2584
J. Phys. Chem. 1980, 84, 2584-2587
Heats of Mixing of Polyelectrolyte and Simple Electrolyte Solutions J. Skerjanc," A. Regent, and L. Boiovi5 Kocijan Department of Chemistty, Edvard Kardelj University, 6 1000 Ljubljana, Yugoslavia (Received: March 7, 1980)
The heats of mixing of aqueous solutions of alkali metal poly(styrenesulfonates)with solutions of the corresponding alkali metal chlorides of the same concentration of the cation (0.06 mol/L), and of poly(styrenesu1fonicacid) with hydrochloric,perchloric, nitric, p-toluenesulfonic, iodic, and trichloroacetic acids and poly(ethy1enesulfonic acid) were measured at 25 "C. A few measurementshave also been performed at higher and lower concentrations. In most cases the heat effects were endothermic. The observed mixing enthalpy decreases with increasing concentration and is strongly dependent on the ionic radius of the common counterion and the low molecular weight anion. The experimental results, corrected for the heat of dilution of the simple electrolyte,were compared with predictions from the infinite line charge theory. Reasonable agreement between experiment and theory can be expected at concentrations below ca. 0.001 mol/L.
Introduction In most polyelectrolyte theories the individuality of counterions has usually been neglected and they have been frequently treated as point charges. This theoretical simplification, however, has not been supported by various experimental observations. For example, measurements with solutions of the alkali metal poly(styrenesu1fonates) have disclosed that the osmotic coefficient decreases with the decreasing radius of the hydrated counterions.1,2The influence of the size of the counterion on thermodynamic properties of polyelectrolyte solutions has been still more clearly reflected in the enthalpy3 and volume changes4on dilution. In the articles quoted the electrostatic polyelectrolyte theory based on the cylindrical cell modeP6 has been used for the theoretical interpretation. Attempts to treat counterions in this model as hard spheres of different radii explained the experimental observations only qualitatively but proved unsuccessful to explain them quantitatively. On the basis of these findings it was concluded that besides Coulombic, long-range forces also short-range forces should be considered in a future, more general, polyelectrolyte theory. The individuality of counterions, reflected in various studies more or less explicitly, seems to be manifested very drastically in heat of mixing measurements. In our recent article7we report on heat effects accompanying the mixing of two polyelectrolyte solutions containing the same POlyion (poly(styrenesu1fonate) anion) and different counterions. Since mixing of counterions has been performed at constant ionic strength and thus in a constant electrical field of the common polyion, only the interactions of like-charged counterions have been reflected in the enthalpy of mixing. It was found that the heat effects may be endothermic or exothermic, depending on which counterions are mixed. This experimental finding has not been supported by the extended theoretical cell models in which two kinds of monovalent counterions are present, differing in size, and which predicts only positive values of the enthalpy of m i ~ i n g . ~ Another article which is related immediately to the present studies, by Boyd et reports on the enthalpy changes ensuing from mixing an aqueous solution of sodium poly(styrenesu1fonate) with a solution of sodium chloride. It was found that the heat effects are endothermic when simple salt is added to a polysalt solution, and in general they are exothermic when polyelectrolyte is added to a salt solution. The observed mixing enthalpies, corrected for the heat of dilution of the salt, agreed well over a wide composition range with the prediction of 0022-3654/80/2084-2584$0 1 .OO/O
the infinite line charge theory.1° However, in experiments in which salt was added to the polyelectrolyte solution, increasing deviations from the predicted values were observed when the concentration of the salt solution was increasing. The present studies refer to this composition range. Instead of varying the concentrations of the salt and POlysalt solutions, we carried out the measurements at constant concentration of the common cation and changed the composition of the mixed solution by mixing various amounts of the two solutions. The poly(styrenesu1fonate) ion was chosen as a polyanion, and, in most cases, chloride was the simple anion. In a few instances also perchlorate, nitrate, p-toluenesulfonate, iodate, trichloroacetate, and poly(ethylenesu1fonate) ions were chosen as the co-ions. Since a strong dependence of the enthalpy of mixing on the size of the counterion has been observed in previous studies, the radius of the common counterion was systematically increased. The following counterions were used: H', Lif, Naf, K', and Cs'.
