Ind. Eng. Chem. Res. 1994,33, 2426-2433
2426
Swelling and Phase Transitions in Deforming Polymeric Gelst M. V. Badiger, A. K. Lele, M. G. Kulkami, and R. A. Mashelkar’ National Chemical Laboratory, %ne 411 008, India
Deformation of physically cross-linked gels is shown to increase their swelling capacity significantly and induce new volume phase transitions in the gels. Both of these phenomena are novel and are demonstrated here for the first time. The physical origin of the increased swelling lies in the breakage of some of the physical cross-links in the gel due to deformation. A phenomenological kinetic model is developed t o describe the rate of breakage of physical cross-links in the gel due to shearing deformation. Coupling this model with the thermodynamics of swelling of polymeric networks gives quantitative predictions for the time evolution of the increase in the swelling capacity of such a gel. The enhanced swelling capacity of the gels due to deformation is also shown to be retained in the “memory” of the gel during further swelling-collapse cycles, a somewhat surprising result, which needs further elucidation.
Introduction Polymeric gels are molecular networks having a capacity to imbibe large amounts of solvent. The gels exhibit a unique combination of elastic properties and osmotic reactivity (Tanaka, 1981). For example, in the presence of a “good” solvent, the gels swell by absorbing large quantities of the solvent. However,on addition of a “poor” solvent, the gel collapses to its initial state. Under certain conditions,the gel undergoes a discontinuous volume phase transition (Tanaka, 1987). This is shown in Figure 1for a hydrolyzed starch grafted polyacrylonitrile gel based on the data reported by Badiger (1989). The phenomenon of volume phase transition in gels has been extensively studied over the past decade both theoretically (Dusek and Patterson, 1968; Tanaka, 1978; Illavsky, 1981) and experimentally (Janas et al., 1980; Nicoli et at., 1983; Hirotsu et al., 1987). Gels undergo volume phase transitions in response to various external stimuli, such as pH (Katchalsky et al., 1950),light (hie, 1986),temperature (Tanaka, 1978), and electric fields (Tanakaet al., 1982). This stimulus response of gels enables us to exploit them as smart materials. Numerous applications of these “smart” materials have been established. In separations technology, gels have been used to concentrate biomolecules through a size selective extraction process (Cussler et al.,1984; Badiger et al., 1992). In sustained-release technology, gel-based intelligent insulin pumps (Bae et al., 1989) have been devised. Similarly, a diffusion-modulated reversible bilayer gel membrane for sustained release of drugs has been reported (Kulkarni et al., 1992). Kokufata et al., (1991) have indicated the use of gels as molecule-specificsensors. Gel-based soft actuators (Kwon et al., 1991) for applications in robotics and chemomechanical membranes (Osada and Ross-Murphy, 1993) for separations are being investigated. A brief overview of these developments has been provided by Mashelkar (1993). The reversible volume phase transition in gels occurs because of the “osmotic forces” which swell or collapse the network structure. The basic features of this osmotic forces are captured qualitatively by the Flory equation (Flory, 1953):
* To whom correspondence should be addressed. t
NCL Communication No. 4947.
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-
1
a‘4
:- I I-
d
0
01 0
I
40
I
so
I
120
160
SWELLING C A P A C I T Y ( r n l / g )
Figure 1. Volume phase transition of hydrolyzed starch-polyacrylonitrile graft copolymer.
