Dispersion relation of lipid membrane shape fluctuations by neutron spin-echo spectrometry

We have studied the mesoscopic shape fluctuations in aligned multilamellar stacks of 1,2-dimyristoyl-sn-glycero-3-phoshatidylcholine bilayers using the neutron spin-echo technique. The corresponding in plane dispersion relation tau(-1)(q(vertical bar vertical bar)) at different temperatures in the gel (ripple, P-beta(')) and the fluid (L-alpha) phase of this model system has been determined. Two relaxation processes, one at about 10 ns and a second, slower process at about 100 ns can be quantified. The dispersion relation in the fluid phase is fitted to a smectic hydrodynamic theory, with a correction for finite q(z) resolution. We extract values for the bilayer bending rigidity kappa, the compressional modulus of the stacks B, and the effective sliding viscosity eta(3). The softening of a mode which can be associated with the formation of the ripple structure is observed close to the main phase transition.