J . Phys. Chem. 1987, 91, 3845-3848 of the individual bond dissociation energies in these compounds are also quite uncertain.' Acknowledgment. J. W. Simons gratefully acknowledges the financial assistance and kind hospitality of the Photochemistry Group (Chem-4) while on sabbatical leave at Los Alamos National
3845
Laboratory. Support from SDIO/IST is gratefully acknowledged. The technical assistance of Douglas Hof and Kenneth Winn is gratefully acknowledged. Registry No. Pb12, 10101-63-0; Pb, 7439-92-1; I, 7553-56-2; PbI,
13779-93-6.
Free Enthalpies, Enthalpies, and Entropies of Dilution of Aqueous Solutions of Alkaline Earth Poly(styrenesu1fonates) at Different Temperatures G. Vesnaver,* Z. Kranjc, C. Pohar, and J. Skerjanc Department of Chemistry, Edvard Kardelj University, Ljubljana, Yugoslavia (Received: December 16, 1986)
The free enthalpies, enthalpies, and entropies of dilution of aqueous solutions of alkaline earth poly(styrenesu1fonates) were determined at 0, 25, and 40 OC. It is shown that the free enthalpies of dilution are rather insensitive to temperature while the corresponding enthalpies and entropies of dilution increase significantly when temperature is lowered. Such behavior cannot be explained by the electrostatic polyelectrolytetheory based on the cell model. Instead it is suggested that the observed temperature dependence of the measured quantities of dilution is due to the changes in water structure in the immediate vicinity of counterions.
Introduction We recently studied the free enthalpies (AGD), enthalpies (AHD), and entropies ( A S D )of dilution of aqueous solutions of alkali metal poly(styrenesu1fonates) at different temperatures.'.2 The results obtained clearly indicate that the electrostatic polyelectrolyte theory based on the cylindrical cell model3 cannot explain the observed dependence of AGD, AHD, and ASD on the temperature and the type of the counterion. It has been shown that this dependence can be interpreted qualitatively in terms of changes in water structure around the counter ion^.^ In order to gain more information concerning the contributions of the solute-solvent interactions to the quantities of dilution, the present work on AGD, AHD, and ASD of aqueous solutions of poly(styrenesu1fonates) with divalent counterions was undertaken. Experimental results were compared with the predictions of the electrostatic polyelectrolyte theory3 to see whether larger Coulombic interactions between polyion and the divalent counterions lead to any better correlation between the theory and the experiment. As before,2 the deviations from the calculated values were discussed in terms of structural interactions between the counterions and the neighboring water molecules. Experimental Section Aqueous solutions of magnesium (MgPSS), calcium (CaPSS), and strontium (SrPSS) poly(styrenesu1fonates) were prepared by titrating poly(styrenesu1fonic acid) (HPSS) with the corresponding metal carbonate until pH was about 5.5. HPSS was prepared by the usual ion-exchange and dialysis techniques from sodium poly(styrenesu1fonate) (NaPSS) with molecular weight of 70 000 and a degree of sulfonation 1.O (Polysciences, Inc., Warrington, PA). The concentrations of stock solutions were determined complexometrically and spectrophotometrically. Enthalpies of dilution were measured at 0, 25, and 40 O C in an LKB 10700-1 flow microcalorimeter unit thermostat4 within f0.005 OC. Osmotic coefficients were determined at 25 and 40 O C by vapor pressure osmometry while their values at 0 OC were obtained from the l i t e r a t ~ r e . The ~ instrument used was Knauer (1) Vesnaver, G.; Rudei, M.; Pohar, C.; Skerjanc, J. J . Phys. Chem. 1984, 88, 2411. ( 2 ) Vesnaver, G.; Skerjanc, J. J . Phys. Chem. 1986, 90, 4673. (3) (a) Fuoss, R. M.; Katchalsky, A.; Lifson, S . Proc. Natl. Acad. Sci. U.S.A.1951, 37, 579. (b) Alfrey, T. Jr.; Berg, P. W.; Morawetz, H. J . Polym. Sci. 1951, 7 , 543. (4) Frank, H. S.; Wen, W. Y. Discuss. Faraday SOC. 1957, 24, 133.
0022-3654/87/2091-3845$01.50/0
vapor pressure osmometer. Osmotic coefficient, cp, was obtained as described earlier,2 using the relation 4." c p = m
where m is the monomolality of the polyelectrolyte solution with divalent counterions and cp. and m. are the osmotic coefficient6 and molality of the KCI solution with which the same resistance change was measured as with the polyelectrolyte solution.
