J. Phys. Chem. 1988, 92,6997-7001 It is the same difference in the bandgap that determines the difference in the electron affinity (EA) that is in the conduction band edge, as the bulk electronegativity ( x ) of the two compounds is practically the same (4.74 and 4.73 eV for the silver and the copper chalcogenide, respectively). In fact, according to Butler and Ginley2’ EA x - E,/2 and, therefore, the values of -0.39 and -0.29 V versus N H E are obtained for AgInSe2 and CuInSe2, respectively. Note that the value of the electron affinity of CuInSez is in good agreement with that calculated by Cahen and Mirovsky’ for the conduction band edge in the polyiodide electrolyte (-0.30 V versus ”E). Since the energy level of the redox couple in the electrolyte is independent of the electrode material, the silver compound turns out to be slightly (-0.10 V) less stable than the copper compound, assuming that no ion adsorption occurs on the semiconductor surface. Moreover, another very important point should be considered. Owing to the low p-d admixture, more involvement of the anion bonding electrons may be expected in the silver than in the copper compound. In other words, lattice Ag-Se bonds are expected to be broken more readily than Cu-Se ones. In addition, both chalcogenides show an appreciable ionic conductivity, particularly the silver c o m p o ~ n d as ~ ~the J ~mobility of the Ag+(aq) ions is higher than that of the Cu+(aq) ions. Thus, (34) Shay, J. L.; Wernick, J. H. Ternary Chalcopyrite Semiconductors, Growth, Electronic Properties and Applications; Pergamon: Oxford, 1975.
6997
a field-assisted out-diffusion of the cations is to be expected, which leads to a greater surface depletion and lattice instability in AgInSez than in CuInSe2, as primarily suggested by Dagan and Cahem9 Conclusions
In this paper, the energy relations known as thermodynamics are used to show the electrochemical and chemical decomposition reactions that may take place in a PEC cell having n-AgInSe, as the photoanode. The results of such investigation agree with preliminary experimental data. The material is expected to photodecompose and its instability is more pronounced in the polyiodide than in the polysulfide solution since SeO rapidly dissolves in the latter electrolyte, Seobeing the main corrosion product well-known to depress the PEC performance. Moreover, TDM evaluation as well as solid-state considerations evidence that AgInSe? is more prone to hole attack than its copper analogue.
Acknowledgment. I gratefully acknowledge G. Dagan and D. Cahen for their experimental results on AgInSQ (ref 9) on which this work is mainly based. The research was supported by the Progetto Finalizzato Energetica 2, CNR-ENEA Contract No. 86.00908.59 and by Minister0 della Pubblica Istruzione. Registry No. InAgSe’, 12002-76-5;InAgSSe, 1 16128-64-4;Na#04, 7757-82-6; Ag2Se, 1302-09-6; In3+, 7440-74-6; In’s3, 12030-24-9; InAgS2, 12002-75-4;s’-, 18496-25-8;S3’-, 12597-05-6;s,’-, 12597-07-8; HS-,15035-72-0;In203,1312-43-2;In2%,, 12056-07-4;S2Se2-,3168385-9; S3Se2*-,116129-31-8;Ag2S, 21548-73-2; Se, 7782-49-2; H20, 7732-18-5;Ag, 7440-22-4;Se2-, 22541-48-6; I-, 20461-54-5; 13-, 1490004-0; AgI, 7783-96-2; In13, 13510-35-5; Ag20, 20667-12-3; SSe2-, 11089-59-1;S4Se2-,116129-32-9;S3Se2-,116129-33-0.
