1370
NORIOISEAND TSUNEO OKUBO
Mean Activity Coefficient of Polyelectrolytes.
X.
Activity
Coefficients of Polyphosphates of Various Gegenionsl by Norio Ise and Tsuneo Okubo Department of Polymer Chemistry, Kyoto University, Kyoto, J a p a n
(Received August 89,1967)
The osmotic and (mean) activity coefficientsof polyphosphates (PP) of various gegenions in aqueous media have been determined at 25" by means of the isopiestic vapor pressure measurements. The osmotic coefficients of Li-, Na-, and KPP are comparatively small and concentration insensitive, whereas those of N(nCdH9)4-, N(n-C3H7)4-, N(CzHs)4-, N(CHs)h-, and N(CH~)~CHZC~H~PP are large and increase with increasing concentration. The activity coefficients of the polyphosphates decrease linearly with the cube root of polymer concentration, up t o 0.5 equiv/1000 g of water. The order of the magnitude of the activity coefficient is N(n-C4H9)4 > N(n-C3H,)4 > N(C2H5)4 > N(CH& > N(CHI)ICH~C~H~ and Li > Na > K. These relative orders are accounted for in terms of the structural influences of the ions on water. It is inferred that the polyphosphate ion is a structure former, with a mode incompatible to that of sodium ions. The degree of incompatibility is suggested to be intermediate between that of sodium polystyrenesulfonate and sodium polyethylenesulfonate or polyacrylate, owing to a charge-transfer-type interaction of the phosphate group with water molecules. Finally a discrepancy is pointed out between the order of the observed osmotic coefficients and that of the degree of gegenion association. This is interpreted as implying that the solvmtsolute interaction is more important than the gegenion association.
Introduction The systematic study of the (mean) activity coefficients of polyelectrolytes in aqueous solutions is being intensively conducted in this laboratory.2 So far our attention has been paid to organic polyelectrolytes. In this communication, the measurements are extended to various salts of a polyphosphate, which is an inorganic material. A variety of properties of its solution have been studied by many authors, but the activity coefficient has never been discussed. Thus the osmotic and activity coefficients of polyphosphates are now determined by using the isopiestic equilibration method, and the specificity of gegenions on these coefficients is studied.
Experimental Section
p r e v i ~ u s l y . ~The maximum inaccuracy of the present measurements was 2% of the concentration values. Usually 72 hr was necessary to attain the isopiestic equilibrium, and several successive experiments were made with the same solution. In order to examine whether degradation can occur during the equilibration time, the viscosity measurements of a carefully stored solution of NaPP were undertaken at a 30-day interval. The results show that the reduced viscosity stayed consta,nt within 30/& From this we concluded that the degradation is practically negligible. Furthermore, we assumed that this applied also to others than the sodium salt. Degradation in the acid form, however, proceeds easily. Thus the neutralization with various alkali solutions was completed within a period as short as possible. It is believed, however, that this is not a source of serious error in our measurements, because the activity coefficient is rather insensitive toward molecular weight like some other thermodynamic properties of polyelectrolytes.
The sodium polyphosphate (KaPP) was a gift from the Monsanto Company, St. Louis, M o . Its number-average degree of polymerization was 600 in o ~ m o m e t r y . ~A stock solution of NaPP was prepared using conductivity water and was purified by passing Results and Discussion through a column containing cation- and anion-exThe measured concentrations of the isopiestic sochange resins. The polyacid solution thus obtained lutions of the polyphosphate and potassium chloride was neutralized by the aid of conductometric titration (reference electrolyte) are given in Table I. with an aqueous solution of reagent grade LiOH, NaOH, KOH, (CH8)dNOH (TAIAOH), (CzH6)dSOH (1) Presented a t the 16th Symposium of Polymer Sciences, Fukuoka, Japan, Oct 1967. (TEAOH), (?'L-C~HT)~NOH (TPAOH), (n-C4Hs)NOH (2) I n the present work, the mean activity coefficients of polyelec(TBAOH) or (CH3)&H2C6H&OH (T3IBAOH). The trolytes are being dealt with, which should not be confused with the polymer concentration was determined by the titrasingle-ion activity coefficients of any ionic species. tion data. (3) The measurement was done by using a stock solution of the potassium salt which was prepared a s described in the text and The isopiestic measurements were carried out at 25 employed for the isopiestic experiments. 0.005° by using an apparatus described b e f ~ r e . ~ (4) T. Okubo, N. Ise, and F. Matsui, J . Amer. Chem. Soc., 89, 3697 The experimental procedures were also reported (1967).
*
The Journal of Physical Chemistry
MEANACTIVITY COEFFICIENT OF POLYELECTROLYTES
1371
Table I : Concentrations of the Isopiestic Solutions of Potassium Chloride and Polyphosphates at 25'' wcci
0.0344 0.0384 0.0458 0.0541 0.0678 0.0879 0.103 0.143 0.198 0.244 0.351 0.529 1.12 a mKC1
Li
0.127 0.142 0.172 0.207 0.263 0.348 0.406 0.555 0.761 0.915 1.27 1.87
...