Results As shown in Figures 1, 2, and 3 the measured enthalpies of dilution of MgPSS, CaPSS, and SrPSS solutions at 0, 25, and 40 OC become increasingly endothermic with decreasing temperature and when going from Mg2+ through Ca2+ to Sr2+ counterion. Evidently, this behavior is very similar to the one observed with alkali poly(styrenesu1fonate) solutions, even though the AHDvalues obtained for poly(styrenesu1fonates) with divalent counterions are much lower.' Osmotic coefficients of MgPSS, CaPSS, and SrPSS solutions determined at 25 and 40 "C are presented in Figures 4 and 5 . Comparison with the corresponding cp values at 0 "C taken from the literatureS shows that osmotic coefficient depends very little on the temperature, the concentration of the polyelectrolyte solution, and the nature of the divalent counterion. Discussion As shown previously,2 the free enthalpies, enthalpies, and entropies of dilution of polyelectrolyte solution from the initial concentration m to the final concentration mo can be expressed as ACD(m+mo) = AGDo(M+mo)
+ AGDC(m+mo) + AGD"(m+ m0)
AHD(m+mo) = AHDO(m-mo)
AHDc(m+ mo) + AHDn(m+mo)
ASD(m+mo) = hSoo(M+mo) -k aD'(m+Wo)
+ ASD"(m+ mo) (1)
( 5 ) Kozak, D.; Dolar, D. Z . Phys. Chem. (FrankfurtlMain) 1971, 76, 93. (6) Robinson, R. A.; Stokes, R. H. Electrolyte Solufions, 2nd ed.; Butterworths: London, 1959; p 481.
0 1987 American Chemical Society
3846 The Journal of Physical Chemistry, Vol. 91, No. 14, 1987
Vesnaver et ai.
A =1103 /
/
/ /
100
..i=11.34 . MgPSS c
I
s
B
, ,
, 0
, 0
o
8
2 t
-E
I" -
loa
- 200
-loot
- 30C
1
I
2
1
-log m
2
Figure 1. Enthalpy of dilution of aqueous solutions of MgPSS, CaPSS, and SrPSS as a function of monomolality, m, at 0 OC. Dashed line: values calculated from the cell theory (eq 12) with parameter X as indica ted .
where AGOo, AHDO,and ASDo refer to a hypothetical uncharged polyelectrolyte solution and the AG$, AHDc,and ASDcand AGD", AHD", and ASD'' terms represent contributions due to the Coulombic and non-Coulombic interactions that take place in the real polyelectrolyte solutions. With polyelectrolytes having a large number of ionic groups on the polyion the free enthalpy of dilution expressed per monomole of polyelectrolyte can be presented as
1
- log m
I
Figure 2. Enthalpy of dilution of MgPSS, CaPSS, and SrPSS at 25 O C . Other details as in Figure 1.
dilution can be expressed only in terms of the experimentally determined quantities.
Similar expressions relating enthalpies and entropies of dilution to experimental data can be obtained by applying general thermodynamic relations to eq 3 and 4. It is easy to show that
AHDO(m-.mo)= 0
(6)
where z, and z2 are the charge numbers of the ionized groups on the polyion and the counterions, -yh and 7%are the polyelectrolyte mean activity coefficients at the initial and final concentration, and cp and cpo are the corresponding osmotic coefficients. By applying the Gibbs-Duhem relation between y+ and p to eq 2 it follows that
AGo(m-.mo) = ? R T [ In z2
+ LI(1- p) d In m
3
AHD(m+mo) (3)
The corresponding expression for the free enthalpy of dilution of hypothetical uncharged polyelectrolyte solution is obtained from eq 3 assuming that the osmotic coefficient of uncharged polyelectrolyte is equal to 1. z1 m0 AGDo(m-.mo) = -RT In '72 m
(9)
(4)
Finally, it follows from eq 1, 3, and 4 that the sum of the Coulombic and non-Coulombic contributions to the free enthalpy of
T
zI
m
Z2
mo
--RS
(1 - p) d In m (10)
As in previous work2we tried to interpret our experimental results by means of the electrostatic polyelectrolyte theory based on the cylindrical cell modeL3 According to this theory the electrostatic free enthalpy of solution per monomole of polyelectrolyte, G,, the corresponding electrostatic enthalpy, He, entropy, S,, and the osmotic coefficient, cp, are given by7-'' (7) &ifson, S.; Katchalsky, A. J . Polym. Sci. 1954, IS, 43. (8) Skerjanc, J. J . Phys. Chem. 1973, 77, 2225. (9) Skerjanc, J.; Dolar, D.; LeskovSek. D. Z . Phys. Chem. (Frankfurt/ Main) 1967, 56, 207.
