  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.
