Membrane dynamics and structure factor

We investigate the short time and short scale dynamics of membrane phases. The dynamics of the two point displacement correlator of the membrane is shown to be dominated by the transverse mean-square displacement of a tagged membrane point and to vary with time t as similar to t(2/3). As a result, the structure factor of oriented lamellar phases at nearly perpendicular orientations (mean membrane normal parallel to the wavevector (k) over right arrow) decays as a stretched exponential S((k) over right arrow, t) similar to e-((Gammak2t))(2/3) with Gamma(kz) similar to (T/kappa)(1/2) (T/eta)k(3). For isotropic systems, angular averaging retains the stretched exponential decay, S(k, t) similar to e(-(Gammakt)z), but with alpha > 2/3 and no longer universal. We also find Gamma(k) similar to k(z) with z < 3. Agreement with recent. experimental results is elucidated. (C) 2002 Elsevier Science B.V. All rights reserved.