Solute-Solute-Solvent Interactlons Studied through the Kirkwood-Buff Theory. 3. Effect of the Pressure on 0,for Some Aqueous and Nonaqueous Mixturest L. Lepori and E. Matteoli* Istituto di Chimica Quantistica ed Energetica Molecolare del C.N.R.,via Risorgimento 35, 56100 Pisa, Italy (Received: October 9, 1987; In Final Form: March 28, 1988)
From thermodynamic data, the Kirkwood-Buff integrals, Gij,have been obtained in the entire mole fracton range for binary mixtures of tetrachloromethane (TCM) with C,HwlOH (n = 1-4), 2-methyl-2-propano1, 1,Cdioxane, and tetrahydrofuran. The pressure coefficients of Gij, G’j = aGij/aP,are also reported for the above mixtures as well as for the corresponding aqueous solutions. In addition, the values of the excess local concentration are calculated for all mixtures. In aqueous systems, the tendency to homocoordination is observed for both alcohols and ethers as well as for water and is larger the larger the hydrocarbon-like moiety of the compounds; in TCM-containing mixtures, only alcohol molecules show mutual affinity, which, on the contrary, is larger for the lower alcohols. Gtvcurves indicate that the tendency to homocoordination is practically independent of pressure for TCM mixtures, but for aqueous solutions it decreases sensibly with increasing P at high solute concentrations and increases in very dilute solutions. These results are qualitatively discussed in order to point out the type of interactions that may be responsible for the observed G, and Gtijbehavior.
Introduction
In a previous paper we reported and discussed the first results of our study of solute-solute-solvent interactions based on the Kirkwood-Buff theory.’ By means of thermodynamic quantities such as activity coefficients, partial molal volumes, and compressibilities, for aqueous solutions of a number of organic compounds, we were able to calculate the Kirkwood-Buff integrals, Gjj (ij= 1,2), defined by Gij = s a0 ( g i j - 1)4ar2 d r
(1)
+Preliminary results were presented at the 1st Meeting of the Portuguese Electrochemical Society, Coimbra, Portugal, 1984. To whom correspondence should be addressed.
0022-3654/88/2092-6997$01.50/0
gijbeing the radial distribution function. These parameters, which convey information on the tendency of molecules of species i to become more concentrated or more diluted (with respect to the bulk concentration) in the entire surrounding of a given j molecule, were found useful in characterizing the local environment of various molecules in liquid mixtures. We have now determined GI, values for mixtures of tetrachloromethane (TCM) with each of these compounds: methanol, ethanol, 1-propanol, I-butanol, 2-methyl-2-propano1, tetrahydrofuran (THF), and 1,Cdioxane; in addition, the results of a study of the effect of pressure on G, behavior in mixtures of either water or TCM with each of the above compounds are (1) Matteoli, E.; Lepori, L. J. Chem. Phys. 1984, 80, 2856.
0 1988 American Chemical Society
6898 The Journal of Physical Chemistry, Vol. 92, No. 24, 1988
presented; this is the first paper in the literature reporting experimental results on the pressure dependence of Gij quantities. This study was planned to obtain information, by comparing the G, behavior of aqueous and nonaqueous systems and by correlating it with the molecular structure of the components, on (1) how the socalled hydrophobic interaction, the tendency of nonpolar solutes to associate in aqueous solution promoted by the peculiar structure of water, can be revealed by this type of approach; (2) the effect of pressure on the above phenomenon; and (3) the change of composition in the neighborhood of a given molecule with respect to the bulk composition (excess local composition). The main advantage of this method over other thermodynamic means of investigation of solutesolutesolvent interactions consists in the possibility that it can be applied to the whole mole fraction range and that information on i-i, i-j, and j-j interactions and on their dependence on concentration is simultaneously obtained.
