Diffusion dynamics and steady states of systems of hard rods on the square lattice

TL;DR

This paper investigates the diffusion dynamics of hard rods on a square lattice, clarifying the conditions for nematic phase formation and demonstrating how nonequilibrium kinetics influence phase segregation and interface orientation.

Contribution

It shows that previous findings of phase segregation for rods of length six are due to nonequilibrium effects, and establishes equilibrium conditions for phase behavior.

Findings

Nematic phase exists only for rods of length ≥7 in equilibrium.

Nonequilibrium kinetics can induce phase segregation for rods of length 6.

Interface orientation depends on the type of nonequilibrium kinetics.

Abstract

It is known from grand canonical simulations of a system of hard rods on two dimensional lattices that an orientationally ordered nematic phase exists only when the length of the rods is at least seven. However, a recent microcanonical simulation with diffusion kinetics, conserving both total density and zero nematic order, reported the existence of a nematically phase segregated steady state with interfaces in the diagonal direction for rods of length six [Phys. Rev. E 95, 052130 (2017)], violating the equivalence of different ensembles for systems in equilibrium. We resolve this inconsistency by demonstrating that the kinetics violate detailed balance condition and drives the system to a nonequilibrium steady state. By implementing diffusion kinetics that drives the system to equilibrium, even within this constrained ensemble, we recover earlier results showing phase segregation only for rods of length greater than or equal to seven. Furthermore, in contrast to the nonequilibrium steady state, the interface has no preferred orientational direction. In addition, by implementing different nonequilibrium kinetics, we show that the interface between the phase segregated states can lie in different directions depending on the choice of kinetics.