Model of the hydrophobic interaction

Abstract

The potential of mean force between interstitial solute molecules in Ben-Naim's one-dimensional, many-state lattice model (related to the one-dimensional q-state Potts model) is calculated. Since the model is exactly soluble, all results are explicit and analytic. It is found that the magnitude of the effective attractive force between solutes and the range of that attraction vary inversely with each other: the strength of the attraction, as expected, increases with increasing magnitude of the (entropically unfavorable) free energy of “hydrogen-bond’' formation, but at the same time the range decreases. Conversely, when the unfavourable entropy and favourable energy of “hydrogen-bond’' formation are nearly in balance, the attraction between hydrophobes, while then weak, is of very long range. It is remarked that solubility in a one-dimensional solution model, when the direct intermolecular interactions are of short range, can only be defined osmotically. The solubility of the hydrophobe, as so defined, is calculated with the present model. It is found to decrease with increasing temperature, as expected for a hydrophobic solute.

References

1. A. Ben-Naim, Statistical Thermodynamics for Chemists and Biochemists, Plenum, New York, 1992, pp. 220–223.
2. F. Y. Wu, J. Appl. Phys., 1984, 55, 2421.
3. F. H. Stillinger, J. Solution Chem., 1973, 2, 141.
4. J. C. Owicki and H. A. Scheraga, J. Am. Chem. Soc., 1977, 99, 7413.
5. L. R. Pratt and D. Chandler, J. Chem. Phys., 1977, 67, 3683.
6. B. Guillot and Y. Guissani, J. Chem. Phys., 1993, 99, 8075.
7. J. Forsman and B. Jönsson, J. Chem. Phys., 1994, 101, 5116.
8. M. E. Paulaitis, S. Garde and H. S. Ashbaugh, Curr. Opin. Colloid Interface Sci., 1996, 1, 376.
9. M. Pellegrini, N. Grønbech-Jensen and S. Doniach, J. Chem. Phys., 1996, 104, 8639.
10. G. Hummer, S. Garde, A. E. García, A. Pohorille and L. R. Pratt, Proc. Natl. Acad. Sci. USA, 1996, 93, 8951.
11. S. Lüdemann, H. Schreiber, R. Abseher and O. Steinhauser, J. Chem. Phys., 1996, 104, 286.
12. F. M. Floris, M. Selmi, A. Tani and J. Tomasi, J. Chem. Phys., 1997, 107, 6353.
13. N. A. M. Besseling and J. Lyklema, J. Phys. Chem. B, 1997, 101, 7604.
14. R. D. Mountain and D. Thirumalai, Proc. Natl. Acad. Sci. USA, 1998, 95, 8436.
15. K. A. T. Silverstein, A. D. J. Haymet and K. A. Dill, J. Am. Chem. Soc., 1998, 120, 3166.
16. K. Lum, D. Chandler and J. D. Weeks, J. Phys, Chem. B, 1999, 103, 4570.
17. B. Widom, J. Chem. Phys., 1963, 39, 2808.
18. C. Domb, Adv. Phys., 1960, 9, 149.
19. G. R. Andersen and J. C. Wheeler, J. Chem. Phys., 1978, 69, 3403.
20. J. C. Wheeler, personal communication.