Electrostatics of heterogeneous monolayers. Constitutive equations and mathematical models

A new approach for modelling the electrochemistry of complex heterogeneous systems, composed of various bulk, surface and line phases, is proposed. A key step in it is the generalization of standard electrostatic boundary conditions, considered as 2D, 1D Poisson-Boltzmann equations. This viewpoint is applied to experimentally studied systems of two co-existing (e.g. liquid expanded, liquid condensed) monolayer phases. Another important feature of the given model is that, at electrochemical equilibrium, like with bulk double layers, surface double layers emerge on both sides of the contact line dividing the surface phases. A general mathematical formulation of the problem is proposed in respect of the electric potential as distributed in the complex heterogeneous system. Comments are also provided on the methods of solving the problem. The example illustrates a simplified system of two semi-infinite surface phases (monolayers) having equivalent parameters and divided by a contact line. The paper discusses the expressions obtained for the electrical potential, electrostatic energy, etc. and their dependence on the parameters of the system. Special focus is taken of the work of contact line formation.