The hybrid ergodic lattice gas model for critical fluids and the molecular nature of the critical point

Abstract

This paper introduces the hybrid ergodic lattice gas model as a conceptually simple, computationally cheap, yet accurate model that predicts macroscopic fluid pressure along the critical isotherm of a fluid accurately. A key concept is the hybrid evaluation of the properties: the kinetic and repulsive pressure components are calculated from equations of state, representing the ‘global’ nature of these values, whereas the attractive pressure component is calculated from the ‘local’ particle arrangement, in which particle clusters are identified using unsupervised machine learning. The proposed method captures the fluid pressure of the ideal gas regime and near the critical point, and is much more accurate then the Peng Robinson equation of state for liquid states. The predicted molecular structure is then used to identify three distinct stages of molecular behavior along the isotherm: I. cluster formation, II. cluster consolidation, and III. supercluster growth. Specifically, the critical point is shown to correspond to the state in II. where clusters merge together to form a single supercluster, corresponding to the percolation threshold of a cubic site lattice. The foundation of the model in a lattice gas opens the door for the analytical analysis of near-critical fluids using percolation theory and probabilistic analysis. As an example, a lattice-based derivation of a van der Waals attractive term is given. Finally, the lattice fluid is shown to be related to random networks, but deviates from the classical Erdős and Rényi’s G(N, L) model in that the critical point is found at a degree of 〈k〉 = 2 rather than the classical result of 〈k〉 = 1.