J . Phys. Chem. 1984, 88, 3132-3133
3132
Polar, Aprotic Solvents and the Hydrophobic Effect Frank A. Greco Department of Physiology and Biophysics, Harvard Medical School, Boston, Massachusetts 021 15 (Received: May 20, 1983; In Final Form: November 2, 1983)
A current theory of the hydrophobic effect assigns the decrease in entropy upon mixing water and alkane to an increase in hydrogen bonding. This paper shows that the entropy of formation of a water-decane interface (-0.162 erg/(deg cm2)) has a magnitude similar to those of decane and N,N-dimethylacetamide (-0.1 52 erg/(deg cm*)), dimethyl sulfoxide (-0.125 erg/(deg cm2)), and acetonitrile (-0.159 erg/(deg cm2)). Since these polar, aprotic solvents cannot form hydrogen bonds among themselves, a mechanism must exist by which entropy can decrease without invoking properties unique to hydrogen bonds. A qualitative model relating entropy changes to free volume is proposed.
Theories concerning the immiscibility of water and alkane have created a useful framework in which to discuss factors affecting micelles, proteins, and biological membranes.’-3 All of these theories focus on the decrease in entropy associated with the interaction of water and alkane, because this decrease accounts for the unfavorable free energy of mixing. Entropy losses of similar magnitude occur when water and alkane interact in two different settings: as two bulk phases separated by an interface and as solute and solvent for alkane in ~ a t e r . ~ Ideally, -~ a complete theory should explain both cases but many authors have focused on the solubility of alkane in water, taking methane in water as paradigm.2,6-8 NBmethy, Scheraga, and Kauzmann9 have clearly stated a widely held belief that “...this entropy term arises owing to changes in the state of water and has to be attributed to increased ordering of water molecules, i.e., to an increase in hydrogen bonding.” However, Miller and Hildebrand’O have emphasized the contribution of hydrogen bonds to the heat capacity of water. They assign the entropy decrease to the notion that “when inert molecules are introduced ... H bonds are deactivated or destroyed to an extent depending upon the total surface of the solute.” While both approaches attempt to link the entropy change to the number and strength of hydrogen bonds, they lead to opposite results. Hence, it seemed of interest to examine the role played by hydrogen bonds and, in the first place, to determine its necessity for entropy loss. Since polar, aprotic solvents behave similarly to water in some respects, their interaction with alkane would provide for comparison a system without hydrogen bonding. The aprotic solvents used in the following experiments do not mix with decane; therefore, interfacial measurements were the simplest way to make the comparison. Surface and interfacial energies were determined by drop volume using the correction factors derived by Harkins.” Each drop depended from a stainless steel tip of mean diameter 0.5990 f 0.0002 cm as measured by micrometer. Mean volume was calculated from the number of drops formed by about 1.0 mL (fO.OO1) of fluid expressed from a micrometer syringe (MicroMetric Instrument Co., Cleveland, OH). Drops were formed in a glass vessel which was completely closed except for connection to the atmosphere through a drying tube and which was immersed (1) Hartley, G. S. “Aqueous Solutions of Paraffin-Chain Salts”; Hermann: Paris, 1936. (2) Kauzmann, W. J. Adv. Protein Chem. 1959, 14, 1-63. (3) Tanford, C. Science 1978, 200, 1012-8. (4) Aveyard, R.; Haydon, D. A. Trans. Faraday SOC.1965,61,2255-61. ( 5 ) Davies, J. T.; Rideal, E. K. “Interfacial Phenomena”;Academic Press: New York, 1963; pp 18-19. (6) Linford, R. G.; Powell, R. J.; Hildebrand, J. H. J . Phys. Chem. 1970, 74, 3024-5. (7) Abraham, M. H. J . Am. Chem. SOC.1982, 104, 2085-94. (8) Wfrtz, D. H. J . Am. Chem. SOC.1980, 102, 5316-22. (9) Nemethy, G.; Scheraga, H. A.; Kauzmann, W. J. J. Phys. Chem. 1968, 72, 1842. (10) Miller, K. W.; Hildebrand, J. H. J . Am. Chem. SOC.1968, 90, 300 1-4. (1 1). Weissberger, A., Ed. “Physical Methods of Organic Chemistry”; Interscience: New York, 1945; p 168.
