Surface relaxation of lyotropic lamellar phases

We study the relaxation modes of an interface between a lyotropic lamellar phase and a gas or a simple liquid. The response is found to be qualitatively different from those of both simple liquids and single-component smectic-A liquid crystals. At low rates it is governed by a non-inertial, diffusive mode whose decay rate increases quadratically with wave number, |ω| = Aq2. The coefficient A depends on the restoring forces of surface tension, compressibility and bending, while the dissipation is dominated by the so-called slip mechanism, i.e., relative motion of the two components of the phase parallel to the lamellae. This surface mode has a large penetration depth which, for sterically stabilised phases, is of order (dq2) − 1, where d is the microscopic lamellar spacing.