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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.
Growth of hard--rod monolayers via deposition is studied in a lattice model using rods with discrete orientations and in a continuum model with hard spherocylinders. The lattice model is treated with kinetic Monte Carlo simulations and dynamic densit
Based on the collision rules for hard needles we derive a hydrodynamic equation that determines the coupled translational and rotational dynamics of a tagged thin rod in an ensemble of identical rods. Specifically, based on a Pseudo-Liouville operato
Based on simplifications of previous numerical calculations [Graf and L{o}wen, Phys. Rev. E textbf{59}, 1932 (1999)], we propose algebraic free energy expressions for the smectic-A liquid crystal phase and the crystal phases of hard spherocylinders.
Phase transitions are uncommon among homogenous one-dimensional fluids of classical particles owing to a general non-existence result due to van Hove. A way to circumvent van Hoves theorem is to consider an interparticle potential that is finite ever
We study a mass transport model, where spherical particles diffusing on a ring can stochastically exchange volume $v$, with the constraint of a fixed total volume $V=sum_{i=1}^N v_i$, $N$ being the total number of particles. The particles, referred t