Extensions to Study Electrochemical Interfaces, A Contribution to the Theory of Ions

In the present study an alternative model allows the extension of the debye-hückel theory (dht) considering time dependence explicitly. from the electro-quasistaticapproach (eqs) done in earlier studies time dependent potentials are suitable to describeseveral phenomena especially conducting media as well as the behaviour of charged particlesin arbitrary solutions acting as electrolytes.this leads to a new formulation of the meaning of the nonlinear poisson-boltzmannequation (pbe). if a concentration and/or flux gradient of particles is considered the originalstructure of the mpbe will be modified leading to a new nonlinear partial differential equation(npde) of the third order. it is shown how one can derive classes of solutions for the potentialfunction analytically by application of an algebraic method. the benefit of the mathematicaltools used here is the fact that closed-form solutions can be calculated without any numericalapproximations.