Smectic and columnar ordering in length-polydisperse fluids of parallel hard cylinders

TL;DR

This study uses a density functional approach to analyze how length-polydispersity influences the stability of smectic versus columnar phases in parallel hard cylinder fluids, revealing a terminal polydispersity point where phase stability switches.

Contribution

It introduces a fundamental-measure density functional for polydisperse cylinders and compares its predictions with virial approximations, improving phase diagram mapping accuracy.

Findings

All approximations agree on a terminal polydispersity where smectic stability decreases.

The fundamental-measure functional outperforms virial approximations in quantitative predictions.

Metastable nematic-nematic demixing is predicted by the fundamental-measure functional.

Abstract

We apply a recently proposed density functional for mixtures of parallel hard cylinders, based on Rosenfeld's fundamental measure theory, to study the effect of length-polydispersity on the relative stability between the smectic and columnar liquid crystal phases.To this purpose we derive from this functional an expression for the direct correlation function and use it to perform a bifurcation analysis. We compare the results with those obtained with a second and a third virial approximation of this function. All three approximations lead to the same conclusion: there is a terminal polydispersity beyond which the smectic phase is less stable than the columnar phase. This result is in agreement with previous Monte Carlo simulations conducted on a freely rotating length-polydisperse hard spherocylinder fluid, although the theories always overestimate the terminal polydispersity because the nematic-columnar phase transition is first order and exhibits a wide coexistence gap. Both, the fundamental-measure functional and the third virial approximation, predict a metastable nematic-nematic demixing. Conversely, according to second virial approximation this demixing might be stable at high values of the polydispersity, something that is observed neither in simulations nor in experiments. The results of the fundamental-measure functional are quantitatively superior to those obtained from the other two approximations. Thus this functional provides a promising route to map out the full phase diagram of this system.