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

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