1361
MEANACTIVITYCOEFFICIENT OF POLYELECTROLYTES absorbancy with time. Furthermore, the observed p H dependence of the reaction (eq 10) was found to be limited to the range of pH >6.0, thus indicating that other protonation equilibria may be involved in more acidic solutions. Considering the above limitations and taking results only from the narrow range of optimum conditions, the thermodynamic equilibrium constant for the reaction in eq 9 was K " , = 0.9 0.1 with AH" = -5.2 f 1.3 kcal/mole and A s " = -18 j-. 5 eu. The wide limits of uncertainty in these results preclude their use in calculating indirectly thermodynamic data for the tris(pyridjne-2-aldoxime)iron(l11-11) couple. The reverse calculation is more meaningful. Thus, taking the data for the above couple as determined experimentally (this paper) together with the data for the
hexacyanoferrate(II1-11) couple as determined experimentally by a similar method2yields for the reaction in eq 9 the following calculated values: Koi = 1.3 f 0.1, AH" = -6.0 f 0.8 kcal/mole, AS" = -19.6 f 2.8 eu. It is noteworthy that although there is an apparent discrepancy between the measured and calculated values of K'i, the enthalpies and entropies are well within limits of uncertainty. The equilibrium constant is clearly very close to unity. I n a sense then, the two redox couples are equivalent. However, whereas pyridine-2-aldoxime complexes have the advantage of small charge and no ion association complications, the hexacyanoferrates have other advantages over the other ligand-they are considerably more stable as complex ions over a wide p H range and are also free from protonation equilibria a t p H >5.
Mean Activity Coefficient of Polyelectrolytes.
VIII.
Osmotic and Activity
Coefficients of Polystyrenesulfonates of Various Gegenions' by Norio Jse and Tsuneo Okubo Department of Polymer Chemistry, Kyoto Unioersity, Kyoto, J a p a n Accepted and Transmitted by The Faraday Society
( J u l y 66, 1967)
The osmotic and mean activity coefficients of polystyrenesulfonates of various gegeiiioiis were investigated by means of the isopiestic vapor-pressure measurements. The order of the magitude of the activity coefficient was H + > Li+ > Na+ > K+, Ca2+ > Ba2+,and N+(n-CdHg) > N+(n-CsH,) > N+(CzH6)4 > N+(CH3)4> N+(CHs)&H2C6H6 > "2. This relative order was accounted for in terms of the structural effects of the ions on water. It was inferred that the polystyreiiesulfonate ion acted as a fairly strong structure former because of the benzene ring. The structure-formingtendency of the polysulfonate ion was suggesbed to be enhanced with increasing concentration, in contrast with the structural influences of simple ions which are so far considered concentration independent. As is well recognized, the mean activity coefficient of electrolytes is a most basic and most important quantity for understanding the thermodynamic properties of the solutions. (In the present work, the mean activity coefficient is discussed, which should not be confused with the single-ion activity coefficient.) For low molecular weight electrolytes, systematic study, experimental and theoretical, on this quantity has been conducted thoroughly, as far as dilute aqueous solutions of 1-1 type electrolytes are concerned. I n the field of high molecular weight electrolytes, however, there is very little information concerning the activity coefficient, the only published data being those measured in aqueous media in this Thus, it is
strongly hoped to extend the experimental work to other polyelectrolyte systems. I n the present paper, we report the results obtained for various salts of a polystyrenesulfonic acid (PSt) in the binary aqueous solutions. The main purpose of this work is to study (1) Part VII: H. Matsui, N . Ise, and T. Okubo, J. Phys. Chem., submitted for publication. (2) N . Ise and T. Okubo, ibid., 65, 4102 (1965). (3) N. Ise and T. Okubo, ibid., 70, 1930 (1966). (4) N. Ise and T. Okubo, ibid., 70, 2400 (1966). (6) N . Ise and T. Okubo, ibid., 71, 1287 (1967). (6) N. Ise and T. Okubo, ibdd., 7 1 , 1886 (1967). (7) T. Okubo, N. Ise, and F. Matsui, J . Am. Chem. floc., 89, 3687 (1967).
