Scaled Particle Theory of solutions: Comparison with Lattice Fluid model

Abstract

An easily implemented off-lattice thermodynamic model of a fluid mixture is developed using Scaled Particle Theory (SPT) in a mean-field approximation. Thermodynamic properties are derived from the random insertion of a hard sphere (HS) chain into a HS mixture and invoking random mixing to calculate energetics. Like the Lattice Fluid (LF) model, the SPT model completely characterizes pure fluids with three parameters that can be calculated from pure component properties. Binary mixtures require only one additional interaction parameter, which can be approximated using a geometric mean combining rule or treated as an adjustable parameter. Phase stability criteria and mixture properties are calculated and compared to both experimental data and LF model predictions. SPT and LF models are comparable when applied to some properties of solutions of small molecules, but the LF model proved superior for polymer solutions, especially with respect to calculation of lower critical solution temperatures. This was an unexpected result because an off-lattice model was assumed superior to any lattice description of a fluid.