Isotropic-to-cholesteric transition in liquid crystal elastomers

A liquid crystal elastomer tries to spontaneously elongate on entering the locally nematic phase, but may have to twist to reduce its Frank elastic energy. The extremes are a conventional, transverse cholesteric structure (where it reduces its Frank energy), and a uniformly aligned state (where it can maximally spontaneously extend and reduce its elastic energy). Between these it can adopt a conical state where there is also bend but equally a partial satisfaction of the elastic requirements. A line of first-order transitions between conical and transverse states ends and becomes a line of second-order transitions, depending on chain anisotropy, the ratio of the Frank bend and twist constants, and on the elastic modulus reduced by the bend energy. Continuous and discontinuous variation of cone angles, and spontaneous elongations and shears are given, as are analytic forms for the singular variation of director as cones are lost to the transverse state. The variation of the multicritical point with the ratio of Frank constants is also given.