Achiral symmetry breaking and positive Gaussian modulus lead to scalloped colloidal membranes

TL;DR

This paper investigates how achiral symmetry breaking and positive Gaussian curvature influence the formation of scalloped edges in colloidal membranes, revealing new insights into their elastic properties and 3D shaping capabilities.

Contribution

It demonstrates that colloidal membranes with scalloped edges have positive Gaussian modulus and introduces a phenomenological model linking edge energy and Gaussian curvature.

Findings

Achiral symmetry breaking leads to scalloped membrane edges.

Membranes exhibit positive Gaussian curvature modulus.

Experimental measurements align with the excluded volume prediction.

Abstract

In the presence of a non-adsorbing polymer, monodisperse rod-like particles assemble into colloidal membranes, which are one rod-length thick liquid-like monolayers of aligned rods. Unlike 3D edgeless bilayer vesicles, colloidal monolayer membranes form open structures with an exposed edge, thus presenting an opportunity to study physics of thin elastic sheets. Membranes assembled from single-component chiral rods form flat disks with uniform edge twist. In comparison, membranes comprised of mixture of rods with opposite chiralities can have the edge twist of either handedness. In this limit disk-shaped membranes become unstable, instead forming structures with scalloped edges, where two adjacent lobes with opposite handedness are separated by a cusp-shaped point defect. Such membranes adopt a 3D configuration, with cusp defects alternatively located above and below the membrane plane. In the achiral regime the cusp defects have repulsive interactions, but away from this limit we measure effective long-ranged attractive binding. A phenomenological model shows that the increase in the edge energy of scalloped membranes is compensated by concomitant decrease in the deformation energy due to Gaussian curvature associated with scalloped edges, demonstrating that colloidal membranes have positive Gaussian modulus. A simple excluded volume argument predicts the sign and magnitude of the Gaussian curvature modulus that is in agreement with experimental measurements. Our results provide insight into how the interplay between membrane elasticity, geometrical frustration and achiral symmetry breaking can be used to fold colloidal membranes into 3D shapes.