4364
J. Phys. Chem. 1986, 90, 4364-4365
Enthalpies of Dilution of Poly(styrenesu1fonate)s in Anhydrous N-Methylformamide J. Skerjanc,* C. Pohar, and A. Fabjan Department of Chemistry, Edvard Kardelj University, Ljubljana, Yugoslavia (Received: February 18, 1986)
The enthalpies of dilution of solutionsof alkali-metal and magnesium poly(styrenesu1fonate)s in anhydrous N-methylformamide were measured at 25 O C in the concentration range from about 0.1 to 0.001 monomol/L. The enthalpy of dilution is practically independent of the ionic radius of the counterions and its values are approximately 8 times higher than those found, for example, for poly(styrenesu1fonic acid) and its lithium salt in water. The experimental data are compared with predictions from electrostatic theories based on the cylindrical cell and infinite line-charge models. A reasonable agreement between theory and experiment is obtained.
Introduction In the period from the early 1950s, when polyelectrolytes became attractive for many polymer chemists, to the present various thermodynamic and transport properties of these charged polymers have been accumulated. The majority of data have been obtained with aqueous solutions, and only a few with nonaqueous solvents or mixtures of water and an organic solvent.I4 With such mixtures it is possible to vary the dielectric constant of the medium continuously over a given range. From the point of view of any electrostatic theory the dielectric constant is the most important physical property of the solvent. It has a direct influence on the electrostatic interactions between charged particles and thus on the behavior of a charged macromolecule in solution. Therefore, studies of polyelectrolytes in solvents with different dielectric constants should provide an additional tcst of electrostatic theories adopted in this field. To our knowledge no studies of polyelectrolyte solutions have been performed in a pure solvent or solvent mixture with a dielectric constant greater than that of water. A particularly attractive representative of these solvents is N-methylformamide. It has one of the highest known dielectric constants (e = 182.4 at 25 0C),5and it is a powerful ionizating solvent. Owing to its high dielectric constant, one would expect that ionic association in this solvent would be small, and consequently the individuality of counterions should be less pronounced than in water. Even anhydrous N-methylformamide readily dissolves strongly ionizing polyelectrolytes such as poly(styrenesu1fonate)s. On the contrary, these polysalts are not soluble in pure organic solvents with dielectric constants lower than that of water, for example, in alcohols and dioxanes3 Therefore, a mixed solvent of water and dioxane has been used in previous s t ~ d i e s . ~It- has ~ to be stated however, that a pure solvent has an essential advantage over a solvent mixture. Its composition in the proximity of a solute is the same as in the bulk of solution, and hence any troubles or vaguenesses ensued from the preferential solvation of the solute are excluded. In this contribution we present the enthalpy of dilution results for the lithium, sodium, potassium, cesium, and magnesium salts of poly(styrenesu1fonic acid) in anhydrous N-methylformamide a t 25 OC over a wide concentration range. The experimental results are compared with predictions of the electrostatic theories based on the cylindrical cell6 and the infinite line charge' models. Experimental Section All salts were derived from one single sample of sodium poly(styrenesulfonate), NaPSS, obtained from Polysciences Inc. (1) Priel, Z.; Silberberg, A. J. Polym. Sci.: Part A-2 1970,8, 689, 705, 713. (2) yesnaver, G.; Dolar, D. Eur. Polym. J. 1975,II,657. 1976,I t , 129. (3) Skerjanc, J.; Vesnaver, G.;Dolar, D. Eur. Polym. J . 1980,16, 179. (4) Skerjanc, J.; Vesnaver, G.Macromolecules 1983,16, 1 164. ( 5 ) Leader, G. R.; Gormley, Y. F. J . A m . Chem. SOC.1951,73, 5731. (6) (a) Fuoss, R. M.; Katchalsky, A.; Lifson, S. Proc. Null. Acad. Sci. U.S.A. 1951.37,579. (b) Alfrey, T., Jr.; Berg, P. W.; Morawetz, H. J . Polym. Sci. 1951,7, 543. (7) Manning, G.S. J . Chem. Phys. 1969,51, 924.