Here V,is the molar volume of the solvent, $I is the volume fraction of the network, R is the gas constant, T is the absolute temperature, xis the interaction parameter, and (v$ VO)is the cross-link density in the as-prepared gel. In eq 1, the first three terms represent a “swelling force” on the network due to the energetically favorable mixing of polymer chains with the solvent molecules, while the last term is an “elastic retractive force” which tries to bring the network back to its unstrained state. The equilibrium swelling capacity of the gel results from a balance of these two forces. Thus for a given gel-solvent system, the swelling capacity of the gel is strongly dependent on its cross-link density. Volume transitions are discontinuous for networks which have charged polymer chains and/or stiff chains (Tanaka, 1987). Whereas phase transitions in chemically cross-linked networks are well understood, the presence of phase transitions in physically cross-linked networks (e.g., hydrogen-bonded networks) has gained attention only recently (Ilmain et al., 1991). The physical cross-links are weak and temporary and can be disrupted reversibly by imposing a deformation. Therefore, deformation is likely to affect the equilibrium swelling capacity and the phase transitions in such gels. Surprisingly, this aspect has not been examined in the literature. Our work examines these effects. In order to account for the reversible breakage of physical cross-links in the gel, we use a simple kinetic model which can predict the time dependence of decrease in cross-link 0 1994 American Chemical Society
-*
Ind. Eng. Chem. Res., Vol. 33,No. 10,1994 2427
Shear
kz
where [SI is multiplied by 2 since every cross-link is formed by the association of two sites. kl and k2 are the rate constants for the breaking and formation of cross-links, respectively. The rate of formation of cross-links is given by
-= cr'
ki
E e 2s
Since the total number of sites [SIT, which can be crosslinked, is conserved, we get from a site balance
Shear
[SI
2[El = [SIT
(4)
Equations 3 and 4 can be easily solved to give the time dependence of breakage of physical cross-links as
Figure 2. Schematic of two types of cross-linked systems. (a) A
physically cross-linked system with occasional chemical cross-links. Slow deformation of this gel can break some of the physical crosslinks. (b) Completely chemically cross-linked system, which when deformed will result in an extended state, while retaining all the cross-links in it.
density due to shear. We show that when the kinetics is coupled with the thermodynamics of gels as given by eq 1, the resulting simple theory can quantitatively fit the experimental data on the swelling of deforming physical gels. Similar kinetic approaches have been used by rheologists to model the rheology of viscoelastic and thixotropic fluids. For example, the "entanglement network" theory for viscoelastic fluids (Lodge, 1964)and the theory for thixotropic materials (Cheng and Evans, 1965;Cheng, 1971) use rate equations for the reversible breakdown of "structure" in the fluid undergoing shear. Furthermore, Mujumdar has recently used a similar kinetic model for quantifying the rheological behavior of thixotropic fluids in oscillatory shear flow (Mujumdar, 1993). Additionally, in this paper we demonstrate some unusual observations of the effect of deformation on swelling, as well as some evidence of new volume phase transitions in deformed gels. We also report some unsuspected memory effects in these gels, which we observed during the course of our work.
Model We consider here a gel which contains a large number of physical cross-links and only a few covalent (chemical) cross-links distributed in the gel matrix. The physical cross-links could be due to entanglements of dangling chains or due to hydrogen-bonding associations between polar groups of two chains. Such cross-links are weak and can be broken down to unassociated "sites" by subjecting the gel to deformation. These "sites" can also re-form into cross-links thereby establishing an equilibrium or steady-state concentration of sites and cross-links. Figure 2 shows a schematic of such a gel and the effect of deformation on it. Let us assume that the gel is initially in a state wherein all the sites are associated to form physical cross-links, and subsequently a t t > 0 a shear deformation is imposed on the gel. Let us denote the concentration of cross-links and unassociated sites by [El and [SIg-mol/cm3,respectively. The dynamics between [El and [SI can be simply written as
- azA exp(-Bt) 1 - A exp(-Bt)
CY,
[El =
(5)
with
where
B = a(al- CY') [El0 is the initial concentration of cross-links in the gel. Equation 5 correctly satisfies both the initial condition of [El = [El0 and the condition of dynamic equilibrium of [El = a1 at large times. Thus, eq 5 predicts a decrease in the concentration of physical cross-links in the gel due to an imposed deformation. The rate constant kl of the breakage reaction will depend on the magnitude of the imposed deformation field. We consider here the simplest relation given by
k , = ki.
