Chemical Education Today
Letters Hydrophobic Solvation NOT via Clathrate Water Cages I read with great interest Konrad and Lankau’s recent article in this Journal (1) on the hydrophobic effect. These authors discuss the thermodynamics underlying Henry’s law to shed light on the process of hydrophobic solvation. The approach strikes me as powerful and useful. There is just one point that bears correcting. As a physical explanation of Frank and Evans’s “iceberg model” of aqueous solvation of nonpolar solutes (2), Konrad and Lankau present in Figure 6 an (H2O)20 clathrate-like cage surrounding the central methane solute molecule. As many other authors have done, Konrad and Lankau go on to discuss changes in entropy and enthalpy of solvation in light of changes in solvent structure as water clathrate cages form, stretch, and break down. Discussions of this type have the advantage that they allow us to visualize, using a fairly simple structure, why ∆S and ∆H are both generally negative for the hydration of nonpolar solutes. The disadvantage of using the clathrate cage model is that it is probably wrong. Konrad and Lankau cite one study that supports the existence of an (H2O)20 clathrate-like cage hydrating krypton (3) and another article that argues for a much smaller water cage surrounding hydrated methane (4). In fact, experimental evidence tends to argue against the very existence of these cages (5, 6). Hildebrand showed that methane diffuses only 40% slower in water than in carbon tetrachloride (7); if clathrate hydration cages existed, aqueous diffusion should be 90–99% slower. Several other studies have presented data that argue against the existence of ordered clathrate structures (7–11). An alternative statistical mechanical model called the “scaled particle cavity theory” has been developed to explain the thermodynamics of hydrophobic solvation (12). Molecular dynamics simulations using this theory suggest that the hydrophobic effect stems from the small size and tight packing of the water molecule, and the resultant low compressibility and high density of liquid water, rather than from macromolecular clathrate cages (13–17). Scaled particle theory has recently been revised and reviewed (6). Konrad and Lankau do correctly state that the “dependence of the Henry’s law constant on the solvent’s density is another clue that the inner structure of the solvent is an important factor in the discussion of hydrophobic solvation”. Unfortunately, the authors’ explanation for the higher density of liquid water relative to ice is wrong. They state that the higher density of water “suggests that the number of hydrogen bonds per water molecule is slightly larger than four”. Although such “penta-coordinated water molecules” have been observed, the required “bifurcated hydrogen bonds” are weaker than the single hydrogen bond that they replace (18). Furthermore, there is no thermodynamic or geometric evidence that such bifurcated H bonds would increase the density of water (18). Recent estimates stemming both from molecular dynamics simulations (19) and X-ray spectroscopy (20) suggest that each molecule in liquid water forms an average of 2.4 hydrogen bonds, as compared to 4 H bonds per molecule in ice. Konrad and Lankau make the logical assumption that increased H bonding leads to increased density; however, liquid
water has less H bonding than ice, but a higher density. How can this be the case? One thing to keep in mind is that the covalent H–O–H bond angle is 104.5° in gaseous and liquid water, but it must widen to 106° to accommodate the tetrahedral symmetry around water oxygens in solid ice (21). This distortion of water’s O–H covalent bonds allows for stronger, more rigid noncovalent hydrogen bonds between water molecules in the ice crystal (21). On the other hand, in liquid water, hydrogen bonds are weaker and more flexible. There is very little long range (>15–20 Å) order in liquid water, thus allowing water molecules to rotate, bend, and translate (19) in such a way as to maximize packing density above that available within the tetrahedrally packed ice crystal. Recently Rezus and