Comparison of the Osmotic Virial Equation with the Margules Activity Model for Solid–Liquid Equilibrium

Predicting freezing points of ternary salt solutions with the multisolute osmotic virial equation

Previously, the multisolute osmotic virial equation with the combining rules of Elliott et al. has been shown to make accurate predictions for multisolute solutions with only single-solute osmotic virial coefficients as inputs. The original combining rules take the form of an arithmetic average for the second-order mixed coefficients and a geometric average for the third-order mixed coefficients. Recently, we derived generalized combining rules from a first principles solution theory, where all mixed coefficients could be expressed as arithmetic averages of suitable binary coefficients. In this work, we empirically extended the new model to account for electrolyte effects, including solute dissociation, and demonstrated its usefulness for calculating the properties of multielectrolyte solutions. First, the osmotic virial coefficients of 31 common salts in water were tabulated based on the available freezing point depression (FPD) data. This was achieved by polynomial fitting, where the degree of the polynomial was determined using a special criterion that accounts for the confidence intervals of the coefficients. Then, the multisolute model was used to predict the FPD of 11 ternary electrolyte solutions. Furthermore, models with the new combining rules and the original combining rules of Elliott et al. were compared using both mole fraction and molality as concentration units. We find that the mole-fraction-based model with the new combining rules performs the best and that the results agree well with independent experimental measurements with an all-system root-mean-square error of 0.24 osmoles/kg (0.45 °C) and close to zero mean bias for the entire dataset (371 data points).

Large Decrease in the Melting Point of Benzoquinones via High-n Eutectic Mixing Predicted by a Regular Solution Model

Decreasing the melting point (T_m) of a mixture is of interest in cryopreservatives, molten salts, and battery electrolytes. One general strategy to decrease T_m, exemplified by deep eutectic solvents, is to mix components with favorable (negative) enthalpic interactions. We demonstrate a complementary strategy to decrease T_m by mixing many components with neutral or slightly positive enthalpic interactions, using the number of components (n) to increase the entropy of mixing and decrease T_m. In theory, under certain conditions this approach could achieve an arbitrarily low T_m. Furthermore, if the components are small redox-active molecules, such as the benzoquinones studied here, this approach could lead to high energy density flow battery electrolytes. Finding the eutectic composition of a high-n mixture can be challenging due to the large compositional space yet is essential for ensuring the existence of a purely liquid phase. We reformulate and apply fundamental thermodynamic equations to describe high-n eutectic mixtures of small redox-active molecules (benzoquinones and hydroquinones). We illustrate a novel application of this theory by tuning the entropy of melting, rather than the enthalpy, in systems highly relevant to energy storage. We demonstrate with differential scanning calorimetry measurements that 1,4-benzoquinone derivatives exhibit eutectic mixing that decreases their T_m, despite slightly positive enthalpies of mixing (0-5 kJ/mol). By rigorously investigating all 21 binary mixtures of a set of seven 1,4-benzoquinone derivatives with alkyl substituents (T_m's between 44 and 120 °C), we find that the eutectic melting point of a mixture of all seven achieves a large decrease in T_m to -6 °C. We further determine that the regular solution model shows improvement over an ideal solution model in predicting the eutectic properties for this newly investigated type of mixture composed of many small redox-active organic molecules.

Gibbsian Surface Thermodynamics

Gibbsian composite-system thermodynamics is the framework governing the equilibrium of composite systems, including systems that at equilibrium have more than one value of pressure because of the action of surface tension, semipermeable membranes, or fields, and thus cannot be treated as simple systems. J. W. Gibbs's paper that lays out composite-system thermodynamics, "On the Equilibrium of Heterogeneous Substances", communicated in two parts in 1876 and 1878, is widely regarded as one of the most important pieces of scientific literature of its century. Many scientists adopted and stressed the importance of Gibbsian thermodynamics. In 1960, H. B. Callen wrote a textbook that made Gibbsian composite-system thermodynamics more accessible to thermodynamicists. However, Callen's book left out Gibbs's work on curved fluid interfaces and did not treat the complicated nonideal systems of interest to today's thermodynamicists. In this Feature Article, I have attempted to convey in a comprehensive manner the framework of Gibbsian composite-system thermodynamics including in detail the treatment of systems with interface effects and with nonideal, multicomponent phases. This work lays out the relationships between important equilibrium equations including the following: the Gibbs-Duhem equation, the Gibbs adsorption equation, the Young-Laplace equation, the Young equation, the Cassie-Baxter equation, the Wenzel equation, the Kelvin equation, the Gibbs-Thompson equation, and the Ostwald-Freundlich equation, including nonideal and multicomponent forms. Equations of state that are often useful for Gibbsian composite-system thermodynamics are reviewed including adsorption isotherms and our own work on two semiempirical equations of state: the Elliott et al. form of the osmotic virial equation and the Shardt-Elliott-Connors-Wright equation for the temperature and composition dependence of surface tension. I summarize the work of our group developing Gibbisan composite-system thermodynamics including new equations for such things as the curvature-induced depression of the eutectic temperature or the removal of azeotropes by nanoscale fluid interface curvature. Gibbsian composite-system thermodynamics has broad applications in biotechnology, nanostructured materials, surface textures and coatings, microfluidics, nanoscience, atmospheric and environmental physics, among others.