Defects in nematic membranes can buckle into pseudospheres

Area of Science:

• Soft matter physics
• Materials science
• Biophysics

Background:

• Membrane shape is influenced by various factors including boundary conditions, surface tension, curvature, and particle ordering.
• Orientational order of embedded particles, such as rodlike particles forming a nematic phase, can significantly impact a membrane's equilibrium shape.
• Nematic membranes are relevant in diverse systems, including biological cells, liquid crystal films, and manufactured materials.

Purpose of the Study:

• To investigate the influence of orientational order on membrane shape.
• To elucidate the elastic terms governing nematic membranes using differential geometry.
• To understand the buckling behavior of nematic membranes due to topological defects.

Main Methods:

• Formulation of the free energy for nematic films using tensor contractions from differential geometry.
• Analysis of elastic terms allowed by symmetry.
• Investigation of the competition between surface tension and in-plane elasticity in defect-induced buckling.

Main Results:

• Topological defects in the orientation field can induce membrane buckling.
• In the absence of bending rigidity, buckling results in a universal shape (parabolic pseudosphere/revolved tractrix).
• Bending rigidity opposes buckling and leads to predictable shape modifications, with anisotropic rigidities causing distinct shapes for aster and vortex defects.

Conclusions:

• The orientational order of particles is a crucial factor in determining membrane shape.
• Buckling induced by topological defects in nematic membranes is a key phenomenon.
• The study provides a framework for measuring specific couplings in nematic membranes by analyzing defect-induced shapes.