Technical note: Adsorption and desorption equilibria from statistical thermodynamics and rates from transition state theory

Abstract

Adsorption and desorption represent the initial processes of the interaction of gas species with the condensed phase. They have important implications for evaluating heterogeneous (gas-to-solid) and multiphase chemical kinetics involved in catalysis; environmental interfaces; and, in particular, aerosol particles. When describing gas uptake, gas-to-particle partitioning, and the chemical transformation of aerosol particles, parameters describing adsorption and desorption rates are crucial to assessing the underlying chemical kinetics such as surface reaction and surface-to-bulk transfer. For instance, the desorption lifetime, in turn, depends on the desorption free energy which is affected by the chosen adsorbate model. To assess the impact of those conditions on desorption energy and, thus, desorption lifetime, we provide a complete classical and statistical thermodynamic treatment of the adsorption and desorption process considering transition state theory for two typically applied adsorbate models, the 2D ideal gas and the 2D ideal lattice gas, the latter being equivalent to Langmuir adsorption. Both models apply to solid and liquid substrate surfaces. We derive the thermodynamic and microscopic relationships for adsorption and desorption equilibrium constants, adsorption and desorption rates, first-order adsorption and desorption rate coefficients, and the corresponding pre-exponential factors. Although some of these derivations can be found in the literature, this study aims to bring all derivations into one place to facilitate the interpretation and analysis of the variables driving adsorption and desorption for their application in multiphase chemical kinetics. This exercise allows for a microscopic interpretation of the underlying processes including the surface accommodation coefficient and highlights the importance of the choice of adsorbate model and standard states when analyzing and interpreting adsorption and desorption processes. We demonstrate how the choice of adsorbate model affects equilibrium surface concentrations and coverages, desorption rates, and decay of the adsorbate species with time. In addition, we show how those results differ when applying a concentration- or activity-based description. Our treatment demonstrates that the pre-exponential factor can differ by orders of magnitude depending on the choice of adsorbate model with similar effects on the desorption lifetime, yielding significant uncertainties in the desorption energy derived from experimentally derived desorption rates. Furthermore, uncertainties in surface coverage and assumptions about standard surface coverage can lead to significant changes in desorption energies derived from measured desorption rates. Providing a comprehensive thermodynamic and microscopic representation aims to guide theoretical and experimental assessments of desorption energies and estimate potential uncertainties in applied desorption energies and corresponding desorption lifetimes important for improving our understanding of multiphase chemical kinetics.