# Perturbative density functional methods for cholesteric liquid crystals

## TL;DR

This paper develops a numerical framework to predict the macroscopic properties of cholesteric liquid crystals from microscopic models, demonstrating high accuracy and efficiency in calculating equilibrium structures using perturbative methods.

## Contribution

It introduces a perturbative approach based on Poniewierski-Stecki equations for cholesteric phases, improving computational efficiency and accuracy over previous methods.

## Key findings

- Predictions align well with full-functional descriptions.
- Perturbative treatment valid for pitch lengths of a few dozen particle diameters.
- Full angle-dependent virial coefficients enhance numerical efficiency.

## Abstract

We introduce a comprehensive numerical framework to generically infer the emergent macroscopic properties of uniaxial nematic and cholesteric phases from that of their microscopic constituent mesogens. This approach, based on the full numerical resolution of the Poniewierski-Stecki equations in the weak chirality limit, may expediently handle a wide range of particle models through the use of Monte-Carlo sampling for all virial-type integrals. Its predictions in terms of equilibrium cholesteric structures are found to be in excellent agreement with previous full-functional descriptions, thereby demonstrating the quantitative validity of the perturbative treatment of chirality for pitch lengths as short as a few dozen particle diameters. Furthermore, the use of the full angle-dependent virial coefficients in the Onsager-Parsons-Lee formalism increases its numerical efficiency by several orders of magnitude over that of these previous methods. The comparison of our results with numerical simulations however reveals some shortcomings of the Parsons-Lee approximation for systems of strongly non-convex particles, notwithstanding the accurate inclusion of their full effective molecular volume. Further potential limitations of our theory in terms of phase symmetry assumptions are also examined, and prospective directions for future improvements discussed.