2868
Macromolecules 1984,17, 2868-2874
the bulk is denoted here as the average fraction of gauche bonds of the unperturbed chain. This value determined here for the cubic-lattice system is not directly relatable to real chains. However, one may relate the ratio ( r 2 )/ L of the mean-square end-to-end distance to the fully extended chain length following the derivation of Flory4 ( r 2 ) / L= @ / g - 1)
(8)
1 being the bond length, or the width of the cubic lattice. This value corresponds to the Kuhn length of the equivalent freely jointed chain and its axial ratio is then simply XK = 2 / g - 1 (9) From the results in Figure 1, the value g of the unperturbed chain at the transition is -0.45 for the system of chains comprising 20 segments and containing voids of -4.8%. The corresponding value of xK is -3.4. This value will decrease for the completely filled system of infinite chains for which the critical value of xK is 2.63 in the mean-field approximation. In this regard, it is interesting to note the predictions of X K ca. 6.4 and ca. 4.5 by the mean-field theories relying on the freely jointed chaina and a wormlike chain model,31 respectively. Hence, the exact value of xK critical to forming an ordered phase depends strongly on the chain model. Nevertheless, it should be noted that the degree of chain stiffness necessary to bring about an ordered state of bulk polymers is not very large. For the cubic-lattice chain considered here, the ordered states below the transition exhibit nearly perfect order both in conformation and in orientation. On the other hand, the degree of order predicted by a recent mean-field theory using a wormlike chain model is much ~maller.~' The degree of order assumed by real chains, therefore, is likely to depend strongly on the details of their conformational characteristics. Furthermore, the disorder-order transition observed here occurs without any assitance from the intermolecular dispersion forces, whereas in real polymers ordered states usually involve more favorable intermolecular interactions. These considerations show clearly that it will be necessary to investigate the effect of chain models as well as the contribution of the inter-
molecular dispersion energy in order to fully understand the details of disordered and ordered states and their phase transitions in real polymers.
Acknowledgment. We thank Professor P. J. Flory for helpful discussions and encouragement during the course of this work. A.B. thanks IBM World Trace of Germany for providing a postdoctoral fellowship. References and Notes Flory, P. J . J . Chem. Phys. 1942,10,51. Huggins, M.L. J. Phys. Chem. 1942,46,151; Ann. N.Y. Acad. Sci. 1942,4, 1. Flory, P. J. "Statistical Mechanics of Chain Molecules"; Interscience: New York, 1969. Florv. P.J . Proc. R. SOC.London. Ser. A 1956.234. 73. Nagie, J . F.Proc. R. Sac. London, Ser. A 1974,337,569. Gordon. M.: KaDadia. P.: Malakis. A. J . Phvs. A 1976., A9.751. , " Malakis, A.'J. bhys.'A i980, A13, 651. Guirati, P. D. J. Phvs. A 1980.A13, L437:J. Stat. Phvs. 1982. 28,-441. Gujrati, P. D.; Goldstein, M. J. Chem. Phys. 1981, 74,2596. Baumgiirtner, A,; Yoon, D. Y. J. Chem. Phys. 1983,79,521. Wall, F. T.;Mandel, F. J. Chem. Phys. 1975,63,4592. Metropolis, N.; Rosenbluth, A. N.; Rosenbluth, M. N.; Teller, A. H.; Teller, E. J. Chem. Phys. 1953,21,1087. Miller, A. R. Proc. Cambridge Philos. 1943,39,54. Orr, W. J . C. Trans. Faraday Sac. 1944,40,320. Guaeenheim, E.A. Proc. R. Sac. London. Ser. A 1944,183.203. GiKgs, J . H: J. Chem. Phys. 1956, 25, 185. Gibbs, J. H.; DiMarzio, E. A. Zbid. 1958,28, 373. Adam, G.; Gibbs, J . H. J . Chek. Phys. 1965,43, 139. Roe, R.-J.; Tonelli, A. E. Macromolecules 1979,12,878. Flory, P. J . Proc. Natl. Acad. Sci. U.S.A. 1982, 79,4510. Carlson, C. W. Ph.D. Dissertation, Stanford University, 1975. Flory, P. J . Faraday Discuss. Chem. SOC.1979, No. 68, 14. Patterson, G. D.; Kennedy, A. P.; Lathan, J. P. Macromolecules 1977,10,667. Fischer, E.W.;Strobl, G. R.; Dettenmaier, M.; Stamm, M.; Steidle, N. Faraday Discuss. Chem. Sac. 1979,No. 68, 26. Snyder, R. G.; Poore, M. W. Macromolecules 1973, 6, 708. Higgins, J . S.; Stein, R. S. J. Appl. Crystallogr. 1978,11,346. Gawriah. W.: Brereton. M. G.: Fischer. E. W. Polvm. Bull. 1981,4,687.' Ballard. D. G.H.: Burgess. A. N.: Cheshire. P.: Janke. E. W.: Niven, A.; Scheltkn, JrPoZymer 1981,22, 1353. Yoon, D. Y.;Flory, P. J. Polym. Bull. 1981,4,693. Kuhn, W. Kolloid 2. 1936, 76,258;1939,87,3. Flory, P. J . Macromolecules 1978, 11, 1141. Flory, P. J.; Ronca, G. Mol. Cryst. Liq. Cryst. 1979,54,289. Ronca, G.; Yoon, D. Y. J. Chem. Phys. 1982,76,3295.
