Kinetics of Isothermal Adsorption on Energetically Heterogeneous Solid Surfaces:  A New Theoretical Description Based on the Statistical Rate Theory of Interfacial Transport

Starting from the fundamental equations of the statistical rate theory of interfacial transport (SRTIT), a set of three equations has been developed, resulting in a new description of the kinetics of localized gas adsorption/desorption on energetically heterogeneous solid surfaces. For the Langmuir model of adsorption, these equations take the following form: dθ t /d t = 2 kT χ c (ε c) K̃ gs Kp e ε c / kT − 1/ (Kp) e -ε c / kT, θ t (ε c, T) = χ (ε) exp ( (ε − ε c) / kT) /1 + exp ( (ε − ε c) kT) dε, and χ c (ε c) = χ (ε) (1/ kT) exp ( (ε − ε c) / kT) /[1 + exp ( (ε − ε c) / kT) 2 ] dε, where θ t is the average surface coverage, t is time, T and k are the absolute temperature and Boltzmann constant, respectively, p is the nonequilibrium pressure in the experiment, K̃ gs is an expression depending on the conditions at which the experiment is carried out, K is a temperature-dependent constant, and χ (ε) is the normalized differential distribution of the number of adsorption sites at various values of the adsorption energy ε. Two adsorption energy distributions, one Gaussian-like and one rectangular, were taken into consideration since they lead to the two well-known isotherm equations, the Langmuir−Freundlich and the Temkin isotherms, commonly used to describe adsorption equilibria. By accepting these energy distributions, one arrives at two kinetic expressions θ t (t) which after several simplifying assumptions reduce to the well-known power-law and Elovich equations. The new equations have been subjected to an exhaustive numerical analysis, and then used to interpret some experimental data reported in the literature. Both the constant K and the adsorption energy distribution χ (ε) can be calculated from equilibrium adsorption isotherms by this analysis. We have therefore shown that by measuring just the adsorption equilibria it is possible to predict the related behavior of adsorption kinetics. In the theoretical procedures available in the literature, only the reverse operation was possible.