Mixing rules for binary Lennard–Jones chains: theory and Monte Carlo simulation

Abstract

Theoretically-based van der Waals one-fluid (vdW1) mixing rules are derived for Lennard–Jones (LJ) chain mixtures. The rules provide equivalent one-fluid segment parameters for LJ size ( σ) and energy ( ε) parameter as well as chain length ( m) based on the parameters of the individual mixture components and the component mole fractions. The mixing rules are tested by performing Monte Carlo simulations of eight different binary mixtures and the equivalent vdW1 pure fluid, each at three densities. The simulations test the effects of changing LJ size parameter, LJ energy parameter and chain length individually and together. The effects of mole fraction and density are also examined. The mixing rules are tested for accuracy in predicting compressibility factors and radial distribution functions. It is found that the vdW1 rules provide excellent agreement when size and energy parameter are varied. Good agreement is found for mixtures with different chain lengths. The discrepancy is worst at very high densities when all component parameters are varied simultaneously.