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Enthalpies of Dilution of Strong Polyelectrolyte Solutions
Enthalpies of Dilution of Strong Polyelectrolyte Solutions. Comparisons with the Cell and Line Charge Theories G. E. Boyd* and D. P. Wilson Department of Chemistry, University of Georgia, Athens, Georgia 30602 (Received August 11, 1975) Publication costs assisted by the University of Georgia
A sensitive, isothermal titration microcalorimeter was used in the measurement of the enthalpies of dilution, AHD,of several strong polyelectrolytes in aqueous solutions a t 298.15 K. The sodium salts of atactic poly(styrenesu1fonic acid), NaPSS, of varying molecular weight, of poly(ethylenesu1fonic acid), NaPES and of poly(3-methacryloyloxypropane-1-sulfonicacid), NaPMOS, were employed in dilutions from 0.2 to monomolar concentration. The NaPSS and the NaPMOS preparations gave AHD values in ca. 3 X agreement with predictions of electrostatic theory based on the cell model for dilution from initial concentration below mi = 3.1 X 10-2 monomolar, using the “structural value” for the charge density parameter, 5 = 2.828. The limiting slope for the change in AHD with log m predicted by the infinite line-charge model also appeared to be approached by the NaPSS and NaPMOS solutions a t high dilutions. The anomalously low AHD values observed with the NaPES solutions could be brought into agreement with the cell model only if an empirical 5 greater than twice the magnitude of the “structural value” was assumed. Alternatively, the small dilution enthalpies of NaPES can be attributed to complex formation between the counterions (i.e., Na+) and the sulfonate groups attached to the chain backbone.
The recent development of sensitive microcalorimeters for the measurement of the heat changes which occur in small volumes of viscous aqueous solutions of macromolecular solutes promises to be of importance in the determination of the thermodynamic properties of these hitherto infrequently examined systems. The property changes accompanying the dilution of synthetic, strong polyelectrolyte and biopolyelectrolyte solutions are of particular interest because of the availability of quantitative electrostatic t h e o r i e ~ l -based ~ on molecular models of cylindrical symmetry which yield predictions with which experimental results may be compared. A sensitive test of the theory is afforded by measurements of the enthalpies of dilution, particularly a t small concentrations of polyelectrolyte where a limiting behavior is predicted which is analogous to the prediction made by the Debye-Huckel theory of simple electrolyte solutions. The sodium salts of three polyvinylsulfonic acids were employed in our enthalpy of dilution (AHD)measurements: (a) poly(styrenesu1fonic acid) of two molecular weights; (b) poly(ethylenesulfonic acid); and, (c) poly(3-methacryloyloxypropane-1-sulfonic acid) to investigate a possible molecular weight dependence of AHD;to determine the effect, if any, of the distance of the sulfonate group from the polyelectrolyte chain backbone; and, whether or not the nature of the substitution of the sulfonate group to the chain backbone affects the magnitude of AHD. Measurements of the concentration dependence of the enthalpies of dilution of poly(styrenesu1fonic acid), of its alkali metal and several of its alkaline earth salts, have been reported p r e v i o ~ s l y . ~In- ~these investigations a large double compartment, Dewar-type solution calorimeter was employed which gave results which appear to agree well with theory. The thermal effects were quite small, however, and, because systematic errors may be introduced in the calorimetry of polyelectrolyte solutions as a result of their appreciable viscosity, it seemed that confirmatory determi-
nations with a radically different type of calorimeter would be worthwhile.
