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We derive an expression relating the static dielectric permittivity profile for a system nonuniform in one dimension to correlations between the net system dipole moment and the local polarization density. The permittivity profile of a dipalmitoylphosphatidylcholine (DPPC) lipid bilayer in water is calculated from an all-atom 20-ns molecular dynamics simulation. The component of the permittivity parallel to the bilayer shows a nonmonotonic decrease from the value in bulk water to the value in the membrane interior; the interfacial region itself has a very large permittivity, greater than that of bulk water. In high-dielectric regions, obtaining a quantitative estimate of the component normal to the bilayer is not possible because of large numerical uncertainty. However, the calculated correlation function is consistent with a value for the interface at least as large as that of bulk water. In general, the transition to a low-dielectric environment is sharp and is located on the inner border of the region where there is significant probability of finding the polar head groups.
Stern et al. (Mon,) studied this question.