THE JOURNAL OF
PHYSICAL CHEMISTRY Registered in U.S. Patent Ofice @ Copyright, 1988, by the Ameriean Chemicrrl Society
VOLUME 70, NUMBER 4 APRIL 15, 1966
Donnan Equilibria in Polystyrenesulfonate Gels
by Richard L. Gustafson Rohm & Haas Company, Research Division, Philadelphia, Pennsylvania
19137
(Received December 87, 1966)
Measurements of sorption of HCl, NaC1, NaI, NaH2P04,CaC12, and LaC4 by the appropriate ionic forms of two polystyrenesulfonate gels, Amberlite XE-100 and Amberlite IR-120, have been capied out in 0 . 0 2 4 m solutions at 25". Mean molal activity coefficients, y+* = yireaV'VRT,of the various electrolytes in the resin phase have been calculated after suitable corrections have been made for occlusion of solution on the surface of the resin. Values of y** decrease with decreasing ionic strength, in accordance with the theoretical predict,ions of Katchalsky and Lifson, except in the case of the dihydrogen phosphate ion. The values of y** decrease in the orders NaI > NaC1 > NaH2P04and NaC1 > CaC12 > Lac&, which are the orders obtained in aqueous solutions of the same salts.
Introduction A number of investigators have studied the electrolyte sorption characteristics of ion-exchange resins as a function of the external concentration in a variety of acid, base, and salt systems.'-I2 They have found that, as the external concentration decreases, the mean molal activity coefficient of the electrolyte in the resin phase also decreases, in contrast to the behavior observed in aqueous solutions of strong electrolytes in which activity coefficients approach unity a t infinite dilution. However, as has been pointed out by other worker^,'^-'^ it is possible that the decreases in the values of the activity coefficients (which are calculated by the use of the modified Donnan relationship) with decreasing solution concentration are caused by occlusion of electrolyte on the bead surfaces and by sorption of co-ions by resin impurities. Hence, some of the electrolyte which is found to be present in the resin phase actually is a component of the solution phase. The relative contribu-
tion of such an error naturally increases as the concentration of electrolyte in the external solution decreases, thus producing the observed effect. (1) W. C. Bauman and J. Eichhorn, J. Am. Chem. SOC.,69, 2830 (1947). (2) H. P. Gregor, F. Gutoff, and J. I. Bregman, J. Colloid Sci., 6 , 245 (1951). (3) H. P. Gregor and M. H. Gottlieb, J. Am. Chem. Soc., 75, 3539 (1953). (4) C. W. Davies and G. D. Yeoman, Trans. Faraday SOC.,49, 968 (1953). (5) J. S. Mackie and P. Meares, Proc. Roy. Soe. (London), A232, 485 (1955). (6) G. J. Hills, P. W. M. Jacobs, and N. Lakshminarayanaiah, ibid., A262, 257 (1961). (7) K. A. Kraus and G. E. Moore, J. Am. Chem. SOC.,75, 1457 (1953). (8) M. H. Gottlieb and H. P. Gregor, ibid., 76, 4639 (1954). (9) F. Nelson and K. A. Kraus, ibid., 80, 4154 (1958). (10) J. Danon, J. Phys. Chem., 65, 2039 (1961). (11) N. Lakshminarayanaiah, J. Polymer Sci.. Al, 139 (1963). (12) R. L. Gustafson, J. Phys. Chem., 67, 2549 (1963).
