Technical note: Adsorption and desorption equilibria from statistical thermodynamics and rates from transition state theory
Authors: Knopf Daniel A. , Ammann Markus 
Published: October 2021

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.