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 relaxation is found to be qualitatively different from those of both simple liquids and single-component smectic-A liquid crystals. It is governed by a non-inertial, diffusive mode whose decay rate increases quadratically with wavenumber, |ω| = Aq. The coefficient A depends on the restoring forces of surface tension, compressibility and bending, while the dissipation is dominated by the slip mechanism, i.e., relative motion of the two components parallel to the lamellae. This surface mode has a large penetration depth which, for sterically stabilized phases, is of order (dq), where d is the microscopic lamellar spacing. Lyotropic lamellar phases occupy large portions in the phase diagrams of amphiphilic molecules (surfactants) in solution [1, 2]. They consist of stacks of parallel fluid membranes separated by microscopic (∼1–10 nm thick) layers of solvent [fig. 1(a)], thus having the symmetry of a smectic-A liquid crystal [3]. These phases appear in numerous applications, e.g., in the cosmetic and detergent industries. Lamellar bodies are found also in biological systems such as the lung [4]. Apart from the surfaces of lamellar phases with air, surfactant phase diagrams contain also large coexistence regions (so-called miscibility gaps) [1], in which a lamellar phase has an equilibrium interface with an isotropic liquid such as a dilute micellar solution or an L3 (sponge) phase [1,2]. Spherical lamellar structures in the form of multilamellar vesicles (onions) dispersed in a solvent are commonly encountered as well [5]. Thus, the surface response of these phases is a fundamental issue relevant to a large variety of experimental systems. The static response of smectics to surface deformations was thoroughly studied [3,6,7]. Dynamic relaxation of surface perturbations in thermotropic (single-component) smectics was addressed briefly in ref. [8] and in more detail in ref. [9]. In the current Letter we analyse the surface relaxation of lyotropic (two-component) lamellar phases and demonstrate the essentially different surface dynamics of this ubiquitous class of materials. Surface modes characterise the relaxation dynamics of surface perturbations whose amplitude decays with increasing distance into the bulk material [fig. 1(a)]. In a simple liquid, having mass density ρ, viscosity η and surface tension γ, the surface dynamics depend on two