Phase Transition in Swollen Gels. 6. Effect of Aging on the Extent of Hydrolysis of Aqueous Polyacrylamide Solutions and on the Collapse of Gels Michal IlavskP,* Jaroslav Hrouz, Jaroslav Stejskal, and Karel Bouchal Institute of Macromolecular Chemistry, Czechoslovak Academy of Sciences, 162 06 Prague 6, Czechoslovakia. Received February 13, 1984
ABSTRACT The aging of aqueous polyacrylamide solutions and gels prepared under similar conditions was investigated in parallel. The colorimetric determination of the concentration of ammonium ions produced by the hydrolysis of amide groups of polyacrylamide in solution proved that with increasing time of aging, T , from 0 to 103 days the mole fraction of COO- groups increased from 0 to 0.052. Light scattering revealed the existence of a polyelectrolyte effect in solutions of aged PAAm. The light scattering data also showed that the hydrolysis of PAAm was not accompanied by degradation processes. For networks with the time of aging, 7,>12 days, a phase transition was observed in acetonewater mixtures. By introducing the effective degree of ionization, an agreement can be reached between the swelling data and those predicted by the molecular theory describing swelling equilibria in polyelectrolyte networks. The discontinuity in volume in the phase transition is accompanied by a jumpwise change in the equilibrium shear modulus of the gel.
Under certain conditions, in polyacrylamide (PAAm) networks swollen in acetone-water mixtures, a transition can be observed between two polymer phases differing in 0024-9297/84/2217-2868$01.50/0
the conformation and Concentration of segments. The time of aging (or curing) of the gels had a decisive influence on the phase transition (collapse). Aging took place either 0 1984 American Chemical Society
Macromolecules, Vol. 17,No. 12, 1984
Phase Transition in Swollen Gels 2869
under the same conditions as those at the gel f~rmationl-~ (i.e., - 4 wt % PAAm and -96 wt % water; due to N,N’-tetramethylethylenediamine being used as the reducing component of the initiation system, the medium has pH -8-9) or in a basic solution4 with pH 12. The time of curing 7 at a higher pH was reflected in the formation and extent of the collapse much more distinctly (T 10 days at pH 12 corresponds to 7 60 days at pH 8-9). During the aging at pH 12, it may be expected that hydrolysis of AAm groups is the most important effect. The collapse thus depends on the existence of charges on the chain. The introduction of charges into the PAAm by copolymerizing acrylamide with sodium methacrylate (MNa) led to a conclusion5that -0.8 mol % of MNa is sufficient to bring about the collapse. The extent of the collapse increases with increasing MNa content, and it appears in mixtures with a higher content of acetone. These experimental findings were in a semiquantitative agreement with the theory of swelling equilibria of polyelectrolyte network^;^^^ also, data obtained on networks of the copolymer of AAm with MNa prepared at various dilutions at network formations or with a varying content of the cross-linking agents could be theoretically described in a semiquantitative way. The decisive effect of ionization of the gel on the existence of the collapse has also been demonstrated recently on PAAm gels1° which contained 0-5 mol 9% of N-acryloxysuccinimideester. The collapse occurred when the network contained more than 1.6 mol % of hydrolyzed N-acryloxysuccinimide ester. As the number of charges arising during the aging of PAAm gels is not known, a quantitative comparison between the formation and extent of the collapse, on the one hand, and the theory of swelling equilibria, on the other, is missing. Although indirect experiments have demonstrated the presence of charges also in PAAm gels cured under the same conditions under which they were formed3 (pH 8-9), a view has been forwarded2*”that in such a case the effect of hydrolysis is less important, and it is probably the heterogeneous structure of the gels (especially in the range of short times, T = 0-15 days) which is responsible for the change in physical properties. The time change in the properties of aqueous PAAm solutions has also been reported in the literature in a number of cases. However, no uniform view has been suggested regarding the interpretation of the aging of solutions (reflected, e.g., in a decrease in the viscosity of solutions with time).12 It has been suggested that aging is accompanied by degradation which is due either to radicals13 or to microorganism^,'^ by disentanglement of chains,15 by a long-term conformational transition inside the chain,16and, under certain conditions, by hydr01ysis.l~On the other hand, in some other carefully performed investigationsls no time changes of the molecular structure of PAAm were observed in pure water. It may be expected that the understanding of processes which take place during curing of aqueous PAAm solutions will also contribute to the elucidation of the formation of phase transition in PAAm gels and vice versa. This study deals with the effect of aging of PAAm solutions and gels at pH -8-9 on the extent of hydrolysis and the formation and extent of the collapse in gels. Since the curing of solutions and gels occurred under the same conditions (gels contain only -2.5 wt ‘70 of the crosslinking agent-methylenebis[acrylamide]-as an additional component), it may be expected that processes which take place during the aging (especially at low degrees of hydrolysis) will be the same in both cases. The knowledge of the extent of hydrolysis of the PAAm from solutions will make possible a quantitative comparison
-
-
-
Table I Effect of the Time of Aging T on the Degree of Hydrolysis of PAAm Solutions 105y; sample T, days mol .e-1 &mn1 2 3 4 5 6 7 8 9 10 11
0.13 3 6 12 20 24 48 65 78 97 103
0 3.36 8.66 14.30 20.08 24.80 49.60 62.77 69.75 74.70 77.60
0 0.0024 0.0060 0.0100 0.0140 0.0172 0.0320 0.0405 0.0500 0.0500 0.0520
O y is the total concentration of ammonium ions corrected for the amount of NH4+ ions in the initiator used; xcoo- is the mole fraction of COO- ions.
