Desorption Times

Abstract

We briefly discussed isothermal and temperature programmed desorption experiments in the introductory chapter. We also collected data on the desorption time t_d for a number of physisorbed gas-solid systems in Table 1.1. Recently, Goodstein and his collaborators have performed a series of low-ternperature experiments on the desorption kinetics of helium on metal surfaces. As these experiments yield time of flight spectra exhibiting a wealth of information in addition to the desorption time, we postpone a detailed discussion to the appropriate chapter, 6. In this chapter, we report on the calculation of desorption times from the master equation, with the various transition probabilities surveyed in Chap. 4. We begin with the simplest model, namely a mobile adsorbate on a uniform surface, with the further simplification that the parallel momentum of the desorbing particle is conserved according to (4.4). The master equation is then (4.6). Splitting the sums into bound state contributions, labeled with an index i, and continuuum contributions, labeled by k, it reads

$${{{\rm{dn}}_{\rm{i}} } \over {{\rm{dt}}}} = \sum\limits_{{\rm{i'}}} {{\rm{W}}\left( {{\rm{i,i'}}} \right){\rm{n}}_{{\rm{i'}}} - \sum\limits_{\rm{i}} {{\rm{W}}\left( {{\rm{i',i}}} \right){\rm{n}}_{\rm{i}} - \sum\limits_{\rm{k}} {{\rm{W}}\left( {{\rm{k,i}}} \right){\rm{n}}_{\rm{i}} + \sum\limits_{\rm{k}} {{\rm{W}}\left( {{\rm{i,k}}} \right){\rm{n}}_{\rm{k}}.} } } }$$

(5.1)

To calculate the isothermal desorption rate, we recall that in an isothermal desorption experiment, starting from a gas-solid system in equilibrium at temperature T, one rapidly pumps away the gas phase keeping the system’s temperature constant. This implies the initial conditions

$${\rm{n}}_{\rm{i}} \left( {{\rm{t}} \mathbin{\lower.3ex\hbox{$\buildrel<\over {\smash{\scriptstyle=}\vphantom{_x}}$}} 0} \right) = {\rm{n}}_{\rm{i}} \,^{{\rm{eq}}},$$

(5.2)

but it also suggests that one should keep the continuum states unoccupied, i.e.,

$${\rm{n}}_{\rm{k}} \left( {{\rm{t}} \mathbin{\lower.3ex\hbox{$\buildrel>\over {\smash{\scriptstyle=}\vphantom{_x}}$}} {\rm{0}}} \right) = 0.$$

(5.3)