Polylogarithmic Adsorption Isotherm at Surface Linear Energetic Heterogeneity
—An exact solution for the monomolecular adsorption isotherm on the surface with linear energetic heterogeneity has been obtained. It is shown that the interpretation of numerous experimental data that were earlier associated with a surface energy heterogeneity (the Temkin adsorption model) may require an extensive revision because of the existence of lengthy linear segments of an isotherm in semilogarithmic coordinates. The new properties of the isotherm are studied and the asymptotic and physical limiting cases have been considered. It has been shown that the surface energetic heterogeneity in the case of the polylogarithmic adsorption model is represented by two parameters: the energy dispersion, which is identical to the Temkin model heterogeneity parameter, and energy gradient. Depending on the sign of the latter, predatory surfaces and are distinguished. For predatory surfaces, the greater the adsorption heat of the surface area, the larger the number of such surface domains. For temperate surfaces, the greater adsorption heat is inherent in fewer surface domains. Physically, the greater adsorption gradient “pushes” the system in the same direction as the greater energy dispersion but less pronouncedly. Similar to the Temkin adsorption model, a simplified form of the polylogarithmic isotherm is obtained for the case of “medium coverage” (the term by Temkin).