Confined polymer nematics: order and packing in a nematic drop

TL;DR

This paper models the packing and orientation of confined nematic polymers inside a sphere, revealing various configurations and defect structures based on chain endpoints and sphere size.

Contribution

It introduces a continuum free energy model incorporating polymer connectivity and density dependence to study nematic polymer packing in confined geometries.

Findings

Multiple chain configurations with different defect geometries identified.

The model predicts an orientational transition between isotropic and nematic phases.

Chain endpoints and sphere size critically influence the packing structure.

Abstract

We investigate the tight packing of nematic polymers inside a confining hard sphere. We model the polymer {\sl via} the continuum Frank elastic free energy augmented by a simple density dependent part as well as by taking proper care of the connectivity of the polymer chains when compared with simple nematics. The free energy {\sl ansatz} is capable of describing an orientational ordering transition within the sample between an isotropic polymer solution and a polymer nematic phase. We solve the Euler-Lagrange equations numerically with the appropriate boundary conditions for the director and density field and investigate the orientation and density profile within a sphere. Two important parameters of the solution are the exact locations of the beginning and the end of the polymer chain. Pending on their spatial distribution and the actual size of the hard sphere enclosure we can get a plethora of various configurations of the chain exhibiting different defect geometry.