(8)
where is the shear rate and k is the proportionality constant. The rate constant k2 can also in principle depend on the magnitude of deformation. The "concentration" of cross-links in the gel is identical to the cross-link density of the gel. Since the gel under consideration here is mostly physically cross-linked and only partially chemically cross-linked, the total cross-link density of the gel can be written as
yo
yo
yo
2428 Ind. Eng. Chem. Res., Vol. 33, No. 10, 1994
in which vc is the moles of chemical cross-links which are permanent and up is the moles of physical cross-links which can be broken due to an imposed shear according to the kinetics given by eqs 5-7. Thus, a decrease in the total cross-link density would result in a less elastic gel. Since the swelling capacity of a gel is strongly dependent on its cross-link density, the gel can swell significantly, when sheared. If the swelling kinetics of the gel is relatively faster as compared to the kinetics of breakage of physical cross-links, then the rate of increase in swelling will be determined by eqs 5-7. In general, this will be valid if
0,851
Here, R, is the size scale of the gel (e.g., particle size) and D is the cooperative diffusion coefficient of the network (Tanaka and Fillmore, 1979). We assume in the following that the size of gel particles is small enough that eq 10 is satisfied. The swelling capacity of the gel can be obtained from eq 1which is now rewritten for a partially chemically crosslinked gel as
Here f is the degree of ionization of the charged polymer chains in the network, Mc is the average molecular weight of chains between cross-link points, which is assumed constant, and the total cross-link density is written as the sum of the chemical and physical cross-links as per eq 9. Now,eqs 5 and 11can be coupled (provided the condition in eq 10 is satisfied) to give the swelling capacity of the gel at any instantaneous value of the total cross-link density. The kinetics of swelling of a deforming physical gel can now be predicted from this simple phenomenological model. This coupling between the kinetics of breakage of physical cross-links and the thermodynamics of swelling of networks is a novel approach to model physical networks and has been formulated here for the first time. In order for the theory to be simple and yet realistic, we wish to maintain as few model parameters as possible. Our phenomenologicalkinetic model has three parameters, which can be suitably chosen to fit the experimental data. These parameters include the two rate constants kl and k2 and the total moles of sites [SITavailable in the gel. On the other hand, the thermodynamic swellingtheory given by eq 11requires three parameters: x , M,, and vPlvc. These can be obtained independently by fitting the Flory theory to the equilibrium swelling data of an undeformed gel. We now present some general predictions of our phenomenological model. Figure 3 shows the change in the density of physical cross-links with time after subjecting the gel to the shear deformation field. The cross-link density reduces as the cross-links break, and it reaches a new dynamic equilibrium value as time increases. As a consequence of this, the swelling capacity of the gel increases and attains a new higher equilibrium value. Figure 4 shows the effect of the intensity of deformation (or the shear rate) on the swelling capacity of the gel. In these calculations kl is considered to be given by eq 8, while k2 is considered to be constant for the sake of simplicity. It is seen that the swelling capacity of the gel
11.12
1.00h
/
II / / /I d 0
0 80 00
0 40
0 20
0 60
0 80
t/Teq
Figure 3. Model predictions of the changes in degree of cross-linking of a physical gel and consequent effect on swelling ratio.
r
O r
frgOO(mih'l
I
I
I
I
I
I
10
20
3.0
40
50
60
TIME ( M I N )
Figure 4. Model predictions of effect of shear rate on kinetics of increase in swelling capacity of a physical gel.
increases with an increase in the shear rate, and that the time required to reach equilibrium, TW,decreases with increase in the shear rate. Figure 5 shows the effect of deforming a charged gel on its volume phase transition. As the quality of the solvent is changed from a "poor" solvent to a "good" solvent, an undeformed gel shows a first-order transition between a collapse state and a swollen state. If the gel is now sheared, then it is realistic to assume that the physical cross-links in the gel will be broken only when the gel is in the swollen state. This is because the collapsed gel is virtually a dry powder and therefore the motions of the solvent molecules outside the gel have no effect on the chains of the gel network. Thus, Figure 5 shows that imposing a shear deformation on the gel neither affects the collapsed state nor shifts the transition point. The swollen state is affected as expected, in that the swelling capacity increases with time and reaches a new dynamic equilibrium value. Finally it is interesting to compare the above predictions with those for a completely chemically cross-linked gel. Such a gel cannot be sheared but can be strained. The change in the free energy of the gel due to deformation
Ind. Eng. Chem. Res., Vol. 33, No. 10, 1994 2429 0-907
1.001
\
0'
o"I
0.50 -10
10
50
30
70
90
v/ vo
Figure 6. Effect of tensile deformation on volume phase transition of a covalently cross-linked gel. Deformation induces an increase in the swelling capacity of the gel. a, is the dimensionless magnitude of the tensile force (a,= F&dkT).