Volume 76, Number 4
A p d 1968
1362
NORIOISEAND TSUNEO OKUBO
the specificity of gegenions on the osmotic and activity coefficients of the polyelectrolyte. In the previous workl6the activity coefficients of alkali metal salts of a polyvinylsulfuric acid were found to be in the same order as Gurney’s empirical rule8 predicts. Since this rule was originally found for uniunivalent simple electrolytes, mainly for alkali halides, the observed concordance was considered rather surprising and it, was tempting to ascribe this result t o the low charge density of the polyelectrolyte used. Thus, the measurements are now extended to polystyrenesulfonates having a high charge density. This polyelectrolyte is a strong acid and stable in the acid form, unlike the polyvinyl sulfate, which can easily undergo saponification at low pH’s. Therefore H + can now be included in the series of gegenions.
calculated from the osmotic coefficient by using the Gibbs-Duhem equation In
(Yl*/Y2*)
=
$921
-
PZZ
+
where the suffixes 1 and 2 of the coefficients refer to concentrations nzl and m2, respectively. This relative values of the activity coefficient thus determined was conveniently standardized at infinite dilution. The assumptions involved were that the mean activity coefficients of the various salts of PSt have the same value at infinite dilution, i.e., yo*, and that the cuberoot rule concerning the polymer concentration dependence of the activity coefficient was valid down to infinite dilution. The activity coefficient given in Table 11, (y*/yo*),was thus obtained. Experimental Section The osmotic coefficient observed is, in most cases, Sodium polystyrenesulfonate (KaPSt) of a degree found to increase with increasing concentration, as of polymerization of 2500 was a gift from the Dow seen from Table 11. Furthermore, the osmotic coeffiChemical Co., Midland, Mich. A solution of the cient is influenced sensitively by the gegenions. The KaPSt was passed through a column of cation- and activity coefficient is generally found to decrease with anion-exchange resins to the acid form. Then the increasing Concentration and increase through a miniaqueous solutions of various salts of PSt such as Li-, Ka-, mum. We note here that the trend of decreasing of K-, Ca-, Ba-, XHd-, N(CH3)4-, N(C2H5)4-,Ii7(n-C3H7)4-, the activity coefficient is representable by the cube-root N(n-CJIQ)d-, and N ( C H ~ ) ~ ( C H ~ C G Hwere B ) Pprepared S~ rule, which has been found to hold for some polyelectroby neutralization with aqueous solutions of the corresl y t e ~ , ~ -but ’ the range of fit of the rule is confined to ponding hydroxides. lower concentrations for the polystyrenesulfonates, Osmotic and activity coefficients were determined by because strong solvent-solute interaction exists in the the isopiestic vapor-pressure measurements at 25 =t present cases, as will be shown. The magnitude of the 0.005’ with an apparatus employed earlier.’ The activity coefficient is in the order reference electrolyte was potassium chloride. The experimental error of the present isopiestic measureH + > Li+ > N a + > E(+ (A) ments was at highest 1.0% of the concentration value, Ca2+ > Ba2+ (B) which was estimated from the duplicate or repeated runs. This order of error was considered gratifying and in the light of rather large uncertainty inherent in N+(~-C~HQ >)N+(n-C3H7)4 A > K+(CzH5)4 > the determination of polyelectrolyte concentration. N+(CH3)4 > K + ( C H ~ ) ~ C H & ~>HKH4+ B (C)
Results and Discussion
