The nature of the ordered phase of the confined self-assembled rigid rod model

Abstract

We investigate the nature of the ordered phase and the orientational correlations between adjacent layers of the confined three-dimensional self-assembled rigid rod model, on the cubic lattice. We find that the ordered phase at finite temperatures becomes uniaxial in the thermodynamic limit, by contrast to the ground state (partial) order where the orientation of the uncorrelated layers is perpendicular to one of the three lattice directions. The increase of the orientational correlation between layers as the number of layers increases suggests that the unconfined model may also exhibit uniaxial ordering at finite temperatures.

Three-dimensional patchy lattice model for empty fluids

“…It follows that the equilibrium state corresponds to the empty lattice when µ < −ǫ, and to the full lattice with M AA bonds when µ > −ǫ. The fully occupied ground state is highly degenerate 32 as a large number of configurations are compatible with U GS = −M ǫ. In general, the order of a fully occupied configuration may be described through the order of a set of planes [i, j, k]: Particles in one plane have the same in-plane orientation but different planes may exhibit different (in-plane) orientations.…”

“…A similar mapping exists when some of the sites are blocked, the main difference being that the effect of the blocked sites enters as a local external field. 32 Considering plaquettes of four sites, 24,38 and defining on each plaquette h A as the sum of the potential energy contributions involving at least one active particle, it can be shown that h A is written in terms of a Potts-like interaction as…”