between the swelling equilibria of variously cured PAAm gels and the theoretical prediction (similarly to gels of the copolymer of acrylamide with sodium methacrylate5).
Experimental Section Sample Preparation. Solutions of polyacrylamide (PAAm) were prepared by mixing 5 g of acrylamide, 150 pL of N,N’tetramethylethylenediamine, and redistilled water up to 96 mL, and the solution was dosed into ampules (diameter D 1cm). Each ampule containing 4.8 mL of solution was flushed with nitrogen, and 0.2 mL of a 1%aqueous solution of ammonium persulfate was added; on stirring, the ampules were sealed. The PAAm gels were prepared in the same way as the solutions, but 0.133 g of N,”-methylenebis[acrylamide] was added to the initial mixture. The samples of solutions and gels were left in ampules for various times, starting from 3 h (completed polymerization, monomer conversion -98%) up to 103 days (Table I). Preparation and subsequent characterization of the samples were performed at room temperature. Determination of the Degree of Hydrolysis. The overall concentration of ammonia and ammonium ions obtained by the hydrolysis of amide groups was determined colorimetrically; in an alkaline medium the released ammonia reacted with thymol, and Bromothymol blue was formed after oxidation with sodium hyp0br0mite.l~The reagent used in colorimetry consisted of two solutions: solution I contained 2 g of thymol, 10 mL of 2N NaOH, and 90 mL of water, and solution I1 was prepared from 100 mL of bromine water and 35 mL of 2 N NaOH. A sample of the solution of PAAm was diluted with the same volume of deionized water; from the solution thus obtained, 5 mL was taken and solutions I and 11, 2 mL of each, were gradually added. After 5 min, the solution was analyzed colorimetrically with a Spekol 10, Zeiss-Jena colorimeter, at a wavelength of 650 nm. The dependence of extinction on the concentration of ammonium ions (ammonia) was calibrated with a standard NH4C1 solution. From the values thus determined, the extent of hydrolysis was determined and characterized by the mole fraction of carboxylic ions xCm- (Table I). In the calculation of xcoo-, the concentration of ammonium ions was corrected to the quantity of the initiator used. Changes in the concentration of hydroxyl ions in the polymerization of AAm and those following its hydrolysis were determined with a Potentiograph pH-meter E 336 A. Light Scattering, Samples of cured PAAm were precipitated into methanol, the polymer was isolated, reprecipitated, and dried. Light scattering from PAAm solutions in water or NaCl solutions was measured with a vertically polarized primary beam in the angular range 30-150O and at a wavelength of 546 nm with a Sofica 42 000 apparatus. Each measurement of molecular weight and other quantities was based on the results of measurements of five solutions each time (polymer concentration 1 X 10-%5 X g/mL). The refractive index increment of PAAm in water 0.187 mL/g; the dependence of the refractive index increment on the degree of hydrolysis was neglected, because the hydrolysis of -5% of amide groups represents only a 1 % change in the
-
Macromolecules, Vol. 17, No. 12, 1984
2870 Ilavskg et al.
of both the swelling ratio X and modulus G on the composition of the acetone-water mixture is given in Figure 1.
