Determination of the reaction order and activation energy for desorption kinetics using TPD spectra: Application to D₂ desorption from Ag(111)

For desorption kinetics which follow the Polanyi-Wigner rate expression, plots of [In( -dθ dt) - nIn(θ)] versus ( 1 T) from TPD spectra can be used to determine both the reaction order and the desorption activation energy for the desorption kinetics of molecules from surfaces. We present a mathematical justification for this method and apply this method to a wide variety of simulated TPD spectra. The plots are linear for all temperatures when the correct value of the reaction order, n, is chosen. When n is incorrectly chosen, the direction of curvature of the plots yields information which can be used in determining the correct reaction order. Compared to the true value of n, the plots curve upward at high temperature when the trial n is too large, and downward when the trial n is too small. This method of determining the reaction order is most sensitive to the choice of n in the region near the desorption peak maximum. We show that the plots are approximately linear for all choices of n at low temperatures and caution others to discontinue using this method over this range of data. We also point out the importance of comparing the measured TPD spectra with computer simulations of TPD spectra using the parameters determined from any analysis method in order to validate the determination of these parameters. In order to illustrate the application of these methods, we reexamine recent TPD data for the desorption of D₂ from Ag(111) [X.-L. Zhou, J.M. White and B.E. Koel, Surface Sci. 218 (1989) 201]. The desorption of D₂ from D adatoms chemisorbed on Ag(111) is found to follow second order kinetics, with a desorption activation energy of 10.5 kcal/mol at low D coverage.