Surface Potential and Surface Dipole Moment of Water and Polar-Quadrupolar Liquids

Nearby interfaces, polar-quadrupolar molecules are orientated by image forces. This produces a macroscopic normal dipole moment and is the reason for the surface potential of liquids like water. The theory of the effect requires higher-order multipole expansion of both the image interactions and the macroscopic equations of electrostatics. The quadrupolar Coulomb law predicts the formation of a dipolar double layer (DDL) at the surface, with an adsorbed layer of dipoles orientated by image forces and oppositely polarized diffuse layer formed as a response to the field of the adsorbed dipoles. We relate the surface dipolar potential to the molecular properties (dipole and quadrupole moments and molecular polarizability), the medium properties (dielectric permittivity and macroscopic quadrupolarizability), and structural characteristics of the surface layer (distance between equimolecular and dielectric surfaces, thickness of the adsorbed layer, and cavity size). The thickness of the DDL is set by the quadrupolar length of the fluid, a quantity analogous to the Debye length. Molecules on the gas-phase side of the Gibbs equimolecular surface have a large contribution to the adsorbed dipole, especially for water. The surface layer is thick enough to produce a diffuse dipole layer also on the gas-phase side of the surface, i.e., three layers of dipoles exist, in agreement with recent simulations data. The calculated unperturbed surface polarization of the adsorbed layer for water agrees with estimates from point of zero dipole of alcohol monolayers. The calculated surface potential of water (between -15 and -85 mV, depending on the assumptions; oxygen toward the gas phase) agrees with existing experimental estimates.