Thermodynamics of interacting hard rods on a lattice

TL;DR

This paper derives an exact analytical framework for the thermodynamics of lattice hard rods with various interactions, enabling numerical analysis of complex systems like ionic liquids and charged multilayers.

Contribution

It provides a novel exact derivation of the isobaric partition function for interacting lattice hard rods, applicable to diverse interaction types and relevant physical phenomena.

Findings

Exact partition function derived for various interactions

Numerical thermodynamic analysis performed using Broyden algorithm

Applicable to systems like ionic liquids and charged multilayers

Abstract

We present an exact derivation of the isobaric partition function of lattice hard rods with arbitrary nearest neighbor interactions. Free energy and all thermodynamics functions are derived accordingly and they written in a form that is a suitable for numerical implementation. As an application, we have considered lattice rods with pure hard core interactions, rods with long range gravitational attraction and finally a charged hard rods with charged boundaries (Bose gas), a model that is relevant for studying several phenomena such as charge regulation, ionic liquids near charged interfaces, and an array of charged smectic layers or lipid multilayers. In all cases, thermodynamic analysis have been done numerically using the Broyden algorithm.