Derivation of the Working Equations The Kirkwood-Buff integrals, Gij, can be expressed in terms of activity coefficients, yi, partial molal volumes, q,and isothermal compressibility coefficients, KT, according to the following equations: Cij
= RTKT- K Q / D V
(i # j )
(2) (3)
D = 1 + Xi(a In y i / a X J T s
(4)
where V is the mean molar volume of mixture, R the universal gas constant, and Xi the mole fraction of the ith component. By differentiation of eq 2-4 with respect to P at constant T , and rearranging, we obtain (aGi,/dP)T = RT(aKT/dP)T + (Xihj/RT + ViVz/D + G’ij KlV2 &Vi - VlV2KT)/DV ( i # j ) ( 5 )
+ G’, E (aG,,/dP)T = C’ij + VKT/Xj - K,/XjD - ?hi/@RT
(6) and Ki is the isothermal partial
In eq 5 and 6 , hi = (aVi;/a&)Tf molal compressibility, K j = - ( d & ; / a P ) ~ . For the discussion of the results, the values at infinite dilution of G , and G’,j, G,” and C;’, respectively, may be useful. Gji’ and G’,,O cannot be obtained directly from eq 3 and 6 as these take an indefinite form in the limit of Xi -* 0. By differentiation of the expressions for G,’ reported in ref 1, we obtain the following relationships: G’,jo(i#j) = lim
C’ij
= RT(aKj/ap)T
+
(7)
Xl-Q
G:,’ = lim G’,, = RT(dKj/aP)T + 2Kj0 - q h i ’ / R T
+
XrO
VjKj 0.95, 1 stands for water or TCM), where more accurate and densely detailed experimental data are available, it is much lesser. We realize that these errors are large but in our opinion are acceptable in consideration of the very high quality of the experimental data that would be required to get more precise Gij results; moreover, we believe that these uncertainties do not invalidate considerations and conclusions based on comparisons among G, or G ; behavior for different mixtures. Source of Thermodynamic Data For the aqueous systems, all thermodynamic data used to calculate G ; were taken from the literature as explained in ref 1. For the remaining mixtures, activity and partial molal volume data were calculated from data measured by us and published e l s e ~ h e r e ;partial ~ . ~ molal compressibility values were calculated from data of other authors” or estimated by correlation methods. The density data available for the water + dioxane system allowed the calculation of G ; in the range X I > 0.5 only.
Results and Discussion In the following sections, with index 1 we will indicate either water or TCM, which also will be referred to as solvents. For the sake of saving space, the results are reported only in the form of figures. To avoid crowding in figures, we omitted to report results for mixtures containing 2-methyl-2-propanol; in fact, the behavior of the system water 2-methyl-2-propanol is similar to that of water 1-propanol, and the system TCM 2-methyl-2-propanol closely follows TCM + 1-butanol. All Gij data for the aqueous systems have been taken from ref 1. The complete set of results in a tabular form is available upon request. The systems TCM methanol, TCM ethanol, and TCM + propanol are the only mixtures for which a comparison with literature data can be made, and only as far as G, are concerned. Not only is the agreement between our results and the data of Kat0 and co-workers’ (obtained from Rayleigh scattering experiments) qualitatively very good, the shapes of the G, curves as function of the mole fraction being practically identical, but also the numerical values agree within declared uncertainty. The binary systems chosen for this study lend themselves to a proper correlation of the Gij behavior with changes in the molecular structure of the compounds: in the same solvent (water or TCM) the effect of hydrocarbon chain lengthening and the effect of the different polar groups (OH or 0)will be examined; these results will be compared between the two solvents considered. The figures reporting the G, values have been assembled in order to facilitate the identification of these effects. As said before, the quantity D, eq 4, and therefore the derivative with mole fraction of the rational activity coefficients yi, is the key factor in determining Gij values; the larger the departure of the D values from unity, the larger the deviation from Raoult’s law and the more complex the shapes of G , and G’, curves. An ideal system obeying Raoult’s law in the whole concentration range is thermodynamically characterized by y l = yz = 1, E. = V,; microscopically, the pair potentials of interaction are the most similar compatibly with the different molecular diameters of the components: and the distribution of molecules in solution approaches a complete randomness. These facts suggest that the behavior of the G, quantities for an ideal system, G$ and G’if, is a useful reference for the discussion of the results. We have calculated C# and G’;! values by substituting D = 1, h = 0, E. = VI,Kj = KiK in eq 2-8; for the molar volumes and compressibility coefficients of the pure components we used the same values
+
+
+
+
+
(2) Lcpori, L.; Matteoli, E. J. Chem. Thermodyn. 1986, 18, 13. (3) Matteoli, E.; Lepori, L. J. Chem. Thermodyn. 1986, 18, 1065. (4) Rao, S. S.; Goplakrishnan, R. J. Acoust. SOC.India 1979, 7, 5 . (5) Ernst, S.; Glinski, J.; Jezowska-Trzebiatowska, B.; Acta Phys. Pol., A 1979, ASS, 501. (6) Hcrbeuval, J.-P.; Gaulard, M.-L. C.R. Acad. Sci. 1971, 273, 189. (7) Kato, T.; Fujiyama, T.; Nomura, H. Bull. Chem. Soc. Jpn. 1982, 55, 3368. ( 8 ) Ben-Naim, A. Water an Aqueous Solution. Introduction to a Molecular Theory; Plenum: New York, 1974.