The concentrations at isopiestic equilibrium are given in Table I. The osmotic and activity coefficients for the polystyrenesulfonates were tabulated in Table 11. The practical osmotic coefficients of the polysalts (pz)were evaluated by using the relation ‘Pz = 2mKCl(PKCl/(Z/ZBg
$. 1)(m/g)
(1)
where m K C l is the molality of reference potassium chloride solution, m the concentration of the polysalts (equiv/1000 g of water), x the stoichiometric valency of the macroion, 2, the valency of gegenions, and PKCl the osmotic coefficient of KC1 at mKC1. It should be noted that the osmotic coefficient dealt with in the present paper is the one defined on the basis of the stoichiometric number of ions, not of the free ions. The (PKC1 values were obtained from l i t e r a t ~ r e . ~The activity coefficients of polystyrenesulfonates, y*, were The Journal of Physical Chemistry
One explanation for this specificity would be possible in terms of the specific way in which the structure of water may be altered by the ions, as suggested by Frank.lo I t has been shown that the concepts of the structural salting-out and salting-in can explain the positions of activity coefficient--concentration curves, if the relative strengths of the influences are postulated. Specifically the salting-out results in the highlying curves, whereas the salting-in results in the lowlying ones. If one accepts this interpretation, it would be possible to infer the most important structural factor from the experimentally found orders: A, B, (8) R. W. Gurney, “Ionic Processes in Solution,” McGraw-Hill Book Co., Inc., New York, N. Y., 1953, Chapter 16. (9) R. A. Robinson and R. H. Stokes, “Electrolytes Solutions,” Butterworth and Co. Ltd., London, 1959, pp 476, 481. (10) H. S. Frank, J. Phus. Chem., 67, 1554 (1963); Z. Physik.
Chem., 228, 364 (1965).
1363
;\I EAK ACTIVITYCOEFFICIENT OF POLYELECTROLYTES Table I : Concentrations of Isopiestic Solutions of Potassium Chloride and Polystyrenesulfonats a t 25' --HPS
-------LiPSt----
t-equiv/ 1000 g
mmi, m
equiv/ 1000 g
mmi,
0.152 0.213 0.271 0.344 0.555 0.868 1.85
0.360 0.469 0.572 0.649 0.848 1.07 1.66
0.0841 0.0851 0.109 0.115 0.154 0.160 0.232 0.297 0.370 0.411 0.562 0.815 0.979 1.48 1.85 3.23
0.217 0.225 0.285 0.303 0.377 0.395 0.503 0.582 0.673 0.709 0.850 1.05 1.18 1.48 1.74 2.19
0.0460 0.0492 0.0637 0.0817 0.0926 0.104 0.115
-CaPSt-
-KPSt--.
m
0.148 0.160 0.249 0.414 0.424 0.565 0.580 0.815 0.880 1.85
-N(CzHs)aPStm,
m,
m
equiv/ 1000 g
mKci, m
equiv/ 1000 g
mKc1, m
equiv/ 1000 g
0.0417 0.0516 0.0595 0.0851 0,109 0.115 0.154 0.160 0.232 0.253 0.297 0.370 0.411 0.562 0.815 0.979 1.48 1.85 3.23
0.115 0.159 0.190 0.259 0.324 0.337 0.422 0.437 0.548 0.590 0.661 0.757 0.811 0.990 1.28 1.40 1.85 2.07 2.59
0.0560 0.0689 0.0752 0.0892 0.113 0.123 0.144 0.180 0.269 0.321 0.472 0.493 0.779 1.85
0.187 0.219 0.241 0.272 0.327 0.354 0.402 0.473 0.616 0.684 0.859 0.889 1.18 1.83
0.0468 0.0516 0.0595 0.0851 0.109 0.115 0.154 0.160 0.232 0.297 0.370 0.411 0.562 0.815 0.979 1.48 1.85 3.23
0.130 0.157 0.180 0.243 0.305 0.315 0.394 0.409 0.523 0.613 0.710 0.756 0.907 1.09 1.23 1.49 2.11
0.0695 0.0841 0.115 0.160 0.232 0.297 0.370 0.411 0.562 0.813 0,979 1.48 1.85 3.23
0.156 0.197 0.265 0.349 0.450 0.536 0.623 0,673 0,780 0.978 1.09 1.38 1.52 1.91
0.0817 0.0841 0.0926 0.104 0.115 0.148 0.160 0.249 0.253 0.269 0,280 0.411 0.424 0.565 0.580 0.815 0.880
0.0349 0.0369 0.0464 0.0470 0.0623 0.0592 0.0661 0 0731 0.0901 0.113 0.124 0.154 0.274 0.682 1.58
0.122 0.129 0.154 0.158 0.172 0.192 0.211 0.229 0.267 0.346 0,379 0.454 0,706 1.29 1.96
equiv/ 1000 g
mmi,
0.143 0.157 0.198 0.250 0.291 0.320 0.334 0.419 0.440 0.587 0.801 0.832 0.996 1.01 1.23 1.29 1.99
1.67
---BaPSt--.--.. m,
m,
m,
(CHa)rPSt---.
