Dispersion relation of lipid membrane shape fluctuations by neutron spin-echo spectrometry
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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 $τ^{-1}$(q$_{||}$) at different temperatures in the gel (ripple, P$_{β'}$) and the fluid (L$_α$) 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 $κ$, the compressional modulus of the stacks $B$, and the effective sliding viscosity $η_3$. The softening of a mode which can be associated with the formation of the ripple structure is observed close to the main phase transition.