The Journal of Physical Chemistry, Vol. 91, No. 14, 1987 3847
Properties of Alkaline Earth Poly(styrenesu1fonates) G, =
-
(e2?- 1)[(1 2x
- f12]
In
""-)
( 1 + d In T
[
z~RT
(1
- (1
- X)2 - pz 1 -pz
2Xe2Y
+2zzh 1 - P2 - E 1
S , = -(He - G,) T
+ PZ)Y -
-x
1
(11)
1
d In V ] CT) ( (12)
(13)
where
and all other symbols have the same meaning as defined earlier.2,7-10
The Coulombic contributions AGD', AHD', and ASD' as well as non-Coulombic contributions AGD", A&", and ASD" were then estimated by assuming that the real AGD', AHD', and ASD' values may be equated with the corresponding values of AGDe, AHD', and ASDecalculated from eq 1 1 , 12, and 13. The values of AGD, AHD, and ASD determined at 0, 25, and 40 "C for the dilution of MgPSS, CaPSS, and SrPSS solutions from m = 0.4 to mo = 0.04 monomol/kg of H 2 0 are reported in Table I. The AHD values were obtained directly from the AH, vs. log m curves presented in Figures 1-3 while the AGD and ASD values were determined from the experimental data by using eq 3 and 8. The s ( l - p) d In m terms needed in these calculations were obtained by graphic integrations of the measured p vs. m relations (Figures 4 and 5 and ref 5). Inspection of results given in Table I shows that the measured AGD values are rather insensitive to temperature while the corresponding AHD and ASD values become increasingly endothermic and positive at lower temperature, a behavior very similar to the one observed with solutions of poly(styrenesu1fonates)with monovalent counterions.'J Comparison of results obtained for poly(styrenesu1fonates) with monovalent and divalent counterions (Table I, ref 2) shows that the influence of the nature of the counterion on AH, and ASD is much less important when counterions are doubly charged. Similar behavior has also been observed with simple electrolyte solutions whose various thermodynamic properties seem to be less influenced by the size of divalent than by the size of monovalent
I
2
Figure 3. Enthalpy of dilution of MgPSS, CaPSS, and SrPSS at 40 OC. Other details as in Figure 1. TABLE I: Values of ACm AHm and A S D for MgPSS, CaPSS, and StpSS at 273.15, 298.15, and 313.15 K and the Corresponding ACDo, AHDO, and ASDo Values for a Hypothetical Uncharged Polyelectrolyte Solution' AGD, J monomol-l ACDo, T, K J monomol-i MgPSS CaPSS SrPSS -26 1 -282 -28 1
273.15 298.15 313.15
-2615 -2854 -2998
-342 -356 -317
T, K
AHDO, J monomol-I
MgPSS
CaPSS
SrPSS
273.15 298.15 313.15
0 0 0
14 -99 -174
81 -24 -113
153 38 -54
The AG$, AHD', and ASD' values for the same dilution process were calculated by using eq 1 1 , 12, and 13 and the characteristic parameters a = 0.8 nm, b = 0.252 nm, and t = 87.896, 78.358, and 73.151; d In t/d In T = -1.257, -1.368, and -1.434; d In V/d T, K In T = -0.0161, 0.0767, and 0.120; and Xeff = 11.03, 11.34, and 273.15 11.56 at 0, 25, and 40 "C, respe~tive1y.l~Effective v a l ~ e s ~ ~ ~298.15 ~ ~ of the charging parameter X 2 times higher than the corresponding 313.15
-248 -272
AH,, J monomol-I
hsD,
ASDO,
J monomol-' K-I
J monomol-I K-I
MgPSS
CaPSS
SrPSS
9.57 9.57 9.57
1.30 0.86 0.46
1.25 0.87 0.54
0.96 0.70
aInitial concentration m = (10) Marcus, R. A. J . Chem. Phys. 1955, 23, 1057. (11) Frank, H.S.;Robinson, A. L. J . Chem. Phys. 1940, 8, 933. (12) Wood, R. H. J . Phys. Chem. 1959.63, 1347. (13) Wood, R. H.; Anderson, H. L. J . Phys. Chem. 1966, 70, 992. (14) Owen, B. B.; Miller, R. C.; Milner, C. E.; Cogan, H. L. J . Phys. Chem. 1961.65, 2065. (1 5) Katchalsky, A,; Alexandrowicz, Z.; Kedem, 0. In Chemical Physics of Ionic Solutions; Conway, B. E., and Barradas, R. G., Ed.; Wiley: New York, 1966; p 295. (1 6) Armstrong, R. W.; Strauss, U. P. In Encyclopedia of Polymer Science and Technology; Mark, H. F., Gaylord, N. G., Bikales, N. M., Ed.; Interscience: New York, 1968; Vol. 10, p 797.