m,
m,
mKci m
-N
-NHaPSt--
----NaPStm,
m,
mmi, m
esu:v/ 1000 g
mKci, m
equiv/ 1000 g
~KCI,
m
equiv/ 1000 g
0.0460 0.0492 0,0637 0.0817 0.0926 0.104 0.148 0.249 0.253 0.269 0.280 0.411 0.424 0.580 0.815 0.880 1.85
0.154: 0.170 0.214: 0.269 0.304 0.331 0.439 0,623 0.621 0.677 0.683 0,908 0.899 1.12 1.39 1.47 2.34
0.0349 0.0369 0.0464 0.0470 0.0523 0.0592 0.0661 0.0731 0.0901 0.113 0.124 0.154 0.274 0.682 1.58
0.177 0.189 0.226 0.236 0.256 0.282 0.311 0.339 0.397 0.505 0.552 0.638 0.912 1.45 2.11
0.0447 0.0560 0.0689 0.0752 0.0892 0.113 0.123 0.144 0.180 0.269 0.321 0.411 0.472 0.493 0.779 1.85
0.242 0.271 0.308 0.348 0 395 0.484 0.551 0.672 0.864 1.19 1.40 1.58 1.80 1.88 2.61 3.45 I
0.156 0.167 0.190 0.216 0.228 0.293 0.304 0.413 0.415 0.468 0.462 0.603 0.604 0.721 0.737 0.911 0.945
and C. As is duly supported by the partial molal most weakly, provided that this effect outweighs the entropy data,ll the structure-forming tendency deself-salting-in of cation by cation and of anion by anion. creases in the order H+ > Li+ > Na+ > K+. The I n other words, the polystyrenesulfonate ion would hydronium ion is the strongest structure former in this have to be either a strong structure breaker or a strucseries. Also Ca2+ has a smaller entropy value than ture former of a mode incompatible with the cations. Ba2+. For the aliphatic organic cations, the more The first possibility may be excluded from further carbon atoms surrounding the nitrogen, the more consideration, since the polystyrenesulfonate ion hydrophobic and stronger structure former these cations has a large hydrocarbon tail (benzene ring), which will be.12 I n other words, the strength of the strucwould promote the water structure.13 The partial H ~ ) ~molal entropy of HS03- is reported to be +32.6 eu ture-forming tendency is in the order: ? ; + ( ~ L - C ~> N + ( ~ L - C ~ H> , ) ~S+(C2Hs)4 > N+(CH3)4 > KH4f. Then, the polystyrenesulfonate ion would be ex(11) Reference 8, p 267. (12) H. S. Frank and W, Y. Wen, Discussions Faraday Sac., 24, pected to salt-out hydronium, calcium, and tetra133 (1957). butylammonium ions most strongly, in the respective (13) G . NBmethy and H. A. Soheraga, J . Chem. Phys., 36, 3401 series, and potassium, barium, and ammonium ions (1962). Volume 78, Number 4 April 1968
1364
KORIOISEAND TSUNEO OKUBO
Table TI : Osmotic and Activity Coefficients of Polystyrenesulfonates a t 25" NaPSt log Q2
1 2 3 4 5 6 7 8 9 10 11 12 13 14
1 2 3 4 5 6 7 8 9 10 11 12 13 14
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.2 1.4 1.6 1.8 2.0
0.562 0,566 0.602 0.651 0,699 0.744 0,794 0.834 0,880 0.96 1.05 1.14 1.23 1.32
0.786 0.841 0.918 1.01 1.12 1.23 1.35 1.57 1.78 1.97
-0.601 -0.680 .- 0.714 -0.714 -0.730 -0.726 -0.720 -0.717 -0.702 -0.668 -0.629 -0.589 - 0.552 -0.512
0.705 0.747 0.830 0.921 1.01 1.12 1.22 1.32 1.52 1.70 1.85 2.00 2.38
0.001 0.002 0.015 0,050 0.101 0.159 0.223 0.344 0.471 0.612