0022-3654/86/2090-4364$01.50/0
(Warrington, PA), with a molecular weight of about 70000 and a degree of sulfonation of 1.O. For purification and preparation of solutions, dialysis and ion-exchange techniques were used as described in detail elsewhere.* From concentrated aqueous solutions the dry salts were isolated by lyophilization. N-Methylformamide, N M F (purum, Fluka), was purified following the procedure given in the l i t e r a t ~ r e .The ~ solvent was shaken with N a O H pellets and BaO overnight, then decanted, and vacuum distilled from BaO through a 40-cm Vigreux column. After a second distillation the product had a specific conductance E'cm-*, in agreement with the literature value. of 3 X Immediately after distillation the stock solution of a given salt was prepared. The lyophilized salts dissolved in the solvent within a few hours, leaving a small amount (1-2%) of undissolved residue which was removed by centrifugation. It is well-known that the conductivity of the solvent increases slightly with time, indicating a slow degradation. Care was taken therefore that a given set of calorimetric experiments was finished within 24 h of preparing the solutions. Enthalpies of dilution at 25 OC were obtained by mixing 2 mL of solution with 4 mL of solvent in an LKB 10700-2 batch microcalorimeter which utilizes a twin heat conduction principle.
Results and Discussion The results of the calorimetric measurements are presented in Figure 1 where the enthalpy of dilution, AHD,is plotted against the logarithm of monomolarity, c (mol of SO3- groups/L). Experimental points for each salt are the average of three independent runs, with the relative experimental error up to 10%. Various features of experimental results are noticeable. First, AHD is practically independent of the ionic radius of the monovalent counterions, an observation which is entirely different from that found in AHD measurements in waterlo and dioxane-water mixture^.^ Although the observed differences in the experimental results are practically within the limits of the experimental errors, it can be seen that there is a slight tendency for AHD to increase in the order LiPSS < NaPSS < KPSS < CsPSS, just the reverse of what has been found in water and dioxane-water media. In solvent with a high dielectric constant one would expect complete ionization of electrolytes. This expectation has been confirmed by conductivity" and electromotive force studies'* of the alkali metal halides in N-methylformamide which have shown that ionic association in this solvent is only slight, if at all. Also, the reverse order in activity coefficients has been found for the alkali metal chlorides in N-methylformamide12 compared to that in water. If one extrapolates these observations to polyelectrolytes the slightly expressed individuality of various polysalts observed in the present ~~~~
~~
(8) Skerjanc, J.; Pavlin, M. J . Pfiys. Cfiem. 1977,81, 1166. (9) Held, R. P.; Criss, C. M. J. Phys. C;hem. 1965, 69, 2611. (10) Vesnaver, G.; Rude?, M.; Pohar, C.; Skerjanc, J. J . Phys. Cfiem.1%. 88, 241 1. (11) French, C. M.; Glover, K. H, Trans. Furaday SOC 1955,51, 1418, 1427 (12) Luksha, E.; Criss, C. M J. Phys. Chem. 1966,70, 1496.
0 1986 American Chemical Society
, The Journal of Physical Chemistry, Vol. 90, No. 18, 1986 4365
Enthalpies of Dilution of Poly(styrenesu1fonate)s
I
2.5
15
2.0
I
1.0
log c
Figure 1. Enthalpy of dilution of alkali-metal and magnesium poly-
(styrenesu1fonate)sin anhydrous N-methylformamide at 25 OC (circles). Full lines: values calculated from the cell theory (eq 1 and 2) with parameter X as indicated. Dashed lines: limiting slopes (eq 4). AHD studies can be understood. Another feature of the results presented in Figure 1 is the fact that the values of AHDin N M F are approximately 8 times higher than those found, for example, for poly(styrenesu1fonic acid) and its lithium salt in water.I0 The general shape of the AHD curves is, however, similar to those found in aqueous solutions, e.g., an almost linear dependence of AHD on the logarithm of the concentration. It is well-known now that such concentration dependence is also theoretically founded by polyelectrolyte theories. The cylindrical cell theory6 for polyelectrolyte solutions leads to an expression for the electrostatic contribution to the dilution enthalpy AHDewhich is related to the observed enthalpy of dilution AHD by
