1268
A. Ben-Naim
Structure-Breaking and Structure-Promoting Processes in Aqueous Solutions A. Ben-Naim* Laboratory of Molecular Biology, National lnstitute of Arthritis, Metabollsm, and Digestive Diseases, National Institutes of Health, Bethesda, Maryland 200 14 (Received November 13, 1974; Revlsed Manuscript Received March 7, 1975) Publication costs assisted by the National Institutes of Health
A new measure is devised to estimate the structural changes in the solvent induced by processes occurring in aqueous solutions. This measure relates the isotope effect in the standard free energy of the process involved, in light and heavy water, with the change in the average number of hydrogen bonds that occurs in the solvent. Some numerical examples for the process of dissolution are presented, from which one can classify solutes as either structure promoters or structure breakers. A possible generalization of this method for more complicated processes is also indicated.
1. Introduction
The classification of solutes, dissolved in water, as “structure breakers” and “structure promoters” has been the subject of a great number of research w o r k ~ . l -These ~ concepts have evolved from the two fundamental works of Bernal and Fowler? and Frank and Evans: on the properties of aqueous solutions. These authors were, perhaps, the first to recognize and to stress the importance of the role of the “structure of water” in the understanding of the unusual properties of aqueous solutions. Yet in spite of the large number of articles written on this subject, the very basic questions of how to define the “structure of water” and which experiment should be done to measure the “structural changes” in water were left unanswered. T o be sure, there has been a great deal of discussion on this topic, nevertheless in most cases it appears that this subject has evaded a quantitative treatment. To cite one example out of many, suppose one measures the viscosity of pure water. Then the same measurement is carried out in aqueous solutions of various solutes. Now if a solution is found to have a larger viscosity than that of pure water, the traditional interpretation of such an observation is that the added solute has increased the “structure of the solvent”. Clearly because of the ambiguity in the very meaning of the “structure of water” as conceived by different authors, and because of a lack of a clear-cut relationship between the measurable quantity on one hand, and the changes of the structure of water on the other, there has been a widespread disagreement among authors who have used different experimental techniques. The central purpose of this article is, in a way, to fill the gap in this field. In the first place we shall present a quantitative measure of the “structure of water” which we believe is in close conformity with current views on this concept as expressed by many authors. Furthermore we devise an approximate relationship between a simple experimental quantity on one hand and a change in the structure of water induced by the pertinent process. To the best of the authors knowledge this is the first relation that makes such a connection. Although it involves certain approximations,
* After August 1975 correspondence should be addressed to the author a t the Department of Physical Chemistry, the Hebrew University, Jerusalem, Israel. The Journal of Physical Chemistry, Vol. 79, No. 13, 1975
the application of this relationship leads to results that are in qualitative agreement with conclusions reached earlier using other methods. As a subsidiary result, this work provides new and independent support to the theoretical argument presented earlier,’~~ that simple solutes such as argon, methane, and the like do indeed stabilize the structure of water, in the sense which is described in sections 3 and 4. This topic has been continuously discussed and debated in the literature ever since it was originally conjectured by Frank and Evans.6 The next two sections contain the assumptions leading to, and the derivation of a relation between the isotope effect in the standard free energy of solution and structural changes in water. Section 4 provides a few numerical results and section 5 indicates possible generalizations of this relationship to include more complex processes taking place in aqueous media. 2. Definitions and Assumptions In this section we consider the simplest process that occurs in aqueous solution; Le., the dissolution of a spherical nonpolar solute, such as argon, methane, and the like, in a system of N water molecules at a given temperature T and pressure P. The standard free energy of solution of a solute, S, is related to the Ostwald absorption coefficient, ys,by * A F s 0 = -kT In ys
