Two New Thermodynamic Constraints for a Solid/Supercritical Fluid System

Abstract

One of the phenomenological observations in any supercritical system is the common pressure where all the solubility isotherms intersect. Thus, this crossover pressure addresses a thermodynamic constraint or a key set of conditions for supercritical mixtures. In this paper, a phase stability analysis has been performed for the formulation and estimation of the crossover pressure. This absolute theoretical approach includes two subsequent steps. At the first step, it has been formulated in terms of an abstract quantity, i.e., Gibbs free energy. However, the system should be treated more quantitatively in order to estimate the crossover pressure. Therefore, at the second step, which is based on the solute behavior at the infinite dilution limit, the equations formerly used have been further manipulated, which ultimately leads to two equations that are given in terms of estimable properties. They are actually two thermodynamic constraints for solid/SCF mixtures. One of them has been used to predict the crossover pressure of certain mixtures. The other one has not been used for this task due to a theoretical restriction. However, the successfully prediction of the crossover pressure by using either of the equations confirms the other one since they are subsequent and related equations. Crossover PressureAccording to Foster et al. [1], the crossover pressure is a phenomenological observation. In other words, researchers who measure the solubility of solids in supercritical fluids (SCFs), observe that there is a common pressure where all the solubility isotherms intersect [1-10]. As a result, this point can be assumed to be a thermodynamic constraint over the supercritical mixtures. This common pressure is mathematically represented by Eq. (1) 1) :The schematic intersection of the solubility isotherms is shown in Fig. 1. According to Fig. 1, at pressures below the crossover pressure, an increase in temperature induces a decrease in solubility of the solid in the SCF phase while the opposite effect occurs above the upper crossover pressure. This behavior can be explained by the reasoning that at pressures below the crossover pressure, the density of the SCF phase is more sensitive to temperature changes than that at higher pressures. A temperature increase in this region affects the sol- -1) List of symbols at the end of the paper.