$n$-alkanes on MgO(100). I. Coverage-dependent desorption kinetics of $n$-butane

High-quality temperature-programmed desorption (TPD) measurements of $n$-butane from MgO(100) have been made for a large number of initial butane coverages (0–3.70 ML, ML–monolayers) and a wide range of heating ramp rates $(0.3–10K∕s)$⁠. We present a TPD analysis technique which allows the coverage-dependent desorption energy to be accurately determined by mathematical inversion of a TPD spectrum, assuming only that the preexponential factor (prefactor) is coverage independent. A variational method is used to determine the prefactor that minimizes the difference between a set of simulated TPD spectra and corresponding experimental data. The best fit for butane desorption from MgO is obtained with a prefactor of $1015.7±1.6s−1$⁠. The desorption energy is $34.9±3.4kJ∕mol$ at 0.5-ML coverage, and varies with coverage approximately as $Ed(θ)=34.5+0.566θ+8.37exp(−θ∕0.101)$⁠. Simulations based on these results can accurately reproduce TPD experiments for submonolayer initial coverages over a wide range of heating ramp rates $(0.3–10K∕s)$⁠. Advantages and limitations of this method are discussed.