Effects of orientational order on modulated cylindrical interfaces

TL;DR

This paper investigates how orientational order influences shape modulations in cylindrical interfaces, revealing defect patterns and phase transitions driven by curvature and order interactions.

Contribution

It provides an analytical and simulation-based analysis of defect-free and defect-rich modulated cylindrical interfaces with orientational order, highlighting shape transition behaviors.

Findings

Modulated cylinders exhibit banded isotropic and ordered regions.

Type I systems are defect-free, Type II have up to 4n excess defects.

Shape transitions can be continuous or discontinuous depending on defect states.

Abstract

Cylindrical interfaces occur in sheared or deformed emulsions and as biological or technological lipid monolayer or bilayer tubules. Like the corresponding spherical droplets and vesicles, these cylinder-like surfaces may host orientaional order with $n$-fold rotational symmetry, for example in the positions of lipid molecules or of spherical nanoparticles. We examine how that order interacts with and induces shape modulations of cylindrical interfaces. While on spherical droplets $2n$ topological defects necessarily exist and can induce icosahedral droplet shapes, the cylindrical topology is compatible with a defect-free patterning. Nevertheless, once a modulation is introduced by a mechanism such as spontaneous curvature, nontrivial patterns of order, including ones with excess defects, emerge and have nonlinear effects on the shape of the tube. Examining the equilibrium energetics of the system analytically and with a lattice-based Markov chain Monte Carlo simulation, we predict low-temperature morphologies of modulated cylindrical interfaces hosting orientational order. A shape modulation induces a banded pattern of alternatingly isotropic and ordered interfacial material. Furthermore cylindrical systems can be divided into Type I, without defects, and Type II, which go through a spectrum of defect states with up to $4n$ excess defects. The character of the curvature-induced shape transition from unmodulated to modulated cylinders is continuous or discontinuous accordingly.