The Journal of Physical Chemistry, Vol. 92, No. 24, 1988 6999
Solute-Solute-Solvent Interactions
.
- .
0
il
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'M
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____-----
0
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1
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1
I
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.?
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.?
"- E: 0
.9
'TCM
Figure 1. Plots of G,) (in cm3 mol-') and of G',, (cm' mol-' bar-') for a
hypothetical ideal system (left side) and for the system TCM (1) + THF (2) (right side), at 298.15 K: (---), G12;(-), GII;(-1, G22.
as for the system TCM + THF. In Figure 1 we have compared this ideal case with the experimental results of TCM THF, a mixture which is the 'most ideal" of those here s t ~ d i e d .G~ t and G'i: are characterized by a smooth monotonic trend with the mole fraction and take values of the order of magnitude of the molar volumes and compressibilities, respectively; the slope of the curves is determined by the difference between these quantities for the two components. The G, curves for TCM + THF on the whole show a behavior very similar to the ideal case. It may be observed that since G, values are calculated from thermodynamic quantities, the information that they convey cannot add anything to what can be deduced from the conventional examination of the properties involved, yi, 6, Ri, and particularly (a In y,/aXi). Actually, although the G, parameters are mainly determined by the quantity D which is independent of the species (D - 1 = X,a In y l / a X I = X2a In y 2 / a X 2 ) separate , and independent information is obtained on GI1,Guyand G12. For example, the fact that the shapes of the y i curves for the system water propanol are similar to those of the yi for TCM + propanol might suggest that GI1and Gzzcurves of the former system are quite similar to GI, and Gz2curves, respectively, of the latter mixture; instead, a completely different behavior is found between GI, of water and GI, of T C M (see next section). Comparison between Gv of Aqueous and Nonaqueous Systems. Figure 2 represents the trends of Gij values in the whole mole fraction range for water-containing mixtures (left side) and for the TCM-containing systems (right side). By looking first at alcohol solutions, it can be seen that Gz2and GI2curves have maxima and minima, respectively, a t XI N 0.7-0.9 both in aqueous and in nonaqueous systems (upper four rectangles); this indicates a tendency of alcohol molecules to be coordinated by other alcohol molecules and also a tendency of alcohol molecules to stay away from water and from TCM. In the aqueous systems, the absolute value of the extremum increases with increasing chain length of alcohols; in TCM-containing mixtures an opposite trend is observed, and the peak values in these mixtures are more marked than in aqueous solutions. This opposite trend of Gzzof alcohols in the two solvents is also observed at infinite dilution, as is demonstrated in Table I. The behavior of GI,is particularly interesting (Figure 2, third couple from top of rectangles): the four GI, curves of TCM in each of its mixtures with alcohols are practically identical and show monotonic trend and magnitude similar to an ideal case (see Figure 1). On the contrary, the G l l functions of water show maxima for solutions of ethanol, propanol, and (not shown) 2-methyl-2-propano1, thus indicating a tendency to mutual coordination of water molecules, and the values at maximum are much larger than the corresponding maximum values of GZ2.This phenomenology suggests and confirms that water, presumably by changing its structure, plays an active and major role in the mechanism responsible for the tendency toward association of solutes with large hydrocarbon-like moieties; in TCM
+
+
"i 1
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.?