AG = AGmix+ AG,,
- We,
(12)
where AGmix is the mixing free energy, AGe1 is the elastic energy,and Wat is the external work done by the deforming force. For a cylindrical piece of gel under tension the free energy of the gel has been given by Hirotsu and Onuki (1989) as
AGIkT =
In
+ xd4,) +
V
+ 2ff,2-
-
where a a and ar are the expansion factors in the axial and the radical directions, Fs is the tensile force, L is the length of the gel under tension, and LOis the length of the undeformed gel. The volume fraction of the gel is given by
Following Hirotsu and Onuki (1989), the equilibrium swelling of the gel under tension can be obtained by minimizing the free energy with respect to a a and ar.This provides two simultaneous equations to calculate aaand ar and hence the swelling capacity from eq 14. Hirotsu and Onuki (1989) observed and qualitatively predicted volume transitions of a uniaxially strained poly(N-isopropylacrylamide) gel. However, they did not obviously recognize that the swelling capacity of the gel can also be increased due to the imposed deformation. Figure 6 shows the volume phase transition of a completely chemically cross-linked gel under uniaxial tension. I t is seen that, similar to the physically cross-linked gel, the chemically cross-linked gel also shows an increased swelling capacity under deformation. A small shift in the transition temperature is also observed. However, a t a microscopic
scale, the origin of this phenomenon is different than that for a physically cross-linked gel. In the former case, the tensile force acts on the chains which stretch between the cross-link points of the gel and therefore increases the volume occupied by them. This force will be experienced by the chains in the collapsed as well as the swollen states of the gel. As a result, an increase in the swelling capacity and a shift in the transition temperature is observed in Figure 6. Also, there is no breakage of any cross-links in this gel. On the other hand, in the physically cross-linked gel, an increase in swellingis due to the breakage of physical cross-links in the swollen state only. Thus we have seen that, shearing a physically crosslinked gel or straining a chemically cross-linked gel can cause an increase in the swelling capacity of the gel. In the following section we present a preliminary experimental validation for some of the predicted effects and also attempt quantitative fitting of the data with our phenomenologicalmodel. We also demonstrate some other unusual results, which cannot be predicted by any simplistic theory such as the one presented above.
Experimental Section We have chosen hydrolyzed starch-g-polyacrylonitrile (HSPAN) gel for our experimental studies. The chemical structure of HSPAN gel is shown in Figure 7. The long chains of hydrolyzed polyacrylonitrile, which are grafted on to the starch backbone, can undergo intermolecular hydrogen bonding as well as entanglements. These constitute the physical cross-links in the gel. During the graft copolymerization,the growing polyacrylonitrile macroradicals can combine to form covalent bonds between two pendant chains. However,Rodehed and Ranby (1986) have argued that the number of chemical cross-links formed due to such a bimolecular termination are not likely to be significant. Also, the unusually high swellingcapacity of HSPAN gel indicates a very low degree of chemical cross-links (Fanta et al., 1982). On the other hand, the presence of a large number of physical cross-links is evidenced by the film-forming property of HSPAN gel particles (Weaver et al., 1974). The formation of films from individual gel particles is considered to be due to the
2430 Ind. Eng. Chem. Res., Vol. 33, No. 10, 1994
/
Entanglements
CH -CONH2
I
C H -COONa
1 CH20H
CH$H
CH20H
CH20H
CH2OH
Figure 7. Chemical structure of hydrolyzed starch-g-polyacrylonitrileand also schematic of type of physical and chemical crow-linking that the gel might undergo.