Experimental Section Poly(styrenesu1fonic acid) (HPSS) and its alkali metal salts were all derived from one single sample of sodium poly(styrenesu1fonate) (NaPSS) obtained from Polysciences Inc. (Rydal, PA). According to the manufacturer's specification the NaPSS had a molecular weight of 100000 and a degree of sulfonation of 1.00. Poly(ethylenesu1fonic acid) (HPES) was derived from its sodium salt which was prepared by the polymerization of sodium ethylenesulfonate following the procedure of Breslow and Kutner.ll The sodium ethylenesulfonate monomer was synthesized from 1,2-dibromoethane by the Stecker reaction.12 The weight-average molecular weight of the HPES was estimated to be 45 000 from viscosity measurements in 0.1 M Na2S04at 25 OC.ll For purification and preparation of polyelectrolyte solutions, dialysis and ion exchange techniques were used as described elsewhere in detail.7 All inorganic chemicals were obtained commercially in reagent grade form. Calorimetric measurements were carried out at 25 "C in an LKB 10700-2 batch microcalorimeter with golden cells. Into one compartment of the reaction cell the polyelectrolyte solution was pipetted, and into the other an appropriate volume of the simple electrolyte solution, so that the total volume of both solutions was 5.00 mL. The reference cell was charged with the corresponding amounts of water. T h e solutions were pipetted by means of Hamilton syringes. 0 1980 American Chemical Society
The Journal of Physical Chemistry, Vol. 84, No. 20, 1980 2585
Heats of Mixing of Electrolyte Solutions
20
t
LiPSS -LiCI
HPSS-HCIO, 20
~
15 L.
I
/
HPSS-HCI
y 15
n
E" 10 -a I
1 Y
E
%
5
CsPSS-CaCI ~
1
0
-
I
-
0.2
I
-
0.6
0.4
XP
--0.8
1.0
Figure 1. Heat of mixing lof 0.150 monomolar of poly(styrenesu1fonic acid) (HPSS) and its alkali metal salts with 0.150 M chlorides in water at 25 O C as a function of the mole fraction of the polymer.
r---
LiPSS-LiCI
20
-5
0
0.2
0.4
0.6
0.8
1.0
XP Flgure 3. Heat of mixing of 0.0600 monomolar poly(styrenesu1fonic acid) with 0.0600 M solutions of perchloric, nitric, hydrochloric, ptoluenesulfonic, iodic, and trichloroaceticacids and poly(ethylenesu1fonic acid) at 25 O C as a function of the mole fraction of HPSS.
simple electrolyte solution, S, of the same concentration of the common counterion. By mixing appropriate amounts of both solutions we obtained the dependence of AHmon the mole fraction of the polysalt, Xp. I t is convenient to express the results of mixing processes in terms of the enthalpy change divided by (np + ns),the total amount of polyelectrolyte and simple electrolyte in monomoles and moles, respectively. Then AHmis related to the enthalpies of the mixed and both single solutions, containing 1 mol of the salts, by eq 1.
15
F-7
-I
E .
10
1
Y
5
0
-5
0
0.2
0.4
0.6
0.8
1.0
XP
Figure 2. Heats of mixing of 0.0600 monomolar poly(styrenesu1fonate) solutions with 0.0800 M clhloride solutions at 25 OC.
