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Elucidation of the mechanism and control of the kinetics of complex electrode reactions is often complicated by peculiarities such as memory effects, hystereses, switching, oscillations etc., all these being effects of the system's non-linearity. The model of the electrocatalytic reaction involves two consecutive electroadsorption reactions with charge numbers n1, n2, possibly also fractional. A Butler-Colmer-type kinetic equation conforming to a Frumkin adsorption isotherm is analyzed in a state variable approach with surface concentration used as the state variable and electrode potential as the input (control) variable. With transport limitations neglected, the process has one degree of freedom; its evolution is governed by a single ordinary differential equation and the only peculiarity resulting from non-linearity may be multiplicity of steady states. Numerical solutions of steady states without the simplifying assumption of irreversibility were obtained using the Mathematica program. The relation of the states without the simplifying assumption of irreversibility were obtained using the Mathematica program. The relation of the surface concentration of adsorbed intermediate and the electrode potential in the steady-state was defined as the analogue of the equilibrium adsorption isotherm and it was termed the steady-state isotherm. For strong attractive interactions its plots present the whole variety of shapes including N-, S- or Z-like shapes. The case intermediate between S- and Z-shape non-linearity corresponds to the constant surface concentration and vanishing adsorption capacitance. Accordingly, the reaction in the electrochemical test can be seen as a non-adsorptive one despite apparent adsorption.
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