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Orientations of dipoles restricted by two oppositely charged walls

We considered the system of two oppositely charged surfaces in a solution composed of dipoles and monovalent ions. The functional density theory for dipoles of arbitrary length was introduced. The spatial distribution of electric charge within the dipoles, the orientations of dipoles and their restrictions near the charged surface were taken into account. The result of the variational procedure gave the nonlinear integro-differential equation for the electrostatic potential. It was numerically solved by restating it as a fixed-point equation in an infinite-dimensional space of functions and then by looking for an approximated solution in the finite-dimensional space of functions defined in a mesh of Chebyshev nodes. The numerical solution showed that the dipoles are predominantly oriented parallel to the electric field, i.e. perpendicular to the charged surfaces. The interaction between oppositely charged surfaces mediated by dipoles was discussed.