X from the structural value are discussed by Katchalsky et al.14 The theoretical curves presented in Figure 1 were calculated with two structural and two effective values of A, for monovalent counterions: Xstructursl = 1.22, Xeffective = 1.83 giving the ratio Xeffcctivc/Xstmctural = 1.5, and for divalent counterions: Xstructural 2.44, Xeffectlve = 4.38 with the ratio Xeffeclivc/Xstructural = 1.8. The coefficient d In a/d In T was assumed to be, in the first approximation, negligible and set equal to zero. The value 0.8 nm was taken for the macromolecular radius, a, needed to obtain For b, the length the relation between y and the con~entration.'~ of a monomeric unit, the value 0.252 nm, typical for vinylic polyelectrolyte, was used, and for parameters characteristic for the solvent the values for NMF53l5at 298.15 K were used: t = 182.4, d In t/d In T = -2.681; d lnV/d In T = 0.260. Comparison of the experimental and calculated values in Figure 1 shows a reasonable agreement for monovalent and divalent counterions when the effective values of A, 1.83 and 4.38, respectively, are used. It is noticeable that the theoretical curve for monovalent salts is rather insensitive of the value of the charging parameter. It can be seen that with Xeffective 1.5 times the slope of the theoretical curve diminishes larger than hstructural about 7% only, contrary to the observation in water where the slope of the AH, curve is roughly inversely proportional to X. Experimental data at high dilution are in reasonable agreement also with predictions of another popular polyelectrolyte theory, the infinite line charge theory of Manning.' According to this theory the limiting slope for AHD reads16
- -
which can be readily obtained also from eq 1 and 2 in the limit c 0 (8 0). In eq 4 the charging parameter C; = X must have its structural value. Limiting slopes calculated from eq 4 are presented in Figure 1 as dotted lines. It can be seen that the experimental slopes appear to approach the limiting slopes for monovalent and divalent salts. AHD = AHD' AHD" (1 1 Finally, it may be mentioned that similar measurements of the enthalpy of solution of selected simple electrolytes in anhydrous where A H D O is the nonelectrostatic contribution. The comparison N-methylf~rmamide~J'gave much less satisfactory agreement with of the observed and calculated data is based on the usual asthe theoretical prediction. Whereas, for example, cesium and sumption that only electrostatic interactions are significant, and potassium chlorides and strontium and barium chlorates had thus AHDO may be neglected. limiting slopes that were consistent with the limiting slope for AHD The electrostatic enthalpy Hc is given by the expressionI3 predicted by the Debye-Hiickel theory, sodium chloride, bromide, and iodide had slopes between 7 and 10 times the theoretical slope, and, most outstandingly, lithium chloride had even a slope on the order of 280 times the predicted one. On the basis of these and conductance data" it was suggested that there was ionic assod In 6 ziRT 1 - 8 2 ciation for the latter electrolytes, a finding, which one would hardly d In T 2z2X expect for a high-dielectric-constant solvent such as NMF. Although the polymeric electrolytes studied in the present work where the charging parameter X is defined by display a thermodynamic behavior which differs strikingly in many X = zlz2e02/ekTb (3) instances from the classical behavior characteristic of low-molecular-weight electrolytes, and therefore looking for two close All symbols have the same meaning as defined p r e v i o ~ s l y . ~ , ~ , ~ ~ ,analogies '~ between them is often risky, it may be pointed out in Equation 2 has two adjustable parameters, X and d In a/d In conclusion that the results of the present studies do not yield any T. The first one, A, is the principal parameter of the cell theory. evidence for appreciable ionic association in these systems. It appears in theoretical expressions for all thermodynamic Registry No. LiPSS, 9016-91-5; NaPSS, 9080-79-9;KPSS, 901 1properties and usually has to be properly adjusted in order to bring 99-8;CSPSS, 37286-93-4;MgPSS, 37286-95-6; HCONHCH3,123-39-7. theory and experiment into agreement. It has been found that the ratio between this empirical X (Xeffeaivc) and the structural X, (14) Katchalsky, A.; Alexandrowitz, 2.;Kedem, 0. In Chemical Physics given by eq 3, is always Xcffcctive/Xstructural 1 1, and, further, that Of Ionic Solutions, Conway, B. E.,Barradas, R.s., Eds.; Wiley: New York, this ratio is to the extent of coiling of the polyion, 1966;p 295. The possible reasons for the deviation of the effective values of (15) de Visser, C.;Pel, P.; Somsen, G. J . Solution Chem. 1977, 9, 571.
+
-)+-[
(13) Skerjanc, J.; Dolar, D.; Leskodek, D. Z . Phys. Chem. (Frankfurt am Main) 1967, 56, 207. 1970, 70, 31.
(16)Skerjanc, J.; HoEevar, S.; Dolar, D. Z . Phys. Chem. (Frankfurt am Main) 1973. 86. 3 11. (li) Finch, A.; Gardner, P. J.; Steadman, C. J. J . Phys. Chem. 1967, 71, 2996.
