Calculation of local dielectric permittivity of confined liquids from spatial dipolar correlations

We report the working expressions of calculation of local dielectric permittivity ((r)) under nanoconfinement from dipolar spatial correlations. Three confined geometries are investigated: planar, cylindrical and spherical interfaces. We apply these relations to the calculation of the local components of (r) of water confined in a porous silica framework. Microscopically we highlight that the dielectric profile is correlated to the density of water and hydrogen bonding network.