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We consider a theoretical model for the chiral smectic A twisted ribbonsobserved in assemblies of fd viruses condensed by depletion forces. Thedepletion interaction is modeled by an edge energy assumed to be proportionalto the depletant polymer in solution. Our model is based on the Helfrich energyfor surface bending and the de Gennes model of chiral smectic A liquid crystalswith twist penetration at the edge. We consider two variants of this model, onewith the conventional Helfrich Gaussian curvature term, and a second withsaddle-splay energy. A mean field analysis of both models yields a first-orderphase transition between ribbons and semi-infinite flat membranes as the edgeenergy is varied. The phase transition line and tilt angle profile are found tobe nearly identical for the two models; the pitch of the ribbon, however, doesshow some differences. Our model yields good qualitative agreement withexperimental observations if the sign of the Gaussian curvature or saddle-splaymodulus is chosen to favor negative Gaussian curvature.

Theory of depletion induced phase transition from chiral smectic A twisted ribbons to semi-infinite flat membranes