Comment on “Determination of the quaternary phase diagram of the water–ethylene glycol–sucrose–NaCl system and a comparison between two theoretical methods for synthetic phase diagrams” Cryobiology 61 (2010) 52–57

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).

Multicomponent solutions: Combining rules for multisolute osmotic virial coefficients

This paper presents an exploration of a specific type of a generalized multicomponent solution model, which appears to be first given by Saulov in the current explicit form. The assumptions of the underlying theory and a brief derivation of the main equation have been provided preliminarily for completeness and notational consistency. The resulting formulae for the Gibbs free energy of mixing and the chemical potentials are multivariate polynomials with physically meaningful coefficients and the mole fractions of the components as variables. With one additional assumption about the relative magnitudes of the solvent-solute and solute-solute interaction exchange energies, combining rules were obtained that express the mixed coefficients of the polynomial in terms of its pure coefficients. This was done by exploiting the mathematical structure of the asymmetric form of the solvent chemical potential equation. The combining rules allow one to calculate the thermodynamic properties of the solvent with multiple solutes from binary mixture data only (i.e., each solute with the solvent), and hence, are of practical importance. Furthermore, a connection was established between the osmotic virial coefficients derived in this work and the original osmotic virial coefficients of Hill found by employing a different procedure, illustrating the equivalency of what appears to be two different theories. A validation of the combining rules derived here has been provided in a separate paper where they were successfully used to predict the freezing points of ternary salt solutions of water.

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.