Results and DiscusBion The heats of mixing, AHm,were obtained in experiments in which a polyelectrolyte solution, P, was mixed with a
Hmixedsoln - XPHP -
(1 - xP)Hs
(1) The calorimetric results of mixing poly(styrenesulfonates) with the corresponding chlorides are shown in Figures 1 and 2 for two concentrations. Two explicit conclusions can be drawn from the results: (1)The enthalpy of mixing decreases with increasing concentration. This conclusion is supported by results presented in Figures 1and 2 and by experiments carried out at the lower concentration of 0.006 mol/L. The values of AH, at the maximum (at Xp = 0.6) are 25, 22, 19, 17, and 7 cal mol-l of counterions for the Li salt, the acid, Na, K, and Cs salts, respectively. (2) The enthalpy of mixing of the polysalt with the simple salt varies strongly with the size of the common counterion; it increases in the order Cs+ < K+ < Na+ C H+< Li+. Hence, the larger the ionic radius of the hydrated counterion, the higher AH,. The nature of the simple anion is also important, as can be seen in Figure 3. The enthalpy of mixing of poly(styrenesulfonic acid) with simple acids decreases in the order: perchloric, nitric, hydrochloric, p-toluenesulfonic, and iodic acid, becomes negligible when HPSS is mixed m r n
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The Journal of Physical ChemiStry, Vol, 84, No. 20, 1980
with another vinylsulfonic polyacid, poly(ethylenesu1fonic acid), and turns negative for trichloroacetic acid. It seems that there is no simple relation between the heat effect on mixing and the size of the co-ion; the conventional partial 44.12, 29.00, 17.83, 119.6, molal volumes at 25 "C arel3>l4 25.3, and -4.9 mL/mol for perchlorate, nitrate, chloride, p-toluenesulfonate, iodate, and poly(ethylenesu1fonate) anions, respectively. Previous studies7 showed, however, that polyelectrolyte solutions follow Young's sign rule15J6 which has been suggested for simple electrolyte solutions. This rule predicts for charge-symmetrical mixtures that at constant and low ionic strength and in the presence of a common ion the mixing of two structure-making or two structure-breaking ions gives a positive enthalpy of mixing, while the mixing of a structure maker with a structure breaker gives negative AH,. The perchlorate, nitrate, and chloride ions are structure breakers,17 while the p toluenesulfonate,18 iodate, and trichloroacetate ions are structure makers.17 The structure-breaking influence of these anions decreases in the order C10, > NO< > C1- > IO3- > CCl3C0O-, which is also the order of the observed enthalpy changes in Figure 3. It is very likely that the huge poly(styrenesu1fonate) ion is a structure breaker; hence, we can see that, except for the pairs HPSS-HTS and HPSS-HI03, Young's sign rule holds even for the highly charge-asymmetrical mixture of polyanion and low molecular weight anion. For the theoretical interpretation of experimental results, the cell5 and the infinite line chargelo theories have frequently been used. When simple salt is present in a polyelectrolyte solution, the theoretical treatment based on the line charge theory seems to be much simpler although the results are limited to dilute solutions. The theory gives the following expression for the excess Helmholtz free energy of a solution containing one monomole of polyelectrolyte: Fex/RT = -4 In x (2) where x is the Debye screening parameter, while R and T have their usual significances. The charge density parameter, (, the principle parameter of the theory, is for monovalent ions given by eq 3, where eo is the protonic f = e:/tkTb (3) charge, E is the dielectric constant of the solvent, h is the Boltzmann constant, and b is the length of a monomer unit. A slight difference between Helmholtz and Gibbs free energies may be negle~ted.~ Application of the GibbsHelmholtz equation to eq 2 gives an expression for the electrostatic enthalpy of a solution containing polysalt and simple salt, He. By subtracting the corresponding enthalpy of solution containing only polysalt, Heo,one obtains the electrostatic enthalpy of transfer, AHt = He - Heo,of polysalt from an aqueous solution to a solution of simple salt? This can be comparedgwith the observed enthalpy changes on mixing solutions of polysalt and simple salt, AH,, corrected for the enthalpy of dilution of the salt solutions from the initial concentration C,' to the final concentration C,f. For our experimental condition for which the initial concentrations of polysalt and simple salt are equal, C,f = (1- XP)Csi,and the final expression for the enthalpy of transfer, AHt, calculated per total amount of solute is given by ( E > 1) eq 4. The value of ,$ for the vinylic poly-
sulfonates in water is ( = 2.83 at T = 298.15 K and for water d In t/d In T = -1.327. Thus, the theory predicts
Skerjanc et al.
