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, Japan
(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 polystyrenesulfonatesand 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
MEANACTIVITYCOEFFICIENT OF POLYELECTROLYTES form an ordered structure of water. This ability has been ascribed to the presence of benzene rings. I n order to study whether this conclusion is of general validity, we extend the measurements to polyethylenesulfonate. This material lacks the benzene ring, so one might expect much weaker solvent-solute interaction than in the polystyrenesulfonate case. Another purpose of this work is to investigate the specificity of various gegenions in the osmotic and activity coefficients. I n previous publications, the specificity of gegenions observed for polystyrenesulfonates2 and polyvinyl sulfates3 could successfully be accounted for in terms of the structural influences of the ions on ~ a t e r . ~ Though -~ the explanation appears to be reasonable, it is not yet cogent enough to lead us to the recognition of the basic similarity between polyelectrolyte and simple electrolyte solutions, since the structural factor of the ions mas found originally for simple electrolyte solutions. Thus it is interesting to accumulate further experimental data for various polyelectrolyte systems. Experimental Section Sodium polyethylenesulfonate (NaPES) was a gift from the Hercules Powder Co., Wilmington, Del. The degree of polymerization was 770 by viscometry. An aqueous solution of this salt was passed through a column of cation- and anion-exchange resins to the acid form. Then the aqueous solutioris of various salts, such as Li-, Sa-, K-, iSH4-, N(CH3)4-, N(C2H6)4-, N(n-C3H7)4-,N(n-C4H9)4-,and N(CH3)3(CH2C6H6)PES, were prepared by neutralization with aqueous solutions of the corresponding hydroxides (reagent grade). The elementary analyses of the final products showed that the sodium contents were within the range of the experimental error. The analyses indicated that the lithium, potassium, tetraethylammonium, and tetrabutylammonium salts were hydrated with 0.78, 0.39, 8.8, and 9.3 molecules of water/base molecule, respectively. Taking into account these hydration numbers, the degree of sulfonation was determined as 0.99. Osmotic and activity coefficients were determined by the isopiestic equilibration method at 25 =t 0.005' with an apparatus described before.7 The reference electrolyte was potassium chloride. The experimental error of the present measurements was, at the highest, 2% of the concentration value. Results and Discussion The measured concentrations of the solutions of PES salts and potassium chloride in isopiestic equilibria are listed in Table I. The practical osmotic coefficient of the polyelectrolyte (&) was calculated by the condition of the equal solvent vapor pressure, Le. (62
= 2mKCIdKCI/(Z/Z2g
+ 1)(m/z>
(1)
1367
Table I : Isopiestic Concentrations of Potassium Chloride and Polyethylenesulfonates at 25'" mKcl
H
Li
"KC1
Na
0.0309 0.0362 0.0461 0.0502 0.0587 0.0715 0.0914 0.117 0.147 0.224 0.299 0.557 0.896
0.286 0.306 0.340 0.360 0.404 0.472 0.574 0.698 0.827 1.13 1.40 2.07 2.78
0.288 0.311 0.354 0.374 0.419 0.488 0.602 0.736 0.878 1.19 1.51 2.25 3.08
0.0337 0.0391 0.0437 0.0523 0.0611 0.0747 0.0988 0.106 0.129 0.138 0.213 0.226 0,350 0.451
0.268 0.288 0.333 0.397 0.469 0.586 0.777 0.894 1.12 1.13 1.91 2.04 3.35 3.84
mKCl
NH4
0.0732 0.177 0.239 0.386 0.520 1.20 1.42
0.274 0.592 0,763 1.09 1.33 1.91 2.03
mKCl
K
0.0455 0.0634 0.0837 0.134 0,173 0.245 0.365 0.584
0.432 0.594 0.790 1.35 1.79 2.69 4.16 6.09
N(CHs)sN(nCHaCsHs N(CHa)a N(CzHs)r CsHi)a 0.205 0.285 0,502 0.716 0.885 1.45 1.58
0.204 0.374 0.482 0.669 0.817 1.31 1.43
0.202 0.357 0.4.56 0.626 0.756 1.20 1.32
0.195 0.334 0.410 0.549 0.659 1.04 1.14
N(nC~HP)~ 0.185 0.304 0.382 0.515 0.622 1.02 1.13
a rn1Cc1 is in molality; polysulfonate concentration is in equiv/ 1000 g of water.
