Mercedes-Benz water molecules near hydrophobic wall: integral equation theories vs Monte Carlo simulations

Abstract

Associative version of Henderson-Abraham-Barker theory is applied for the study of Mercedes-Benz model of water near hydrophobic surface. We calculated density profiles and adsorption coefficients using Percus-Yevick and soft mean spherical associative approximations. The results are compared with Monte Carlo simulation data. It is shown that at higher temperatures both approximations satisfactory reproduce the simulation data. For lower temperatures, soft mean spherical approximation gives good agreement at low and at high densities while in at mid range densities, the prediction is only qualitative. The formation of a depletion layer between water and hydrophobic surface was also demonstrated and studied.

Figure 1

Two molecules of MB water (i and j), separated by the distance r_ij. Each molecule has three bonding vectors denoted by $\overrightarrow{i_k}$ (or $\overrightarrow{j_l}$); k, l = 1, 2, 3.

Figure 2

The water-water radial distribution function, g(r*), at (a) T* = 0.18, P* = 0.19 and (b) T* = 0.36, P* = 0.19. The MB model Monte Carlo result is presented by symbols, the PY results by red continuous line, and the SMSA results by green dashed line.

Figure 3

Density profile of MB water close to LJ plane. The MB model Monte Carlo result is presented by symbols, the PY results by red continuous line, and the SMSA results by green dashed line for pressure p* = 0.19 and (a) T* = 0.36, ρ* = 0.534, (b) T* = 0.28, ρ* = 0.741, (c) T* = 0.24, ρ* = 0.870, and (d) T* = 0.18, ρ* = 0.990.

Figure 4

Same as Fig. 3, results are for T* = 0.18 and (a) ρ* = 0.1, (b) ρ* = 0.534, (c) ρ* = 0.741, and (d) ρ* = 0.990.

Figure 5

Same as Fig. 4, results are for T* = 0.36.

Figure 6

Dependence of maximum density of MB water close to LJ plane on density. The SMSA results from Eq. 26 are presented by red solid line and from IET by green dashed line and from Monte Carlo simulations by symbols for (a) T* = 0.36 and (b) T* = 0.18.

Figure 7

Dependence of absorption coefficient of MB water close to LJ plane on density. The MB model Monte Carlo result is presented by symbols and the SMSA results by red solid line for (a) T* = 0.36 and (b) T* = 0.18.

Figure 8

Average number of hydrogen bonds per MB water molecule depending on distance from LJ plane. The MB model Monte Carlo result is presented by symbols and the SMSA results by red solid line for pressure p* = 0.19 and (a) T* = 0.36, ρ* = 0.534 and (b) T* = 0.18, ρ* = 0.990.

Figure 9

Population p_i of (a) nonbonded, (b) once bonded, (c) twice bonded, and (d) triple bonded MB water molecule depending on distance from LJ plane. The MB model Monte Carlo result is presented by symbols and the SMSA results by red solid line for pressure p* = 0.19 and T* = 0.18, ρ* = 0.990.

Figure 10

Same as Fig. 8, results are for T* = 0.36, ρ* = 0.534.