Gibbsian Surface Thermodynamics

Abstract

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.