Thermodynamics and Phase Transitions of Electrolytes on Lattices with Different Discretization Parameters

TL;DR

This paper explores how discretization parameters in lattice models affect the thermodynamics and phase transitions of electrolytes, bridging discrete and continuum descriptions through analytic and numerical methods.

Contribution

It introduces a detailed analysis of the impact of discretization parameters on electrolyte phase behavior, connecting lattice models with continuum theories.

Findings

Discretization parameter influences critical temperature and density.

Gas-liquid phase separation occurs at low densities across lattice types.

Fine discretization suppresses phase transitions due to order-disorder transformations.

Abstract

Lattice models are crucial for studying thermodynamic properties in many physical, biological and chemical systems. We investigate Lattice Restricted Primitive Model (LRPM) of electrolytes with different discretization parameters in order to understand thermodynamics and the nature of phase transitions in the systems with charged particles. A discretization parameter is defined as a number of lattice sites that can be occupied by each particle, and it allows to study the transition from the discrete picture to the continuum-space description. Explicit analytic and numerical calculations are performed using lattice Debye-H\"{u}ckel approach, which takes into account the formation of dipoles, the dipole-ion interactions and correct lattice Coulomb potentials. The gas-liquid phase separation is found at low densities of charged particles for different types of lattices. The increase in the discretization parameter lowers the critical temperature and the critical density, in agreement with Monte Carlo computer simulations results. In the limit of infinitely large discretization our results approach the predictions from the continuum model of electrolytes. However, for the very fine discretization, where each particle can only occupy one lattice site, the gas-liquid phase transitions are suppressed by order-disorder phase transformations.