Temperature and length scale dependence of solvophobic solvation in a single-site water-like liquid

Crustwater: Modeling Hydrophobic Solvation

We describe Crustwater, a statistical mechanical model of nonpolar solvation in water. It treats bulk water using the Cage Water model and introduces a crust, i.e., a solvation shell of coordinated partially structured waters. Crustwater is analytical and fast to compute. We compute here solvation vs temperature over the liquid range, and vs pressure and solute size. Its thermal predictions are as accurate as much more costly explicit models such as TIP4P/2005. This modeling gives new insights into the hydrophobic effect: (1) that oil–water insolubility in cold water is due to solute–water (SW) translational entropy and not water–water (WW) orientations, even while hot water is dominated by WW cage breaking, and (2) that a size transition at the Angstrom scale, not the nanometer scale, takes place as previously predicted.

Temperature, Pressure, and Length-Scale Dependence of Solvation in Water-like Solvents. II. Large Solvophovic Solutes

We use molecular simulation to determine solvation free energies, isochoric solvation energies and entropies, isobaric solvation enthalpies and entropies, partial molecular volumes, and isothermal density derivatives of the solvation free energy as a function of temperature and pressure for hard-sphere solutes with diameters ranging from 4 to 36 Å in TIP4P/2005 and Jagla water-like solvents exhibiting unusual thermodynamics. An important piece of our discussion focuses on the nanometer-sized solutes, for which simulation results are found to be accounted for by the most basic classical thermodynamic treatment contemplating bulk and interfacial contributions to the solvation free energy. Thus, since water's liquid-vapor surface tension is only special inasmuch as it takes unusually large values, solvent's water-like unusual thermodynamics manifests through a term proportional to the pressure in the solvation free energy. As a result, such solvent's unusual thermodynamics is found to be relevant to the temperature and pressure dependence of the isochoric solvation energy and entropy as well as to the isothermal density derivative of the solvation free energy. This sharply contrasts with the findings of the first part of this series indicating that the solvation free energy of small hard spheres responds to temperature and pressure changes as solvent's density does, with such a contrasting picture embodying a "pressure-density dichotomy." As for the length-scale dependence, we find the zero nominal pressure and the solvent's temperature of the maximum density as singular conditions for cavity surface-area size scaling of large solutes to occur for all solvation quantities. We finally argue that the overall study undertaken in this series suggests that water's unusual thermodynamics may be relevant to the thermodynamic stability of clusters of solvophobic units in the temperature-pressure plane. Some comments on the role of solute-solvent attractive interactions are also depicted.

Analytical 2-Dimensional Model of Nonpolar and Ionic Solvation in Water

A goal in computational chemistry is computing hydration free energies of nonpolar and charged solutes accurately, but with much greater computational speeds than in today's explicit-water simulations. Here, we take one step in that direction: a simple model of solvating waters that is analytical and thus essentially instantaneous to compute. Each water molecule is a 2-dimensional dipolar hydrogen-bonding disk that interacts around small circular solutes with different nonpolar and charge interactions. The model gives good qualitative agreement with experiments. As a function of the solute radius, it gives the solvation free energy, enthalpy and entropy as a function of temperature for the inert gas series Ne, Ar, Kr, and Xe. For anions and cations, it captures relatively well the trends versus ion radius. This approach should be readily generalizable to three dimensions.

Temperature, Pressure, and Concentration Derivatives of Nonpolar Gas Hydration: Impact on the Heat Capacity, Temperature of Maximum Density, and Speed of Sound of Aqueous Mixtures

The hydrophobic effect is an umbrella term encompassing a number of solvation phenomena associated with solutions of nonpolar species in water, including the following: a meager solubility opposed by entropy at room temperature; large positive hydration heat capacities; positive shifts in the temperature of maximum density of aqueous mixtures; increases in the speed of sound of dilute aqueous mixtures; and negative volumes of association between interacting solutes. Here we present a molecular simulation study of nonpolar gas hydration over the temperature range 273.15-373.15 K and a pressure range -500 to 1000 bar to investigate the interrelationships between distinct hydrophobic phenomena. We develop a new free energy correlation for the solute chemical potentials founded on the Tait equation description of the equation-of-state of liquid water. This analytical correlation is shown to provide a quantitatively accurate description of nonpolar gas hydration over the entire range of thermodynamic state points simulated, with an error of ∼0.02 k_BT or lower in the fitted chemical potentials. Our simulations and the correlation accurately reproduce many of the available experimental results for the hydration of the solutes examined here. Moreover, the correlation reproduces the characteristic entropies of hydration, temperature dependence of the hydration heat capacity, perturbations in the temperature of maximum density, and changes in the speed of sound. While negative volumes of association result from pairwise interactions in solution, beyond the limits of our simulations performed at infinite dilution, we discuss how our correlation could be supplemented with second virial coefficient information to expand to finite concentrations. In total, this work demonstrates that many distinct phenomena associated with the hydrophobic effect can be captured within a single thermodynamically consistent correlation for solute hydration free energies.