0,800 0,828 0.850 0,880 0.936 1.00 1.08 1.16 1.35 1.61 1.88 2.18 2.50
(on a scale of zero for a proton),ll comparable with +26.4 eu for NH4+, which is believed not to alter greatly the water structure.14 Thus, we may expect that the structural influence of the polystyrenesulfonate ion is determined by that of the benzene ring. I n other words, this ion is structure forming. It would furthermore be accepted that the water structure around the inorganic cations is different from that in the vicinity of polystyrenesulfonate Also, the organic cations tend to enhance the cage-like structure, whereas the polystyrenesulfonate ion may interact with OH groups in water molecules through the intermediary of T electrons of the benzene ring,l6'l7so that the orientation of water molecules in contact with the benzene ring is largely restricted. Thus the polystyrenesulfonate ion influences mater structure in a different way from the other inorganic and organic cations. I n the light of the interaction between OH groups and T electrons just mentioned, it may be inferred that the aromatic hydrocarbons are weaker structure formers than the aliphatic ones.l3 Therefore, the relative position of trimethylbenzylammonium ion and tetraThe Journal of Physical Chemistry
-0.437 -0.464 -0.439 -0.405 -0.362 -0.314 -0.260 -0.207 -0.097 0.018 0.134 0.242 0.396
-0.239 -0,250 -0.263 -0.265 -0.249 -0.217 -0.173 -0.125 -0.006 0.131 0.293 0.479 0.685
0.604 0.600 0.648 0.709 0,780 0.828 0.902 0.960 1.03 1.16 1.29 1.42 1.55 1.69
0.833 0.820 0.804 0.794 0.792 0.792 0.792 0,800 0.822 0.834 0.924 0.946 1.04
-
("/*/YO*)
-0.503 -0.577 -0.602 -0.604 -0.595 - 0 . ,376 -0.&51 -0.536 -0.506 -0.431 -0.368 -0.289 -0.221 -0 129
-0.302 -0.323 -0.335 -0.367 -0.392 -0.413 -0.421 -0.421 -0.427 -0.433 -0.412 -0.382 -0.370
methylammonium ion, in the observed order, can be accounted for by the structural factor of the benzene ring in the former, which would cause a less efficient salting-out (or a more efficient salting-in) between the cation and polyanion. It would then be interesting to compare the polystyrenesulfonate ion with other macro- and simple anions in relation to their structural influences. Figure 1 shows the osmotic coefficients of sodium polystyrenesulfonate (NaPSt), sodium polyethylenesulfonate (NaPES), and sodium polyacrylate (NaPAA) . (The osmotic coefficient cnn be more conveniently used for comparison between polyelectrolytes and simple electrolytes than the activity coefficient of the solute, since yo*, the limiting value of the activity coefficient, cannot uniquely be determined for polyelectrolytes at present.') The data of KaPES have been obtained in this (14) P. hf. Vollmar, J . Chem. Phys., 39, 2236 (1963). (15) W.-Y. Wen, S. Saito, and C. Lee, J . Phys. Chem., 70, 1244 (1966). (16) I. M. Goldman and R. 0. Crisler, J,Org. Chem., 23,751 (1958). (17) M. Oki and H. Iwamura, Bull. Chem. Soc. Japan, 33, 717 (19fN).
