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

We have studied the mesoscopic shape fluctuations in aligned multilamellar stacks of DMPC bilayers using the neutron spin-echo technique. The corresponding in plane dispersion relation ${\tau }^{-1}$(q${}_{\mathrm{\mid }\mathrm{\mid }}$) at different temperatures in the gel (ripple, P${}_{{\beta }^{\mathrm{\prime }}}$) and the fluid (L${}_{\alpha }$) phase of this model system has been determined. Two relaxation processes, one at about 10ns and a second, slower process at about 100ns 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.