Quantum Theory of Chiral Interactions in Cholesteric Liquid Crystals

TL;DR

This paper develops a quantum mechanical model to analyze chiral interactions in cholesteric liquid crystals, focusing on dispersion interactions and molecular excitation states, providing new insights into the microscopic origins of chirality.

Contribution

It introduces a novel expansion method considering transverse coordinates and identifies new interaction terms involving local dipoles, advancing understanding of quantum chiral interactions.

Findings

Results align with previous models when both molecules are excited.

Identifies new interaction terms involving local dipole moments.

Does not determine whether quantum or steric interactions dominate in cholesterics.

Abstract

We study the effective chiral interaction between molecules arising from quantum dispersion interactions within a model in which a) the dominant excited states of a molecule form a band whose width is small compared to the average excitation energy and b) biaxial orientational correlation between adjacent molecules can be neglected. Previous treatments of quantum chiral interactions were based on a multipole expansion of the intermolecular interaction. However, because real liquid crystals are composed of elongated molecules, we utilize an expansion in terms of only coordinates transverse to the long molecular axes. We identify two distinct physical limits depending on whether one or both of the interacting molecules are excited in the virtual state. When both molecules are excited, our results are similar to those found previously by van der Meer et al. Previously unidentified terms in which only one molecule is excited involve the interactions of local dipole moments, which exist even when the global dipole moment of the molecule vanishes. We present analytic and numerical results for helical molecules. Our results do not indicate whether the dominant chiral interaction in cholesterics results from quantum or from steric interactions.