Modeling of Phase Coexistence via Thermodynamic Potentials

Thermodynamic potentials can be used to study various phase phenomena. In particular, they can be used to determine the phase coexistence of a liquid and vapor for a simple van der Waals fluid, which relates the interactions and size of particles (molecules/atoms) represented by spheres as simple constants a and b, respectively. Phase coexistence at a given temperature for a simple fluid is determined using Newton’s method, thermodynamic potentials, and the conditions of phase coexistence. From this information, we are able to construct a phase diagram of the vapor and liquid densities versus the temperature. The constructed phase diagram shows how the simple van der Waals fluid predicts the occurrence of a critical point (point at which the fluid is no longer simply characterized as a gas or liquid but rather a liquid and gaseous fluid or critical fluid) as opposed to the ideal gas law. This phase diagram can then be further used to study homogeneous (a pure solution or solution containing a single molecule/atoms) and inhomogeneous (mixture or solution containing multiple molecules/atoms or a substrate/wall) nucleation by classical density functional theory in statistical mechanics.