where W L K C ~is the molality of the reference potassium chloride solution, m is the concentration of polyethylenesulfonate (equiv/1000 g of water), 2 is the stoichiometric valency of the macroion, Z 2 , is the valency of gegenion, and ( ~ K c I is the practical osmotic coefficient of potassium chloride solution. The activity coefficients of the polyelectrolytes (y*) were calculated by using the Gibbs-Duhem equation In
(YI*/YZ*)
=
(6zl
- (622
+
where the subscripts 1 and 2 correspond t o in1 and m2, respectively. The osmotic coefficients of various polyethylenesulfonates are given in Figures 1A and 1B. Evidently, the 9, values of the sulfonates having inorganic gegenions are small compared to those of salts of organic cations. In the concentration range studied, 92 of KPES is smaller than 0.2, whereas the coefficient ex(3) N.Ise and T. Okubo, J . Phgs. Chem., 71, 1886 (1967). (4) H. S. Frank and W. Y . Wen, Discussion Faraday SOC.,24, 133 (1957). (5) H. S. Frank, J. Phys. Chem., 67, 1554 (1963). (6) H. S. Frank, 2. Phys. Chem. (Leipzig), 228, 364 (1965). (7) T. Okubo, N. Ise, and F. Matsui, J. Amer. Chem. Soc., 89, 3697 (1967). Volume 72,Number 4 April 1968
1368
NORIOISEAND KIYOTSUGU ASAI
2.0
-
1.0
-
4
0.0
I 0
I
I
,
0.5 1.0 m, equiv/1000 g.
1
1.5
0.5
Figure 1A. Osmotic coefficients of aqueous solutions of polyethylenesulfonates a t 25": 1, N ( T L - C ~ H ~2,) ~N(n-CaH,)a; ; 3, N(CzHd4; 4, N(CHs)4; 5, I\;(CH~)~CH&OHS; 6, "4.
I
I
1.0 d/a.
1.6
Figure 2. Activity Coefficientsof polyethylenesulfonic acid and its alkali salts as a function of the cube-root of polymer concentration a t 25': 1, H : 2, Li; 3, Na; 4, K.
0.6 0.4
4 0.2
0.0
0
1 2 m, equiv/1000 g.
3
Figure 1B. Osmotic coefficients of aqueous solutions of polyethylenesulfonates a t 25': 7, H ; 8, Li; 9, Na; 10, K.
ceeds over unity frequently for organic cations. Furthermore, the osmotic coefficient increases with increasing polymer concentration, except for the sodium and potassium cases. For H-, Li-, Na-, and KPES, the relative value of the activity coefficient (y1*/y2*) obtained by eq 2 was standardized to yo* at infinite dilution by using the cube-root relation, as bef01-e.~ The final results denoted by y*/yo* are given in Figure 2 as a function of the cube root of polymer concentration. Clearly the cube-root rule is valid for these salts at low concentrations. The slopes of the straight lines are -1.03, - 1.09, - 1.25, and - 1.32, for H-, Li-, Na-, and KPES, respectively. The activity coefficient is seen to be in the order
H + > Li+ > Na+ > K+
(A)
This order is the same as found for HzO-polystyrenesulfonate. As for the alkali metal ions, the same order was found for polyvinyl sulfate in water.3 The slope values are found to be larger than those observed previously for lithium-, sodium-, and potassium polyvinyl sulfate (ranging from -0.60 to -0.973). This difference is, however, in accord with our previous finding8 that the magnitude increases with increasing (linear) charge density of the macroion, since the degree of esterification of the polyvinyl sulfate was only 0.227 whereas the degree of sulfonation of the PES almost 1.0. From Figure 2, the upper bound of the range of fit of the rule is about 1 equiv/1000 g of water for all salts. It should be remarked that this value is approximately equal to the ones reported for sodium The Journal of Physical Chemistry
polyacrylate9 and polyethylenimine salt'O but is much larger than that observed for simple electrolytes (e.g., 0.10 mol/l. for XaCl1*). Furthermore, the upper bound for the PES is much higher than that observed for polystyrenesulfonates (0.3 equiv/1000 g of water). The reason for this is the strong solvent-solute interaction in the latter case, as mentioned above. For polyethylenesulfonates of organic gegenions, on the other hand, the activity coefficient increases with increasing concentration. In other words, the cuberoot rule does not apply for these salts in the concentration range studied. As a consequence, the standardization could not be carried out at infinite dilution by using the cube-root relationship. Thus the activity coefficient was expediently standardized at 0.2 equiv/ 1000 g of water and was denoted as ?*/yo 2*. Figure 3 is the graphical presentation of the activity coefficient thus determined. The activity coefficient is seen to be in the order N+(n-C4H9)4 > Nf(n-C3H7)4 > N+(CsH5)4 >
N+(CH3)4 > iY+(C€I3)3CHzCBHb> XH4f
(13)
We note here that an ambiguity is associated with the order because of the absence of experimental data in the more dilute region. In the light of the osmotic coefficient data given in Figures 1A and l B , however, the subsequent discussion appears to be meaningful. Furthermore, it should be remembered that the activity coefficients of polystyrenesulfonates2 decrease in the same order as found in the present work. According to the theory of structural influences of ion^,^-^ the salting out between ions causes large osmotic and activity coefficients, whereas the salting in causes small ones. Thus the data given in Figures 1A and 1B indicate that the salting-in effect is strong in the (8) N . Ise and T.Okubo, J. Phys. Chem., 69, 1930 (1966). (9) N . Ise and T. Okubo, ibid., 71, 1287 (1967). (10) N. Ise and T. Okubo, ibid., 70, 2400 (1966). (11) H. S. Frank and .'l T. Thompson, "The Structure of Electrolytic Solutions," W. J. Hamer, Ed., John Wiley and Sons, New York, N. Y . , 1959.
