Hexagonal and lamellar mesophases induced by shear

The role of a shear flow in the formation of an hexagonal mesophase is investigated and the transition between the isotropic, lamellar and hexagonal phases described in a three dimensional phase diagram [τ, u, Δ] where τ is a temperature-related parameter, u a measure of the intrinsic asymmetry of the system and Δ the strength of the shear rate. At zero shear rate the microphase separation transition (M.S.T.) is dominated by fluctuations but it acquires a strong mean-field character as Δ is increased. We find a region in the phase diagram where the same isotropic phase may undergo a transition to a lamellar or an hexagonal structure according to whether is cooled or sheared. The relevance of our results for diblock copolymers and for microemulsions is discussed.