1365
MEANACTIVITY COEFFICIENT OF POLYELECTROLYTES
P N ( C H d 4 P S t log (P,
0.594 0.621 0.633 0.709 0.788 0.864 0.940 1.01 1,06 1.21 1.37 1.57 1.81
-0.851 -0.904 -0.936 -0.939 -0.927 -0.916 -0.898 -0.877 -0.849 -0.801 -0.738 -0.672 -0.618 -0.570
0.593 0.622 0.654 0.711 0.785 0.842 0.905 1.00 1,02 1.11 1.22 1.82 1.92 1.61
1 2 3 4 5 6 7 8 9 10 11 12 13 14
(r*/ro*)
-0.429 -0.481 -0.511 -0,516 -0.515 -0.493 -0.462 -0.432 -0.401 -0.335 -0.228 -0.118 0.013
0.632 0.670 0.733 0.784 0.864 0.932 1.01 1.11 1.20 1.41 1.65 1.92 2.23 2.60 YN
-0.393 -0.448 -0.462 -0.458 -0.429 -0.410 -0.379 -0.337 -0.283 -0.181 -0.040 0.130 0.321 0.522 (CHs)sCHzCaHsPS-t log
(r*/ro*)
9 2
-0.352 -0.392 -0.373 -0.339 -0.301 - 0,255 -0.178 -0,113 -0.044 0,088 0.262 0.534 1.02
0.790 0.824 0,888 0,958 1.05 1.15 1.27 1,38 1.50 1.74 2.01 2.32 2.72
1 2 3 4 5 6 7 8 9 10 11 12 13
2,
I
I
I
10
15
0.900 0.962 1.03 1.12 1.24 1.34 1.47 1.60
x - -w
0
1
05
m (equiv/1000gI
20
Figure 1. Osmotic coefficients of aqueous solutions of polystyrenesulfonate, polyethylenesulfonate, polyacrylate, and ethylberixenesulfonates at 25’ : (1) sodium polystyrenesulfonate, (2) lithium ethylbenxenesulfonate, (3) sodium ethylbenzenesulfonate, (4) sodium polyacrylate, and ( 5 ) sodium polyethylenesulfonate.
laboratory,18and those of iYaPAA have been calculated from published values of the osmotic coefficient defined on the basis of the number of free ions.5 These three macroions have approximately the same (linear) charge density. It is seen from Figure 1 that the osmotic coefficient is strongly influenced by the nature of the macroions. According to the structural explanation mentioned above, the experimental results
-0.325 -0.322 -0.284 -0.243 -0.177 -0.099 -0.027 0.050
0.582 0.613 0.610 0.638 0.672 0,705 0.742 0.780 0.818 0.894 1.00 1.14 1.29
-0.471 -0.530 -0.579 -0.606 -0.620 -0.623 -0.632 -0.637 -0.630 -0.602 -0.549 -0.480 -0.401
show that the salting-out effect between polystyrenesulfonate ions and sodium ions is stronger than between polyethylenesulfonate ions and sodium ions. It is reasonable to ascribe the difference to the hydrocarbon tail ( L e . , benzene ring) present in the polystyrenesulfonate ion, which has a structure-forming tendency as mentioned above, since the sodium ion can be considered a structure former. The relative position of the osmotic coefficients of XaPAA and NaPES at higher concentrations can be accounted for by the stronger structure-forming nature of the former, which is supported by the smaller entropy value for CHBCOO- (about 15 eu6) than that for HSOa- (about 32 eu). Further remarks appear necessary with regard to differences between macroions and simple ions. I n Figure 1, the osmotic coefficients of sodium and lithium salts of p-ethylbenzenesulfonic acid (EBS) l9 are presented. The coefficient of LiEBS is larger than that of NaEBS. This indicates either the structure(18) N. Ise and K. Asai, J. Phys. Chem., in press. (19) S. Lindenbaum and G. E. Boyd, ibid., 71, 681 (1967). Volume 72,Number 4
April 1968
NORIOISEAND KIYOTSUGU ASAI
1366 breaking nature of ethylbenzenesulfonate ion or the presence of an ordered structure around this ion, which is formed in an incompatible way with that around the cation. Clearly the second possibility is acceptable, since this is in accord with the previously concluded structural influence of polystyrenesulfonate ion. However, the osmotic coefficient of NaPSt increases with increasing concentration, whereas that of NaEBS decreases; accordingly, a crossing appears. It is believed that the structural influence of the polyanion sharply