Thermodynamics and the hydrophobic effect in a core-softened model and comparison with experiments

A simple and computationally inexpensive core-softened model, originally proposed by Franzese [G. Franzese, J. Mol. Liq. 136, 267 (2007)], was adopted to show that it exhibits properties of waterlike fluid and hydrophobic effect. The potential used between particles is spherically symmetric with two characteristic lengths. Thermodynamics of nonpolar solvation were modeled as an insertion of a modified Lennard-Jones particle. It was investigated how the anomalous predictions of the model as well as the nonpolar solvation compare with the experimental data for water anomalies and the temperature dependence of noble gases hydration. It was shown that the model qualitatively follows the same trends as water. The model is able to reproduce waterlike anomalous properties (density maximum, heat capacity minimum, isothermal compressibility, etc.) and hydrophobic effect (minimum solubility for nonpolar solutes near ambient conditions, increased solubility of larger noble gases, etc.). It is argued that the model yields similar results as more complex and computationally expensive models.

Figure 1

Two characteristic lengths in a pair potential suffice to reproduce the behavior of water. (a) Inversion of the experimental oxygen-oxygen radial distribution function [36, 37] yields an effective pair potential. Competition between orientational order due to strong angular-dependent interactions (hydrogen bonding) and translational order manifests as two characteristic lengths in a potential. (b) The soft-core potential (solid line) used in our simulations (CSW) can be thought of as a first-order approximation of the experimental potential. Also, a modified Lennard-Jones potential for solute-solvent interaction for two particle sizes (dashed and dotted lines) is shown, which is used to simulate hydrophobic particles.

Figure 2

(a) Oxygen-oxygen radial distribution function in liquid water at ${25}^{°}\mathrm{C}$ and 1 atm from neutron scattering experiment [91]. (b) Radial distribution function from a simulation in the CSW solvent slightly above the melting point and at subcritical pressure, $T^{*}=0.6$ and $p^{*}=0.0002$, corresponding to ${30}^{°}\mathrm{C}$ and 2.6 atm.

Figure 3

Comparison of (a)–(d) experimental data for water properties at 1 atm [1, 92] and (e)–(h) simulation results of the CSW fluid at subcritical pressure, $p^{*}=0.024$. The CSW model captures the appearance of the temperature of maximum density (TMD), the negative thermal expansion coefficient, and minima in the heat capacity and the isothermal compressibility. [Note a different scale and pressure $p^{*}=0.10$ for (h).]

Figure 4

Comparison of experimental data on (a) the change of thermodynamic properties and (b) volume for transfer of argon into water at 300 atm [68, 97, 98] and (c)–(d) simulation results for transfer of a modified Lennard-Jones particle with ${\sigma }_{\mathrm{LJ}}=1.0$ and $\epsilon =0.1$ into the CSW solvent at $p^{*}=0.02$.

Figure 5

Free energy of transfer of nonpolar gases into water at ${25}^{°}\mathrm{C}$ and 1 atm (left scale) [68] and results from CSW model (right) at different temperatures ($T^{*}=0.6$, $0.8$, $1.0$) for $p^{*}=0.024$. See Table 1 for the parameters used.

Figure 6

(a)–(b) Excess chemical potential for transfer of a hard sphere with radius $r$ in water [72] is in agreement with (c)–(d) the calculated trends for insertion of modified LJ solutes of various sizes in the CSW fluid at $T^{*}=1.0$ and $p^{*}=0.1$.