interdiffusion and entanglements of chain ends between neighboring particles (Fanta et al., 1982). Hence, HSPAN can be considered as mainly physically cross-linked hydrogel containing only occasional chemical cross-links. Thus HSPAN gel is a representative of the structure depicted in Figure 2. Hydrolyzed starch-g-polyacrylonitrile was synthesized in our laboratory by using the standard technique (Fanta et al., 1982) which involves graft copolymerization of acrylonitrile onto gelatinized starch at 30 "C with ceric ammonium nitrate as a redox initiator for the free radical polymerization. The graft copolymer was subsequently alkali hydrolyzed and isolated in the form of dry powder. It had an equilibrium water absorption capacity of 170178 mL of water/g of dry polymer. The particles size of our HSPAN gel in the dry state was in the range of 0.1-0.2 mm, and in the swollen state it was in the range of 0.6-1.2 mm. The molecular weight of the grafted polyacrylonitrile pendant chain was determined by thoroughly extracting the crude graft with pure dimethylformamide, thus dissolving the ungrafted polyacrylonitrile homopolymer, and then acid hydrolyzing the resulting pure graft copolymer to remove the starch backbone. The grafted polyacrylonitrile was recovered and dried, and its molecular weight was estimated viscometrically in dimethylformamide to be 120000. The percent grafting was determined to be 48%. A new experimental technique had to be designed for determining the swellingof the gel under in situ conditions, as shown schematically in Figure 8. In effect, it is a Couette device with the facility of holding the swollen gel between rotating surfaces and maintaining the swelling at an equilibrium level by continuous water addition with a provision to suck out the excess water by vacuum. More specifically,the apparatus consisted of a jacketed sintered funnel, which was connected to a measuring jar. The swollen superabsorbent polymer was sheared in the annular gap between the walls of the sintered funnel and a rotating spindle, which was attached to the coaxial
JACKET
.SUP SHEARED ERA BSOR P
TlON
POLYMER
POROUS DISC
I I
I
--
L
TO VACUUM
Figure 8. Experimental apparatus for in situ measurement of swelling capacity of deforming gels.
cylinder fixure of a Couette viscometer (Rheotest-2). The gap width was 1.5 cm, which was much bigger than the individual particle sizes in the swollen gel. The temperature was maintained a t 25 "C by circulating water through the jacket with a temperature-controlled bath. The spindle was rotated at different rotational speeds to vary the shear rate. It was not possible to assign an exact value to the shear rate as there was a noticeable slip the rotating surface. During the process of shearing; water was continuously added from the top and the excess water was collected by using a slight vacuum. From the instantaneous volume of the gel, the level of swelling could be calculated at any time.
250.00
250
3
A
A
240
C
-8
>
RPM=243
-
/
I/
220c
c 220.00
RPM.243
35
.-+-0
a 2 1 0.00 L.
0
2 200.00
SAMPLE-HSPIN TEMP.-25'C
Q 190 0 0 Q, CI
0
3
SAMPLE-HSPAN TEMP.-25'C
18000
I
1 , 8 0 0 0 160.00 240.00 320.00 40000 480.00
170 0 0 000
Time (mi.) Figure 9. Experimental observations of effect of deformation on swelling capacity of HSPAN gels. The solid lines through these data are the model predictions using model parameters listed in Table 1. Table 1. Model Parameters for Obtaining Quantitative Fit to the Experimental Data in Figure 9
parameters
i. (min-1) k kz (g-mol/(cm38)) vJVo (g-mol/cm3)
vM/VO(g-mol/cm3) u8 (cm*/g-mol)
M,(g/g-mol)
r""
81 rpm
speed 135 rpm
Kinetic Model 126.0 201.6 4.67X 10-8 4.67 X 10-8 0.010 34 0.007 34 0.1 0.1 0.9 0.9 Flory's Theory 18 18 30 OOO 30 000 0.01 0.01 0.03 0.03
243 rpm 363.0 4.67X 10-8 0.00480 0.1 0.9 18 30 OOO 0.01 0.03
Results and Discussion Experimental Validationof Swelling in Deforming Gels. Figure 9 shows the experimental data of increased swelling capacity of the gel when subjected to shear deformation. The equilibrium absorption capacity of the gel increased from 178 mL/g to 205, 215, and 258 mL/g with an increase in the revolutions per minute (rprn; 80245). The lines through the data are the model predictions, which are obtained by using model parameters listed in Table 1. It is seen that the model can provide a quantitative fit to the experimental data. It is prudent to note here that the values of the shear rate used in the model calculations are those which would have existed at the wall of the rotating spindle in the absence of any wall slippage. This is certainly an assumption and is used here only for simplicity in calculations. A quantitative fit to the data was obtained when both rate constants, kl and kz, were made to depend on the shear rate. More specifically, while kl increased proportionally with the shear rate (eq 8), ka had to be decreased with increasing shear rate. Whether any physical reasoning can be assigned to this trend is not clear at the moment. Figure 10 summarizes our complete experimental data on the effect of shearingon swellingcapacity of the HSPAN gel. The lines through the data here are not model predictions. Path A shows data which are already reported in Figure 9. A t point C on each curve in Figure 10, the shearing was stopped. Subsequently, the swelling capacity was measured without shear and this is shown on path B. It can be seen that, when the shearing was stopped in all the cases, the new equilibrium value attained decreased only slightly (path B) which indicates a partial recovery
!
