Dynamical behavior of microemulsion and sponge phases in thermal equilibrium

The dynamical behavior of microemulsion and sponge phases is studied with a time-dependent Ginzburg-Landau model. The model has been shown previously to capture many of the essential static properties of these systems. Using a field-theoretic perturbation theory, we calculate the frequency-dependent (complex) viscosity eta(omega), sound velocity c(omega) and damping D(omega), and the scattering intensity S(k,t) in bulk and film contrast. The viscosity is almost frequency independent for small omega, then drops sharply at a characteristic frequency omega*, corresponding to a characteristic relaxation time tau similar to 1/omega*. The same relaxation rime is also found to dominate the sound velocity and damping. The characteristic frequency has the scaling form omega*similar to xi(-6)Omega(q xi), where xi is the correlation length and q is the inverse domain size of the microemulsion structure. The scattering intensity S(k,t) decays exponentially in time t for large t with an algebraic prefactor t(-alpha), both in bulk and in film contrast. In the latter case, we find there are several regimes of the wave vector k with different exponents alpha.