Shear-induced structural transitions of a micellar cubic phase during large amplitude oscillatory shear flow is studied with time-resolved oscillatory rheological small angle neutron scattering. This technique allows us to resolve the structural changes within a cycle of oscillation. By applying a strain rate near the critical melting shear rate, melting and recrystallization occurs in a cyclic mode. The maximum degree of order is observed when the shear stress reaches a plateau value during the large amplitude oscillatory shear cycle, whereas melting is maximized at the strain rate wave peaks. This structural evolution confirms the cyclic mechanism of sticking and sliding of 2D hexagonal close-packed layers [I. W. Hamley et al., Phys. Rev. E 58, 7620 (1998)].
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