What Promotes Smectic Order: Applying Mean Field Theory to the Ends

TL;DR

This paper uses a mean field theoretical model to investigate how particle tip shape and tail length influence the formation of smectic order in liquid crystals, revealing that rounded tips and longer tails promote smectic phase stability.

Contribution

It introduces a simple two-dimensional model to analyze the role of particle tip shape and tail length in smectic phase formation, providing new insights into the microscopic factors involved.

Findings

Rounded tips and longer tails lower the density threshold for smectic formation.

Particle tip shape critically affects the stability of smectic order.

Longer polymer tails destabilize the nematic phase, favoring smectic ordering.

Abstract

Not every particle that forms a nematic liquid crystal makes a smectic. The particle tip is critical for this behaviour. Ellipsoids do not make a smectic, but sphero-cylinders do. Similarly, only those N-CB alkylcyanobiphenyls with sufficiently long ($N\ge 8$ carbons) alkane tails form smectics. We understand the role of the particle tip in the smectic transition by means of a simple two-dimensional model. We model sphero-cylinders by "boubas" with rounded tips, and ellipsoids by "kikis" with pointed tips. The N-CB molecules are modelled by a small body with a polymer tail. We find that rounded tips and longer polymer tails lead to a smectic at lower densities by making the space between layers less accessible, destabilizing the nematic.