1369
MEANACTIVITY COEFFICIENT OF POLYELECTROLYTES
L
0
0.5
1.0
1.5
m, equiv/1000 g.
Figure 3. Activity coefficients of polyethylenesulfonates having large organic gegenions a t 2 5 O : 1, N(n-C4Hg)a; 2, N(n-CJ37)a; 3, N(CzHs)a; 4, N(CHa)a; 5, N(CH3)3CH2CeHs; 6, "4.
2.0
I
0
0.5
'A' 1
I
1.0
0
0.5
1.0
1.5
m, equiv/1000 g.
Figure 4. Osmotic coefficients of aqueous solutions of polystyrenesulfonates, polyethylenesulfonates, and polyacrylates a t 26'. 1, sodium polystyrenesulfonate; 2, sodium polyacrylate; 3, sodium polyethylenesulfonate; 4, tetrabutylammonium polyethylenesulfonate; 5, tetrabutylammonium polystyrenesulfonate; 6, ammonium polystyrenesulfonate; 7 , ammonium polyethyleiiesulfonate.
cases of inorganic gegenions, whereas the salting-out effect is predominant for the PES having organic gegenions. Since the inorganic cations under consideration are structure forming in the order H + > Li+ > Xa+ > K+,12the experimental data suggest that the PES ion should be also a structure former of a mode compatible to that of these gegeni~ns.'~Because the PES anion does not contain benzene rings, it is not structure producing to the same extent as the PSt ion. However, in view of the ionic entropy value of HS03- (+32.6 eui2) being close to that of KH4+ (+26.4 euizj, which is considered not to alter the water structure muchJ14 the PES ion can be regarded as a structure former. Furthermore, it would be admitted that the sulfonate group of the PES ion and the inorganic cations immobilize water molecules around themselves by the electrostatic action so that they make a similar water
structure and, accordingly, can strongly salt in each other. The stronger salting-in effect in the PES systems than in the PSt cases is understandable in the light of hydrophobic nature of the benzene ring in PSt ions and is clearly demonstrated in Figure 4 (left). It is seen that sodium polyacrylate having hydrophilic carboxylate groups also exhibits a marked salting-in effect. Unlike the inorganic cation, the organic gegenions are hydrophobic and tend to make the "cage-like" structure of water.4 Thus the mode of structure making by these large gegenions is incompatible with that by the PES ion. Furthermore, the structuremaking tendency is enhanced with increasing numbers of carbon atoms around n i t r ~ g e n . ~Thus the PES anion salts out tetrabutylammonium ion most strongly, as is shown in Figure 1A. The relatively weak saltingout effect in the trimethylbenzylammoniurn case, as demonstrated in Figure lA, can be accounted for by the less strong structure-making ability of the aromatic (benzene) group than an aliphatic one.16 The weakest effect for the ammonium salt is due to the inability of this gegenion to alter the water structure. Comparison between the alkylaminonium polyethylenesulfonate and polystyrenesulfonate invites some comments. We note that these two kinds of macroions and also the tetraalkylammonium ions being considered are structure formers. The mode of structure formation by these gegenions is less incompatible with that of the PSt anion'than that of the PES anion because of the hydrophobicity of the former anion. Accordingly, a weaker salting-in (or stronger salting-out) effect can be expected in the PES cases. This is substantiated experimentally as shown in Figure 4 (right). (Compare curves 4 and 5.) For ammonium salts, on the other hand, the relative order of 4zis reversed (curves Since 6 and 7) ; NH,PSt has larger cbz than ",PES. the ammonium ion has little influence on water structure, as mentioned above, and the PSt anion is a stronger structure former than the PES anion, the ammonium ion may be expected to salt out the PSt ion more strongly than the PES ion.
Acknowledgments. The sodium polyethylenesulfonate mas kindly furnished from the Hercules Powder Co., Wilmington, Del., by courtesy of Dr. D. S. Breslow. (12) R. W. Gurney, "Ionic Processes in Solution," iMcGraw-Hill Book Co., Inc., New York, N. Y., 1953, Chapter 16. (13) W.-Y. Wen, S. Saito, and C. Lee, J . Phys. Chem., 70, 1244 (1966). (14) P. M. Vollmar, J. Chem. Phys., 39, 2236 (1963). (15) G. NBmethy and T I . A . Scherags, ibid., 36, 3401 (1962).
Volume 72, Number 4
April 1968