(2.1) where h is the Boltzmann constant. The statistical mechanical expression for ys is Ys =
SdV.fdXNexp[-pUN(XN) - pBs (XN) - pPV] SdVSdXN exp[-pUN(XN) - pPV]
= (exp(-ml (2.2) Here 6 = ( k T ) - l , U N ( X ~represents ) the total potential energy of interaction among the solvent molecules being a t a fixed configuration X N = XI, Xz, -, XN (Xi comprises the six coordinates required to describe the position and the orientation of a single water molecule, the latter is treated here as a rigid particle). The quantity B s ( X N )represents the total interaction energy between a solute particle, at some fixed position, e.g., Rs, and the solvent molecules a t the configuration X N . The integrations in (2.2) is over all possible volumes V and con-
1269
Structure-Breaking and -Promoting in Aqueous Solutions
figurations XN. The symbol ( )O designates an average, in the TPN ensemble, over all the configurations of the solvent molecules. In addition to the very usage of the classical expression (2.2) for the Ostwald absorption coefficient we also employ the following assumptions. a. The water molecules are viewed as rigid particles interacting via a pair potential U(X,,X,). For the total potential energy of interaction we assume the full pairwise addit i ~ i t ynamely ,~
c
U(X,,X,)
(2.3)
= CU(X,,RS)
(2.4)
U,(XN) =
f W > S
= Nlim S-0
(3.6)
T,P,N
The last equality on the right-hand side of (3.6) follows from the extensive character of the function ( G ) s , Le., in the macroscopic limit, the derivative with respect to N s may be approximated by the change due to the addition of one solute particle S. Substituting (3.6) into (3.1) we get the first-order expansion of ys(D) as “is(D) = ”is(H)[1 - P ( E D - EH)((G)s - (G),)
+
*
*
I
(3.7) Thus the isotope effect in ys is determined by the quantity ( G ) s - (G)o which we now show has the meaning of a structural change in the solvent, induced by the addition of S. Consider the function G(Xi,Xj) which has been introduced as a part of the pair potential in (2.5). As we have stated before, there is no need, for the present purpose, to provide an explicit form for this function, though this may be done in various ways.8 It is sufficient to acknowledge the property that G(X,,X,) attains the maximum value of unity whenever the pair of molecules are in a “good” configuration to form a H B (e.g., the 0-0 distance is about 2.76 %, The Journal of Physical Chemistry, Vol. 79,No. 13, 1975
(3.9)
Thus either the average number of HB’s ( G ) o in the system, or the average number of HB’s formed by a specific particle of the system may be used as a measure of the degree of the structure of water. Similarly one may define the conditional average
-
$63 =
J”dVSdXNP(XN,V/%)Q1(XN) 2 = -N0 3 s (3 .lo) Hence the quantity A ( G ) s = ( G ) s - (G)o may be assigned the meaning of the structural change in the solvent induced by the dissolution of the solute S. We believe that A ( G ) s reflects in its content, the concept of structural changes in the solvent as referred to by many authors. Having assigned meaning to A (G ) s we may view relation 3.6 as an exact relation for a system of model particles obeying the assumptions of section 2. Alternatively, adopting the first-order expansion in (3.7) to account for the isotope effect in ys (or in AfisO), we get the following approximate relation: AF~O(D)
- ALL~O(H)
=
(ED
-
€H)A(G)S
(3.11)
where on the left-hand side we have an experimental quantity, whereas on the right-hand side we have molecular quantities. Once we agree upon the numerical value for t~ - t ~we, may extract information on A ( G ) s by the application of this relation. Some numerical values for A ( G ) s are presented in the next section. Finally we note that in deriving relation 3.11 we did not make use of the full pairwise additivity (2.3). Instead, i t is sufficient to assume the split of the total potential energy as in (2.6). The more refined split in (2.7) was employed, however, in the interpretation of the quantity (G)as a measure of the structure of water.
