Shear-induced ordering of nano-pores and instabilities in concentrated surfactant mesh phases

Mixed surfactant systems with strongly bound counterions show many interesting phases such as the random mesh phase consisting of a disordered array of defects (water-filled nano-pores in the bilayers). The present study addresses the non-equilibrium phase transition of the random mesh phase under shear to an ordered mesh phase with a high degree of coherence between nano-pores in three-dimension. In-situ small-angle synchrotron X-ray study under different shear stress conditions shows sharp Bragg peaks in the X-ray diffraction, successfully indexed to the rhombohedral lattice with R$\bar{3}$m space group symmetry. The ordered mesh phase shows isomorphic twinning and buckling at higher shear stress. Our experimental studies bring out rich non-equilibrium phase transitions in concentrated cationic surfactant systems with strongly bound counterions hitherto not well-explored and provide motivation for a quantitative understanding.