On the behavior of the osmotic second virial coefficients of gases in aqueous solutions: Rigorous results, accurate approximations, and experimental evidence

Molecular-Based Description of the Osmotic Second Virial Coefficients of Electrolytes: Rigorous Formal Links to Solute-Solvent Interaction Asymmetry, Virial Expansion Paths, and Experimental Evidence

We introduce a molecular-based route to the evaluation of the osmotic second virial coefficients of dissociative solutes in dilute binary solutions, according to a general molecular thermodynamic solvation formalism of electrolyte solutions. We discuss the underlying solvation fundamentals and derive rigorous expressions leading to (i) the functional relationship among the osmotic second virial coefficients and the limiting composition behavior of the non-Coulombic contribution to the Kirkwood-Buff integral of the solute-solute interactions, the corresponding composition slope of the mean activity coefficient of the electrolyte solute, and a precisely defined solute-solvent intermolecular interaction asymmetry that characterizes unambiguously the solution non-ideality; (ii) the self-consistent calculation of the osmotic second virial coefficients of electrolytes as defined by the composition expansion along different thermodynamic paths and/or composition variables; (iii) the microstructural interpretation of Hill's isobaric-isothermal osmotic second virial coefficient in terms of Kirkwood-Buff correlation function integrals and its relationships to other osmotic coefficients from composition expansions along alternative thermodynamic paths; and (iv) the identification of drawbacks in the implementation of previous methods, originally intended for non-electrolyte systems, to systems involving dissociative solutes. The proposed formalism provides the fundamentally based foundations to the determination of the osmotic second virial coefficients of any type of electrolyte solute, whose thermodynamic expressions converge naturally to the non-electrolyte ones by setting to unity the solute stoichiometric coefficient ν. Following the formal results, we illustrate the formalism with the calculation of a variety of osmotic second virial coefficients involving a wide selection of aqueous solutions at ambient conditions and comprising a wide range of anion-cation type combinations characterized by 2 ≤ ν ≤ 6. Finally, we interpret the behavior of the resulting osmotic virial coefficients in terms of the solute-solvent intermolecular interaction asymmetry, discuss the experimental data requirements for the accurate evaluation of the osmotic second virial coefficients, and provide some observations as well as their modeling implications.

Evaluation of Osmotic Virial Coefficients via Restricted Gibbs Ensemble Simulations, with Support from Gas-Phase Mixture Coefficients

We present a method for computing osmotic virial coefficients in explicit solvent via simulation in a restricted Gibbs ensemble. Two equivalent phases are simulated at once, each in a separate box at constant volume and temperature and each in equilibrium with a solvent reservoir. For osmotic coefficient BN, a total of N solutes are individually exchanged back and forth between the boxes, and the average distribution of solute numbers between the boxes provides the key information needed to compute BN. Separately, expressions are developed for BN as a series in solvent reservoir density ρ₁, with the coefficients of the series expressed in terms of the usual gas-phase mixture coefficients B_ij. Normally, the B_ij are defined for an infinite volume, but we suggest that the observed dependence of B_ij on system size L can be used to estimate L dependence of the BN, allowing them to be computed accurately at L → ∞ while simulating much smaller system sizes than otherwise possible. The methods for N = 2 and 3 are demonstrated for two-component mixtures of size-asymmetric additive hard spheres. The proposed methods are demonstrated to have greater precision than established techniques, for a given amount of computational effort. The ρ₁ series for BN when applied by itself is (for this noncondensing model) found to be the most efficient in computing accurate osmotic coefficients for the solvent densities considered here.

Osmolyte-Induced Effects on the Hydration Behavior and the Osmotic Second Virial Coefficients of Alkyl-Substituted Urea Derivatives: Critical Assessment of Their Structure-Making/Breaking Behavior

We analyzed the hydration behavior of alkyl-substituted urea osmolytes in terms of their deviation from Lewis-Randall solution ideality and characterized their structure-making/breaking tendency according to a proposed solvation formalism that provides a rigorous cause-effect connection between the system microstructure and its solution thermodynamic nonidealities. After a brief introduction of the rationale behind the use of Lewis-Randall over alternative solution ideality references, we (i) assessed the effect of the nature and type of alkyl substitution on the osmolyte-induced perturbation of the solution microstructure as a function of composition, (ii) analyzed their microstructural responses to changes in temperature and pressure, and (iii) demonstrated the structure-breaking nature of urea and the magnifying behavior of its alkyl-substituted osmolytes, whose trend follows the increasingly positive deviation of the osmolyte solutions from Lewis-Randall ideality. Then, we discussed the falsifiability of a pair of frequently used conjectured structure-making/breaking criteria, supported by the derived exact relationships between the structure-making/breaking parameter, the solution thermodynamic nonideality, and the osmotic second virial coefficient of the aqueous osmolytes. Finally, we provided an outlook on how the proposed approach could guide the quest for a truly (microstructural to free energy) causative explanation for the denaturation mechanism of proteins.

On the Solvation Thermodynamics Involving Species with Large Intermolecular Asymmetries: A Rigorous Molecular-Based Approach to Simple Systems with Unconventionally Complex Behaviors

This work deals with the solvation thermodynamics of systems containing extreme intermolecular interaction asymmetries, such as binary mixtures comprising ideal gas species plus other real species, and analyzes the composition dependence of relevant solvation properties from a rigorous molecular-based theoretical viewpoint. It focuses on the effect of large intermolecular interaction asymmetries, involving simple model species for which we have available rigorous results, to advance our understanding of the true molecular-based origin of their unconventional solvation behavior. This effort involves a statistical mechanics approach to identify the thermodynamic constraints and microstructural manifestation underlying the nonmonotonous composition behavior of the species' partial molar properties, as well as to describe formally the explicit link between the intermolecular asymmetries and the observed anomalous behavior. The outcome of the analysis provides sound support to the depiction of the solvation of a weakly interacting solute in a real solvent, a scenario that facilitates the molecular thermodynamic interpretation of gas solvation characterized by low solubility and thermodynamic stability gaps. Moreover, this work illustrates direct comparisons between real aqueous systems and the ideal gas-aqueous system counterparts to highlight and discuss the usefulness of invoking the ideal gas species as a reference solute to gain understanding of the solvation of real gas species.