Results and Discussion Effect of the Time of Aging on the Hydrolysis of PAAm. T h e use of N,N'-tetramethylethylenediamine (TEMED) as the reducing component of the initiation system determined not only the rate of t h e initiation reaction but also t h e concentration of hydroxyl ions catalyzing the subsequent hydrolysis of amide groups on the polyacrylamide chain. Before persulfate was added to the reaction mixture, the potentiometrically determined concentration of hydroxyl ions had been 2.5 X lo4 mol/L (pH 10.4) and had decreased due to the initiation reaction t o 1.7 X mol/L (pH -9.2). Such change in the concentration of hydroxyl ions is caused by a loss in T E M E D due to the redox reaction with persulfate and to t h e basicity of the reaction products. T h e p H value of -9.2 determined the initial conditions of the alkaline hydrolysis of amide groups on polymer chains. In the course of the reaction, t h e concentration of hydroxyl ions dropped further, as low as 1 X 10+ mol/L (pH -8) after -100 days of aging. T h e change from p H -9.2 t o p H -8 is a consequence of t h e hydrolytic reactions of t h e cation NH4+ and of carboxylic anions bound on polymer chains, which are products of t h e hydrolysis of amide groups. T h e hydrolytic reactions can be characterized by t h e scheme
-
[-COO-
NH:
t H20 t H20
e [-COOH
4
t OH-
NH40H t H+
T h e alkaline hydrolysis of amides proceeds as a firstorder reaction with respect both to amide and to hydroxyl ions, and its mechanism is characterized by t h e following schemez4 Figure 1. Dependence of the swelling ratio X and modulus G (g cm-2) on the acetone content a: (a) samples of series A-D; (b) samples of series E-H;series of gels A-H correspond to networks X values; ( 0 )G values. in Table 111; (0)
i
0-
t OH-
7 -2r
-CCNH2 OH
refractive index increment.21 In view of low concentrations of the low molecular weight electrolyte added, its effect on the refractive index increment was disregarded. The results of light scattering were evaluated by the usual Zimm method.22 Swelling and Mechanical Characteristics. After a given time of aging, the gels were removed from the ampules, cut into specimens -1 cm long, and left to swell in 200 mL of an acetone-water mixture (20 mixtures in the range 0-80 vol % acetone). After swelling (-28 days), the swelling ratio X related to the state of network formation
x = ( D * / D ) 3 = V*/V
(1)
was determined with the individual specimens; here, D and V respectively are the diameter and volume of specimen after swelling in a given solvent mixture, and D* and V* respectively are the diameter and volume of the specimen after preparation. The diameter was measured with an Abbe comparator (accuracy f0.0002 mm); the X values in Figure 1 are the averages from at least three measurements. The volume fraction of the polymer in the swollen state, u2 = uoX, can be determined by using the X values (uo is the volume fraction of the polymer at network formation; uo = 0.037). Deformation experiments in compression were carried out by using an apparatus described earlier23and the same specimens as those used in the determination of X. The dependence of force f on compression X = l / l o ( l and lo respectively are the deformed and initial height of the specimen) was measured in the range 0.7 < X < 1. The shear modulus G was determined from
e
[-!
t NH2-
OH
T h e scheme shows t h e equivalency between t h e concentration of carboxylic anions and the overall concentration of ammonia a n d t h e NH4+ cation on which t h e determination of the degree of alkaline hydrolysis was based. In the range of low conversion, the concentration of carboxylic ions generated on the polymer chain should have increased linearly with time. However, under the given experimental conditions there was a considerable deviation from the linear dependence (Table I), which was probably due t o a decrease in t h e concentration of hydroxyl ions in the course of t h e hydrolysis of amide groups bound on the polyacrylamide chain. T h e colorimetric method could not be employed in the determination of the concentration of ammonia and NH4+ cations in the gels because in the tridimensional structure the rate of formation of Bromothymol blue is determined by diffusion processes, and an extension of the reaction time above 5 min causes irreproducibility of the measurement.
(2)
Characterization of the Molecular Structure of PAAm by Light Scattering. In the light scattering
So is the initial cross section of the specimen. The dependence
measurements of PAAm solutions in pure water, the sam-
G = f/SO(X-'
-
A)
Macromolecules, Vol. 17, No. 12, 1984
10
Phase Transition in Swollen Gels 2871
c
I
1
I
0
05
10 SI"?
2
0
05
0 2
10
5,172
Figure 2. Angular dependences of light scattered from solutions of aged PAAm: (a) PAAm solutions in water; (b) PAAm solutions in 0.01 M NaCl; PAAm concentration 5 X g/mL; numbers at lines correspond to the time of aging in days.
