Isotropic-nematic transition for hard rods on a three-dimensional cubic lattice

Abstract

Using grand-canonical Monte Carlo (GCMC) simulations, we investigate the isotropic-nematic phase transition for hard rods of size L×1×1 on a three-dimensional cubic lattice. We observe such a transition for L≥6. For L=6, the nematic state has a negative order parameter, reflecting the co-occurrence of two dominating orientations. For L≥7, the nematic state has a positive order parameter, corresponding to the dominance of one orientation. We investigate rod lengths up to L=25 and find evidence for a very weakly first-order isotropic-nematic transition, while we cannot completely rule out a second-order transition. It was not possible to detect a density jump at the transition, despite using large systems containing several 10^{5} particles. The probability density distributions P(Q) from the GCMC simulations near the transition are very broad, pointing to strong fluctuations. Our results complement earlier results on the demixing (pseudonematic) transition for an equivalent system in two dimensions, which is presumably of Ising type and occurs for L≥7. We compare our results to lattice fundamental measure theory (FMT) and find that FMT strongly overestimates nematic order and consequently predicts a strong first-order transition. The rod packing fraction of the nematic coexisting states, however, agree reasonably well between FMT and GCMC.

Nematic and gas-liquid transitions for sticky rods on square and cubic lattices

“…Phase diagram for L = 5 in 3D for a system size M 3 = 64 3 . The hard rod transition corresponds to T * = ∞ and is located at a packing fraction η nem c ≈ 0.88 (in agreement with Refs [21]. and[22]).…”

“…This version of a nematic phase is the stable one for a = 5 and 6. Furthermore, the nematic transition is of very weak first order for the aspect ratios studied (up to 25) [21]. A coexistence density gap is not detectable and the first order character is only visible through a finite-size-scaling analysis for large lattices.…”

“…This discussion on possible types of ordering transitions points to a general difference between rod models on the lattice and in the continuum. Previous studies of hard rods with unit square cross section on a cubic lattice in 3D [21,22] have detected a nematic transition for a ≥ 5. In stark contrast to continuum models, the nematic phase can be manifested in a peculiar manner, where there is a 'negatively-preferred' direction instead.…”

“…The isotropic-nematic transition is presumably of very weak first order [21]. A finite coexistence gap (difference between packing fractions of the coexisting isotropic and nematic state) was not resolvable.…”

“…Previous work has considered purely hard-core rods (T * = ∞) [21,22]. For such hard rods with lengths L ≤ 4, the isotropic phase is stable up to packing fractions close to 1.…”