ~ 1 + T I r l

i j i j

r 1 V i j - - ~ d~ I n v~/vio) - ~ 1 jj In V J V o j )m n r a n

+ r I V* g -- (12)

where

/ ~ - 1- e ~ - - 2 ~ 1 2 ( t ~ 1 / l * ) 0 5X12 (13)

R T

Here, the terms on the first, second, third and the fourth linein eq. (12) account for ent ropy and enthalpy o f mixingthrough physical interaction, equation of state properties ofcomponents, hydrogen bond ing interactions and elasticity ofthe entangled network, respectively. Subscripts 1 and 2 cor-respond to the solvent and polymer, respectively. Different

symbols are explained in the nomenclature. ~ and v o are thereduced density and the number of hydrogen bonds evalu-ated using

~3(AG) •(AG)= 0 and =0 . (14)

~fi avq

N~ is the number of moles of physical entanglements. Assum-ing physical entanglements as being equivalent to chemicalcrosslinks (Papanu e t a l . , 1989b; Devotta e t a l . , 1995), Are isgiven by

V~ = Pe - . (15)

Here, M and Mc are the molecular weight of the polymer and

the critical molecular weight for entanglement, respectively,and pp is the density of polymer (g/m3). Assuming that thesolvent phase is a pure solvent, the equilibrium interfaceconcentration of the polymer can be obtained by setting thedifference between the chemical potential of the solvent inthe gel phase and that of pure solvent to zero. The massbalance equations were made dimensionless by defininga dimensionless time 0 = D o t / L o ) and position x / L o ) .

The equilibrium concentration was obtained by New-ton-Raphson technique. The values of equation of stateparameters used are given in Table 1. These are typicalvalues repo rted in the litera ture for many solvents and poly-mers. The governing equations were solved usingCrank-Nicholson technique. ~bl in eq. (12) is the closedpacked volume fraction and is rela ted to ~b~ in eq. (4) as

The average dissolution rate is defined as the ratio of theinitial thickness o f film to the total time required for the film todissolve. In o rder to evaluate this, the total dimensionless timerequired for the film to dissolve is determined. Its inverse isdefined as the average dimensionless dissolu tion rate.

Table 1. Typical values of the parameters used(a) Molecular parameters

3883

P* T * p*(bar) (K) (kg/m 3)

6050 541 15724760 499 1709

(b) Standard state hydrogen bonding parameters

o s oj V o

(k J/tool) (J/tool K) (cm3/mol)

- l 1.44 - 9.74 - 0.85- 11.44 - 19.7 -0 .8 5

RESULTS AND DISCUSSION

Before we predict the effect of temperature on the dissolu-tion rate of the polymer film, it will be useful to see the effect

of temperature on the surface concentration of the solvent atthe gel -liquid interface. Figure 2(a) presents the change in theconcentration of the solvent at the interface with temper-ature. It can be seen that increase in temperature decreasesthe solvent volume fraction at the gel- liquid interface. Thisindicates a decrease in the extent of swelling of the polymerfilm with an increase in temperature. Increase in tempera tureresults in a substantial decrease in the hydrogen bondinginteraction and a marginal increase in physical interactionbetween the polymer and solvent molecules. The net effect isthat the affinity o f the polymer to the solvent is reduced andtherefore the equilibrium concentration of the solvent at thegel-liquid interface is reduced.

In Fig. 2, curve (b) shows the effect of temperature on thesolvent volume fraction at the gel-li quid interface, when the

hydrogen bonding association is not considered. It can beclearly seen that the solvent volume frac tion increases withtemperature, indicating increase in swelling with temper-ature. However, the solvent volume fractions at all temper-atures are seen to be much lower compared to curve (a). Thisindicates that the swelling of the polymer is essentially due tothe hydrogen bonding interaction.

Figure 3 shows the effect of temperature on the dissolutionrate of the polymer film. The dissolution rate increases withan increase in temperature initially, although the extent ofswelling, which is determined by the concentration of thesolvent at the gel-liquid interface, is reduced. This is due tothe faster diffusion of the solvent into the polymer film andthe enhancement of the chain mobility with an increase intemperature. This results in faster disengagement of the

chains at the gel-l iquid interface. However, a further increasein temper ature results in a substantial reduc tion in swelling.Therefore, the mobility of the chains gets reduced. Thiscounterbalances the thermal effects. As a result, the dissolu-tion rate starts decreasing, thus showing a maximum. Thistrend predicted by the model is in line with the experimentalobservations shown in Fig. 1. We are thus able to capturetheoretically the presence of an optimum temperature atwhich the dissolution rate is maximum with minimum swell-ing. As mentioned earlier, this feature has important implica-tions in microli thography, where high dissolution rate withminimum swelling is critical.

It may be interesting to show a continuous increase indissolution rate with temperature, for a case without hydro-gen bonding interaction. However, as seen in Fig. 2(b) the

solvent concentrations are very low at all temperatures asthe chemical interaction is not considered. At such lowconcentr ations of solvent, the polymer mobility is not suffi-ciently high and t he disengagement rates are extremely low.Therefore, the variation of dissolution rate with tem peratureis predicted for a case where the polymer swells appreciably



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0 . 5 0 3 0 2

0 . 4 5 t i = I t 02 7 0 2 8 0 2 9 0 3 0 0 3 1 0 3 2 0 3 3 0


F i g . 2 . P r e d i c t e d v a r i a t i o n o f e q u i l i b r i u m s o l v e n t v o l u m e f r a c t io n a t t h e g e l - l i q u i d i n t e r f a c e w i t h t e m p e r -

a t u r e: a ) w i t h h y d r o g e n b o n d i n g a n d b ) w i t h o u t h y d r o g e n b o n d i n g .