Structure-Breaking and -Promoting in Aqueous Solutions
1271
4. Some Numerical Examples In this section we make use of relation 3.11 to estimate the magnitude and direction of the structural changes in water induced by the dissolution of different solutes. We note that in the past the isotope effect in the thermodynamic properties of aqueous solution was frequently interpreted in terms of structural changes in the solvent.14-ls We believe that relation 3.11 provide a more direct and explicit means for that goal. Experimental values for Apso(H) and Aps0(D) were collected from the 1 i t e r a t ~ r e .As l ~ for e~ - e ~ it, is well known that there exist no universally agreed method of estimating the HB energy.l3 We believe, however, that the estimates made by NBmethy and Scheraga11,20are quite reasonable for our purposes. They used the values of E H = -3.57 kcal/ mol of bonds, and e~ = -3.80 kcal/mol of bonds, for their model of liquid water. (These estimates were based on the experimental values for the energies of sublimation and vaporization of light and heavy ice.4J1,21)Using these values we get E,, -
cH = -0.23 kcal/rnol of bonds
(4.1)
which we shall adopt in all the forthcoming calculation. Note that e~ - CH is indeed small compared with the value of the HB energy. This fact supports the use of only firstorder terms in the expansion in (3.1). Clearly the exact values of t~ and E D depends strongly on the method one chooses to measure the strength of the HB. However in relation 3.11 the difference CD - EH appears as a proportionality factor, therefore different choices of ED - t~ would have no effect on the relative magnitude of A ( G ) s for different solutes. Table I reports some values for the isotope effect in Apso for argon in H2O and in D2O along with the computed values of A ( G ) s a t different temperatures. In accordance with many previous conclusions, based on either experimental or theoretical arguments, the dissolution of argon in water increases, or stabilizes, the structure of water, in the sense that the average number of HB's becomes larger in the presence of the solute. This effect diminishes with the increase of temperature. The plot of A ( G ) s vs. temperature shows a clearcut positive curvature, Figure 1. Table I1 includes values of A ( G ) s for methane, ethane, propane, and butane. The temperature dependence is similar to. the one observed for argon in Table I. From these data it appears that the extent of the stabilization effect becomes smaller the larger the hydrocarbon molecule. This finding suggests that geometrical restrictions on the shape of the molecule are important in achieving a large stabilization effect, a topic which clearly deserves further study. In Table I11 we report similar results for ionic solutions. Note however that we are using only the final relation (3.11) which was derived for nonionic solutes. The fact that a salt dissociates into ions in water may alter the whole argument leading to (3.11), therefore these figures should be regarded as tentative ones only. We have used part of Table 6-9 from Arnett and McKelvey4 as a source for our computations. Perhaps the most remarkable difference between the values of A ( G ) s in this table and in the previous two tables is the appearance of negative values for most of the salts, i.e., most ionic solutions have a destabilizing effect on the structure of water. Exceptional cases are the fluoride salts such as LiF and NaF, and the tetraalkylammonium salts such as (n-Bu)dNCl.
TABLE I: Values of Apso(D) - Ap,O(H), in cal/mol, and for Argon at Different Temperaturesa
t , "C
5
10
Ap;(D) - -63.9 AF;(H) A (G) s 0.278 a Based
-58.5
15 -53.9
0.254
20
25
-49.8
-46.2
0.234
0.216
0.201
on data from Ben-Naim.22
TABLE 11: Values of A(G),for Some Hydrocarbons at Different Temperaturesa
t , "C
5
10
15
20
25
Methane Ethane Propane
0.21 0.19 (0.14) (4")
0.19 0.14
0.17 0.12
0.15 0.12
0.13 0.14 (0.11)
Butane
0.17 0.13 0.08 0.03 -0.03 (0.17) (0.14) (4") a B a ~ e don data from Ben-Kaim et al.23 and Kresheck et al.24 Values in brackets were computed from Kresheck et al.,24who reported some values at 4 and 25'.
TABLE 111:Values of A(G)+for Some Ionic Solutionsa c1-
Br-
I-
BPhd-
-0.10 4.51 -0.56 -0.55 -0.31 4.71 -0.58 +O .45
-0.31 -0.72 4.78 -0.76 4.52 4.93 4.79 +O .23
-0.53 4.95 -1 .oo 4.98 4.74 -1.15 -1 -02 -0.01
4.71 -1.13 -1.18 -1.16 4.92 -1.33 -1.19 -4.16
FLi
+O .42 +o .01 -0.04 K' 4.03 Rb' +0.21 cs4.19 '4" -0.06 (Me + ( I ~ - B U ) ~ N + -0.97
Na'
a All entries are for one temperature, 25'. Data taken from Tables 6-9 of ref 4.