ples with T > 6 days begin to show the polyelectrolyte effect. This effect is characterized by a distinct decrease in the intensity of scattered light (Figure 2a); i.e., the Kc/RB values increase ( K is the optical constant, c is polymer concentration, and RBis the so-called Rayleigh ratio for the scattering angle e), due to the destructive interference of scattered light. This is a consequence of strong intermolecular interactions of electrostatic nature. With increasing degree of hydrolysis, the dissymmetry of radiation envelopes of scattered light decreases and eventually assumes even values lower than unity (Figure 2a). After the addition of a sufficient amount of low molecular weight electrolyte (sodium chloride in this case), the polyelectrolyte effect is screened and the Kc/RBvalues of more hydrolyzed samples decrease considerably (Figure 2b), compared with salt-free solutions. Depending on the time of aging, in the case of the screened polyelectrolyte effect there also is a slight rise in the Kc/RBvalues, which reflects the increasing values of the second virial coefficient with increasing charge density on chains. Molecular parameters of the dissolved polymer may be determined by light scattering only in the absence of the polyelectrolyte effect. The concentration of the added electrolyte, 0.001 M NaC1, is sufficient for screening the effect just mentioned in all samples, even if the most cured samples seem to be close to the limit after which the polyelectrolyte effect becomes operative. At this concentration of sodium chloride, the increase in the second virial coefficient as a function of the increasing charge density (time of aging) becomes well discernible (Table 11). A similar trend is also observed for the dimensions of macromolecules characterized by the radius of gyration. At the increased concentration of the low molecular weight electrolyte (0.01 M NaCl), the presence of charges on polyelectrolyte chains has virtually no effect at all, and the increase of the second virial coefficient is small (Table 11). The molecular weight of PAAm determined in 0.001 and 0.01 M NaCl (conditions where the polyelectrolyte effect does not exist) is independent within the limits of experimental error on the time of aging (Table 11). Certain differences in the molecular weights of variously cured samples are obviously caused by minor deviations in the dosage of the initiation system. Thus, the aging of PAAm is not accompanied by degradation processes. This conclusion is also in agreement with the results of earlier measurements. 15916
Table I1 Molecular Parameters of Polyacrylamide (Aged for the Time T ) Determined by Light Scattering from Aqueous Solulioub of Sodium Chloride" 7, (RG2)z1/2, ~ O ~ A ~ ,1O4Az0, days lOW3M, nm mol mL g-2 mol mL g-2 0.13 820 64 5.6 0 3 670 65 5.6 2.8 6 760 71 5.1 17.8 12 880 94 7.0 49.6 24 560 88 6.4 147 48 700 87 17.6 508 930' 112 19.2 1004 78 97 910' 181 29.0 1240 0.13 3 6 12
24 48 78 97
740 600 7 50
650 640 530 660 650
0.01 M NaCl 65 57 55 57 54 64 69 73
5.6 5.4 4.4
5.5 5.8 6.6 6.4 8.6
0
0.28 1.78 4.96 14.7 50.8 100.4 124.0
" M , is molecular weight, is the radius of gyration, A2 is the second virial coefficient of polyacrylamide in aqueous NaCl solutions, and A; is the Donnan term calculated according to eq 3. The result is subjected to a considerable error owing t o the onset of the polyelectrolyte effect.
From the mole fraction of carboxylic ions xcoo- (Table I), it is possible, for the sake of illustration, to calculate the so-called ideal Donnan term A 2 by using the relation (3)
in which C,is the molar concentration of the low molecular weight electrolyte and Mo is the molecular weight of the monomer unit; xcoo-/Mois the number of charges per unit molecular weight of the polyelectrolyte (Table 11). The considerably higher A? values compared with the experimentally determined second virial coefficient A2 at higher degrees of ionization suggest low values of the activity coefficients of counterions of the polyelectrolyte. This observation is in agreement with numerous data reported in the l i t e r a t ~ r e .The ~ ~ low accuracy of determination of second virial coefficients impedes quantitative conclusions. Swelling and Mechanical Behavior of Cured PAAm Gels. Comparison between Theory and Experiment. For low-cured samples (A-C) the dependence of X on the acetone content is continuous; for the other gels, phase transition may be found; the extent of the collapse, A(1og X)= log X"- log X', and also the acetone concentration in the mixture at which the transition takes place, a,, increase with increasing time of aging (Figure 1,Table 111). This result is in accordance with previous mea~urements.l-~ A dependence similar to that of X on the acetone concentration can be seen also for the shear modulus G (Figure 1). For networks A-C, the dependence of G on a is continuous; for the other networks, there is a discontinuity A(1og G) = log G"- log G'which increases with the time of curing. The value of the modulus Go measured for cured networks prior to swelling in acetone-water mixtures is virtually independent of the time of aging, T (Table 111); this finding is in agreement with earlier measurements.2J1The modulus G measured in acetone-water mixtures increases with increasing T (at constant X), and the log G vs. log X dependence of the individual networks in the range of low X may be represented by parallel straight lines with the slope s = 0.45 (Figure 3). A somewhat higher slope value
Macromolecules, Vol. 17, No. 12, 1984
2872 Ilavskjl et al.
Table I11 Basic Characteristics and Parameters of Phase Transition" Go9
7,
series A B C D E F G H
days 0.13 3 6 12
24 48 78 97
XCW-
0
0.0024 0.0056 0.0100 0.0172 0.0320 0.0450 0.0500
g cm-' 34.6 31.8 33.9 35.9 34.7 33.1 33.8 36.8
GI,
g cm-' 34.6 41.1 43.9 51.4 54.2 60.7 63.5 63.5
lo%&
mol cm-3 3.7 4.4 4.7 5.5 5.8 6.5 6.8
6.8
A(1og X)
1.30 1.44 1.56 1.78 1.84
A(1og G)
0.57 0.62 0.67 0.74 0.76
A
0.210 0.247 0.253 0.256 0.283
xc
0.591 0.631 0.690 0.730 0.776
a,,
vol
70
44 48 50 53 55
4
0.99 0.88 0.75 0.60
0.53 0.56 0.51
7 is the time of aging of gels, XCOO- is the mole fraction of COO- ions, Go is th8 modulus of cured networks before swelling in acetonewater mixtures (X= l),GIis the modulus extrapolated from the G vs. X dependence for X = 1 (Figure 3), w d is the network density related to the dry volume, A(1og X)is a change in the gel volume at collapse, A(1og G) is a change in the modulus at collapse, A = vp - vpl is the extent of the collapse, xC corresponds to the x value of the acetone-water mixture at which the collapse takes place, a, is the acetone concentration in the acetone-water mixture in which the phase transition takes place, and 4 is the activity coefficient of polyelectrolyte counterions.
