We report a high energy-resolution neutron backscattering study to investigate slow motions on nanosecond time scales in highly oriented solid supported phospholipid bilayers of the model system DMPC -d54 (deuterated 1,2-dimyristoyl-sn-glycero-3-phoshatidylcholine), hydrated with heavy water. Wave vector resolved quasi-elastic neutron scattering (QENS) is used to determine relaxation times $tau$, which can be associated with different molecular components, i.e., the lipid acyl chains and the interstitial water molecules in the different phases of the model membrane system. The inelastic data are complemented both by energy resolved and energy integrated in-situ diffraction. From a combined analysis of the inelastic data in the energy and time domain, the respective character of the relaxation, i.e., the exponent of the exponential decay is also determined. From this analysis we quantify two relaxation processes. We associate the fast relaxation with translational diffusion of lipid and water molecules while the slow process likely stems from collective dynamics.
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