957
RICHARD L. GUSTAFSON
958
In the present study, measurements of sorption of HC1, KaCl, NaI, NaH2P04, CaC12, and L a c & by the appropriate forms of Amberlite XE-100, a polystyrenesulfonate resin which has been cross-linked with 4.8% divinylbenxene (DVB) and Amberlite IR-120, a similar resin containing 8.0% DVB, have been carried out in 0.02-4 m solutions at 25". Corrections have been made for the amounts of electrolyte occluded on the bead surfaces, and mean molal activity coefficients of electrolytes in the resin phase have been calculated,
Experimental Section Resins. Samples of 20-30 mesh Amberlite XE-100 and Amberlite IR-120 polystyrenesulfonate resins which contain 4.8 and 8.0% divinylbenzene (DVB), respectively, were placed in glass columns and treated three times with alternate washings with 1 M HC1 and 1 M NaOH. After exhaustive treatment with the NaOH the resins were washed until the p H of the effluent was equal to that of the influent. Approximately 5 ml of resin was taken for each experiment. The capacities of the resins were determined by conversion of the resins to the hydrogen form, washing with water, displacement of the hydrogen ions by treatment with 1 M NaC1, and titration of the effluent with standard NaOH to a phenolphthalein end point. After the capacity determinations, some of the samples were converted to the calcium and lanthanum forms by exhaustive treatment with the corresponding chloride salts. Equilibrations and Swelling Measurements. The resin samples, approximately 7 mequiv in capacity, were equilibrated for several days with 0.01-3 m HC1, NaCl, NaI, NaH2P04,CaCI2, and Lac& solutions a t 25'. The measurements of resin volumes were carried out pycnometrically, and determinations of the weights of swollen resin were made after centrifugation in a manner similar to that described by Gregor, et all7 The amount of water imbibed by each resin sample was calculated by difference. Measurenzents of Imbibed Electrolyte. The imbibed salts were eluted from the resins by 15-20 washings with deionized water whose resistance was greater than lo6 ohms, and the solutions were made to the desired volumes. Chloride and iodide determinations were carried out coulometrically with the use of an AmincoCotlove chloride titrator. Phosphate analyses were carried out colorimetrically by the method of Rockstein and Herron.l* Some of the eluted salt is present in a liquid film at the surfaces of the beads and must not be included in the calculation of imbibed electrolyte. Corrections for the amount of salt in the liquid film, and in any internal cracks or voids, were determined on the basis of measThe Journal of Phyeical Chemistry
urements of sorption of disodium indigodisulfonate from 0.003 M aqueous solutions. It was assumed that, because of Donnan exclusion of the divalent dye anion, a negligible amount of dye enters the gel phase. Rough calculations, made without consideration of activity coefficients, show that the dye concentration in the gel phase will be in the order of lo-' m. Known quantities of resin were contacted with the dye solutions for 1-2 hr, after which time the resin phases were separated by centrifugation under the same conditions as those employed for all of the experiments, i.e., 3000 rpm for 10 min. After the resin samples were weighed, the dye was eluted with water, the resulting solutions were made to 100 ml in a volumetric flask, and the dye concentrations were determined spectrophotometrically at a wavelength of 605 mp. With the knowledge of the densities and dye concentrations of the solution phase and the volumes of the resins, it was possible to calculate the volumes of solution occluded on the resin surface. See Table I. Table I : Solution Occluded on Resin (ml/mequiv) IR-120
0.00694 0.00732 0.00729 0.00763 Av 0.00730 f 0.00018
XE-100
0.00557 0.00541
0.00549 f0.00008
The results given in Table I correspond to occluded volumes of 0.0286 f 0.0007and 0.0132 f 0.0002 ml/ml of bead in the cases of IR-120 and XE-100, respectively. The greater occlusion by IR-120 is caused by the presence of a greater percentage of surface cracks and fissures in this material. The above corrections apply only to fully swollen resins. The volumes of solution occluded by resins which were equilibrated in salt solutions were calculated by multiplying the above values by a factor equal to the ratio of the surface area of the partially swollen bead to that of the completely swollen resin. It is assumed that the film thickness is equivalent in the salt and dye solutions. The final calculations of activity coefficients are not seriously affected by (13) D. H. Freeman, J . Phye. Chem., 64,1048 (1960). (14) E.Glueckauf and R. E. Watts, Nature, 191, 904 (1961). (15) E.Glueckauf and R. E. Watts, Proc. Roy. SOC.(London), A268, 339 (1962). (16) E. Glueckauf, ibid., A268, 350 (1962). (17) H. P.Gregor, K. M. Held, and J. Bellin, Anal. Chem., 23, 620 (1951). (18) M. Rockstein and P. W. Herron, ibid., 23, 1500 (1951).