parameters of the network may be found in eq 2-5 of ref 7. By using known molecular parameters (density of dry 25 t polymer p = 1.35 g ~ m - T~ = , 298 K, uo = 0.037, molar log G volumes of the acetone-water mixture V1 (determined earlier*), molecular weight of the monomer unit Mo = 71 g mol-l, experimental network density Vd, degree of ionization xcoo-, and experimental values of the volume fractions of polymer in the swollen state u,) and by means of eq 4, the dependence of the interaction parameter x on u2 was calculated (due to free swelling, the swelling pressure in eq 4 was taken as P = 0).The same procedure has been employed earlier5 in the treatment of data of the AAm_ _ ~ ~ ___ _ .______MNa copolymers. -IC -0 5 3 05 10 09 x In the case under study, however, the use of the degree of ionization expressed by xcoo- has led to x values in the Figure 3. Dependence of modulus G (g cm-*) on the swelling ratio X (0) series A; ( 0 )series B; ( 0 )series C; (e)series D; ( 8 )series range 0.48-5.75 for samples of the A-H networks swollen E; (@) series F; (a) series G; (a) series H. in water with increasing time of aging T from 0 to 97 days. The value x = 0.48 of the unhydrolyzed network A (xcoo(s = 0.65) was found earlier for the copolymer of AAm with = 0, Table I) has been determined both for sodium metha~rylate.~ The modulus G1 extrapolated from aqueous solutions of PAAm and for PAAm networks the log G vs. log X dependence for X = 1 was increasing swollen in water. Since x is a measure of the polymerwith increasing 7 by some 80%;a similar somewhat greater, solvent affinity when all the charges are screened6 (effect increase in the modulus has been observed5for copolymers of charges on the degree of swelling in eq 4 is included in of AAm with MNa with increasing MNa content. The the terms P, and Pels),it may be expected that the small concentrations of elastically active chains related to the extent of hydrolysis should not be reflected in x to any dry state, Vd = Gl/voRT,were determined by using the considerable degree. The requirement that x should be modulus G1 (Table 111). The low Vd values suggest a low the same (x = 0.48) for cured networks B-H swollen in efficiency of the cross-linking reaction (-lo%), which is water may be satisfied if the effective degree of ionization probably a consequence of large cyclization a t the high a is lower than xcOo-, i.e., a = 4xco0- (where 4 is a semidilution used in network formation. With respect to high empirical correction factor which is related to the activity cyclization, one may expect a certain inhomogeneity of coefficient of counterions). The 4 values determined using networks reflected in higher density fluctuations of polythese conditions vary in the range 1-0.5 for networks with mer segments in comparison with equally concentrated T = 3-97 days (i.e., for XCOO- = 0.0024-0.05, Table 111). solutions; recently," differences in the swelling of diluted Qualitatively similar conclusions regarding the necessity PAAm networks with 7 = 0-15 days have been interpreted of introduction of the activity coefficient were obtained'O by inherent inhomogeneities in these gels. All our gels were in the analysis of swelling data determined for PAAm optically transparent and did not possess birefringence in networks containing hydrolyzed ester of N-acryloxythe undeformed state. succinimide. Inclusion of the effect of electrostatic interactions of The dependence of 6 on xcOo- is given in Figure 4, along chain charges in the kinetic theory of rubberlike elasticity with that of 4 on the mole fraction of sodium methacrylate gave for the swelling pressure7 xMNa (earlier swelling data of networks of the AAm-MNa (4) P = P, + Po,+ Pel+ Pels copolymers5 were treated similarly). We believe that the difference observed in the 4 vs. xcoo- or x m a dependences where the contribution P, is determined by the mixing of the chain segments with the solvent (the Flory-Huggins are related to the fact that, while for the AAm-MNa coterm with the interaction parameter x),P, is given by the polymers the copolymerization proceeds roughly statistimixing of gel ions with the solvent, Pel is determined by cally (statistical charge distribution of the chains), in the a change in the elastic network energy with the degree of hydrolysis of PAAm due to aging the grouping of charges swelling, and Pel,is given by a change in the free energy is preferred which leads to lower 4 values. It should be of electrostatic interactions with the degree of swelling. A pointed out, however, that also an opposite view may be detailed description of the contributions Pi in molecular found in the literature regarding the distribution of
1 ,.
I
I
Phase Transition in Swollen Gels 2873
Macromolecules, Vol. 17,No. 12, 1984
I
' I
I
I
0201
O l O t
/
/.