Experimental Section Materials. Sodium poly(styrenesu1fonate) (NaPSS) preparations NC 1557 and NC 1585 with viscosity molecular weights of 40 000 f 2 000 and 450 000 f 20 000, respectively, were obtained through the courtesy of the Dow Chemical Co., Midland, Mich. These para-substituted salts were purified by dialysis of their aqueous solutions in a hollow-fiber dialysis cell, concentrated with a rotary evaporator and pure, dry, colorless powdered solids were obtained by vacuum freeze drying. Their equivalent weights, determined by acidimetric weight titration of the poly(su1fonic acid) produced from them by cation exchange, were 207.4 f 0.5 and 206.5 f 0.3, respectively, indicating a degree of substitution close to 100%. Ultraviolet absorption spectra were measured with a Cary Model 16 recording spectrophotometer to establish the purity of the preparation^.^ The changes in their optical density a t 261.5 nm as a function of NaCl concentration showed them to be hyperchromic from which the atactic character of the polymer chain was inferred following the recent report of Aylward.8 The sodium poly(ethylenesu1fonate) (NaPES) used was a pure compound received from Professor U. P. Straws of Rutgers University who has described its preparation and p~rification.~ The viscosity average molecular weight estimated by him was ca. 100 000. Attempts by us to measure the ultraviolet absorption of dilute aqueous solutions of NaPES were unsuccessful; very little absorption could be detected down to 200 nm in agreement with Eisenberg and Mohan.lo Small quantities of pure sodium poly(3-methacryloyloxypropane-1-sulfonate), NaPMOS, were kindly given to us by Dr. J. S. Tan of the Eastman Kodak Co., Rochester, N.Y., who has described its preparation and purification elsewhere.ll Its weight average molecular weight, Mw,has The Journal of Physical Chemistry, Vol. SO, No. 8, 1976
G. E. Boyd and D. P. Wilson
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been reported as ca. 530 000. No absorption either in the ultraviolet or visible by dilute aqueous solutions of NaPMOS was detected. Calorimetry. An isothermal titration microcalorimeter of recent design12 capable of detecting and measuring heat effects as small as a few millicalories was employed. (1cal = 4.1840 J.) The major components of the system included a 90-1. water bath controlled to f 3 x OC, a stainless steel reaction vessel, and an isothermal control circuit utilizing constant Peltier thermoelectric cooling and variable Joule heating controlled by a thermistor in an ac Wheatstone bridge. The calorimeter was tested periodically by measuring the heats of dilution of aqueous sodium chloride solutions (Le., 1the constant /3 is imaginary and eq 6a becomes
t = (1 + lPi2)/[l+ lpl cot (IpIY)] (6b) In eq 2 and 3b also, P2 must be replaced by Id2and a change in sign when [ > 1. In the limit of high dilution when the concentration becomes vanishingly small, eq 6 requires that the constant P also approach zero; eq 2a then takes on the limiting form which is given also by the infinite line charge theory4
+
lim -dAHD - - zpRT (1 d In Dld In T ) (7) -0 dln c 2zc[ The enthalpy of dilution values in Figure 1, which include those published by Skerjanc and Dolar? appear to agree well over a wide range in concentration with the curve computed from eq 2 with a high-speed computer. The experimental precision of the AHDvalues is indicated by vertical bars or by duplicate points a t constant -log mi. Below -log mi = 1.8 (i.e., mi = 1.85 X with NaPSS there is no dependence on molecular weight. All of the data taken with sodium poly(styrenesu1fonate) suggests that the limiting slope predicted by the infinite line charge model (eq 7 ) is approached a t concentrations below ca. 3 X IOb3 m (Figure 2). Interestingly, the measurements taken with the NaPMOS solutions (Figure 1) appear to agree well with eq 2 whereas the AHD values for the NaPES solutions depart widely from both the cell and line charge theories. The behavior of this latter polyelectrolyte is quite similar to that of aqueous solutions of sodium poly(acrylate), NaPA, which recently also have been found13 to show much smaller enthalpies of dilution than those estimated from eq 2 assuming the “structural value” of ( = 2.828.
