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

Abstract

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 B T 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.

Bridging Gaussian Density Fluctuations from Microscopic to Macroscopic Volumes: Applications to Non-Polar Solute Hydration Thermodynamics

“…The enthalpy, entropy, and heat capacity of hydrophobic hydration can be determined by fitting the temperature-dependent simulation results and theoretical predictions to the expression where T 0 is a reference temperature, taken here to be 298.15 K (25 °C), and the a i ’s are fitted constants. The form of this expression assumes the hydration heat capacity has a parabolic dependence on the temperature (i.e., c A ex = − T ∂ 2 μ A ex /∂ T 2 | P = − a 3 – 2 a 4 T – 6 a 5 T ( T – T 0 )), which is reasonable for fitting over a wide temperature range given that the hydration heat capacity is expected to be a decreasing function of temperature at lower temperatures and an increasing function of temperature as the critical point is approached. − The hydration enthalpy ( h A ex = − T 2 ∂(μ A ex / T )/∂ T | P ) and entropy ( s A ex = −∂μ A ex /∂ T | P ) similarly follow from appropriate temperature derivatives of eq .…”

“…The form of this expression assumes the hydration heat capacity has a parabolic dependence on the temperature (i.e., c A ex = − T ∂ 2 μ A ex /∂ T 2 | P = − a 3 – 2 a 4 T – 6 a 5 T ( T – T 0 )), which is reasonable for fitting over a wide temperature range given that the hydration heat capacity is expected to be a decreasing function of temperature at lower temperatures and an increasing function of temperature as the critical point is approached. 56 − 59 The hydration enthalpy ( h A ex = − T 2 ∂(μ A ex / T )/∂ T | P ) and entropy ( s A ex = −∂μ A ex /∂ T | P ) similarly follow from appropriate temperature derivatives of eq 15 .…”

“…As anticipated above, these heat capacities are large and positive. Moreover, they exhibit a non-monotonic temperature dependence as observed experimentally, − passing through a minimum above the normal boiling point of water. The agreement between the simulation and IGFT is excellent for solutes of 3 Å radius and smaller.…”

Temperature, Pressure, and Length-Scale Dependence of Solvation in Water-like Solvents. I. Small Solvophobic Solutes

“…The latter pertains to a family of model fluids characterized by isotropic pair potentials with two relevant energy scales that make them to exhibit water-like unusual thermodynamics . Accordingly, there is a strong suggestion that the corresponding thermodynamics of solvophobic solvation should reflect Jagla-fluid unusual thermodynamics just as the thermodynamics of aqueous solvation reflects that of water. , While previous work on this indicates that “Jagla-solvation is aqueous-like”, , it merits our attention to jointly approach isochoric and isobaric solvation for TIP4P/2005 and Jagla water-like solvents and thereby to expand the work on comparative studies of solvation in distinct solvents ,, as well as on the temperature and pressure dependence of solvation. − To this end, we report μ ̅ *­( T , p ), u̅ V * ( T , p ), s̅ V * ( T , p ), h̅ p * ( T , p ), s̅ p * ( T , p ), v p ( T , p ), and v̅ p ( T , p ) data as obtained from molecular simulation and analyze them with the aid of scaled-particle theory (SPT), the Gaussian model of small-length-scale solvation, ,, and our current knowledge of water-like thermodynamics. Methods are described in Section and results presented and thoroughly discussed in Section .…”

Reversal of the Temperature Dependence of Hydrophobic Hydration in Supercooled Water

“…Structural and dynamic properties of the solvent indicate that it remains a liquid over the simulation time even in the supercooled regime. Solute excess chemical potentials were evaluated using Widom test particle insertion. , The solutes considered were helium (He), neon (Ne), argon (Ar), krypton (Kr), xenon (Xe), and methane (Me), modeled using Lennard-Jones (LJ) potentials optimized to aqueous solubilities along with their repulsive Weeks–Chandler–Andersen (WCA) cores . In addition, the solubilities of hard sphere (HS) solutes with radii R (indicating the solvent-excluded size) of up to 3.6 Å were evaluated.…”