DONNAN EQUILIBRIA IN POLYSTYRENESULFONATE GELS
959
Table 11: Values of Mean Molal Activity Coefficients,y**, for Electrolytes in Styrene-DVB Gels a t 25” mcr
111.1
mAr
Y I *
mu
0.1863 0.0538 0.0110 0.0031
0.98 0.88 0.82 0.81
1.636 1.070 0.525 0.256 0.1001 0.0523 0.0258 0.01068
0.655 0.513 0.449 0.461 0.518 0.575 0.643 0.725
CaC12-XE-100 3.33 2.84 2.44 2.25 2.14 2.11 2.09 2.06
1.233 0.711 0.293 0.123 0.0403 0.0191 0.0083 0.0028
0.99 0.77 0.63 0.58 0.54 0.52 0.50 0.48
0.246 0.1140 0.0451 0.0228 0.01129 0.00453
Lac&-XE-100 0.268 1.784 0.306 1.724 1.680 0.419 1.677 0.482 1.672 0.5554 1.666 0.650
0.237 0.1110 0.0445 0.0234 0.0122 0.0051
0.38 0.36 0.39 0.37 0.34 0.31
1.024 0.509 0.203 0.1009 0.0504 0.0204
0.655 0.679 0.732 0.778 0.820 0.872
0.1189 0.0392 0.00831 0.00306 0.00136 0.00067
0.74 0.68 0.65 0.57 0.45 0.28
1.084 0.529 0.208 0.1041
NaH2POk-IR-120 0.456 6.70 6.52 0.556 6.29 0.670 6.24 0.740
0.0952 0.0358 0.0073 0.0020
0.62 0.61 0.65 0.69
1.010 0.493 0.197 0.0993
0.811 0.757 0.767 0.796
HC1-XE-100 3.75 3.37 3.14 3.09
3.275 2.151 1.043 0.521 0.210 0.1039
0.737 0.676 0.655 0.677 0.729 0.778
NaC1-XE-100 6.84 5.63 4.55 4.02 3.67 3.58
1.201 0.672 0.233 0.0791 0.0179 0.0055
0.84 0.75 0.66 0.63 0.60 0.58
3.37 2.25 1.04 0.533 0.207 0.107 0.0521 0.0209
I .032 0.855 0.740 0.725 0.750 0.785 0.818 0.869
NaI-XE-100 7.56 5.99 4.62 4.07 3.70 3.61 3.55 3.50
1.488 0.798 0.242 0.0814 0.0161 0.0048 0.00176 0.00050
1.04 0.88 0.73 0.67 0.64 0.64 0.54 0.43
3.69 2.11 1.00 0.488 0.197 0.0983 0.0501 0.0210
NaHZP04-XE-100 6.08 0.300 0.365 5.17 0.468 4.34 3.91 0.566 3.61 0.675 3.52 0.745 3.46 0.820 3.42 0.869
0.775 0.469 0.1894 0.0702 0.01816 0.00587 0.00193 0.00040
0.51 0.49 0.52 0.53 0.52 0.51 0.50 0.49
small changes in the occluded volume. For instance, a 3% error in this quantity will change a value of y** for NaI sorption by XE-100 from 1.037 to 1.039 in a 3.4 m solution and, in the most sensitive case studied, y** changed from 0.435 to 0.442 in a 0.02 in NaI solution. These errors are small relative to the large variations of y&* which are observed with changes in ionic strength in many cases.
Y i *
the number of anions produced by dissociation of 1 mole of electrolyte, and v is the total number of anions plus cations produced by such dissociation. Values of activity coefficients of the electrolytes were taken from data tabulated by Harned and Owen1gexcept in cases in which the concentration was less than 0.1 m. Here, values were calculated by the use of the Debye-Huckel expression Az +x -p1/2
Results Donnan Equilibria. Mean molal activit,y coefficients of the various salts in the resin phase were calculated by the use of the equatior,
NaCl-IR-120 6.83 6.51 6.27 6.21 6.18 6.17
Yi =
- 1 + dBpcla
where
A =
e3 2.303(Dk5”)
=
0.509
and Here m refers to molality, superscripts r and s refer to resin and solution phases, respectively, P is the partial molar volume of the electrolyte, C and A represent the cationic and anionic component, respectively, VA is
(19) H. 5. Harned and B. B. Owen, “The Physical Chemistry of Electrolytic Solutions,” 3rd ed, Reinhold Publishing Corp., New York, N. Y . , 1958.
