Scaling with temperature and concentration of the nonlinear rheology of a soft hexagonal phase

The nonlinear rheology of a soft surfactant hexagonal phase is examined. The system exhibits a shear-melting transition from a two-dimensional polycrystalline texture to a liquid of cylinders aligned along the flow [Ramos et al., Langmuir 16, 5846 (2000)]. This dynamic transition is associated with a discontinuity in the stress-strain curve (flow curve). A detailed study of the temperature and concentration dependence of the flow curves is presented. The nonlinear rheology is found to display a scaling behavior, when temperature or concentration are varied. We demonstrate that the whole behavior of the hexagonal phase under shear is essentially governed by the linear shear modulus of the sample, ${G}_{0}.$ When temperature is varied, we show that the two key parameters, which control ${G}_{0}$ and in turn, the flow curve, are a transition temperature ${T}_{c}$ and an activation energy ${E}_{A}.$ We propose ${E}_{A}$ to be related to the scission energy of one cylinder into two pieces.