Hydration thermodynamics beyond the linear response approximation.

The solvation energetics associated with the transformation of a solute molecule at infinite dilution in water from an initial state A to a final state B is reconsidered. The two solute states have different potentials energies of interaction, [Formula: see text] and [Formula: see text], with the solvent environment. Throughout the A [Formula: see text] B transformation of the solute, the solvation system is described by a Hamiltonian [Formula: see text] that changes linearly with the coupling parameter ξ. By focusing on the characterization of the probability density [Formula: see text] that the dimensionless perturbational solute-solvent interaction energy [Formula: see text] has numerical value y when the coupling parameter is ξ, we derive a hierarchy of differential equation relations between the ξ-dependent cumulant functions of various orders in the expansion of the appropriate cumulant generating function. On the basis of this theoretical framework we then introduce an inherently nonlinear solvation model for which we are able to find analytical results for both [Formula: see text] and for the solvation thermodynamic functions. The solvation model is based on the premise that there is an upper or a lower bound (depending on the nature of the interactions considered) to the amplitude of the fluctuations of Y in the solution system at equilibrium. The results reveal essential differences in behavior for the model when compared with the linear response approximation to solvation, particularly with regards to the probability density [Formula: see text]. The analytical expressions for the solvation properties show, however, that the linear response behavior is recovered from the new model when the room for the thermal fluctuations in Y is not restricted by the existence of a nearby bound. We compare the predictions of the model with the results from molecular dynamics computer simulations for aqueous solvation, in which either (1) the solute-solvent electrostatic interactions, or (2) the shorter-range attractive interactions are switched-on in the A [Formula: see text] B process.

How is charge transport different in ionic liquids and electrolyte solutions?

In this article we show that, analyzed in a barycentric reference frame, the deviation in conductivity measured directly from impedance experiments with respect to that estimated indirectly from NMR diffusion experiments has different origins in electrolyte solutions and pure salts. In the case of electrolyte solutions, the momentum conservation law is satisfied by solvent + ions. Instead, in a molten salt or ionic liquid momentum conservation must be satisfied solely by the ions. This has significant implications. While positively correlated motion of ions of opposite charge is a well justified explanation for the reduction in impedance conductivity in the case of electrolyte solutions, it is not so in the case of ionic liquids and molten salts. This work presents a set of equations that in the case of ionic liquids and molten salts can be used to obtain from direct measurements of impedance and NMR the distinct part of the diffusion coefficient matrix in the barycentric reference frame. In other words, by using experimentally measurable quantities, these equations allow us to access the motional coupling between ions for which there is no single direct experimental measurement technique. While equations of this type have been proposed before, the ones presented here can be easily derived from the momentum conservation law and linear response theory. Our results indicate that the decrease in the impedance conductivity with respect to NMR conductivity in ionic liquids and molten salts is due to anticorrelated motion of ions of same charge. This scenario is different in electrolyte solutions, where the positively correlated motion of ions of opposite charge makes a significant contribution to the decrease in the impedance conductivity. In contrast, in a system comprising a single binary salt (a room temperature ionic liquid or a molten salt), the cation-anion distinct diffusion coefficient is negative definite and opposes the contribution from the cation-cation and anion-anion distinct diffusion coefficients. This property of the cation-anion distinct diffusion coefficient in systems comprising just two ion-constituents holds true not just in the barycentric reference frame but also in any of the internal reference frames of nonequilibrium thermodynamics.

Solvation thermodynamics: theory and applications.

Potential distribution and coupling parameter theories are combined to interrelate previous solvation thermodynamic results and derive several new expressions for the solvent reorganization energy at both constant volume and constant pressure. We further demonstrate that the usual decomposition of the chemical potential into noncompensating energetic and entropic contributions may be extended to obtain a Gaussian fluctuation approximation for the chemical potential plus an exact cumulant expansion for the remainder. These exact expressions are further related to approximate first-order thermodynamic perturbation theory predictions and used to obtain a coupling-parameter integral expression for the sum of all higher-order terms in the perturbation series. The results are compared with the experimental global solvation thermodynamic functions for xenon dissolved in n-hexane and water (under ambient conditions). These comparisons imply that the constant-volume solvent reorganization energy has a magnitude of at most approximately kT in both experimental solutions. The results are used to extract numerical values of the solute-solvent mean interaction energy and associated fluctuation entropy directly from experimental solvation thermodynamic measurements.