All twist and no bend makes raft edges splay: Spontaneous curvature of domain edges in colloidal membranes

TL;DR

This study combines theory and experiments to reveal how length asymmetry in colloidal membranes causes spontaneous edge curvature and complex domain shapes due to tilt-splay coupling.

Contribution

It introduces a thermodynamic model explaining tilt-curvature coupling at domain edges in colloidal membranes with different rod lengths.

Findings

Short-rod domains exhibit more twist than long-rod domains.

Edge tilt induces splay and spontaneous curvature dependent on rod length asymmetry.

Experimental observations include non-monotonic edge twist and annular domain shapes.

Abstract

Using a combination of theory and experiments we study the interface between two immiscible domains in a colloidal membrane composed of rigid rods of different lengths. Geometric considerations of rigid rod packing imply that a domain of sufficiently short rods in a background membrane of long rods is more susceptible to twist than the inverse structure, a long-rod domain in a short-rod membrane background. The tilt at the inter-domain edge forces splay, which in turn manifests as a spontaneous edge curvature whose energetics are controlled by the length asymmetry of constituent rods. A thermodynamic model of such tilt-curvature coupling at inter-domain edges explains a number of experimental observations, including a non-monotonic dependence of the edge twist on the domain radius, and annularly shaped domains of long rods. Our work shows how coupling between orientational and compositional degrees of freedom in two-dimensional fluids give rise to complex shapes and thermodynamics of domains, analogous to shape transitions in 3D fluid vesicles.