Bakker (22) used mid-infrared pumpprobe spectroscopy to study the rotational reorientation of water molecules in the solvation shell of apolar solutes. They found that four water OH groups were immobilized per methyl group in the solute. Considering that 10 water molecules (with 20 OH groups) may solvate a single methyl group (23), 20% of the total solvating OH groups fall into this immobilized population, while the other 80% maintain the same reorientational mobility as bulk water. If each immobilized OH group is on a separate water molecule, then 40% of the ten solvated water molecules become immobilized: 4 immobilized OH groups per 10 solvating water molecules. (Might this explain why methane diffuses 40% more slowly in water than in CCl4, as quoted above?) Rezus and Bakker interpret their results in light of recent molecular dynamics studies (23–25) that suggest that the high orientational mobility of liquid water molecules is due to packing defects caused by over-coordinated molecules with five H bonds. Fast water reorientation involves over-coordinated water molecules in the first hydration shell rotating to interact with under-coordinated water molecules in the second hydration shell. Adding nonpolar solutes to water displaces over-coordinated water molecules, thus decreasing defects, decreasing fast reorientation, and lowering entropy. Rezus and Bakker conclude that hydration shells around nonpolar solutes are partially (20%?) “frozen” from “a dynamical perspective, but waterlike as far as structure is concerned” (22). This could explain some of the confusion in the field of hydrophobic solvation: the icebergs are dynamic, but not structural. Literature Cited 1. Konrad, O.; Lankau, T. J. Chem. Educ. 2007, 84, 864–869. 2. Frank, H. S.; Evans, M. W. J. Chem. Phys. 1945, 13, 507–532. 3. Bowron, D. T.; Filipponi, A.; Roberts, M. A.; Finney, J. L. Phys. Rev. Lett. 1998, 81, 4164–4167. 4. Koh, C. A.; Wisbey, R. P.; Wu, X.; Westacott, R. E.; Soper, A. K. J. Chem. Phys. 2000, 113, 6390–6397. 5. Silverstein, T. P. J. Chem. Educ. 1998, 75, 116–118. 6. Ashbaugh, H. S.; Pratt, L. R. Rev. Mod. Phys. 2006, 78, 159– 178. 7. Hildebrand, J. H. Proc. Natl. Acad. Sci. U.S.A. 1979, 76, 194. 8. Ashbaugh, H. S.; Asthagiri, D.; Pratt, L. R.; Rempe, S. B. Biophys. Chem. 2003, 105, 323.
© Division of Chemical Education • www.JCE.DivCHED.org • Vol. 85 No. 7 July 2008 • Journal of Chemical Education
917
Chemical Education Today
Letters 9. Cramer, R. D. J. Am. Chem. Soc. 1978, 99, 5408–5412. 10. Wilhelm, E.; Battino, R.; Wilcock, R. J. Chem. Rev. 1977, 77, 219–262; see especially pp 240–245. 11. Blokzijl, W.; Engberts, J. B. F. N. Angew. Chem., Int. Ed. Engl. 1993, 28, 1545–1579. 12. Pierotti, R. A. Chem. Rev. 1976, 76, 717–726. 13. Lucas, M. J. J. Chem. Phys. 1976, 80, 359. 14. Lee, B. Biopolymers 1991, 31, 993–1008. 15. Pratt, L. R.; Pohorille, A. Proc. Natl. Acad. Sci. U.S.A. 1992, 89, 2995–2999. 16. Wallqvist, A.; Covell, D. G. Biophys. J. 1996, 71, 600–608. 17. Durell, S. R.; Wallquist, A. Biophys. J. 1996, 71, 1695–1706. 18. Keutsch, F. N.; Saykally, R. J. Proc. Natl. Acad. Sci. U.S.A. 2001, 98, 10533–10540. 19. Zielkiewicz, J. J. Chem. Phys. 2005, 123, 104501. 20. Wernet, Ph.; Nordlund, D.; Bergmann, U.; Cavalleri, M.; Odelius, M.; Ogasawara, H.; Näslund, L. Å.; Hirsch, T. K.; Ojamäe, L.; Glatzel, P.; Pettersson, L. G. M.; Nilsson A. Science 2004, 304, 995–999.
918
21. Marechal, Y. The Hydrogen Bond and the Water Molecule, Elsevier:Amsterdam, 1998; pp 200–225. 22. Rezus, Y. L. A.; Bakker, H. J. Phys. Rev. Lett. 2007, 99, 148301. 23. Gallagher, K. R.; Sharp, K. A. J. Am. Chem. Soc. 2003, 125, 9853–9860. 24. Sciortino, F.; Geiger, A.; Stanley, H. E. Nature 1991, 354, 218–221. 25. Laage, D.; Hynes, J. T. Science 2006, 311, 832–835.
Supporting JCE Online Material
http://www.jce.divched.org/Journal/Issues/2008/Jul/abs917_2.html Full text (HTML and PDF) with links to cited JCE articles Todd P. Silverstein Department of Chemistry Willamette University Salem, OR 97301
[email protected] Journal of Chemical Education • Vol. 85 No. 7 July 2008 • www.JCE.DivCHED.org • © Division of Chemical Education
