Phase equilibria and solvation forces for fluids confined between parallel walls

TLDR: In this article, the phase equilibria of an open system characterized by the variables μ (chemical potential), T (temperature), and H (wall separation) are derived for the shape of lines of coexistence.

Abstract: The thermodynamics of fluids confined between two adsorbing solid substrates (walls) is revisited. Attention is focused on the phase equilibria of an open system characterized by the variables μ (chemical potential), T (temperature), and H (wall separation). Clapeyron equations for the shape of lines of coexistence are derived and used to interpret the results of earlier calculations of two first‐order transitions, namely capillary condensation of an undersaturated ‘‘gas’’ to ‘‘liquid’’ and prewetting (thick–thin film transition) at finite H. At such transitions the adsorption Γ and the solvation force f jump discontinuously. Criticality of a confined fluid is associated with the divergence of the derivatives (∂Γ/∂μ)T,H and (∂2Γ/∂μ2)T,H or equivalently, with the divergence of (∂f/∂H)T,μ and (∂2f/∂H2)T,μ. The presence of the additional field variable H, and its conjugate density f, implies that the phase equilibria of a confined fluid can be much richer than those of a bulk fluid or of a single interface (H=∞). By extending the formalism to multicomponent systems Clapeyron equations are derived for the coexistence of phases in confined fluid mixtures. An equation for the shift in chemical potential (or concentration) of the phase separation curve of a binary liquid mixture resulting from confinement at constant pressure and temperature is presented. This equation, which becomes exact for large separations H, is the appropriate analog for mixtures of the Kelvin equation used to describe capillary condensation in pure fluids; it can also be regarded as a generalization to nonzero concentrations of the Ostwald–Freundlich formula for the dependence of solubility on particle size. Our analysis provides a framework for interpreting recent solvation force measurements on phase‐separating liquid mixtures.