1
0.3
0'
I
I
I
10
20
30
1
t"C
Figure 1. Values of A ( G)s for argon in water as a function of tem-
perature. In the case of small ions such as Li+ or F-, the strong electrical field in the immediate surroundings of the ion produce a large perturbation effect on the internal properties of the water molecules in that region. If this effect is large then the factorization of the internal partition funcThe Journal of Physical Chemistry, Vol. 79, No. 13, 1975
1272
A. Ben-Naim
tion for single water molecules may not be justified and hence relation 2.2 will not be valid. For this reason one should interpret with some care the figures of Table I11 for small ions. In the case of tetralkylammonium salts, we probably have a competitive effect of stabilization and destabilization by the two ions involved. This conclusion is similar to the ones reached by others using different experimental techniques.1-2 From Table I11 it is difficult to draw a clear-cut relation between the ionic size and the extent of the effect that ion has on the structure of water. I t appears that the larger the anion the larger the destabilization effect. No such a simple relation appears to exist for cations. 5. Further Generalizations for Other Processes In previous sections we treated the process of dissolution of simple molecules in water. This process is sufficient to establish a classification of solutes as “structure breakers” or “structure promoters” in aqueous solutions. However by a simple generalization of the result of section 3 one can deal with more complex processes, such as conformational changes or association of subunits to form a multisubunit biopolymer, etc. In fact information gathered for such processes is more important and interesting than the mere knowledge of which solutes stabilizes or destabilizes the structure of water. The ability to predict the effect of various processes on the structure of water will eventually prove helpful in the understanding of the role of liquid water as a medium in which most biochemical processes take pIace. Consider as a simple example the isomerization reaction
TABLE IV: Structural Changes Induced by the Process of Hydrophobic Interactiona t , “C (G)Et
- (G)2Me
(5.2) and the isotope effect in Apo ma3 be approximated by AIo(D) - Ap0(H) = [pB0(D) - pB0(H)]LpAo(D) - pAo(H)] (ED - EH)[(G)B - (G)A]
(5.3)
The quantity in the squared brackets on the right-hand side of (5.3) may be interpreted as the structural change in the solvent induced by reaction 5.1. Care must be exercised in interpreting ( G ) B - ( G ) A when A and B are complex molecules. In the first place, one has to interpret the quantity ( G ) B as an average over all the conformations of the molecules that are included in the definition of the isomer B. Similar comment applies to ( G ) A . More important, if the reaction in (5.1) involve formation or breaking of hydrogen bonds within the molecules A and B, or between these molecules and the solvent, relation 5.3 no longer applies since it has been based on the assumption (see section 2 ) that the solute-solvent interaction does not change when we replace H2O by D2O. In such a case we have to modify (5.3) to account for the fact that the B involve different HB energies execution of reaction A in the two solvents. A simple example of such a case would be the dissociation of carboxylic acids, for which the isotope effect in the dissociation constants have been tabulated.25 We now turn to one specific example for which we can cite some numerical values. The process to be considered is
-
The Journal of Physical Chemistry, Vol. 79, No. 13, 1975
10
15
20
25
-0.23
-0.23
-0.22
-0.18
-0.12
These figures refer to the process of bringing two methane molecules from a fixed position a t infinite separation to a distance R = 6 1 = 1.533A. Based on data from ref 23. a
the so-called “hydrophobic interaction” (HI) process.26-28 The change in the Gibbs free energy for the process of bringing two simple solutes from infinite separation to some close distance R may be written as W R ) = U(R)
+
~ G ~ I ( R )
(5.4)
where U ( R )is the direct pair potential between the two solutes and 6G“ ( R ) is referred to as the strength of the HI a t the distance R.8 For a specific distance R = u1 = 1.53 A we have recently suggested the following approximate relation:8928 6GH’(o,) = A p E t o - 2ApMe0
(5.5)
where &Eto and are the standard free energies of solution of ethane and methane, respectively. The corresponding isotope effect in the strength of the H I at R = u1 is 6GH‘(Dl, D) - 6GH‘(Ul, H) = hpEto(D) - hlJ.Eto(H)2[ApMeo(D)
- APM~O(H)]
( 5 .I)
A c l B
The standard free energy for this reaction is
5
[(G)Et
- 2(G)Me + (G)01 x (ED - EH) (5.6)
(Note the different meaning of the letter G on the two sides of eq (5.6).) The expression in the squared brackets on the righthand side of (5.6) can be readily interpreted as the structural change in the solvent involved in the HI process, in fact this term may be shown to equal the quantity ( G ) E t ( G ) 2Me which has a more obvious meaning, see also Appendix B. Table IV lists some values for the structural changes in the solvent for the HI process. As is expected all the figures are negative, a result which is consistent with previous conclusions that the net effect of the HI process is a breakdown of the structure of ~ a t e r . ~ . ~ ~ 6. Conclusion