Temperature and pressure dependence of the interfacial free energy against a hard surface in contact with water and decane

Theoretical descriptions of molecular-scale solvation frequently invoke contributions proportional to the solvent exposed area, under the tacit expectation that those contributions are tied to a surface tension for macroscopic surfaces. Here we examine the application of revised scaled-particle theory (RSPT) to extrapolate molecular simulation results for the wetting of molecular-to-meso-scale repulsive solutes in liquid water and decane to determine the interfacial free energies of hard, flat surfaces. We show that the RSPT yields interfacial free energies at ambient pressures that are consistently greater than that obtained from the liquid-vapor surface tensions of water and decane by ∼4%. Nevertheless, the hard surface and liquid-vapor interfacial free energies are parallel over a broad temperature range at 1 bar indicating similar entropic contributions. With increasing pressure, the hard, flat interfacial free energies exhibit a maximum in the vicinity of ∼1000 bars. This non-monotonic behavior in both water and decane reflects solvent dewetting at low pressures, followed by wetting at higher pressures as the solvents are pushed onto the solute. By comparing the results of RSPT against classic scaled-particle theory (CSPT), we show that CSPT systematically predicts greater entropic penalties for interface formation and makes inconsistent predictions between the pressure dependence of the interfacial free energy and solvent contact density with the solute surface.

Scaled-particle theory analysis of cylindrical cavities in solution

The solvation of hard spherocylindrical solutes is analyzed within the context of scaled-particle theory, which takes the view that the free energy of solvating an empty cavitylike solute is equal to the pressure-volume work required to inflate a solute from nothing to the desired size and shape within the solvent. Based on our analysis, an end cap approximation is proposed to predict the solvation free energy as a function of the spherocylinder length from knowledge regarding only the solvent density in contact with a spherical solute. The framework developed is applied to extend Reiss's classic implementation of scaled-particle theory and a previously developed revised scaled-particle theory to spherocylindrical solutes. To test the theoretical descriptions developed, molecular simulations of the solvation of infinitely long cylindrical solutes are performed. In hard-sphere solvents classic scaled-particle theory is shown to provide a reasonably accurate description of the solvent contact correlation and resulting solvation free energy per unit length of cylinders, while the revised scaled-particle theory fitted to measured values of the contact correlation provides a quantitative free energy. Applied to the Lennard-Jones solvent at a state-point along the liquid-vapor coexistence curve, however, classic scaled-particle theory fails to correctly capture the dependence of the contact correlation. Revised scaled-particle theory, on the other hand, provides a quantitative description of cylinder solvation in the Lennard-Jones solvent with a fitted interfacial free energy in good agreement with that determined for purely spherical solutes. The breakdown of classical scaled-particle theory does not result from the failure of the end cap approximation, however, but is indicative of neglected higher-order curvature dependences on the solvation free energy.

Existence of a liquid-liquid phase transition in methanol

A simple model is constructed to study the phase diagram and thermodynamic properties of methanol, which is described as a dimer of an apolar sphere mimicking the methyl group and a sphere with core-softened potential as the hydroxyl group. Performing classical Monte Carlo simulations, we obtained the phase diagram, showing a second critical point between two different liquid phases. Evaluating systems with a different number of particles, we extrapolate to infinite size in accordance with Ising universality class to obtain bulk values for critical temperature, pressure, and density. Strong evidence that the structure of the liquid changes upon transition from high- to low-density phase was provided. From the experimentally determined hydrogen bond strength and length in methanol and water, we propose where the second critical point of methanol should be.

Properties of a soft-core model of methanol: an integral equation theory and computer simulation study

Thermodynamic and structural properties of a coarse-grained model of methanol are examined by Monte Carlo simulations and reference interaction site model (RISM) integral equation theory. Methanol particles are described as dimers formed from an apolar Lennard-Jones sphere, mimicking the methyl group, and a sphere with a core-softened potential as the hydroxyl group. Different closure approximations of the RISM theory are compared and discussed. The liquid structure of methanol is investigated by calculating site-site radial distribution functions and static structure factors for a wide range of temperatures and densities. Results obtained show a good agreement between RISM and Monte Carlo simulations. The phase behavior of methanol is investigated by employing different thermodynamic routes for the calculation of the RISM free energy, drawing gas-liquid coexistence curves that match the simulation data. Preliminary indications for a putative second critical point between two different liquid phases of methanol are also discussed.

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.

The hydrophobic effect in a simple isotropic water-like model: Monte Carlo study

Using Monte Carlo computer simulations, we show that a simple isotropic water-like model with two characteristic lengths can reproduce the hydrophobic effect and the solvation properties of small and large non-polar solutes. Influence of temperature, pressure, and solute size on the thermodynamic properties of apolar solute solvation in a water model was systematically studied, showing two different solvation regimes. Small particles can fit into the cavities around the solvent particles, inducing additional order in the system and lowering the overall entropy. Large particles force the solvent to disrupt their network, increasing the entropy of the system. At low temperatures, the ordering effect of small solutes is very pronounced. Above the cross-over temperature, which strongly depends on the solute size, the entropy change becomes strictly positive. Pressure dependence was also investigated, showing a "cross-over pressure" where the entropy and enthalpy of solvation are the lowest. These results suggest two fundamentally different solvation mechanisms, as observed experimentally in water and computationally in various water-like models.