Na
0.126 0.142 0.178 0.217 0.282 0.378 0.438 0.613 0.862 1.05 1.53 2.31
...
K
0.128 0.147 0.188 0.232 0.305
...
0.446 0.593 0.838 1.01 1.48 2.28
...
N(CzHa)r
N(CHa)r
...
...
0.178 0.214 0.263 0.306 0.409 0.531 0.636 0.841 1.14 1.87
0.156 0.177 0.210 0.256 0.289 0.379 0.481 0,580 0.764 1.00 1.63
... ...
N (n-CrHe)r
N(n-CaHdr
...
...
... ...
N( C H b (CHzCsHs)
...
...
... ...
0.154 0.176 0.213 0.265 0,300 0.405 0.535 0.656 0,901 1.24 2.15
...
*..
0.164 0.193 0.230 0,259 0.340 0.428 0.520 0.673 0,885 1.40
0.177 0.208 0.242 0.317 0.392 0.481 0.625 0.820 1.35
is in molality; polyphosphate concentration is in equiv/1000 g of water.
The practical osmotic coefficient of the polyelectrolyte (4,) was calculated by the condition of equal solvent vapor pressure, as previously described.6 The osmotic coefficients of potassium chloride solutions were taken from the literature.6 The 6, values of various polyphosphates are presented in Figures 1 and 2. It is seen that polyphosphates having metal ions as gegenions have generally much smaller osmotic coefficients than those of organic gegenions. Furthermore, the coefficients of LiPP, KPP, and NaPP are almost concentration independent in the studied range of concentration and do not change markedly with gegenions. On the other hand, as seen from Figure 2, the & values of polyphosphates of organic gegenions increase with increasing concentration and vary remarkably with gegenions. The activity coefficient ( y * ) was calculated using the Gibbs-Duhem relation, as reported previous1ya6 The assumptions involved in the calculation7 were : first, the cube-root rule holds down to infinite dilution; and second, the polyphosphates have the same activity coefficient yo* at infinite dilution, irrespective of the gegenions. The results are plotted against the cube root of polymer concentration in Figure 3. It is seen that the cube-root rule is valid at low concentrations. The upper bound of the range of fit of the rule is about 0.5 equiv/1000 g of water. The slopes are -1.21, -1.33, -1.42, -0.06, -0.18, -0.45, -0.61, and -0.70 for Li-, Na-, K-, TBA-, TPA-, TEA-, TMA-, and TMBAPP, respectively. As was mentioned in a previous paper,a the cube-soot rule is related to the local regular distribution of ions, which is caused mainly by the electrostatic interaction. When the nonelectrostatic interaction is strong enough, the rule does not hold, or the range of fit shifts toward lower concentrations. For example, in polystyrenesulfonate solution,* in which the strong solvent-solute interaction owing to the benzene ring exists, the rule is
I
I
I
I
-€cN
m (equiv/IOOOg)
Figure 1. Osmotic coefficients of aqueous solutions of lithium, potassium, and sodium polyphosphates (25'): 1, LiPP; 2, KPP; 3, NaPP.
. _I
t
/
Figure 2. Osmotic coefficients of aqueous solutions of tetrabutylammonium, tetrapropylammonium, tetraethylammonium, tetramethylammonium, and trimethylbenzylammonium polyphosphates (25'): 1, TBAPP; 2, TPAPP; 3, TEAPP; 4, TMAPP, 5, TMBAPP.
valid up to in = 0.3. Sodium polyacrylate and polyethylenimine salt, on the other hand, showed a long straight segment of the cube-root plot up to in = 1, in which the solvent-solute interaction is much weaker than in the polystyrenesulfonate case^.^^^ From ( 5 ) N. Ise and T. Okubo, J . Phys. Chem., 71, 1287 (1967). (6) R. A. Robinson and R. H. Stokes, "Electrolyte Solutions," Butterworth nnd Co. Ltd., London, 1959, pp 476, 481. (7) For earlier references on the cube-root rule and for the yo* problem, see N. Ise and T. Okubo, J . Phys. Chem., 71, 1886 (1967). (8) N. Ise and T. Okubo, ibid., 72, 1361 (1968). (9) N. Ise and T. Okubo, ibid., 70, 2400 (1966).
Volume 7gPNumber 4 April 1968
1372
KORIOISEAKD TSCNEO OKUBO effect between the organic gegenion? and polyphosphate ion, as was earlier suggested for low molecular weight fluorides by Wen, et nZ.l4 Sext me compare struct'ural influences of various macroions. The existing data shorn that the osmotic coeficjent of sodium salts decreases in the order polystyrenesulfonate* > polyphosphate > polyacrylate5 = polyethylenesu1fonatel0 (C)
Figure 3. Activity coefficients of polyphosphates in aqueous solutions as a function of the cube root of polymer concentration ( 2 5 ' ) : 1, TBAPP; 2, TPBPP; 3, TEAPP; 4, TRIAPP; 5, TMBAPP; 6, LiPP; 7 , NaPP; 8, KPP.
