Simple Model of Hydrophobic Hydration

Abstract

Water is an unusual liquid in its solvation properties. Here, we model the process of transferring a nonpolar solute into water. Our goal was to capture the physical balance between water’s hydrogen bonding and van der Waals interactions in a model that is simple enough to be nearly analytical and not heavily computational. We develop a 2-dimensional Mercedes-Benz-like model of water with which we compute the free energy, enthalpy, entropy, and the heat capacity of transfer as a function of temperature, pressure and solute size. As validation, we find that this model gives the same trends as Monte Carlo simulations of the underlying 2D model and gives qualitative agreement with experiments. The advantages of this model are that it gives simple insights and that computational time is negligible. It may provide a useful starting point for developing more efficient and more realistic 3D models of aqueous solvation.

Analytical theory of the hydrophobic effect of solutes in water

“…To develop the theory for the solvation of nonpolar solutes, we followed the same steps as in Luksic et al [12]. A nonpolar solute molecule of diameter σ s is inserted into water.…”

“…It is smaller than the $v_{\text{mol}}^{\mathrm{normalb}}$ by the overlap volume $\mathrm{\Delta }v(v_{\text{mol}}^{\mathrm{normalh}}=v_{\text{mol}}^{\mathrm{normalb}}-\mathrm{\Delta }v)$ (see Fig. 4) [12]. We compute the Gibbs free energy of transferring a hydrophobic solute into water using [43]…”

“…(4) And, even the disadvantage—that some details of molecular structure must be left out of the model—can actually be an advantage, because they provide an opportunity to explore which details matter and which don’t. Here we give an analytical model of the hydrophobic effect; it builds upon earlier work by Luksic et al [12]. …”

“…[43] required the results of a reference Monte Carlo simulation of pure bulk water phase. That approach was improved by Luksic et al [12], which is simpler and circumvents any computer simulation steps by using an analytical model of the pure phase of water. Both solvation methods were for 2D cases.…”

Analytical model for three-dimensional Mercedes-Benz water molecules

“…These models are able to qualitatively reproduce the known thermodynamic behavior of water including the behavior of supercooled water and describe how the predictions of lattice-gas models are relevant to understanding liquid and amorphous solid water, but it is more difficult to use it for description of solvation effects. This model of MB water can be used to describe the effect of solvation as recently done for the two-dimensional MB model [54]. …”