Monolayers of hard rods on planar substrates: I. Equilibrium

TL;DR

This paper investigates the equilibrium behavior of hard rod monolayers using lattice and off-lattice models, revealing a continuous 'standing up' transition in rod orientation that persists under external potentials, validated by density functional theory and simulations.

Contribution

It introduces a comprehensive analysis of hard rod monolayers with both lattice and continuum models, demonstrating a persistent continuous orientational transition and validating DFT with simulations.

Findings

Continuous 'standing up' transition observed with increasing density.

Good agreement between DFT results and Monte Carlo simulations.

Phase diagrams of bulk hard rods characterized in 2D and 3D.

Abstract

The equilibrium properties of hard rod monolayers are investigated in a lattice model (where position and orientation of a rod are restricted to discrete values) as well as in an off--lattice model featuring spherocylinders with continuous positional and orientational degrees of freedom. Both models are treated using density functional theory and Monte Carlo simulations. Upon increasing the density of rods in the monolayer, there is a continuous ordering of the rods along the monolayer normal ("standing up" transition). The continuous transition also persists in the case of an external potential which favors flat--lying rods in the monolayer. This behavior is found in both the lattice and the continuum model. For the lattice model, we find very good agreement between the results from the specific DFT used (lattice fundamental measure theory) and simulations. The properties of lattice fundamental measure theory are further illustrated by the phase diagrams of bulk hard rods in two and three dimensions.