The enthalpy of dilution values observed with sodium polyacrylate solutions have been accounted for by Skerjanc13 who has followed Katchalsky and coworkers14 in using an empirical, or “effective”, value of the charge density parameter, teff,to fit the data. The ratio, Eeff/tstruct, between the empirical and the structural value, eq 4, of t is always greater than or equal to unity, and appears to be proportional to the extent of coiling of the macroion. The ratio of teffto [struct for highly charged vinylic polymers is close to 2.0 using osmotic coefficient data. If teff= 5.66 is used in eq 2 the estimated concentration dependence of AHD on -log rn for NaPA is found to agree with experiment for concentrations between m = 0.1 and 0.0094 monomolar. There are difficulties with the foregoing proposed explanation in addition to the fact that a value of teff= 5.66 would require excessive polyion coiling. Other measurements, such as those of ionic and mean ionic activity coefficients, Donnan distributions, etc. are consistent with the structural value of = 2.83. Thus, it would seem that the cause of the failure of eq 2 and 7 with E = tstruct to describe the conD NaPA and NaPES solucentration dependence of ~ H for tions (Figure 1)should be looked for elsewhere. Several properties of NaPSS, NaPES, and NaPA solutions support the hypothesis that the counterions (Le., Na+) are the most strongly bound to the PES- polyion. The sequences of the osmotic coefficients7J5 and of the sodium ion activity coefficients16 are NaPSS > NaPA > NaPES. Further, the volume increase on forming NaPSS, NaPA, and NaPES in dilute aqueous media from their respective tetramethylammonium salts have been reported17 as 1.2,4.1, and 4.7 ml per equivalent of total cation present. If, as these results suggest, substantial solvation changes occur in the formation of NaPES and NaPA the calorimetric measurements would be expected to show deviations from the electrostatic theory. The relatively smaller A V for NaPSS can be attributed to difference from NaPES in the spacing of the sulfonate groups making the cooperation of adjacent groups in the binding of Na+ ion more difficult for the PSS- polyion. Thus, NaPSS is more suitable for studying long-range electrostatic forces with minimum interference from short-range interactions, and it is not surprising that the enthalpies of dilution of NaPSS follow the predictions of electrostatic theory. The conclusions from recent light scattering and intrinsic viscosity determinations with NaPMOS, NaPSS, NaPA, The Journal of Physical Chemistry, Vol. 80, No. 8, 1976
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G.E. Boyd, D. P. Wilson, and G. S. Manning
and NaPES solutions,ls which show the latter polyelectrolyte to be the most flexible of the group, are not inconsistent with the occurrence of the strongest binding of Na+ ion by it: sodium ions shield the negative charges on the PESpolyion efficiently, and hence reduce the sulfonate group repulsions to the greatest extent. The virtually identical concentration dependence of AHD (Figure 1) found with NaPSS and NaPMOS is of interest in that dilute solutions of both polyelectrolytes obey the predictions of electrostatic theory. Both polyanions have bulky sidechains and their sulfonate groups are approximately equidistant from the chain backbone, although there are differences in their hydrophobic characters and molecular rigidities. Both polyelectrolytes are well extended in the absence of salt because of the mutual repulsion of their sulfonate groups, but, because of its flexible, hydrated sidechain, these groups in NaPMOS may be approached more readily by counterions. The extent of Na+ ion binding in NaPMOS, therefore, is larger than in NaPSS. However, in both polyelectrolytes there is little or no short-range interaction with the Na+ ion.