0022-3654/84/2088-3 132$01S O / O
in a constant-temperature water bath (fO.l “C). A priori accuracy was about 1%. To confirm this the surface free energy of glass-distilled water was determined as a function of temperature. The value at 20 OC (72.70 erg/cm2) and the temperature coefficient (-0.158 erg/(deg cm2)) agreed within 1% with the data of Harkins” (72.79 erg/cm2 and -0.159 erg/(deg cm2)). Decane (Aldrich Chemical Co., Milwaukee, WI) was further purified by passage over silica. Dimethyl sulfoxide acetonitrile, and N,Ndimethylacetamide were also obtained from Aldrich, specified to be 99+% pure, and used without further purification. To prevent absorption of water all transfers were done by syringe; solvents were stored over molecular sieve 4A. Densities were measured in a 25-mL density bottle and agreed within 0.1%with the values reported in the literature for decane,12N,N-dimethylacetamide,12 dimethyl sulfoxide,13and a~etonitri1e.I~The surface free energy of each solvent was measured against air saturated with vapor. Surface free energy varied linearly with temperature from 20 to 35 OC and the slope was determined by the method of averages. Surface entropy was estimated as the negative of this slope, Le., as -(dF/dT); standard error of the entropy was always less than 10%. Corresponding experiments were performed with the solvent-decane interface. The entropy of formation of the interface (ASf) from the two free surfaces was calculated as the difference between the interfacial entropy and the sum of the solvent and decane surface entropies. The results are summarized in Table
I. Aveyard and Haydon4 have extensively studied the water-alkane interface. These data agree with theirs within experimental error and also show a decrease in entropy at the formation of the interface. However, decreases of similar magnitude occur with the polar, aprotic solvents as well. Hence, there must exist a mechanism by which entropy can decrease that does not invoke properties unique to hydrogen bonds. What connection do these data have with the hydrophobic effect? The answer depends in part upon definition and in part upon nature. In 1953 Kauzmann15 introduced the term “hydrophobic bond” to indicate that the free energy of interaction between nonpolar amino acids in proteins exceeded that expected from van der Waals forces. Following the approach of Hartley’ to micelle formation, Kauzmann2 sought to explain the unexpected free energy as a consequence of the same factors that make nonpolar molecules poorly soluble in water. In particular, the connection was made to the work of Butler,16 Eley,” and Frank and Evansl8 on the solubility of gases in yater. In 1968 Ngmethy, Scheraga, and Kauzmann9 defended the term “hydrophobic bond” and wrote the following: “Because the source of immiscibility (12) Riddick, J. A.; Bunger, W. B. “Organic Solvents”;Wiley-Interscience: New York, 1970. (13) Cleaver, H. L.; Snead, C. C. J . Phys. Chem. 1963, 67, 918-20. (14) J e f h y , G . H.; Vogel, A . I. J . Chem. SOC.1948, 658. (15) McElroy, W. D.; Glass, B. “The Mechanism of Enzyme Action”; Johns Hopkins Press: Baltimore, 1954; pp 70-120. (16) Butler, J. A. Trans. Faraday SOC.1937, 33, 235. (17) Eley, D. D. Trans. Faraday SOC.1939, 35, 1283. (18) Frank, H. S.; Evans, M. W. J . Chem. Phys. 1945, 13, 507-32.
0 1984 American Chemical Society
Polar, Aprotic Solvents and the Hydrophobic Effect
The Journal of Physical Chemistry, Vol. 88, No. 14, 1984 3133
TABLE I
free energy,O erg/cm2 surfaceb interfaceC 72.70 52.19 36.39 1.74 43.27 10.85 29.60 6.48 23.95
compd water N,N-dimethylacetamide dimethyl sulfoxide acetonitrile decane "At 20
OC.
entropy, erg/(deg cm2) surfaceb interfaceC 0.158 0.085 0.126 0.063 0.116 0.080 0.158 0.088 0.089
M
f
-0.162 -0.152 -0.125 -0.159
bVapor. cDecane.
