The Kuznetsov Tensor as a Foundation of the Electric Double Layer Theory at the Metal–Electrolyte Interface

This paper presents a generalized theoretical framework for describing the electric double layer (EDL) at the metal–electrolyte interface based on the introduction of the Kuznetsov tensor. In contrast to classical EDL models, which rely on a scalar electrostatic potential and assume integer ionic charges, the proposed approach accounts for the tensorial nature of interactions arising from specific ion adsorption and partial charge transfer between ions and the metal surface. The Kuznetsov tensor is formulated as a generalized interfacial field tensor that incorporates contributions from energy and momentum transport, charge density, adsorption effects, and entropy fluxes. It is shown that the equilibrium state of the electric double layer corresponds to the condition of vanishing divergence of the Kuznetsov tensor, allowing the EDL to be interpreted as a stationary tensor field rather than a simple superposition of compact and diffuse layers. Within this formalism, fractional effective ionic charges, ion competition in multicomponent electrolytes, and the influence of the chemical nature of the electrode surface are naturally captured. It is demonstrated that classical Poisson–Nernst–Planck equations and Stern-type models can be recovered as limiting cases of the tensor description under appropriate simplifying assumptions. The proposed theory provides a unified mathematical foundation for multiscale modeling of electrochemical interfaces and offers a consistent framework for analyzing charge storage, capacitance, and interfacial phenomena in batteries, supercapacitors, and electrocatalytic systems.