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2432 Ind. Eng. Chem. Res., Vol. 33, No. 10,1994
for 60 min, there appeared to be a second transition. We believe that this is the first instance where the emergence of such additional transitions as a result of deforming the gels has been demonstrated.
Table 2. Effect of Spinning Time on Swelling (Spinning Speed 1800 rpm) swelling capacity (mL/g) time of spinning (rnin) 0.0 169.2 10.0 231.3 20.0 241.9 30.0 245.9 40.0 238.5 60.0 239.4 loo,,
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Conclusions
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1
We have shown that physically cross-linked gels, when sheared, shown an increased swelling capacity. We believe this enhanced swelling is due to the breakage of weak physical bonds in the gel. A simple phenomenological model has been developed, which involves a coupling between the kinetics of breakage of such cross-links and the thermodynamics of swelling of polymeric networks. The model in its simplest form contains three parameters, which cannot be estimated a priori. The model predicts (i) an increase in the swelling capacity of the gel with an increase in the intensity of the deformation field, (ii) a faster approach to the new dynamic equilibrium swelling as the shear rate is increased, and (iii)no shift in the volume phase transition of the gel. This model can quantitatively fit the experimental data on the kinetics of increase in swelling due to imposition of shear. We have also compared the above results with those of a completely chemicallycross-linked gel which is subjected to a tensile strain. We show that such a gel also shows an increase in the swellingcapacity when stretched. However, the physical origin of this swelling is different than that for the physically cross-linked gel in that the chains of the chemically cross-linked gel expand under the influence of the tensile force resulting in the swelling of the gel. The volume phase transition also shifts slightly because of the same reason. Unlike the physical gel, the cross-links in the covalently cross-linked gel do not break easily under the normal deformation fields. The observation of increased superabsorption of gels reported in this work has pragmatic significance in the manufacturing of superabsorbent polymers. We believe that the “memory” of HSPAN gels is demonstrated here for the first time. Such nonequilibrium effects are important from a fundamental point of view since they lead to the necessity of formulating new theories. The observation of a second phase transition in HSPAN gels due to shearing shows that deformation could be another stimulus, which may induce a phase transition in gels. This is a new finding, since so far only pH, temperature, nonsolvent, light, electric field, etc. have been shown to induce volume phase transitions in gels. A force field may have other subtle effects on the gel which have not been addressed in this work. For example, Ianniruberto et al. (1994)have shown that, on application of a “pinching” force to the gel, the distribution of the network density can be changed. This might result in the formation of a nonhomogeneous structure in the gel which could affect ita swelling behavior. Our work may have significance in some other related fields. The problem of swelling and dissolving polymers in shear fields is being addressed on both molecular level (Brochard and de Gennes, 1983;Herman and Edwards, 1990;Devotta et al., 1994)and macroscopic level (Devotta et al., 1993,Devotta et al., 1994;Ranade and Mashelkar, 1994). It is quite likely that the effects of the kind elucidated here may have direct or indirect bearing in these situations. An additional area pertains to the formation of high-performance fibers of ultra high molecular weight, high-density polyethylene by the “swelldraw” process (Mackley and Solbai, 19871, where the polymer is swollen but not dissolved and then drawn. Once again our findings may have bearing on such processes.
Ind. Eng. Chem. Res., Vol. 33, No. 10, 1994 2433 Finally, flow through gel-walled tubes (Krindel and Silberberg, 1979) has been further explored recently (Kumaran, 1993). Our work may have a bearing in such flow situations as well.
