A New Time Dependent Approach for Solving Electrochemical Interfaces Theoretical Considerations Using Algebraic Approaches

Recently we introduced a nonlinear partial differential equation (nPDE) of the third order for the first time. This new model equation allows the extension of the Debye-Hückel Theory (DHT) considering time dependence explicitly. This also leads to a new formulation in the meaning of the nonlinear Poisson-Boltzmann Equation (nPBE) and therefore we call it the modified PoissonBoltzmann Equation (mPBE). The purpose of the present paper is to analyze the new model equation by algebraic methods without using any approximations and numerical methods. We show how we can integrate a highly nPDE leading to suitable classes of solutions importantly in electrochemical applications. Generalized relations for the potential, the charge density, and the electric field are given in an analytical way for special classes of solutions involving time dependence explicitly. Conclusions are supported by studying some test examples such like potassium chloride and other many-valued electrolytes. 1. Preliminaries To evaluate the potential distribution around a central ion and/or describing the potential of electrodes the classical Debye-Hückel Theory (DHT) is used. Here the electric double layer interaction is the central point or to be more precisely, the electrode-electrolyte interface is assumed as a basis of electrodics. Under equilibrium conditions the time-average forces are the same in all directions and at all points in the bulk of the electrolyte (assuming to be isotropic perfectly and homogeneous) and there are no net preferentially directed electrical fields. MATCH Communications in Mathematical and in Computer Chemistry MATCH Commun. Math. Comput. Chem. 67 (2012) 91-107