I
1
-log m
0.4
and final concentration m =
0.04
monomol/kg of H,O.
structural values (eq 15) were chosen because their use in eq 14 gives in the measured concentration range a reasonably good agreement between the measured and calculated osmotic coefficients (Figures 4 and 5 and ref 5). Results of these calculations are presented in Table I1 together with the values of AGD", AHD", and ASD" estimated according to eq 5, 7, and 10. Comparison of the measured free enthalpies, enthalpies, and entropies of dilution (Table I) with those calculated from the cell
The Journal of Physical Chemistry, Vol. 91, No. 14, 1987
3848
0.31
0
I
CaPSS
0 SrPSS F
e?,-
0.2
h'_. ,
1
0
1.5
0
0.5
1.0 - log m
Figure 4. Osmotic coefficient of aqueous solutions of MgPSS, CaPSS, and SrPSS as a function of monomolality, m, at 25 OC. Dashed line: values calculated from the cell theory (eq 14) with parameter A as indicated.
TABLE II: Computed Coulombic Contributions of Dilution, AGUE, muc, and Mucand the Corresponding Non-Coulombic Contributions AGUE,AHu", and ASD@for MgPSS, CaPSS, and SrPSS at 273.15, 298.15. and 313.15 K O AGD", J monomot-] AGD', T, K J monomol-' MgPSS CaPSS SrPSS 273.15 2414 -141 -60 2645 -146 -7 3 -39 298.15 2784 -103 -6 7 -58 313.15 AHD'.
313.15
J monomol-' -7 4 -1 I9 -143
T, K 273.15 298.15 313.15
ASS$, J m ~ n o m o l -K-I ~ -9 I 1 -9.27 -9.35
T, K 273.15 298.15
Vesnaver et al.
A H D ~J, monomol-' MgPSS CaPSS SrPSS 88 I55 227 20 95 157 -3 1 30 89 ASDn,
MgPSS 0.84 0.56 0.24
J monomol-l CaPSS 0.79 0.57 0.32
K-' SrPSS 0.66 0.48
"Initial concentration m = 0.4 and final concentration m = 0.04 monomol/kg of H20.
theory (Table 11) shows that in spite of strong Coulombic interactions between the polyion and the divalent counterions this electrostatic polyelectrolyte theory fails to explain the observed behavior of AGD, AH,, and ASD. Therefore, in attempting to discuss the measured quantities of dilution the same approach has
1.5
I
-1ogm
0.5
Figure 5. Osmotic coefficient of MgPSS, CaPSS, and SrPSS solutions at 40 OC. Details as in Figure 4.
been used as with poly(styrenesu1fonates) with monovalent counterions.2 The suggested interpretation of AGD, AHD,and ASD is based on the assumption that at higher concentrations there is some overlapping of those outer regions around the divalent counterions in which the water structure is broken down! Reduced overlapping of these regions caused by the dilution process should therefore lead to increased disruption of the water structure around the ions and thus to an increase in enthalpy and entropy of the solution. Such structural contributions to AHD and ASDshould of course be more significant at lower temperatures where water is more structured. On the other hand, the AGD values should not depend much on the temperature or the type of the counterion because the structural contributions to AHD and ASD largely cancel. Our results (Table I and 11) are consistent with such a qualitative explanation. They show that for poly(styrenesu1fonates) with divalent counterions the observed variations in AGD, AHD, and ASD can be fully accounted for in terms of changes of water structure in the immediate vicinity of the counterions. Since the same conclusion has also been reached with the solutions of poly(styrenesu1fonates) with monovalent counterions,* it seems very likely that in aqueous polyelectrolyte solutions the nonCoulombic solute-solvent interactions in general yield significant contributions to the enthalpies and entropies of dilution. Acknowledgment. The partial financial support of the Yugoslav American Joint Fund for Scientific Cooperation (Pr.No 8509373) and the Research Community of Slovenia is gratefully acknowledged. Registry No. MgPSS, 37286-95-6; CaPSS, 37286-92-3; SrPSS, 52624-75-6.
