NORIO ISEAND TSUNEO OKUBO
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The parameter v/rO3 can be replaced by Proa/eo and correspondingly, V / V , by PV,/RT,, but not, without some loss of accuracy, by P/Polcontrary to current practice. These results may be carried over readily to any
bulk property which has been put into the appropriate reduced form. Acknowledgment. The author is grateful to the Faculty Research Committee of Michigan Technological University for financial assistance.
Mean Activity Coefficient of Polyelectrolytes.
V.
Measurements of
Polyvinyl Sulfates of Various Gegenions
by Norio Ise and Tsuneo Okubo Department of Polymer Chemistry, Kyoto University, Kyoto, Japan
(Received November 17, 1966)
The mean activity coefficients of various salts of polyvinyl sulfuric acid (PVAS) have been determined by the isopiestic vapor pressure measurements. It has been found that the logarithm of the mean activity coefficient decreases linearly with the cube root of polymer concentration up to 0.5 equiv/1000 g of water. The slopes of the cube-root plots are -0.60, -0.65, -0.97, - 1.31, and - 1.52 for lithium, sodium, potassium, calcium, and barium salts, respectively. This order of the slope is in accord with what is expected from Gurney’s rule. The magnitude of the slope for the sodium salt is found to be smaller than that of sodium polycarboxylate. This is accounted for in terms of the difference in the structural effects of sulfate ion and carboxylate ion.
Introduction In previous papers, the mean activity coefficients of polyelectrolytes have been determined by the emf measurements of a concentration cell with transfere n ~ e l - and ~ the isopiestic vapor pressure measurem e n t ~ . The ~ results showed that first, the logarithm of the mean activity coefficient decreased linearly with the cube root of polymer concentration (“cube-root” rule). The magnitude of the slope of the cube-root plot increased with increasing charge density and decreased with increasing degree of polymerization of macroion. This cube-root rule suggested the existence of a “linkage” between macroions through the intermediary of gegenions. Second, it was found that the mean activity coefficients of polyelectrolytes could not be equal to the single-ion activity coefficients of its gegenions and the discrepancy between the two The Journal of Phyeical Chemistry
coefficients could be small for the low molecular weight electrolytes. In the present paper, experimental data are reported on various salts of a polyvinyl sulfuric acid (PVAS). The isopiestic vapor pressure measurements were carried out in order to determine the osmotic and mean activity coefficients in a comparatively concentrated region of polymer concentration. One purpose of the present research is to see whether the cuberoot rule holds for the sulfates and to study the specific gegenion effects on the osmotic and mean activity coefficients. Gegenion effects are expected to arise (1) N.Ise and T. Okubo, J . Phys. Chem., 69, 4102 (1965). (2) N. Ise and T.Okubo, ibid., 70, 1930 (1966). (3) N. Ise and T.Okubo, ibid., 70, 2400 (1966). (4) N. Ise and T. Okubo, ibid., 71, 1287 (1967).
MEANACTIVITYCOEFFICIENT OF POLYELECTROLYTES
Table I: Isopiestic Measurements of Salts of PVAS (25') Polyelectrolyte, m,
equiv/
KC1,
Sample"
1000 g
m
(Prb
LiPVAS
0.182 0.201 0.238 0.290 0.369 0.461 0.706 1.59
0.0526 0.0591 0.0723 0.0935 0.122 0.165 0.286 0.961
0.544 0.551 0.566 0.597 0.612 0.655 0.734 1.08
-0.333 -0.350 -0.376 -0.400 -0.433 -0.452 -0.474 -0.360
NaPVAS
0.111 0.133 0.188 0.261 0.340 0.431 0.535 0.780 0,806 0.894 1.19
0.0352 0.0422 0.0633 0.0916 0.122 0.161 0.203 0.319 0.342 0.381 0.558
0.600 0.602 0.632 0.651 0.662 0.685 0.692 0.741 0.767 0.769 0.846
-0.298 -0.328 -0.373 -0.418 -0.452 -0.476 -0.502 -0.513 -0.520 -0.510 -0.520
KVPAS
0.229 0.278 0.374 0.459 0.939 1.74 2.17
0.0581 0.0710 0.0966 0.121 0.257 0.491 0.658
0.475 0.476 0.479 0.487 0.499 0.507 0.543
-0.592 -0.635 -0.700 -0.744 -0.901 -1.03 -1.06
0.228 0.275 0.350 0.469 0.563 0.708 0.856 1.23 1.54
0.0352 0.0426 0.0554 0.0736 0.0888 0.115 0.147 0.251 0.382
0.293 0.293 0.297 0.293 0.293 0.300 0.315 0.372 0.448
-0.793 -0.851 -0.922 -1.01 -1.07 -1.14 -1.19 -1.27 -1.29
0.163 0.184 0.207 0.231 0.272 0.312 0.393 0.536 1.62 2.52
0.0260 0.0290 0.0328 0.0357 0.0425 0.0470 0.0580 0.0788 0.268 0.645
0.304 0.299 0.300 0.293 0.295 0.284 0.277 0.274 0.302 0.459
-0.819 -0.859 -0.894 -0.930 -0.979 -1.03 -1.10 -1.20 -1.55 -1.60
CaPVAS
BaPVAS
Log (Y*/-f*d
O The degree o f neutralization is 1.00 for all of the samples. The 9,values were obtained by using VKCI values which were taken from R. A. Robinson and R. H. Stokes, "Electrolyte Solutions," Butterworth and Co., Ltd., London, 1959, p 476, Table I and p 481, Table I.