1
HPSS-HTCA LiPSS- LiCl HPSS-HTS HPSS-HCl HPSS-HJO, 6 HPSS-HNO. 7 HPSS- HCIO. E NaPSS-NaCI 9 KPSS-KCI 10 CsPSS- C I C l 1 2 3 4 5
100
-
EO
2
3 4
5
in
6 Th 7
-n
3
80
5
E
-
\ lo
-!A 4 0
6
f
: 20
9
0
- 20 0.5
0
1.5
1.0
In [29 +(1-25)xP]
Flgure 4. Corrected heats of mixing of poly(styrenesu1fonic acid) with simple acids (empty circles), and alkali metal poiy(styrenesu1fonates) with alkali metal chlorides (solid circles) at the concentration of the common cation 0.0600 mol/L. Dashed straight line: prediction of the infinite line charge theory (eq 4).
MPSS I C.]
2o
-
cs+ P
,
, 1
- MCI :CM]
2
1.5
-log
c.
Figure 5. Corrected heat of mixing of poly(styrenesu1fonates)with the corresponding chlorides at Xp = 0.6 and 25 OC as a function of the concentration of the common cation, M+. Dashed line: prediction from the infinite line charge theory (eq 4).
positive values of AHt, which are more typical for the present studies. The function given by eq 4 is asymmetrical with respect to mole fraction with the maximum at X, = 0.62, a prediction which can be observed in most cases if corrected values of AH, are plotted against X,. To what extent theoretical and experimental values agree quantitatively depends, however, strongly upon the experimental concentration and upon the nature of the common counterion and co-ion. This is clearly demonstrated in Figures 4 and 5. In Figure 4 the theoretical values expressed as AHt/Xpare plotted against the logarithmic term in eq 4. The points are the experimental enthal'pies of mixing for concentration 0.06 mol/L corrected for the enthalpies of dilution, A",,and calculated
J. Phys. Chem. 1980, 84, 2587-2595
per monomole of polyelectrolyte. Values of AHDwere taken from the beiat available literature source;21 the missing data for iodic, p-toluenesulfonic, and trichloroacetic acids were obtained from other source^.^^^^^ As can be seen, the experimental results are spread out like a fan around the theoretical straight line. We must not forget, however, that the infinite line charge theory on which eq 4 is based is strictly valid only for extremely dilute solutions, whereas the experiments were carried out at finite concentrations. Also, the corrected values of AHmare only approximations for the enthalpy of transfer given by eq 4. As expected, the agreement between theory and experiment gets better at lower concentrations (Figure 5), a finding which has been observed also in many previous studies. Although the nature of the counterions is definitely expressed even at concentrations as low as 0.006 mol/L, one may expect that their individuality will disappear at extreme dilution. Acknowledgment. The partial financial support of the Research Council of Slovenia is gratefully acknowledged.
References and Notes (1) P. Chu and J. A. Marinsky, J . Phys. Chem., 71, 4352 (1967). (2) D. Kozak, J. Kristan, and D. Dolar, 2.Phys. Chem. (Frankfurtam Main). 76. 85 (1971). (3) J. Skerjanc, D. Dolar,’and D. LeskovSek, Z. Phys. Chem. (Frankfurt am Main), 56, 207 (1967); 70, 31 (1970).