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I '
1
1
1 . 1
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.5
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XTC M
Figure 2. Plots of G,/ (in cm3mol-'), eq 2 and 3, against mole fraction X at 298.15 K for binary mixtures of either water (left side) or TCM (right side) with alcohols or ethers. Index 1 in G, stands for water or TCM. The number inside the rectangles indicate (1) methanol, (2) ethanol, (3) 1-propanol,and (4) 1-butanol.
TABLE 1: GzZoand Cn0Values of Solutes in either Water or TCM at T = 298.15 K and P = 1 b a f
solute waterb TCM water TCM -45 3600 0.015 0.088 methanol -28 3370 0.044 0.210 ethanol 102 2760 0.055 0.280 1-propanol 1-butanol 160 2340 0.064 0.270 2-methyl-2-propanol 58 1740 0.140 0.330 THF 74 -70 0.080 -0.007 1,4-dioxane -90 28 0.005 -0.015 OThe limiting values of D and h used in the calculations of eq 2-8 were obtained independently of the equations employed to fit the data in the whole X range. bTaken from ref 1. solution, where the GI behavior indicates that solvent-solvent interactions are independent of the solute, the observed strong tendency to homocoordination of alcohols and its dependence on chain length are explained by hydrogen-bonding interactions and by the fact that these, at least statistically, take place more favorably if the alcohol size is small. The above conclusions are supported by the behavior of the solutions of ethers. In the mixtures containing THF and dioxane, in which interaction among ether molecules through hydrogen bonding is not possible, monotonic trends are exhibited by all Gii functions when TCM is the solvent; in aqueous solutions, instead, GI, and Gz2show maxima, and again the values of GI1are much larger than the Gz2ones, and both G I I and Gzzvalues for the solution of THF, which has a more effective hydrophobic moiety
7000 The Journal of Physical Chemistry, Vol. 92, No. 24, 1988 than dioxane, are higher than those for dioxane (Figure 2, bottom rectangles). Evaluation of the Local Concentration. The information conveyed by the G, parameters on the tendency of molecules of species i to stay away from or to gather around molecules of species j can be made quantitative by multiplying Gijvalues by the bulk concentration of i, c,; this product gives the excess (or deficiency) number of moles of species i in the entire surrounding of a central j m~lecule.*~~ Of course, the main contribution to Gii comes from within a short distance from the origin; if the distance d* for which the integral J;. (g, - 1)4& dr makes no contribution were known, the excess number of moles, ciGij,would have to be confined in a sphere of radius d* centered at moleculej, and therefore it would be possible to calculate the local concentration of i species around j . This approach to calculate local mole fraction has been used recently by Rubio et a1.I0 in order to test models of mixtures based on the local composition concept; also, a discussion of the difficulties inherent in the estimation of a proper value for d* has also been conducted, but much controversy still exists."J2 For mixtures of Lennard-Jones particles of comparable size far from critical solution points, either from theoretical groundssJ3or from MC sirnulati~ns,'~ d* has been found of the order of 2.5-4 times the molecular diameter, a. Our mixtures are not that simple, so even taking for our systems the maximum of the above distances, d* = 4a,a crude approximation is certainly made. Nevertheless, we are convinced that it may be useful to see what Giivalues mean in terms of changes of local concentration with respect to the bulk or average concentration, and believe that a nonrigorous choice of d* will have no influence on a discussion based on comparisons among different systems. Even for a pure liquid and for a symmetrical ideal system, the product ciGij is not zero9 (see Figure l), so, to obtain the "net" excess moles of i particles in the surroundings of j , the corresponding value for an ideal system, c@, must be subtracted. By dividing c,(C, - G:) by v* = (4/3)r(d*j3, we obtain the net excess concentration Ac, of i molecules inside the spherical volume v* around a j molecule. From our G, data we have calculated the relative quantity Acij/ci A ~ i j / ~=i
