Isotherm of adsorption at a solid electrode accounting for the electrode elasticity : A general solution

Abstract

To continue work on the basis of a full electrocapillarity equation, the thermodynamically equilibrium single-component adsorption from a dilute liquid solution on a solid electrode is considered with the effect of its surface deformation ϑ. The general case, where the arising new function γϑ≡ \(\gamma _\partial \equiv \frac{{\partial \Gamma }}{{\partial \vartheta }}\) depends on all the three dimensionless variables: surface concentration of adsorbate Γ, electrode potential, and surface deformation is studied. By expanding all the functions into series by small parameter ϑ, a set of equations with respect to linear expansion coefficients of unknown functions is obtained. For the model of two parallel capacitors, the initial equations are reduced to the same common differential first-order equation or to a transcendental equation, where the boundary conditions use the experimental capacitance curves. The unknown constant integration parameter is proposed to be calculated using at least one additional experimental value of a surface concentration. For the same model of non-deformed electrode, the additive component of the full value γϑ, which depends only on Γ, is shown to have no effect on the isotherm equation.