A modified Poisson–Boltzmann equation: I. Basic relations Original Research Article

The fundamental electrostatic and thermodynamic equations governing the local balance approach for the description of a charged interface in solution are revised. Special attention is given to a detailed thermodynamic analysis of space charge regions being subject to an electric field. The equilibrium conditions of the components of the system are derived, without approximations, in terms of their (electro-)chemical potentials. Combined with Poissonʹs equation they yield a fundamental set of self-consistent local balance differential equations as a general basis for further detailed modelling computations. Comparison with literature shows that work done in the field of the Poisson–Boltzmann approach is often based on incorrect or oversimplified equations.