Twisted loxodromes in spindle-shaped polymer nematics

TL;DR

This paper presents an energetic model for the twisting behavior of spindle-shaped polymer nematics, showing that loxodrome spirals describe the twist pattern and exploring conditions where this configuration is energetically preferred.

Contribution

It introduces a new energetic model that captures the unique twisting behavior of spindle-shaped polymer nematics using loxodrome spirals and extends the geometric approach to bulk systems.

Findings

Loxodrome spirals effectively describe the twist pattern in spindle-shaped nematics.

The model identifies parameter regimes where twisted loxodrome configurations are energetically favorable.

Extension of the geometric model from surface to bulk nematic systems.

Abstract

We develop an energetic model that captures the twisting behavior of spindle-shaped polymer microparticles with nematic ordering, which display remarkably different twisting behavior to ordinary nematics confined to spindles. We have previously developed a geometric model of the twisting, based on experimental observations, in which we showed that the twist pattern follows loxodrome spirals [Ansell et. al., Phys. Rev. Lett., 123, 157801 (2019)]. In this study, we first consider a spindle-shaped surface and show that the loxodrome twisting behavior of our system can be captured by the Frank free energy of the nematic with an additional term constraining the length of the integral curves of the system. We then extend the ideas of this model to the bulk and explore the parameter space for which the twisted loxodrome solution is energetically favorable.