(G, - G f ) / V *
(9)
for all mixtures here considered. G; was obtained for each system from eq 2-4 by taking D = 1 and = Vi in the whole concentration range. To take into account the different molecular sizes of the two components, the value of d* was assumed as a linear combination, in the volume fractions, vl and p2,of their hardsphere diameters, CT;
vi
d* = ~ ( W I + M ~ Z ) (10) Expectedly, many features of the Acij/ci curves, reported in Figure 3, are identical with those of G, (Figure 2). For solutions containing TCM, only Ac2,/c2 for alcohols show very high values at some values of mole fraction: for methanol at XI 0.85, the molar concentration of methanol molecules around a given methanol particle is larger by about 50% than the bulk concentration; the relative change of concentration of TCM around TCM, Acll/cl, and of either ether around itself, Aq2/c2,is almost always less than 2%. In water solutions, the largest Acij/ci are observed for the mixtures containing the solute with the largest hydrophobic moiety; particularly interesting, in our opinion, are the maxima shown by A c l l / c l in both alcohol and ether solutions and also the sur-
-
(9) For example, by multiplying GI1 of pure water, Gii', (Gila= RTKT - VI -VI)] by its concentration,cI = l/Vi, we obtain clG,,' N -1, which indicates that there is 1 mol missing in the surroundings of the central molecule and corresponds to the fact that the molecule, on which the origin is centered, cannot be counted. (10) Rubio, R. G.; Prolongo, M. G.; Diaz-Pena, M.; Renuncio, J. A. R. J . Phys. Chem. 1987, 91, 1177. (11) Ali Mansoori, G.; Ely, J. F. Fluid Phase Equilib. 1985, 22, 253. (12) Rubio, R. G.; Prolongo, M. G.; Cabrerizo, U.;Diaz-Pena, M.; Renuncio, J. A. R. Fluid Phase Equilib. 1986, 26, 1 . (13) Hanky, H. J. M.; Evans, D. J. Inr. J . Thermophys. 1981, 2, 1 . (14) Kataoka, Y . J . Chem. Phys. 1984, 80, 4470.
Lepori and Matteoli
I
.
,I
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.9
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D
*?
Yz :: 4
xb4
XTCM
Figure 3. Behavior of Ac,/c,, the relative change of molar concentration of i around j , with respect to bulk concentration ci. Other explanations as in Figure 2.
prisingly large values of Acu/cz at Xz= 0, which are the maxima for the whole concentration range in each system. We can say, therefore, that if the tendency to homocoordination of a given species is measured on a relative scale, in other words, is "normalized" with respect to the concentration of the species itself as is done in the quantity Acij/ci,this tendency of alcohols and ethers with large hydrocarbon-like moieties in aqueous solutions is stronger in the limit of infinite dilution than at higher concentrations. Pressure Effect. By looking at the results for G; reported in Figure 4,the shapes of G; curves appear more complex than Gii; in a number of cases two relative maxima or minima are shown. Interesting differences can be found between aqueous and nonaqueous mixtures, the most evident being the general much lower values of G ; for the latter systems than for the former. In TCM solutions, all G{j curves, except Gl,, of alcohols a t XI > 0.7, take very low absolute values which are of the order of magnitude of the molar compressibility of the components, such as in an ideal system (see Figure 1). An analogous very low dependence on pressure of G, was calculated theoretically by Kojima et al.I5 for mixtures of Lennard-Jones type molecules, and this was the only information available in the literature on the pressure dependence of Gi parameters. These results suggest that the interactions TCM-TdM, TCM-alcohol, and alcohol-alcohol are independent of each other and insensitive to a change of pressure even in the range of concentration where the alcoholalcohol interactions "feel" the pressure (0.7 < X I < 1). No correlation between the alcohol molecular structures and the complex behavior of their G$2curves in the above concentration range can be recognized, except at XI= 1 (Table I), where a clear increase of the C',,O values with molecular size can be seen. In (15) Kojima, K.; Kato, T.; Nomura, H. J . Solution Chem. 1984, 13, 151.
