A continuous model of the interactions among electric dipoles

Abstract

The paper deals with a study of the spatially periodical dipole patterns that result from the interactions among polar lipid heads, whose tails are confined to a planar thin layer. The model is based on a continuous approach that assumes the dipole layer to be a planar region of infinitesimal thickness; according to this approach the dipole distributions are first represented through proper continuous functions, which are a normal dipole vector per unit area and a given surface charge density. Both of them must be periodical with respect to the coordinates of the plane, as they must be compatible with the periodic electric field configurations studied in this paper. It is shown that the periodical patterns associated to discrete dipoles can be derived from the afore-side continuous representation through the definition of “elementary cells” that contain a finite number of “subdomains” each of which corresponds to a single lipid molecule. A set of dipole patterns is obtained and discussed for the case of a square elementary cell. Results point out that both ferroelectric and antiferroelectric organizations of the dipole components on the layer plane do exist.