Volume YO, h’umber 4 April 1966
RICHARD L. GUSTAFSON
960
&Ne2
’/’
= (1000DkT)
=
3.29 X lo7 a t 25”
The following values of d (in centimeters), the distance of the closest approach, were employed: NaC1, 4.4 X NaI, 4.4 X NaH2P04,4.4 X lo-*; CaC12, 5.2 X and LaC13, 6.5 X The values of “/i*r which are presented in Table 11; include the contribution from the pressurevolume term which is of unknown but presumably small magnitude. The values of the resin phase activity coefficients in Table I1 decrease with decreasing ionic strength, except in the experiments involving sorption of Na€12P04. I n the latter case, the values of y&* in the XE-100 resin remain essentially constant throughout the entire range and actually increase with decreasing concentration in the more highly cross-linked IR-120. As was mentioned earlier, several investigators have shown that, as the external electrolyte concentration approaches zero, the mean molal activity coefficient of the sorbed electrolyte in the resin phase decreases markedly. Freeman13 has shown that constant activity coefficients may be calculated if appropriate corrections are made for the electrolyte which is assumed to be occluded on the bead surfaces and in resin fissures and also for that which is sorbed by resin impurities. I n the present case, an overcompensation may have been made for the amount of occluded electrolyte, for, in the case of KaC1 sorption by XE-100, the amount of salt which was calculated to be occluded was slightly greater than the total amount of salt present in the resin in 0.05 and 0.02 m solutions. n’evertheless, the calculated values of yk* decrease with decreasing ionic strength, indicating that the observed effect is not produced by a failure to recognize the contribution of surface occlusion or adsorption by impurities. The theoretical treatments of Katchalsky and Lifson20and Katchalsky and MichaeliZ1predict such a decrease in the activity coefficient of electrolyte in the resin phase with decreasing concentration, although quantitative agreement has not been found by a number of w 0 r k e r s . 5 ~ ~ ~ ~ ~ ~ ~ ~ The values of the activity coefficients in the resin phases decrease in the order NaI > NaCl > NaH2P04 and XaC1 > CaCIz > LaC4, which are the same orders which are observed in aqueous solutions of the same salts. It is not surprising that the ions which form ion pairs of the Bjerrum type most extensively in aqueous solution should be involved to the greatest degree in ionic interactions in the polyelectrolyte gel. Data concerning the swelling of the various forms of Amberlite XE-100 are shown in Figure 1. As the activity coefficients and osmotic coefficients decrease in the order NaI > NaCl > NaH2P04,the swelIing of the The Journal
of
Physical Chemistry
ms Figure 1. Plots of resin volume us. external salt concentration for various forms of Amberlite XE-100.
resin increases in the order NaI < NaCl < YaH2PO4. The volume of resin also decreases in the order Na > Ca > La. Whereas the degree of swelling of the sodium and calcium salts of Amberlite XE-100 increases with decreasing ionic strength in the usual manner, that of the lanthanum salt is virtually independent of the ionic strength of the external solution. This lack of response of the resin to changes in the osmotic pressure of the external solution is probably produced by the extremely high coulombic attraction (between fixed ions and counterions) which is sufficient to prevent swelling or shrinking.