1887
mainly from nonelectrostatic, short-range forces rather than electrostatic, long-range forces which are predominant when macroions are highly charged. Therefore we used a PVAS having a low charge density (degree of esterification 0.227). Another purpose is to compare the mean activity coefficient data of a polycarboxylate with those of a polysulfate.
Experimental Section The aqueous solutions of various salts of PVAS, such as Li, Na, K, Ca, and Ba salts, were prepared as follows. A solution of potassium polyvinyl sulfate (a product of the Seiko Chemical Co., Fukuoka, Japan) was passed through a column of cation- and anion-exchange resins to convert the polymer to the acid form.5 Then, the solution was neutralized with an aqueous solution of reagent grade LiOH, NaOH, KOH, Ca(OH)*, or Ba(OH)*. The degree of polymerization of the parent polyvinyl alcohol was 1700 in viscometry. The degree of esterification was 0.227, determined by both a titration method and sulfur analysis. Osmotic and activity coefficients were determined by the isopiestic vapor pressure method at 25 f 0.005' with an apparatus employed by us earlier.4 The experimental error of the isopiestic measurements was about 2% in the osmotic coefficient value at the highest.
Results The measured concentrations of the solutions of PVAS salts and potassium chloride in isopiestic equilibria are listed in the second and third columns of Table I, respectively. The practical osmotic coefficient of the polyelectrolyte ( cpz) was calculated by the equation
where mKCl is the molality of the reference potassium chloride solution, m the concentration of the salts of PVAS (equiv/1000 g of water), z the stoichiometric valency of macroion, and (OKCI the practical osmotic coefficient of potassium chloride solution. It should be noted here 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.6 The osmotic coefficient obtained was generally found to increase with increasing concentration as is clearly (6) The polyvinyl sulfate was stable in passing through the ionexchange column, which was ascertained by sulfur analysis. (6) In ref 4, the osmotic coefficient of a polyacrylate was determined using 9 = 2mxcl/[(a 4- l)(m/z)]9KCI,where a is the effective valency of the macroion, instead of eq 1 in the present text.
Volume 71,Number 6 Mag 1967
NORIO ISEAND TSUNEO OKUBO
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Or------
-0.5
2
-1.0
4
- 1.5 0
1 m,
0.4
2
1.2
1.4
Figure 2. Cube-root plots of the mean activity coefficients of various polyvinyl sulfates in water (25”).
seen from the fourth column of Table I and Figure 1. This tendency is the same as found by Alexandrowicz7 and us4 for sodium polyacrylate and was earlier discussed in terms of the excluded volume effect by one of the present authors.8 Figure 1 also demonstrates that the osmotic coefficient of the polyelectrolyte depends sharply on the gegenions. The order of the magnitude of the coefficient is
> K > Ca > Ba
1 .o
0.8 m‘/a.
Figure 1. Osmotic coefficients of the aqueous solutions of various polyvinyl sulfates ( 2 5 ” ) .
Li = Na
0.6
equiv/1000 g.
(A)
This order for the polyelectrolytes is the same as that usually found for the salts of a low molecular weight strong acid.g The mean activity coefficients ( y * ) were calculated using the rearranged Gibbs-Duhem relation, Le.