I
1
, 0.02
0.04
0.06
xcoo-
Xh4NQ
Figure 4. Dependence of the activity coefficient of counterion 4 on the mole fraction XCOO- or XMN,: (0) cured PAAm samples; ( 0 )copolymers of AAm and sodium methacrylate.6
06
/
I
Figure 6. Dependence of the extent of collapse A and of the critical value of the interaction parameter xc on the effective degree of ionization for cured PAAm networks d x c and ~ for copolymers of AAm with sodium methacrylate ~ X M N ~ (-): course determined by the Maxwell data constr~ction~~' x vs. u2 (cf. eq 5) from Figure 5; (0) experimental data for cured PAAm networks; ( 0 )experimental data for copolymers of AAm with sodium methacrylate6 (parameter xc corresponds to x of the acetone-water mixture in which the collapse was observed).
4
3F 01
02
03
04 "2
Figure 5. Dependence of the interaction parameter x (eq 4 for P = 0) on the volume fraction of dry polymer in the swollen gel u2.
Samples denoted as in Figure 3.
charged groups along the chain in hydrolyzed PAAm samples, compared with the copolymers of AAm and acrylic acid.26 The jumpwise change in the gel volume at collapse appears as discontinuity in the x vs. u2 dependence (Figure 5; here, the x values were calculated from eq 4 with P = 0 for the degree of ionization a = &coo-). When the x vs. u2 dependence (shows the van der Waals loop) is used, it is possible to determine the extent of the collapse A = u; - u i and the critical value of the interaction parameter xC at which the transition takes place from the relation (Maxwell's data construction; for a detailed description, cf. ref 5 and 7)
A comparison between theory and experiment is given in Figure 6. While for xcthe agreement between theory and experiment is relatively good, for the extent of the collapse A it is less satisfying. It may be said, however, that eq 4 described semiquantitatively experimental data of cured PAAm networks, assuming the effective degree of ionization to be given by a = &ccoo-. The following conclusions can be made: (a) During the aging of aqueous solutions and gels of PAAm at pH -8-9, the amide groups on the PAAm chains are hydrolyzed (the rate and the extent of hydrolysis depend on pH), but no degradation of PAAm chains takes place.
(b) The predominant role which determines the existence and extent of collapse in cured PAAm gels in acetonewater mixtures is played by the presence of charges on chains and apparently also by their distribution along the chain. We believe that the influence of the other effects (such as the inhomogeneous network structure or time conformational changes of the chain) on the formation of the collapse is only secondary. (c) A semiquantitative agreement between experimental results of the swelling equilibria of cured PAAm networks with theory may be reached by assuming that the effective degree of ionization a is lower than the experimentally determined degree of hydrolysis xcoo-. The parameter 4, which is related to the activity coefficient of counterions (a = c#acoo-), has nevertheless the character of semiempirical correction factor and may involve effects connected with a certain heterogeneity of diluted networks or with other effects not considered in the theory. (d) In the phase transition, there is a jumpwise change in the equilibrium shear modulus of the gel. The dependence of the modulus on the degree of swelling is more pronounced in the collapsed state compared with the expanded state of the gel. In the expanded state at the given value of the swelling ratio X,the modulus increases with the time of aging of the network.
References and Notes (1) Tanaka, T. Polymer 1979,20, 1404. (2) Janas, V. F.; Rodriguez, F.; Cohen, C. Macromolecules
1980,
13, 977. (3) Stejskal, J.; Gordon, M.; Torkington, J. A. Polym. Bull. 1980, 3, 621. (4) Tanaka,
(5) (6) (7) (8)
(9) (10)
T.; Filmore, D.; Shao-Tang Sun; Nishio, I.; Swislow, G.; Shah, A. Phys. Rev. Lett. 1980, 45, 1636. Ilavskfr,M. Macromolecules 1982, 15, 782. Hasa, J.; Ilavskfr,M.; Dulrek, K. J. Polym. Sci., Polym. Phys. Ed. 1975, 13, 253. Ilavskfr, M. Polymer 1981, 22, 1687. Ilavsky, M.; Hrouz, J. Polym. Bull. 1983, 9, 159. Ilavskfr, M.; Hrouz, J. Polym. Bull. 1982, 8, 387. Nicoli, D.; Young, C.; Tanaka, T.; Pollak, A.; Whitesides, G. Macromolecules 1983, 16, 887.
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(16) (17) (18)
1273. Kulicke, W.-M.; Kniewske, R.; Klein, J. B o g . Polym. Sci. 1982, 8, 373. Haas. H. C.: MacDonald. R. L. J.Polym. Sci., Polym. Lett. Ed. 1972,' 10, 461. Chmelir, M.; Kiinschner, A.; Barthell, E. Angew. Macromol. Chem. 1980,89, 145. Muller, G.; Laine, J. P.; Fenyo, J. C. J. Polym. Sci., Polym. Chem. Ed. 1979,17,659. Kulicke, W.-M.; Kniewske, R. Makromol. Chem. 1980, 181, 823. Stejskal, J.; Horskfi, J. Makromol. Chem. 1982, 183, 2527. Machtle, W. Makromol. Chem. 1982, 183, 2515.
