Textured domains on tense surfaces and membranes: Effect of tilt and chirality.

We study the shape and texture of finite domains comprising chiral or achiral molecules carrying tilt, embedded in a two-dimensional surface or membrane, using a combination of simulations and exact variational calculations. We find a variety of shapes and textures including rectangular-shaped domains and a spontaneously broken chiral texture, when the molecules are achiral. We show that chiral tilt domains nucleating in a region of two-phase coexistence repel each other, thereby preventing coalescence and further growth. Our work principally addresses observations of domains in multicomponent giant unilamellar vesicles. It may also be relevant in the study of domains in phospholipid monolayers, nucleating domains of Sm-C* in Sm-A films, and chiral emulsions in Sm-A films, in situations where we can ignore dipolar interactions.