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**Analysis of temperature-programmed desorption via equilibrium thermodynamics**

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M. Schmid, G. S. Parkinson, U. Diebold

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Institut für Angewandte Physik,
TU Wien, 1040 Wien, Austria*

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*ACS Phys. Chem. Au 3 (2023) 44-62*

Temperature-programmed desorption (TPD) experiments in surface science are usually analyzed
using the Polanyi–Wigner equation and/or transition-state theory.
These methods are far from straightforward, and the determination
of the pre-exponential factor is often problematic.
We present a different method based on equilibrium thermodynamics,
which builds on an approach previously used for TPD by Kreuzer et al. (Surf. Sci.1988).
Equations for the desorption rate are presented for three different types
of surface–adsorbate interactions:
(i) a 2D ideal hard-sphere gas with a negligible diffusion barrier,
(ii) an ideal lattice gas, that is, fixed adsorption sites without interaction between the adsorbates,
and (iii) a lattice gas with a distribution of (site-dependent) adsorption energies.
We show that the coverage dependence of the sticking coefficient for adsorption
at the desorption temperature determines whether the desorption process
can be described by first- or second-order kinetics.
The sticking coefficient at the desorption temperature must also be known
for a quantitative determination of the adsorption energy,
but it has a rather weak influence (like the pre-exponential factor in a traditional TPD analysis).
Quantitative analysis is also influenced by the vibrational contributions to the energy and entropy.
For the case of a single adsorption energy, we provide equations to directly convert peak temperatures
into adsorption energies.
These equations also provide an approximation of the desorption energy
in cases that cannot be described by a fixed pre-exponential factor.
For the case of a distribution of adsorption energies, the desorption spectra cannot be considered
a superposition of desorption spectra corresponding to the different energies.
Nevertheless, we present a method to extract the distribution of adsorption energies
from TPD spectra, and we rationalize the energy resolution of TPD experiments.
The analytical results are complemented by a program for simulation and analysis of TPD data.

Corresponding author: Michael Schmid (schmid).

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