Universal current–potential relationship for mass-transfer through Formal Graph approach

The Formal Graph theory, a new language able to model graphically instead of algebraically most of basic equations used in physics and chemistry, is applied to mass-transfer occurring in electrochemical reactions. The integral admittance used in electrodynamics is generalized to all domains where energy is defined. Associated with the concept of energy coupling, this leads to very simple relationships between variables and operators describing processes in a system containing several energy varieties. The paradox of two different forms for the electric capacitance, linear in electrostatics and exponential in electrified materials, is treated and understood. The concept of energetic path brings physical meaning into mathematical models by attributing to each link a role in the conservation or dissipation of the energy. Normal transient diffusion, featured by an exponent 1/2, conserves half of energy, while anomalous diffusion, featured by an exponent p different from 1/2, conserves only 100 p%. The principle of every electrochemical measurement is represented in a simple and clear way by associating two Formal Graphs. The use of a mass-transfer operator generalizing all kinds of mass-transfer (diffusion, convection, thin layer, etc.) and for all geometric situations, allows the characterization of unknown process without previous knowledge of an algebraic model.