Thermopermeation in bicontinuous lyotropic crystals

In 1982, P. G. de Gennes wrote two articles on two apparently disjoined subjects: (1) the Ludwig-Soret effect in porous media filled with pure liquids and (2) bicontinuous structures in microemulsions. In the study of bicontinuous cubic lyotropic crystals subjected to temperature gradients which we present here, these two subjects are now intimately related. Our experiments consist of the observation, by means of an optical microscope, of crystal shapes in three types of phase coexistence: Ia3d-in-vapour, Pn3m-in-L1 and Im3m-in-L1. In all three cases, we infer from changes in the crystal shapes that the surfactant is transferred, along the unique periodic bilayer, from the warm to the cold extremities of crystals. In order to explain this phenomenon of 'thermopermeation' of the surfactant, inspired by de Gennes we assume that: (1) the periodic bilayer acts as a viscoelastic matrix and (2) a slip occurs at the surfactant/water interface.