varies with concentration, whereas that of the simple anion does not. We propose that the polyanion becomes progressively structure forming with rising Concentration. This would be plausible because two benzene rings in the polystyrenesulfonate ion (probably neighboring ones) could fix water molecules by hydrogen bonding involving n electrons in a cooperative manner. Such a sandwich-type structure could be more easily formed at higher concentrations than at lower ones, as a consequence of concentration dependence of the chain configuration. The fact that the structural effects of NaEBS and also of NaPES are concentration insensitive can be accounted for by the above interpretation: for NaEBS, the hydrogen
bond is not strong enough to link two benzene rings of independent molecules through the intermediary of water molecules; and NaPES lacks the benzene ring. It is to be remarked that the structure-forming nature of polystyrenesulfonate ion was also concluded from the solubility measurement.20 The argument presented in the above paragraphs has been based on the structure concepts which have been originally developed for simple electrolytes. If it can be regarded as successful also in the case of polyelectrolytes, it should be noted that the ad hoc postulates, e.g., gegenion association by macroions, have been unnecessary, at least as far as the osmotic and activity coefficients and polystyrenesulfonates are concerned. Though the association does really take place, our results show that the structural factor is of primary importance.
Acknowledgment. The sodium polystyrenesulfonate was kindly furnished from the Dow Chemical Co., Midland, Mich., by courtesy of Drs. W. N. Vanderkooi and
5. C. Moore. (20) J. Steigman and J. L. Lando: J . Phys. Chem., 69, 2896 (1966).
Mean Activity Coefficient of Polyelectrolytes.
IX.
Activity Coefficients
of Polyethylenesulfonates of Various Gegenionsl by Norio Ise and Kiyotsugu Asai Department of Polymer Chemistry, Kyoto University, Icyoto, J a p a n
(Received October $0, 1967)
The osmotic and activity coefficients of polyethylenesulfonates of various gegenions in aqueous media have been determined at 25' by means of isopiestic vapor pressure measurements. The polysalts of inorganic gegenions such as H+, Li+, Na+, and K + have comparatively small osmotic coefficients. The activity coefficients of these salts decrease linearly with the cube root of polymer concentration, up to about 1 equiv/1000 g of water and decrease in the order H > Li > Na > K. The osmotic coefficients of tetraalkylammonium salts have large values and increase with increasing concentration. The magnitude of the activity coefficient is in the order N ( T I - C ~ H >~N(n-C3H,)4 )~ > N(CzHd4 > N(CH2)d > N(CHI)~CH&~H~ > "4. These relative orders are the same as the ones found for polystyrenesulfonates and are accounted for in terms of the structural effects of the ions on water. It is inferred that the polyethylenesulfonate ion is a structure former.
Introduction In a previous paper, the (mean) activity coefficients of polystyrenesulfonates of various gegenions have been determined by the isopiestic vapor pressure measurements.2 The mean activity coefficient to be discussed in the present work should be carefully disThe Journal of Physical Chemistry
tinguished from the single-ion activity coefficient having no sound thermodynamic basis. The results have shown that the polystyrenesulfonate ions could (1) Presented at the 16th Symposium of Polymer Sciences, Fukota, ~ ~ ~ . - ~ . Oct 1967, (2) N . Ise and T. Okubo, J. Phys. Chem., 72, 1361 (1968).
J