is an entropy factor, the water-hydrocarbon system differs qualitatively and in a unique manner from most systems of low miscibility. Thus the interactions in this system do represent a special concept." Recently, Tanford19 has reintroduced surface quantities to define hydrophobicity and has claimed "... that the special character of hydrocarbon-water antipathy can be demonstrated in this way even more clearly than on the basis of bulk solubility data, which have in recent years been the most common vehicle for introducing the concept of hydrophobicity." Thus, the term "hydrophobic bond" grew out of questions arising from the colloid chemistry of proteins and entered the field of the solubility of nonpolar molecules because of the negative entropy common to both processes. Provided the same physical mechanisms underlie the phenomena in colloidal and noncolloidal domains, no confusion results from the use of the term "hydrophobic" in both settings. Since entropy loss accounts for the excess free energy, it seems reasonable to look for a single mechanism that encompasses both domains. However, several difficulties arise. For methane in water, as remarked by Kauzmann,*Othe small radius of curvature might allow a clathrate to form which could not occur at a planar interface. Furthermore, the elegant Pratt-Chandler predicts that as two methane molecules approach each other in water, the favored configuration retains a water molecule between them, which does not correspond to a "hydrophobic bond". It is not the intent of this article to assert that colloidal and noncolloidal entropy losses must derive from a single mechanism, nor to advocate which domain should claim the term "hydrophobic" should these losses derive from different mechanisms, nor even to endorse the term "hydrophobic". It is the intent of this article to answer the following question: are hydrogen bonds necessary to explain entropy loss at the colloidal level? The answer is no. And the answer bears on the theories of proteins, micelles, and biological membranes by eliminating the need to conceive of icelike barriers around these structures. How does entropy decrease when decane and polar, aprotic solvents interact? It is to the nature of such a mechanism that we now turn. The hypothesis that changes in entropy reflect changes in free volume can qualitatively account for the interfacial data. Thus, the surface entropy, associated with the transfer of a molecule from bulk phase to the surface, is positive because of the greater free volume available at the surface.24 The loss of entropy at ~~~~
(19) Tanford, C. Proc. Natl. Acad. Sci. U.S.A. 1979, 76, 4175-6. (20) Kauzmann, W. J., personal communication. (21) Pratt, L. R.; Chandler, D. J . Chem. Phys. 1977, 67, 3683-704. (22) Geiger, A.; Rahman, A.; Stillinger, F. H. J . Chem. Phys. 1979, 70, 263-76 (23) Pangali, C.; Rao, M.; Berne, B. J. J. Chem. Phys. 1979, 71,2975-81. (24) van der Waals, J. D.; Kohstam, P. "Lehrbuch der Thermcdynamik"; Maas and van Suchtelen: Amsterdam, 1908; p 207ff.
the formation of the interface would indicate compression of the surface layers by the attractive forces between the bulk phases. The greater cohesiveness of the polar molecules prevents penetration by decane, notwithstanding the attractive forces between the two phases. From this point of view, the entropy loss occurs as a consequence of the immiscibility, in contradistinction to being the cause of it. The cause of the immiscibility lies in the large forces of cohesion in the polar phases. This point may be underscored by adapting an argument recently employed by Tanford19 to the data for MezSO. The work of adhesion is that required to separate 1 cm2 of two bulk phases in contact and in the case of Me2SO/decane is 56.37 erg/cm2. Comparison of this term with the work of cohesion of Me2S0 (86.54 erg/cmz) and the work of cohesion of decane (47.90 erg/cm2) shows that the attractive forces between Me2S0 and decane exceed those between decane and decane; it is the high cohesion of MezSO that prevents mixing. Similar arguments can be made for acetonitrile and N,N-dimethylacetamide, reinforcing the hypothesis that the underlying mechanisms for water and polar, aprotic solvents are similar. While it is premature to connect rigorously the interfacial phenomena with bulk solubility, some insight can be gained from a sketch of how this might be done. To do this we need further to consider that cohesive forces will vary with thermal fluctuations in density and to postulate that decane can enter the polar phase after such a fluctuation has sufficiently reduced the local density. The entry of a molecule of decane into an area of low density would reduce free volume and hence decrease entropy in a manner analogous to that occurring at the interface. Needless to say, the interpretation of the interfacial data is independent of this limited attempt to extend these ideas to bulk solubility. This explantion has drawn from the work of previous authors.1,2)6,z"2sIt differs by not invoking a special role for hydrogen bonds but it does not exclude a contribution from hydrogen bonds in the case of aqueous solutions. Futhermore, it differs by attempting to connect interfacial phenomena and solubility along the lines drawn by L a n g m ~ i r . ~ ~ Acknowledgment. I was supported in part by grant G M 28992-01 from the National Institutes of Health during this work. I thank F. Brink, W. Kauzmann, R. Latorre, J. Lindsey, K. Miller, and M. Tosteson for helpful discussions. Registry No. Me2S0, 67-68-5;water, 7732-18-5; decane, 124-18-5; acetonitrile, 75-05-8; N,N-dimethylacetamide, 127- 19-5. (25) (26) (27) (28) (29)
Pierotti, R. A. Chem. Rev.
1976, 76, 717-26. Cramer, R. D. J . Am. Chem. SOC.1977, 99, 5408-12. Aranow, R.; Witten, L. J . Phys. Chem. 1960, 64, 1643-48. Howarth, 0.W. J . Chem. SOC.,Faraday Trans. I 1975, 71,2303-9. Langmuir, I. Chem. Reu. 1929, 6, 451-79.