Discussion In view of the results of this paper, it is of interest to compare the values of activity coefficients of NaCl in various types of resin systems. Such data have been obtained from several sources and are shown in Table 111. All results obtained from Gustafson and Lirio’2,22 are based on data which have been corrected for the effects of surface occlusion. Of the various systems for which data are available, the greatest degree of salt sorption, and hence the lowest values of the activity coefficients, is found in the polymethacrylic acid resin. The high degree of ionic interaction in this case is probably produced by the close proximity of functional groups along the polymer chains, relative to that which is found in polystyrene or phenol-formaldehyde polymers. In order to reduce the greater electrostatic po(20) A. Katchalsky and S. Lifson, J . Polymer Sci., 11, 409 (1953). (21) A. Katchalsky and I. Michaeli, ibid., 15, 69 (1955). (22) J. A. Lirio and R. L. Gustafson, unpublished results.
DONNAN EQUILIBRIA IN POLYSTYRENESULFONATE GELS
tential in the polymethacrylate systems, more electrolyte is imbibed than in the other systems. I n the cases of the Amberlite resins, in which surface occlusion effects have been taken into account, the values of ?A* obtained in quaternary ammonium resin (IRA-400, -401, -410, and -411) are less than those obtained in the sulfonic systems, despite the fact that the distances between charged groups are approximately equivalent for the two resins. Similar results were shown by Gregor and Gottlieb3pSwho found that values of yi* for KC1 in polystyrenesulfonatelO% DVB resins were somewhat higher than those obtained in polystyrenebenzyldimethylethanolammonium-8% DVB resins. The two systems are quite different in the sense that, whereas the sodium and chloride ions are counterions and co-ions in the case of the cation exchanger, the roles of the ions are reversed in the case of the anion-exchange resin. The lack of a self-consistent picture may be shown by comparison of data obtained for the Amberlite anion-exchange resins and Dowex 1-X10. Whereas activity coefficients of 0.49-0.52 were obtained in a 1 m medium in the case of the four former resins, which vary over a considerable range in moisture and cross-linker content, a much higher value of 0.69 may be interpolated from the Dowex 1-X10 data of Nelson and Krausgat the same concentration. Although the contents of the present paper lend support to the view that the extent of ion pairing in the resin phase increases as the concentration in the external phase decreases, an unambiguous solution to the problem of electrolyte sorption has not yet been attained. Freeman, et U Z . , ~ have ~ recently measured the uptake of KC1 and XgC1, by low cross-linked (2% DVB) cation and anion exchangers by the use of a technique which circumvents the problems associated with the presence of the liquid film and have found rather constant values of y** over a 0.002-0.26 m concentration range. It would appear that simultaneous measurements by the Freeman technique and by the conventional method on a series of resin systems would be invaluable in attempting to resolve the problem. Hopefully, identical results will be obtained by the two methods. Armed with undisputedly valid data, the
961
Table 111: Values of Mean Molal Activity Coefficients for NaCl in Various Resin Systems Resin
"sC1'
Y**
Ref
Polymethacrylic acid5% DVB
1.o 0.40 0.10 0.020
0.55 0.43 0.30 0.20
12 12 12 12
Amberlite IRA-400" Amberlite IRA-401" Amberlite IRA-410b Amberlite IRA-411b
1.02 1.03 1.02 1.03
0.52 0.52 0.49 0.50
22 22 22 22
Dowex 1-XlO"
2.24 0.91 0.25 0.100 0.050 0,010
0.73 0.68 0.52 0.39 0.29 0.09
9 9 9 9 9 9
Amberlite XE-100
1.04 0.52 0.21 0.104
0.66 0.63 0.60 0.58
1.02 0.51 0.20 0.101 0.050 0.020
0.74 0.68 0.65 0.57 0.45 0.28
1.02 0.51 0.101 0.0100
0.63 0.54 0.37 0.09
Amberlite IR-120
Phenol-f ormaldehydesulfonate
C C C C C
C C
C C C
11 11 11 11
" Polystyrenebenzyltrimethylammonium chloride-DVB. Polystyrenebenzyldimethylethanolammonium chloride-DVB. This work.
final step should involve a search for a theoretical treatment of co-ion uptake which will be in satisfactory agreement with the experimental data over a wide range of salt concentration and resin composition. (23) D. H. Freeman, V. C. Patel, and T. M. Buchanan, J. Phys. Chem., 69, 1477 (1965).
Volunte 70, Number 4 April 1966