9 5 1 0

9 - 0

x

uJ

ty

z

or - - 8 - 5

: 3. . J

o(/)( /)

( /)t n 8 - 0U.l_1z

o

Zh i

=E

7 . 5

( a )

( b )

7 - 0 = = = i t 22 7 0 2 8 0 2 9 0 3 0 0 3 1 0 3 2 0


8

¢¢

z_oI.-

=.1o

6 o~

Q

~0

h i..J

_o3

z4 w

=E

F

F i g. 3 . P r e d i c te d v a r i a t i o n o f d i m e n s i o n l e s s d i s s o l u t io n r a t e w i t h t e m p e r a t u r e : a ) w i t h h y d r o g e n b o n d i n g

a n d b ) w i t h o u t h y d r o g e n b o n d i n g . [KL~ Do= 1 . 0 x 1 0 s ; B d = 1 . 5 ; a p = 6 . 0 × 1 0 - 5 ; ~ s = 7 . 0 × 1 0 - 4 ;

f p T g ) = 0 . 0 2 5 ; f ~ T g ) = 0 . 0 9 . ]

e v e n w i t h o u t h y d r o g e n b o n d i n g . A n o b v i o u s t r e n d o f c o n -

t i n u o u s i n c re a s e i n d i s s o lu t i o n r a t e w i t h t e m p e r a t u r e i s se e n

i n F i g . 3 b ) i n l i n e w i t h t h e e x p e r i m e n t a l t r e n d s h o w n i n

F ig . l a ) .

C O N C L U S I O N S

A m a t h e m a t i c a l m o d e l f o r d i s so l u t i o n o f p o l y m e r f il m h a s

b e e n d e v e l o p e d b y i n c o r p o r a t i n g t h e h y d r o g e n b o n d i n g i n -

t e r a c t io n o f t h e p o l y m e r w i t h t h e s o l v e n t . A n i n t e r e s ti n g



O pt i m a l t e m pe r a t u r e f o r d i s s o lu t i on o f po l ym e r s

p r e d i c t ion o f m a x i m um i n d i s s o lu t i on r a t e v s t e m pe r a t u r e i s s s o l ve n tobserved in l ine wi th the exper im enta l da ta repor ted in the oo va lue a t l a rge t imesl i t e ra ture . The m odel a l so predic t s redu ct ion in swel ling wi thi nc r e a s e i n t e m pe r a t u r e due t o r e duc t i on i n t he hyd r oge n Superscr ip ts

bon ding in terac t ions . The resul t s have pragm at ic impl ica- i surface va luet ions in de term ining the opt im um temp era ture for d i ssolu- * c lose packedt ion wi th the requis i t es of h igher d i ssolut ion ra te an d low erswelling.

I . D E V O T T ANat i ona l Che mi c a l Labor a t o r y

Pune 411 008, India

R . A. M A S H E L K A R *Counc i l o f Sc i e n t i fi c and I ndus t r i a l Re s e ar c h

Ra f t Mar y , Ne w De l h i 110 001 , I nd i a

NOTATION

a num be r o f p r o t on a c c e p t o r s pe r m o l e c u l eAd f ree-volume param eterBd f ree-volume param eterd num be r o f p r o t on donor s pe r m o l e c u l eDm diffusivity of the solve nt

f f ree-volume f rac t ionAG tota l f ree energyk d d i s e nga ge m e n t r a t eK kinet ic cons tantl swol len th ickness of the f ilmm p m ob i l i t y o f t he po l ym e r c ha i nsM m ol e c u l a r w e i gh t o f t he po l ym e rM c cr i t i ca l molecular weight for entanglementN e c onc e n t r a t i on o f e n t a ng le m e n t sP reduced pressure

r s e gm e n t l e ng t hR ga s c ons t a n tt t ime

t r e p r e p ta t io n t i m eT a bs o l u t e t e m pe r a t u r e

Tg glass t rans i t ion temp era turer e duc e d vo l um e

V swol len volum e of the ge lVo volu me of ge l as synthes izedx di s tance f rom the cent re of the s labX 2 b i na r y i n t e r a c t ion pa r a m e t e r

Greek le t tersOt

It

V U

f)

Pp~7

9

therma l expa ns ion coeff ic ient o f free volumef lexibi li ty param eter of an r -m erm e a n- f ie l d i n t e ra c t i on e ne r gy pe r m e rb i na r y i n t e r a c t i on pa r a m e t e rchemical potent ia lf r a c ti ona l num be r o f hyd r oge n bonds o f the ij pai rreduced dens i tyde ns i ty o f t he po l ym e rs ym m e t r y pa r a m e t e r o f a n r - m e tvo l um e f r a c ti on6 r / a e - 1

Subscr ip ts1 solvent2 po l ym e ra a c c e p t o rd d o n o ry gel phasei do no r of type i i = 1, m)i 0 non - bond e d dono r o f t ype ij accep tor of type j j = 1 , n)

0 j non - bond e d a c c e p t o r s o f t ype jp po l ym e r

tCorres pon ding author . Fax: 91 11 3710618. E-mai l :[email protected].

3885

R E F E R E N C E S

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