(19) Lapin, L.; Hein, W. 2.Anal. Chem. 1934, 98, 238. (20) Klein, J.; Conrad, K.-D. Makromol. Chem. 1980, 181, 227. (21) Schwartz, T.; Francois, J. Makromol. Chem. 1981, 182, 2775. (22) Zimm, B. H. J. Chem. Phys. 1948, 16, 1099. (23) Hrouz, J.;Ilavsky, M.; HavliEek, I.; DuEiek, K. Collect. Czech. Chem. Commun. 1979, 44, 1942. (24) Ingold, C. K. "Structure and Mechanism in Organic Chemistry"; Cornell University Press: Ithaca, NY, 1953. (25) Nagasawa, M.; Takahashi, A. In "Light Scattering from Polymer Solutions"; Huglin, M. B., Ed.; Academic Press: New York, 1972; pp 671-719. (26) Truong, N.; Francois, J. InternationalSymposium on Macromolecules, IUPAC MACRO 1983, Bucharest,Romania 1983, paper IV, p 423.
Thermodynamics of Proton Ionization from Poly(viny1ammonium salts) Edwin A. Lewis,* Thomas J. Barkley, R. Renee Reams, and Lee D. Hansen* Thermochemical Institute' and Chemistry Department, Brigham Young University, Provo, Utah 84602
Thomas St. Pierre* Chemistry Department, The University of Alabama i n Birmingham, Birmingham, Alabama 35294. Received January 16, 1984
ABSTRACT: The thermodynamic parameters AG, AH, and AS for proton ionization from the hydrochloride, hydrobromide, hydroiodide, and hydroperchlorate salts of poly(viny1amine) (PVA) have been determined by calorimetric and potentiometric titration. The thermodynamic data are reported as a function of the fraction of sites protonated (a),polymer concentration, electrolyte concentration, counterion type, and temperature. The AH and A S curve3 are much more sensitive than the corresponding AG curve to temperature, concentration, salt, and counterion effects. The largest anomalies in all of the curves are observed to occur at a values between 0.5 and 1. The counterion dependence is indicative of ion pairing between the polyion and the counterion with the association constant decreasing in the order C1- > Br- > I- > ClOi. The enthalpy and the entropy changes show a strong dependence on temperature, characterized by a large positive ACp for all charge states with the maximum in ACp occurring at a = 1. Current polyelectrolyte theories, including those allowing for counterion condensation, fail to predict these titration data.
Introduction We propose here that the difference in the apparent pKa values at t h e extremes of the titration curve for a polyacid or polybase defines the "polyelectrolyte effect". In other words, a polymer exhibiting a strong polyelectrolyte effect shows a large change in pKa on going from t h e uncharged s t a t e t o t h e charged state. T h e polyelectrolyte n a t u r e of poly(viny1amine) (PVA)
was first examined by Katchalsky and co-workers.' They reported that PVA was unique in showing a stronger than usual dependence of the apparent pK, on the charge state of the polymer, a. T h e fully charged polymer (a= 1) was a stronger acid than the uncharged polymer ( a = 0) by about 5 orders of magnitude. Katchalsky explained this unusual behavior by postulating that there were two different ammonium groups. One group was hydrogen bonded while the other was not and each type had a unique intrinsic pK,. Recently, t h e acid-base behavior of PVA has been reexamined by Bloys van Treslong* and Lewis et aL3 Bloys van Treslong has concentrated his efforts on obtaining precise pKa and dpKalda data. In our preliminary report on t h e calorimetric a n d potentiometric study of proton ionization from PVA-HC1 and poly(iminoethy1ene hydrochloride), we showed that t h e changes in t h e enthalpy and Contribution no. 340.
entropy for ionization are more sensitive functions of polymer charge state t h a n is t h e free energy change, pKa, or AG.3 In this paper, we explore the effects of polymer concentration, t h e nature of t h e counterion, supporting electrolyte concentration, and temperature on t h e titration behavior of PVA.
Experimental Section Polymer Synthesis. Poly(viny1amine) (PVA) was synthesized by the procedure reported by Hughes and St. PierreS4By this procedure, acrylic acid was converted to tert-butyl vinylcarbamate and then polymerized with azobis(isobutyronitri1e). The tertbutoxycarbonyl group was removed by acid hydrolysis. NMR and IR analyses indicated complete hydrolysis. The polymer was isolated as the hydrochloride salt and characterizedby elemental analysis, 'H and 13C NMR spectroscopy, and specific viscosity measurements. PVA in the free base form was prepared from the hydrochloride salt by neutralizationwith a 10% excess of NaOH and exhaustive dialysis against water. The PVA free base was isolated by lyophilization and characterized by elemental analysis. PVA-HX, where X = Br, I, or C104,was prepared in two ways. Procedure I involved exhaustive dialysis of a PVA-HC1 solution against first a solution of HX, then water, and finally isolation of the PVA-HX salt by lyophilization. The PVA-HC1 starting solution had a nominal concentration of 0.1 monomolar and the HX solutions nominal concentrations of 0.15 M. The dialysis against either HX or water was done with three changes of the dialyzing solution at 4-h intervals to give a final dilution factor
0024-9297/84/2217-2874$01.50/0 0 1984 American Chemical Society
