Exact Local Composition Model for Two-Dimensional Lattice Fluids
Journal
Industrial and Engineering Chemistry Research
Journal Volume
58
Journal Issue
45
Pages
20779-20787
Date Issued
2019
Author(s)
Abstract
The knowledge on the deviation of local composition from bulk composition has been proven to be powerful for modeling the excess thermodynamic properties of liquid mixtures. However, the exact solution to the local compositions is available for a few cases, such as the one-dimensional (1D) lattice fluids and for certain two-dimensional (2D) lattice fluids (the Ising models). We discover that the long-range correlation in the fluid structure, which is not present in 1D but is important in 2D, is the main reason for the complication of getting the exact local compositions for general 2D lattice fluids. In this work, a general approach for calculating the local compositions in 2D lattice fluids is developed. We show that for any stripe-like 2D lattices, the long-range correlations can be avoided by transforming the system to a multicomponent 1D system. The local compositions of such a system can be determined by minimization of the free energy of the mixture. We found that the local compositions, energy, and entropy predicted from this model, referred to as the Liu-Lin model, are in excellent agreement with those obtained from Monte Carlo simulations and Wang-Landau sampling. By increasing the width of the stripe, the thermodynamic properties predicted from the Liu-Lin model approaches the exact Onsager solution for 2D systems to arbitrary precision. This model can be applied also to conditions where the Onsager model is no longer applicable, such as systems under external magnetic field or with fixed species compositions.
SDGs
Type
journal article