Microdomain morphology, curvature and twist in colloidal membranes of bidisperse rod mixtures

Long and short rod-like viral particles condense into a single-layer membrane driven by a dextran depletant. The organization of the micron-sized rods is more easily probed experimentally than nanometer scale structures in phospholipid membranes, yet both systems are described by liquid crystalline models. In the colloidal membrane system, rods microphase separate and form circular raft domains with self-limiting domain size in equilibrium, much larger than the range of rod-rod interactions. Recent experimental evidence shows that the intra-membrane domain boundaries discriminate between long-rod and short-rod sides, so that short-rod rafts twist significantly more than long-rod rafts. Also, long-rod rafts are unstable to asymmetric and concave morphologies. We develop a model to describe the microstructure and thermodynamic effects of the intra-rod domain edge, and we predict a thermodynamic coupling between domain edge curvature and rod-tilt. This coupling is achiral and distinct from the aspects of raft formation previously captured by a chirality driven model. We argue that this curvature/tilt coupling should exist in any model of phase-separating membranes as a coupling between in-plane tilt and second-derivatives of composition.