In view of the fact that concepts such as “structure-making” and “structure-breaking” solutes are so ubiquitous in the literature on aqueous solutions, it is desirable to have a simple and well-defined measure of these quantities. We believe that the approximate relation 3.11 achieves that goal. Of course the numerical values given in Tables I-IV may not have absolute significance, since they depend on the assumptions listed in section 2 as well as on the numerical . we believe that the relavalue chosen for t~ - t ~ However tive magnitude of these quantities is meaningful, so that different solutes may be compared as to the extent of their effect on the structure of water. The knowledge of the effect of solute on the structure of water is clearly crucial in the understanding the properties of aqueous solutions. It is difficult to claim any practical advantages to such a knowledge, except, perhaps, in con-
1273
Structure-Breaking and -Promoting in Aqueous Solutions
nection with the Pauling theory of anesthesia, where it has been suggested that gaseous molecules such as xenon form “microcrystals of ice” around them. If this occurs in the brain, the theory argues, it may affect the passage of electrical impulses in the nerve system.29 A more important aspect of this work is its potential application to more complex processes. This possibility has been indicated in section 5. However, because of lack of the relevant data on the isotope effect for such processes this aspect has not been developed to the point where numerical quantities could have been computed. We believe that effort in generalizing the relation discussed in sections 3 and 4, as well as in measuring the pertinent isotope effect, would be quite rewarding in understanding the role of water as a medium where most biochemical processes take place.30
Acknowledgment. The author is very grateful to Drs. R. Tenne and W. Kauzmann for reading the manuscript and offering helpful comments. Appendix A I t is often claimed in the literature4J4 that D20 is more “structured” than H20. We show here that the “structure” as measured by ( G ) o is a monotonic increasing function of -CHB. Hence the above statement is equivalent to the assumption (2.8). To show that we consider the derivative of ( G ) o with respect to CHB, i.e. (G)o =
J”dVJdXNe x p [ - / 3 U N ( X N )- PPV]G(XN) (A.1) JdVJdXN exp[-/3UN(XN) - PPV]
‘ @
@I
m -
Figure 2. Schematic processes referred to in Appendix B.
is the correct one. Nevertheless, it is clear from the above relations that it is much safer to correlate changes of structure with changes in HB energies rather than with changes in temperature.
Appendix B In section 5 we have interpreted the quantity in the squared brackets on the right-hand side of (5.6) as the change in the structure of water for the hydrophobic interaction process. This statement needs further clarification. ) value of To simplify our notation we denote by @ ( S ; Nthe ( G ) s in a system of N water molecules. The quantity on the right-hand side of (5.6) strictly refers to the change of the structure due to process I in Figure 2, Le. A+(I) = +(Et;N) - 2$(Me;N) + @(O;N)
Hence increasing the strength of the HB energy for a model system obeying the assumptions of section 2 will result in an increase of the structure of the system. This result is almost self-evident on intuitive grounds. At this junction it is interesting to show that (G)o is not necessarily a monotonic decreasing function of the temperature. This assumption underlies the usage of the concept of “structural temperature” for aqueous solution^.^^^ The temperature derivative of (G)o is
- (G)o(V)o)I (A.3) I t may be shown that the cross fluctuation ( G V ) o J‘((GI?o
( G ) o (V ) Ois related to the difference in the molar volumes of HzO and DzO. Since the latter is small a t room temperature, we expect that this will have negligible contribution to the right-hand side of (A.3). Putting UN = UN’ CHBGas in (2.6) we get
+
= EHB((G2)0 - (G)02) + ((GUN’)0 - (G)o(UN‘ >o) (-4.4) In order to secure a negative temperature dependence to ( G ) o we must assume that the term (GUN), - (G),(U,)o
(B.1)
where @(O;N) is the structure of N water molecules without any solutes. However, we are interested in the change of structure for process I1 which may be written as
W ( I D = @(Et;N) - @(2Me;N)
(B.2)
where by 2Me we denote two methane molecules at infinite separation (for more details see ref 8). We want to show that in macroscopic systems A@(I) and A@(II) are equal to each other. T o do that we note that in macroscopic systems the quantity A4(II) does not depend on N. This is true since all the changes of the structure must occur in the local environments of the solute. In particular, if we take 2 N instead of N we get the same quantity, i.e. (note that T and P are constants)
A@(II) = @ ( E t ; 2 N - @(2Me;2N)
(€3.3)
Since the solutes are a t fixed positions, and the systems are macroscopically large, the two processes depicted as I11 and IV in Figure 2 involve the same, if any, structural change, due to the introduction of a partition in the system, i.e.