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J. Skerjanc, J. Phys. Chem., 77, 2225 (1973). (a) R. M. Fuoss, A. Katchalsky, and S.Lifson, Proc. Natl. Acad. Sci. U.S.A.,37, 579 (1951); (b) T. Alfrey, Jr., P. W. Berg, and H. Morawetr, J. Polym. Sci., 7, 543 (1951). S.bifson and A. Katchaisky, J. Polym. Scl., 13, 43 (1954). J. Skerjanc and M. Pavlin, J. Phys. Chem., 81, 1166 (1977). D. Dolar and J. Skerjanc, J. Polym. Sci., Polym. Phys. Ed., 14, 1005 (1976). G. E. Boyd, D. W. Wilson, and G. S. Manning, J . Phys. Chem., 80, 808 (1976). 0. S. Manning, J . Chem. Phys., 51, 924 (1969). D. S. Breslow and A. Kutner, J . Polym. Sci., 27, 295 (1958). C. E. Schlldknecht, “Vinyl and Related Polymers”, Wiley, New York, 1952, p 645. F. J. Mlllero, Chem. Rev., 71, 147 (1971). N. Ise and T. Okubo, J . Am. Chem. Soc., 90, 4527 (1968). T. F. Young, Y. C. Wu, and A. A. Krawetz., Discuss. Faraday Soc., 24, 37 (1957). Y. C. Wu, M. B. Smith, and T. F. Young, J. Phys. Chem., 69, 1868 (1965). H. L. Anderson and R. H. Wood in “Water, a Comprehensive Treatise”, Vol. 3, F. Franks, Ed., Plenum Press, New York, 1973, p 139; H. G. Hertz, ibid., pp 362, 369. he p+ihyibenzenesuifonate anioni9 and the benzenesuifonate anion” are structure makers. 0.E. Boyd, F. Vasbw, A. Schwarz, and J. W. Chase,J. Phys. Chem., 71, 3879 (1967). R. E. Robertson, S. E. Sugamori, R. Tse, and C. Y. Wu, Can. J. Chem., 44, 487 (1966). V. 6.Parker, Natl. Stand. Ref. Data Ser. (U.S., Nati. Bur. Stand.), No. 2 (1965). E. M. Woollev, J. 0. Hill. W. K. Hannan. and L. G. HeDler. J. Solution Chgm., 7, 385 (1978): J. Skerjanc, unpublished results.
Isotope Effects in Aqueous Systems. 9. Partial Molar Volumes of NaCI/H,O and NaCI/D,O Solutions at 15, 30, and 45 OC Geralld Dessauges, Nada Miljevic,+and W. Alexander Van Hook“ Chemistry Department, University of Tennessee, Knoxvlle, Tennessee 379 16 (Received: November 5, 1979; In Final Form: Msrch 14, 1980)
Densities of NaCl solutions in H20 and D20have been measured with high precision at 15,30, and 45 “C by using a Mettler/Paar densitometer. The data in H20 are compared with the best results of earlier workers. Solvent isotope effects onbpparent molar volumes of NaCl solutions are large and, within experimental error, are proportional to m’/2. They are interpreted in the context of available extended Debye-Huckel theories and cliscussed in terms of the molecular structure of the solvents.
Introduction Dessauges and Van Hook’ (DVH) have recently presented a semiempirical analysis of the electrostatic contribution to excess free energies of aqueous electrolyte solutions at moderate concentrations. The model, like other extended theories2“ reduces to the exact DebyeHuckel (DH) so1utio.d in the limit of high dilution. The Debye model predicts that the various partial molar and apparent molar thermodynamic properties should extrapolate to zero concentration according to m1/2and with a slope which is theoretically defined in terms of the properties of the solvent. Nonetheless difficulties arise since most, if not all, of the thermodynamic properties at the lower limit of practical experiment are not yet in the region where the limiting law is obeyed. It therefore becomes necessary to extend the theory into the experimentally accessible region with theoretical, empirical, or Boris Kidric Institute of Nuclear Science, Physical Chemistry Department, Belgrade, Yugoslavia. 0022-3654/80/2084-2587$0 1.0010
semiempirical arguments. These attempts are collectively labeled “extended Deybe-Huckel theories”. Our interest in this general area stems from the observations of Van Hook and co-workers that solvent isotope effects on osmotic coefficients7 and relative excess enthalpiese phenomonologically display approximate m1l2 dependences out to concentrations of several molal with slopes in excess of those predicted from known isotope effects on the first-order Debye-Huckel limiting-law terms. This observation was not consistent with then available extended t h e ~ r i e s . ~It- ~led to a new one-parameter extended theory1 which successfully rationalizes excess free energies and solvent isotope effects on excess free energies out to relatively high concentrations. In the present paper we turn attention to the solvent isotope effect on molar volume and report new data over a wide concentration range at three temperatures, 15,30, and 45 “C, for the NaC1/H20 and NaCl/D20 systems. Previous measurements of the solvent molar volume isotope effect of NaCl have been reported by Conway and 0 1980 American Chemical Society