these data it is inferred that the solvent-solute interaction in the polyphosphate solutions is intermediate between the polyacrylate and the polystyrenesulfonate. This matter will be discussed again in the latter part of this paper. Figure 3 shows that the activity coefficients of the polyphosphates decrease in the order Li
> Na > K
(A)
and TBA
> TPA > TEA > TMA > TMBA
(B)
These orders were already found for polystyrenesulfonates8 and polyethylenesulfonates.lo Figure 3 also shows that the activity coefficients of the alkali polyphosphates are smaller than those of the organic salts. According to the existing theories of structural influences of ions on ~ a t e r , ~ l -the ' ~ structural salting-out effect is more preponderant for the organic salts than for the alkali salts. The alkali metal ions can immobilize water molecules, owing to the electrostatic interaction, and hence can be regarded as structure formers. Similarly, the polyphosphate ion can form an ordered structure as a consequence of the intense electric field around the charged site. Therefore, it is also a structure former. This is in line with the .fairly large hydration number of the polyphosphate ion as found by Conway, et a1.l6 Thus we may expect strong salting-in effect between the metal ion and the polyphosphate ion. It is believed, on the other hand, that the tetraalliylammonium ions have a tendency of forming cage-like water structure around themselves. l1 The incompatibleness of the modes of structure formation causes a strong salting-out The Journal of Physical Chemistry
Since the polystyrenesulfonate anion has large hydrocarbon parts, an ordered water structure would be formed around this macroion in a way incompatible to that of sodium ion. Thus t,his macroion would salt out sodium ion strongly. Therefore the & is large.'B The polyacrylate ion can be regarded as a structure former, in the light of the ionic entropy value of CH&OO- (+15.0 eul'). Similarly, the polyethylenesulfonate ion was also concluded to be a structure former.1° The mode of water structure around these two macroions is believed to be compat'ible with that of sodium ions. Thus the salting-in effect is strong for sodium polyacrylate and sodium polyethylenesulfonate, so t,hat small & values are observed. It is possible now to conclude that the degree of the incompatibility for sodium polyphosphate is intermediate between two extremes, namely polystyrenesulfonate and polyethylenesulfonate. I n this respect, it may be suggested that the polyst'yrenesulfonate can interact with water molecules through the intermediary of n-electrons of the benzene ring, whereas the polyethylenesulfonate cannot. The situation is the same as found for sodium naphthalenesulfonate arid sodium butane-l-sulfonate.'8 Then it is tempting to suggest further that the polyphosphate can interact. with water molecules more weakly than the polystyrene, and the polyacrylate interacts as weakly as the polyethylenesulfonate. Though no conclusive proof is available a t present, we suggest that the charge-transfer interaction might be a, factor determining the observed order (C). Since the charge-transfer interaction can be described by the ionization potential to the first appro~imation,'~ (10) N. Ise and K. Asai, J . Phys. Chem., 72, 1366 (1968). (11) H. S. Frank and W.-Y. Wen, Discussion Faraday Soc., 24, 133 (1957). (12) H. S. Frank, J . Phys. Chem., 67, 1554 (1965). (13) H. S. Frank, 2. Physik. Chem. (Leipzig), 228, 364 (1965). (14) W.-Y. Wen, S. Saito, and C. Lee, J . Phys. Chem., 70, 1244 (1966). (15) B. E. Conway, J . E. Desnoyers, and A. C. Smith, Phil. Trans. Roy. Sac. London, 256, 389 (1964). (16) The structural influences can be discussed in terms of the osmotic coefficient, instead of the activity coefficient. When comparison of various polyelectrolytes is sought, the use of the osmotic coefficient is convenient because the activity coefficient a t infinite dilution (yo*) varies from polyelectrolyte to polyelectrolyte. For the yo* problem, see ref 17. (17) N. Ise and T. Okubo, J . Phys. Chem., 71, 1886, 4588 (1967). (18) E. Yoshida, E. Cjsawa, and R. Oda, ibid., 68, 2895 (1964). (19) R. S. Mulliken, J . Amer. Chem. Soc., 74, 811 (1952); J . Phys. Chem., 56, 801 (1952).
MEANACTIVITY COEFFICIENT OF POLYELECTROLYTES our experimental data indicate that the phosphate group has a lower ionization potential than the acrylate group, which.would enable the former t o form a stronger charge-transfer-type hydrogen bond.20 Anyway, the mode of the immobilization of water molecules due t o the electrostatic forces, which may occur in the cases of simple ions such as metal, carboxylate, or sulfate ioi-.+, can be altered by the hydrogen bond formation to the largest extent for the polystyrenesulfonate and to a lesser extent for the polyphosphate. The order of the incompatibility series mentioned above, therefore, can be understood. Also, this explanation is in line with the conclusion in the previous paragraph which was derived on the solvent-solute interaction from the cuberoot relationship. Finally, mention should be made of the gegeriion association. This phenomenon has been studied by many authors, since it is characteristic of polyelectrolytes. Experimental data21 show that the extent of gegenion association by polyphosphate ions decreases in the order Li
> Na > K > Cs
(D)
We may expect that the larger the extent the smaller the number of free gegenions and hence the smaller the c $ ~ value. Therefore, +z should decrease in the order Cs > I< > Ka > Li. This is evidently contrary to the observed order Li > K’a = I