Solute-Solute-Solvent I
1
'
The Journal of Physical Chemistry, Vol. 92, No. 24, 1988 7001
Interactions I
'
I
-I
'
THF
I
.I
.s
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Figure 5. Comparison between G22values of THF in water at P = 1 bar (experimental) and at P = 1000 bar (calculated).
I
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'
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XW X TCM Figure 4. Shapes of the derivative G$,(in cm3 mol-' bar-'), eq 5 and 6, against X at 298.15 K for binary mixtures of either water (left side) or
TCM (right side) with alcohols or ethers. Other explanations as in Figure 2.
spite of these relatively large values of G i , of alcohols, no significant change of the Gzzshapes from 1 bar to high pressures can be expected. Indeed, by assuming a linear behavior of G,, with respect to P,that is, in the approximation that G',, is constant with respect to P u p to, say, lo00 bar, we can easily calculate that at this pressure the shapes of the G, curves of our systems containing T C M remain practically the same as at 1 bar. In aqueous solutions, hydrophobic solutes such as propanol, THF, and 2-methyl-2-propanol (the system water 2-methyl2-propanol is not shown in Figure 4 as the shapes of Gi, practically overlap those of water 1-propanol) show large negative values of G i 2 and G I l 1 and positive values for G'12. Compounds with small hydrophobic portions or with two polar groups, such as methanol and dioxane, show monotonic trends and small values of G',,, At X1> 0.95, G'22values are positive and the maxima, reached at infinite dilution, are larger the larger the hydrocarbon-like part of the molecule (see Table I). In contrast to what is found for TCM solutions, the G, behavior of aqueous mixtures of hydrophobic solutes which can be calcu-
+
+
lated a t high P and a t 0.6 < X1 < 0.95 is completely different with respect to room pressure. The large and positive values shown at 1 bar by Gu and Gll and the negative values of G12(see Figure 2) are strongly reduced in magnitude a t 1000 bar becuase of the large negative G'z2and Ql1 and positive W12(Figure 4), and in some cases even a change of sign is predicted. As an example, in Figure 5 is shown what the shape of Gu of THF in water looks like at 1000 bar. The strong tendency to homocoordination of water and of THF observed at room pressure in the range 0.4 < Xl < 0.8 (high values of Gll, and Gzz)is no more found a t 1000 bar, where instead each molecule has a tendency to be surrounded by molecules of the other species. The negative values of G i Zof large-size solutes in water at 0 < Xl < 0.95 are contrasted by the small positive values at X1> 0.95.The change of sign of Gh at X , N 0.95 when Gu maintains positive values suggests that two mechanisms, which behave differently with respect to an increase of P, are responsible for the tendency of hydrophobic solutes to associate in water. In the very dilute region, an increase of solute concentration favors homocoordination, and this is still promoted by a pressure increase. This phenomenon may be explained by the formation of clathrate-type structures into which solute molecules may be accommodated; this causes a decrease of volume and so is favored by a pressure increase; the positive Gu values observed are the results of negative volume changes brought about by closer packing. When the concentration is increased, this process is gradually substituted by another, which prevails a t Xz> 0.05 and which presumably involves contacts between like molecules similarly to what happens in systems undergoing incipient micellization or phase separation. Acknowledgmenr. We thank Prof. G. Ali M a m r i (University of Illinois at Chicago) for reading the manuscript and making valuable comments and suggestions. Registry No. THF, 109-99-9; CCl,, 56-23-5; methanol, 67-56-1; ethanol, 64-17-5; 1-propanol, 7 1-23-8; 1-butanol, 71-36-3; 2-methyl-2propanol, 75-65-0; 1,4-dioxanc, 123-91- 1 .
