Hidden inner potential of electrolyte solutions and their application to ionic conductance and the Wien effect

The Poisson equation for the electrolytic solution was rigorously solved using a charge distribution model in a nanospace without using the linearized Poisson-Boltzmann approximation. The model is based on the dynamic behavior of the system, which fluctuates in the time, space, and energy domains. An action sphere concept was introduced as a tool to describe the electrolytic solution to bridge from the nanometer to the bulk scale. Based on this concept, the solution details were clarified. The results encompass concentration fluctuations in the nanometer region, the size of the action sphere as a function of concentration, and the inner potential profile, which we subsequently utilized to investigate the ionic conductivity of the solution. The derived relaxation field differed from that of the conventionally accepted Debye-Hückel-Onsager model. The derived conductivity was compared with the experimental results with more than 98% accuracy for the concentration range from micromoles to 2.25 M. The derived model potential (self-trapping potential) well explained the Wien effect up to a field of 300 kV cm^-1. By examining the Wien effect in a 1.22 mM MgSO₄ solution, the lifetime of an action sphere was determined to be 8.93 × 10^-9 s. The relaxation part of the electric conductance analysis for the 1 mM NaCl solution yielded a lifetime of 3 × 10^-8 s.