References and Notes (1) R. M. Fuoss, A. Katchalsky, and S. L. Lifson, Proc. Nat. Acad. Sci., 37, 579 (1951). (2) S. Lifson and A. Katchalsky, J. Polym. Sci., 13, 43 (1954). (3) T. Alfrey, P. W. Berg, and H. Morawetz, J. Polym. Sch. 7, 543 (1951). (4) G. S. Manning, J. Chem. Phys., 51, 924 (1969). (5) J. Skerjanc, D. Dolar, and D. Leskovsek, 2.Phys. Chem. (Frankfurt am Main), 56, 207, 218 (1967); 70, 31 (1970). (6) J. Skerjanc, S. Hocervar, and D. Dolar, 2.Phys. Chem. (Frankfurt am Main), 86, 311 (1973). (7) G. E. Boyd, “Polyelectrolytes”, Vol. I., E. Selegny, Ed., D. Reidel Publlshing Co., Dordrecht, Holland, 1974, pp 135-155. (8) N. N. Aylward, J. Polym. Sci, Polym. Chem. Ed., 13, 373 (1975). (9) J. Hen and U. P. Strauss, J. Phys. Chem., 78, 1013 (1974). (IO) H. Eisenberg and G. R. Mohan, J. Phys. Chem., 63, 671 (1959). (11) J. S. Tan and S.P. Gasper, J. Polym. Sci., Phys. Ed., 12, 1785 (1974). (12) J. J. Chrlstensen, J. W. Gardner, D. J. Eatough, and R. M. Izatt, Rev. Sci. Instrum., 44, 481 (1973). (13) J. Skerjanc, Biophys. Chem., 1, 376 (1974). (14) A. Katchalsky, 2. Alexandrowicz, and 0. Kedem, “Chemical Physics of Ionic Solutions”, B. E. Conway and R. G. Barradas, Ed., Wiley, New York, N.Y., 1966, pp 295ff. (15) N. Ise and K. Asai, J. Phys. Chem., 72, 1366 (1968). (16) R . W. Armstrong and U. P. Strauss, Encycl. Polym. Sci. Techno/,. IO, 781-861 (1969); seep 811. Figure 12. (17) U. P. Strauss and Y. P. Leung, J. Am. Chem. SOC.,87, 1475 (1965). (18) J. S. Tan and S. P. Gasper, J. Polym. Sci., Polym. Phys. Ed., 13 [9], 1705 (1975).
Enthalpies of Mixing of Polyelectrolytes with Simple Aqueous Electrolyte Solutions G. E. Boyd,* David P. Wllson, Department of Chemistry, University o f Georgia, Athens, Georgia 30602
and Gerald S. Manning School o f Chemistry, Rutgers University, New Erunswick, New Jersey 0890 1 (Received September 19, 1975) Publication costs assisted by the University of Georgia
The enthalpy changes on mixing dilute aqueous solutions of atactic sodium poly(styrenesulfonate), NaPSS, and sodium chloride were measured at 298.15 K with a sensitive isothermal microcalorimeter. The addition of salt to a NaPSS solution in general was accompanied by the absorption of heat, while the addition of polyelectrolyte to a salt solution became less exothermic with increasing NaCl concentration. The observed mixing enthalpies departed widely from values predicted on the basis of the “additivity rule” (i.e., no interaction between salt and polyelectrolyte), but, when they were corrected for the heat of dilution of the salt, they agreed well over a wide composition range with predictions from the infinite line charge theory.
Introduction The fundamental assumption that the addition of simple salt to an aqueous polyelectrolyte solution does not significantly alter the immediate ionic atmosphere around the polyions has been the starting point for a number of investigations of the properties of such mixtures. If the foregoing hypothesis accurately describes the structure of electrolyte-polyelectrolyte mixtures it may be expected that the separate contributions of the added salt and of the polyion with its counterions to a given thermodynamic property of a mixture will be distinguishable and independent of each other. Additivity of several properties related to the excess free energy of salt-polyelectrolyte mixtures (viz. osmotic and activity coefficients, Donnan distributions, etc.) have The Journal of Physical Chemistry, Vol. 80, No. 8, 1976
been reported and discussed most notably by Katchalsky and his co-worker~.l-~ The empirical nature of the “additivity rule” derived from observations on colligative properties is now recognized, and, in fact, strict additivity has been shown not to be obeyed when precise measurements are a ~ a i l a b l e . ~ - ~ Furthermore, results from the infinite line charge theory of polyelectrolyte^^^^ which is based on a different model suggest that the assumption that the salt does not interact with the polyions cannot be correct. On the other hand, good approximations to the measured properties of mixtures can be inferred from additivity, and thus the “rule” may have useful applications to systems of biological interest or of industrial importance.