results are given in the fifth column of Table I and in Figure 2. As is readily seen from the figure, the cube-root dependence holds for all salts studied except at higher concentrations. The slopes of the straight lines are -0.60, -0.65, -0.97, -1.31, and -1.52 for Li-, Na-, K-, Ca-, and BaPVAS, respectively. The magnitude of the slope is in the order Li
< Na < (I < Ca < Ba
(B)
Thus the nature of gegenions is seen to be an important factor influencing the solution property of polyelectrolytes.12
Discussion
In the above sections, the experimental data of the osmotic and mean activity coefficients of the PVAS salts were presented. These two coefficients are interrelated to each other so that our subsequent discussion will be limited to the mean activity coefficient. In previous paper^,^-^ it was reported that the cubewhere the subscripts 1 and 2 correspond to ml and m2, root plot has long straight segments for the mean activrespectively. As previously mentioned, the familiar ity coefficients of some polyelectrolytes. Figure 2 assumpt’ion that the activity coefficient of electrolytes shows that the rule also holds for the PVAS salts, up is unity at infinite dilution cannot generally be acto about 0.5 equiv/1000 g of water. Again we notice cepted for polyelectrolytes. This is due to the polythat the upper limit of concentration, a t which the It appears ionic work, using Hayman’s terminology. reasonable, however, to regard this work a t infinite dilution as independent of the nature of the gegenions, (7) 2. Alexandrowicz, J , Polymer Sci., 56, 115 (1962). since it is determined by the dielectric constant, elec(8) N. Ise and hl. Hosono, ibid., 39, 389 (1959). (9) H. S. Harned and B. B. Owen, “The Physical Chemistry of tric charge, distance between ionized groups, and Electrolytic Solutions,” Reinhold Publishing Corp., New York, number of the groups. Thus, we may assume that the N. Y.,1958, Chapter 12. activity coefficients of the various salts of PVAS have (10) H. J. G. Hayman, J. Chem. Phys., 2 2 , 1234 (1954). the same value at infinite dilution, Le., y*,,. By as(11) This is a rather crude assumption at present. There exists neither theoretical nor experimental support for this concentration suming that the cube-root rule holds down to infinite dependence in very dilute regions. dilution,ll log y * / y * o can be calculated for various salts (12) The degree of polymerization and charge density of the macroion and concentrations from the osmotic coefficient. The are also influential factors as was clearly demonstrated in ref 2. The Journal of Physical Chemistry
MEANACTIVITYCOEFFICIENT
1889
OF POLYELECTROLYTES
mentioned in the preceding section. In the light of experimental data begin to deviate upward from the the difference in the charge density, such a comparison straight line, is much higher for the PVAS salts than is not fully significant. In order to obtain information for 1-1 type electr01ytes.l~ Thus the previous inon the essential difference between the sulfate and terpretation, that the local regularity in ionic distribucarboxylate, therefore, it is necessary to compare tion can be more easily formed in polyelectrolyte soluNaPVAS with the sodium salt of a polyvinyl alcohol tions than in simple electrolyte solutions, proves to partially acetalized with glyoxylic acid (KaPVAG). have obtained a new experimental support. Our experimental finding2 has shown that the magniDiscussion is now desirable on the relative order of tude of the slope of the cube-root plot for NaPVAG the mean activity coefficients of the PVAS salts. For (ranging from 1.6 to 3.2) decreases with increasing 1-1 type electrolytes, as is well known, Gurney found degree of polymerization and increases with increasing a rule that electrolytes composed of ions of dissimilar number of charges. If this finding also applies to the influence on the water structure have larger mean polysulfate, the magnitude of the slope of KaPVAS activity coefficients than those of ions of similar char(degree of polymerization 1700, charge density 23/ 100 acter.14 In other words, the mean activity coefficient vinyl alcohol units) should be larger than 3.2, which decreases most sharply with increasing concentration was found for NaPVAG-N3 (degree of polymerization when the anion and cation are most similar in their 1700, charge density 10.5). The value actually found structure effect, according to Frank and Thompson.13 for NaPVAS, however, is 0.65. In the light of the Since the entropy value, a measure of the structure degree of polymerization dependence of the slope value effect, is not available for the macroions, we expediently mentioned above, it is difficult to escape the conclusion use the value of HSOs- for ionized group of the polythat NaPVAS molecules have a more highly stretched sulfates. The conventional partial molal entropy configuration than KaPVAG molecules. Correspondof this anion is reported as $32.6 h 1.5 eu on the scale ingly, the specific viscosity of a salt of PVAS was higher of zero for proton, indicating the structure-breaking than that of PVAG with the same gegenion, when nature of the anion, and the values for Li+, S a + , and these polyelectrolytes have the same degree of polyK + are +4.7 k 1.0, +14.0 0.4, and +24.2. f 0.2, merization and number of charges.” re~pective1y.l~Therefore it is clear that the experiDiscussion can now be carried