-A+(III) = @(Et;2N) - +(Et;N) - +(O;N) -A@(rV) = +(2Me;2N) - 2@(Me;N) A@(III) = A@(IV)
(B.4) (B.5) (B.6)
Using (B.4) to (B.6) in (B.3) we get the equality P((GV)o - (G)o(V)o) + (GUN’), - (G)o(UN‘)o
(-4.5)
is either negative or positive but small compared with CHB((G’)O - (G)02).We believe that the second possibility
A m ) = AW)
(B.7)
which is the required relation. The Journal of Physical Chemistry, Vol. 79, No. 13, 1975
1274
R. Williams
NOTEADDED IN PROOF. Recently Jolicoeur and Lacroix (Can. J. Chem., 51,3051 (1973)) have published an interesting paper on the free energies of transfer from HzO to DzO for a series of ketones. Processing their data according to relation 3.11 leads to the following conclusion. Most unsaturated ketones show a positive stabilization of the structure of water, whereas most of the unsaturated and polycyclic isomers have an opposite effect. There are also some interesting effects due to the degree of branching in the hydrocarbon chains that certainly deserve further detailed study both experimentally and theoretically. I am indebted to Dr. Jolicoeur for drawing my attention to this paper. References and Notes (1) R. A. Horne, Ed., "Water and Aqueous Solutions, Structure, Thermodynamics and Transport Processes", Wiley-Interscience, New York, N.Y.,
section 2 becomes simpler by using the more explicit forms (2.3)and
(2.5). (10)A. Ben-Naim in "Water, A Comprehensive Treatise", Vol. I, F. Franks, Ed., Plenum Press, New York, N.Y., 1972. (11) G. Nemethy and H. A. Scheraga, J. Chem. Phys., 41,680 (1964). (12)C. G. Swain and R. F. W. Bader, Tetrahedron, IO, 182 (1960). (13)D. Eisenberg and W. Kauzmann, "The Structure and Properties of Water", Oxford University Press, Oxford. 1969. (14)H. L. Friedman and C. V. Krishman in "Water, A Comprehensive Treatise", Vol. 111, F. Franks, Ed., Plenum Press, New York, N.Y., 1973. (15) B. E. Conway and L. H. Laliberte, Trans. faraday SOC.,66, 3032 (1970). (16) W. Y. Wen and K. Nara, J. Phys. Chem., 72, 1137 (1968). (17)B. E. Conway and L. H. Laliberte, J. Phys. Chem., 72, 4317 (1968). (18)J. Greyson, J. Phys. Chem., 71,2210 (1967). (19) Note that we have defined A/.&' in (2.1)in terms of the Ostwaid absorption coefficient, which is a ratio of molar concentrations. The advantages of using this particular definition have been discussed elsewhere.8 In the literature, Apso is often reported in terms of a ratio in mole fractions. However, since the molar volumes of H20 and D20 are almost identical, around room temperature, the isotope effect in Ahso will be almost insensitive to whether we have chosen molar or mole-fraction concentration scales. (20)G. NBmethy and H. A. Scheraga, J. Chem. Phys., 36, 3362, 3401
1972. (2) F. Franks, Ed., "Water, A Comprehensive Treatise", Vol. Ii and 111, Plenum Press, New York, N.Y., 1973. (3)J. E. Desnoyers and C. Jolicoeur in "Modern Aspects of Eiectrochemistry", Vol. 5,J. O'M Bockris and B. E. Conway, Ed., Plenum Press, New York, N.Y., 1969. (4) E. M. Arnett and D. R. McKeivey in "Solute-Solvent Interaction", J. F. Coetzee and C. D. Ritchie, Ed., Marcel Dekker, New York, N.Y., 1969. (5)J. D. Bernal and R. H. Fowler, J. Chem. Phys., I, 515 (1933). (6) H. S.Frank and M. W. Evans, J. Chem. Phys., 13, 507 (1945). (7)A. Ben-Naim, J. StatisticalPhys., 7, 3 (1973). (8)A. Ben-Naim, "Water and Aqueous Solutions, an Introduction to a Molecular Theory", Plenum Press, New York, N.Y., 1974. (9)The assumption of full pairwise additivity as written in (23)is a very se-
