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

Abstract

Using 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. The midplane tilt at the interdomain edge forces splay, which, in turn, manifests as spontaneous edge curvature with energetics controlled by the length asymmetry of constituent rods. A thermodynamic model of such tilt-curvature coupling at interdomain edges explains a number of experimental observations, including annularly shaped long-rod domains, and a nonmonotonic dependence of edge twist on domain radius. Our work shows how coupling between orientational and compositional degrees of freedom in two-dimensional fluids gives rise to complex shapes of fluid domains, analogous to shape transitions in 3D fluid vesicles.

The thermodynamic origins of chiral twist in monolayer assemblies of rod-like colloids

“…Recent theoretical and experimental work 51–53 has also concluded that the volume change upon twist plays a crucial role in determining the geometry and stability of colloidal membranes of rod-like particles. The geometric frustration between double-twist and splay causes the twisted monolayer to have a hyperbolic edge ( i.e.…”

“…Only when the perpendicular fluctuations of the rods are suppressed and their centers are confined at the 2D midplane (which is the same as the theoretical model in ref. 53), does our monolayer exhibit a hyperboloid-like shape [Fig. S5(b)†].…”

Gnomonious projections for bend-free textures: thoughts on the splay-twist phase

“…As mentioned previously, this means that the characteristic curves from the z = 0 plane never intersect. In a finite geometry, it is possible that a virtual intersection could occur outside the sample as discussed, for instance, in [30] in the context of viral rafts. In that and other cases (15) would be modified by the sample size.…”

Geodesic fibrations for packing diabolic domains

“…For example, one could stack these structures, forming something akin to a hexagonal columnar phase or a Moiré phase (24). Although this would introduce bend defects, it would lower the ever-growing splay of tall diabolic domains (25). Another possibility is to construct an Apollonian packing of circles in the z = 0 plane, leading to an intricate structure of skew domains.…”