on further in terms of mental data given in Figure 2 or inequality B can be the influence of ions on water structure. The entropy accounted for by Gurney’s rule, as far as monovalent value of acetate ion is not available so that we estimate gegenions are concerned. Furthermore, we note that it using the viscosity B coefficient of this ion (+O.250)lB the rule can be extended to Ca2+ and Ba2+, since the and the linear relation between the B coefficient and molal entropy of the former is -11.4 =t 0.3 (strong structure former) and that of the latter is +2.3 f 0.3.15 molal entropy.lg The value thus obtained is about +15 eu on the scale of zero for the proton. If this The magnitude of the slope of the cube-root plot of estimate is correct, it is immediately clear that Na+ the PVAS salts invites some comments. The values and acetate ion are similar in their structure effect experimentally found (ranging from -0.6 to -1.5) and a pair of Na+ and HS03- is rather dissimilar, since are not far from those previously found for a sodium the molal entropy of S a + is about +14.0 eu and that polyacrylate (-0.74) and for a polyethylenimine salt (-0.86),’6 but are much larger than those for 1-1 (13) For the detailed discussion of the cube-root formulation of varitype electrolytes (-0.2 -0.3).13 Frank and ous 1-1 type electrolytes in water, see H. 5. Frank and P. T. ThompThompson, however, pointed out that the magnitude son, “The Structure of Electrolytic Solutions,” W. J. Hamer, Ed., John Wiley and Sons, Inc., New York, N. Y., 1959. Chapter 8. of the slope increases with rising valency and reported (14) Gurney, “Ionic Processes in Solution,” McGraw-Hill a value of -0.726 for CaC12 and -3.9 for Z I & O ~ . ~ Book ~ R.Co.,W.Inc., New York, N. Y., 1953, Chapter 16. The authors have attributed these high values to ion(15) W. M. Latimer, K. S. Pitzer, and W. V. Smith, J. A m . Chem. pair formation, Similarly it is possible that gegenion Soc., 60, 1829 (1938). association by macroion is partly responsible for the (16) These values were obtained by using the equation mentioned in ref 6. These slope values become somewhat large (for example, large slope observed for the polysulfates. - 1.4 for NaP.4A) when use is made of eq 1. This change, which is Since the polysulfates under consideration are Cocompletely due t o a gegenion association phenomenon by macroions, will be discussed fully at a later date, but does not affect our dispo~ye~ectro~ytes of a low charge density, cussion in the text. Of it is rather surprising to find that the (17) I. Sakurada and N. Ise, Makromol. Chem., 40, 126 (1960). the cube-root plot for the PVAS salts (slope and upper (18) See ret 14, 169. limit) are fairly close to those found for homopolymeric (19) It has been pointed out in ref 14 (p 174) that two straight lines can be obtained: the high-lying line is for the large molecular ions po~ye~ectro~ytes of high charge densities such as the such as Nos-, ClOs-, and IOs-. In the present work, the acetate polyacrylates at the full degree Of neutralization 89 ion was assumed to fall on this line.
*
-
Volume 71, Number 6
M a y 1967
NORIOISEAND TSUNEO OKUBO
1890
of HS03- about +32.6 as was mentioned above. Thus, the fact that NaPVAG has a larger slope of the cube-root plot than NaPVAS can be accounted for by Gurney's rule. We note that the foregoing discussion relies on the validity of the approximation by which the real ionized groups I and I1 have been replaced with acetate ion and HSO3-, respectively.
cooI
I1
It is therefore important to know the influence which the oxygen atom connecting COO- or SO3- with the main polymer chain would exert on the water structure. According to existing data,15 the conventional partial molal entropies of C10-, CIOz-, C103-, and C104are 10.0 f 2, 24.1 f 0.5, 39.4 f 0.5, and 43.6 f 0.5 eu, respectively. It is seen from these data that oxygen has a structure-breaking effect and the effect of one oxygen atom becomes progressively small as the ion becomes more complex. This can be found in
The Journal of Physical Chemistry
the pair of S032- and S04z-, which have entropy values of 3 f 3 and 4.4 f 1.0 eu, respectively, and also in the case of NOz- and NO3-, the entropies of which are 29.9 f 1.0 and 35.0 f 0.2 eu, respectively. Thus, it seems possible to conclude that the structural influence of the oxygen under consideration in PVAG and PVAS is rather small. Finally, we would like to comment on the magnitudes of the activity coefficients of NaPVAG and NaPVAS. As was mentioned in a previous paper,' the magnitude of the mean activity coefficients of polyelectrolytes cannot be determined, because it is not known how to estimate the polyionic work experimentally, which determines the mean activity coefficient at infinite dilution. Nevertheless, we know that the polyionic work should be determined by the distance between ionized groups and the number of the groups. Therefore it is expected that polyelectrolytes of the same (linear) charge density and degree of polymerization should have the same mean activity coefficient a t infinite dilution. Then, the mean activity coefficient of NaPVAS should be larger than that of NaPVAG a t finite concentrations, because the magnitude of the slope of the cube-root plot is smaller for the former than for the latter.
Acknowledgment. Sincere thanks are due to Professor I. Sakurada for his encouragement.