Acknowledgment Art Metzner's pioneering contributions have enriched the whole field of engineering analysis of rheologically complex fluids. Art's contributions have also profoundly influenced so many scientists around the world, which includes two of us (A.K.L. and R.A.M.), who had a close association with the Chemical Engineering Department at the University of Delaware. It is a privilege to participate in this tribute to Art. Literature Cited Agarwal, U. S.; Dutta, A.; Mashelkar, R. A. Migration of Molecules Under Flow; The Physical Origin and Engineering Implications. Chem. Eng. Sci. 1994,49, 1693-1717. Badiger, M. V. Transport Phenomena in Polymeric Media. Ph.D. Thesis, University of Bombay, 1989. Badiger, M. V.; Kulkarni, M. G.; Mashelkar, R. A. Concentration of Macromolecules from AqueousSolutions: A New SwellexProcess. Chem. Eng. Sci. 1992,47, 3-9. Bae,Y. H.; Okano,T.; Hsu, E.; Kim, S. W. Thermo-SensitivePolymers as On-Off Switches for Drug Release. Makromol. Chem. Rapid Commun. 1987,8,481-485. Bastide, J.; Candau, S.; Leibler, L. Osmotic Deswelling of Gels by Polymer Solutions. Macromolecules 1981, 14, 719-726. Brochard; De Gennes, P. G. Kinetics of Polymer Dissolution. Physicochemical Hydrodyn. 1983,4 (4), 313-322. Cheng, D. C.-H. "The Characterization of Thixotropic Behavior"; Research Report No. LR 157 (MH); Stevenage: Warren Spring Laboratory, 1971. Cheng, D. C.-H.; Evans, F. Phenomenological Characterization of the Rheological Behavior of Inelastic Reversible Thixotropic and Ani-thixotropic Fluids. Br. J . Appl. Phys. 1965,16,1599-1617. Cussler, E. L.; Stokar, M. R.; Vaarberg, J. E. Gels as Size Selective Extraction Solvents. AICHE J . 1984,30, 578-582. Devotta, I.; Ambeskar, V. D.; Mandhare, A. B.; Mashelkar, R. A. On the Life Time of a Dissolving Polymer Particle. Chem. Eng. Sci. 1994a, 49,645-654. Devotta, I.; Premnath, V.; Badiger, M. V.; Rajmohanan, P. R.; Ganapathy, S.;Mashelkar, R. A. On the Dynamics of Mobilization in Swelling-Dissolving of Polymeric Systems. Macromolecules 1994b, 27,532-539. Dusek, K.; Patterson, D. Transition in Swollen Polymer Networks Induced bv Intramolecular Condensation. J. Polym. Sci. A-2 1968, 6,1209-1216. Fanta, G. F.; Burr, R. C.; Doane, W. M. Cross-linking in Saponified Starch-a-Polv(acwlonitrile). Graft copolymerization of lignocellulosk fibkrs; American Chemkal Sociky: Washin&on,-DC, 1982; pp 195-214. Flory, P. J. Principles of Polymer Chemistry; Cornell University Press: Ithaca, NY, 1953. Herman, M. F.; Edwards, S. F. A Reptation Model for Polymer Dissolution. Macromolecules 1990,15, 3662-3671. Hirotsu, S.; Onuki, A. Volume Phase Transitions of Gels Under Uniaxial Tension. J . Phys. SOC.Jpn. 1989, 58, 1508-1511. Hirotsu, S.;Hirokawa, Y.; Tanaka, T. Volume Phase Transitions of Ionized N-isopropylacrylamide gels. J . Chem. Phys. 1987,87 (2), 1392-1395. Ianniruberto, G.; Marrucci,G. Falling Spheres in Polymeric Solutions. Limiting Results of the Two-Fluid Theory of Migration. J. NonNewtonian Fluid. Mech. 1994, in press. Illavsky, M. Effect of Electrostatic Interactions on Phase Transition in the Swollen Polymeric Network. Polymer 1981,22,1687-1691.
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Received for review February 7, 1994 Accepted July 13, 1994O Abstract published in Advance ACS Abstracts, August 15, 1994.