(1962). (21)I. Kirshenbaum. "Physical Properties and Analysis of Heavy Water", National Nuclear Energy Series, McGraw-Hili, New York, N.Y., 1951. (22) A. Ben-Naim, J. Chem. Phys., 42, 1512 (1965). (23) A. Ben-Naim, J. Wilf, and M. Yaacobi, J. Phys. Chem., 77,95 (1973). (24)G. C. Kresheck, H. Schneider, and H. A. Scheraga, J. Phys. Chem., 69, 3132 (1965). (25) P. M. Laughton and R. E. Robertson in "Solute-Solvent Interaction". J.
vere one for a complex fluid such as water. In fact the derivation in section 3 requires somewhat a weaker assumption, namely, that the total potential energy UN may be written as UN = U,' 4- ~ H B where G the meaning of these symbols are defined in (2.6). However the treatment in
lar Biology, A. Rich and N. Davidson, Ed., W. H. Freeman, San Francisco, Calif., 1968. (30) A. L. Lehninger. "Biochemistry", Worth Publishers, New York, N.Y.,
F. Coetzee and C. D. Ritchie, Ed., Marcel Dekker, New York, N.Y.,
1969. (26)W. Kauzmann, Adv. Protein Chem., 14, 1 (1959). (27)G. Nemethy and H. A. Scheraga, J. Phys. Chem., 66, 1773 (1962). (28)A. Ben-Naim, J. Chem. Phys., 54, 1387,3696 (1971). (29) See, for example, J. F. Catchpool in "Structural Chemistry and Molecu-
1970.
Interfacial Free Energies between Polymers and Aqueous Electrolyte Solutions R. Williams RCA Laboratories, Princeton, New Jersey 08540 (Received December 18, 1974) Publication costs assisted by RCA Laboratories
Contact angle measurements were made for aqueous solutions of CaClz and K&03 on Teflon and polyethylene. The variation of interfacial free energy with salt concentration is the same as that of the surface tension of the solution. This can be understood by considering the effect of the electrostatic image force on the distribution of ions near the interface. The surface tension of water is increased by dissolving an ionic salt 'in it. If we exclude a few materials that are wetting agents this is a general effect. At a given concentration all salts of the same charge type behave about the same. With the possible exception of certain very dilute solutions the surface tension increases monotonically with increasing salt concentration. For concentrated solutions the surface tension can be 50% greater than that of pure water. A recent review of earlier experimental and theoretical work on the problem was given by Rand1es.l The physical basis for the increase in surface tension is the electrostatic image force. A charge, q, in a dielectric The Journal of Physical Chemistry, Vol. 79,No. 13, 1975
medium, 1,is repelled from an interface with a medium, 2, having a smaller dielectric constant. Consider the case for media with dielectric constants, t l and € 2 with €1> ~ 2 If. the interface lies in the x-y plane at z = 0, the image potential, U ( z ) ,is
+
where LY = ( 6 1 - t z ) / ( t l € 2 ) . For the surface tension problem, medium 2 is air and t 2 is 1. For water, t l is 79, giving LY = 0.98. As an ion in the water approaches the interface its energy is increased by the amount, U ( z ) . This becomes
