Fluctuations of Membranes near the Lamellar-Gyroid Transition Point

Abstract

Surfactant/water systems show a variety of three-dimensional structures, where surfactants aggregate spontaneously and avoid water-molecules. The morphology transitions take place by changing temperature (and concentration). The sphere phase, cylinder phase and lamellar phase are well-known. The gyroid phase is observed often between the cylinder and lamellar phases. In the gyroid phase, the cubic structure consists of two three-dimensional networks of water-channels, mutually unconnected. 1) Our purpose is to study the dynamics of membranes, that consist of surfactants, near transition temperatures. According to the scattering experiments by Imai et al., the scattering intensity shows strange peaks in the pre-transition region from the lamellar phase to the gyroid phase. We directly observe the dynamics in this region by the computer simulation of the extended time-dependent Ginzburg-Landau equations. The extended TDGL equations are the followings: { ∂ ∂tφ(r) = (−Aψ + uψ3 −D ψ) − B[ψ − 1 + 2f ],