2.6 The Desorption Process
An adsorbed species present on a surface at low temperatures may remain almost indefinitely in that state. As the temperature of the substrate is increased, however, there will come a point at which the thermal energy of the adsorbed species is such that one of several things may occur :
The last of these options is the desorption process. In the absence of decomposition the desorbing species will generally be the same as that originally adsorbed but this is not necessarily always the case.
(An example where it is not is found in the adsorption of some alkali metals on metallic substrates exhibiting a high work function where, at low coverages, the desorbing species is the alkali metal ion as opposed to the neutral atom. Other examples would include certain isomerisation reactions.)
Desorption Kinetics
The rate of desorption, R_{des }, of an adsorbate from a surface can be expressed in the general form :
R_{des} = k N^{ x} 
where 
x  kinetic order of desorption 
The order of desorption can usually be predicted because we are concerned with an elementary step of a "reaction" : specifically,
I. Atomic or Simple Molecular Desorption
A_{(ads)} → A_{(g)} 

M_{(ads)} → M_{(g)} 
 will usually be a first order process ( i.e. x = 1 ). Examples include …
W / Cu_{ (ads)} → W_{ (s)} + Cu_{ (g)} 
; desorption of Cu atoms from a W surface 
Cu / CO_{ (ads)} → Cu_{ (s)} + CO_{ (g)} 
; desorption of CO molecules from a Cu surface 
II. Recombinative Molecular Desorption
2 A_{ (ads)} → A_{2 (g)} 
 will usually be a second order process ( i.e. x = 2 ). Examples include …
Pt / O_{ (ads)} → Pt_{ (s)} + O_{2 (g)} 
; desorption of O atoms as O_{2} from a Pt surface 
Ni / H_{ (ads)} → Ni_{ (s)} + H_{2 (g)} 
; desorption of H atoms as H_{2} from a Ni surface 
The rate constant for the desorption process may be expressed in an Arrhenius form,
k_{des} = A exp ( E_{a}^{des} / RT )


where 
E_{a}^{des} is the activation energy for desorption , and A is the preexponential factor; this can also be considered to be the "attempt frequency", ν , at overcoming the barrier to desorption. 
This then gives the following general expression for the rate of desorption
In the particular case of simple molecular adsorption, the preexponential/frequency factor (ν) may also be equated with the frequency of vibration of the bond between the molecule and substrate; this is because every time this bond is stretched during the course of a vibrational cycle can be considered an attempt to break the bond and hence an attempt at desorption.
Surface Residence Times
One property of an adsorbed molecule that is intimately related to the desorption kinetics is the surface residence time  this is the average time that a molecule will spend on the surface under a given set of conditions (in particular, for a specified surface temperature) before it desorbs into the gas phase.
For a first order process such as the desorption step of a molecularly adsorbed species :
M_{(ads)} → M_{(g)}
the average time ( τ ) prior to the process occurring is given by :
τ = 1/k_{1}
where k_{1} is the first order rate constant (no proof of this will be given here).
From the previously derived desorption formulae we know that
k_{1} = ν exp ( E_{a}^{des} / RT )
and if we also substitute for E_{a}^{des} using the approximate relation E_{a}^{des} ~ ΔH_{ads} discussed in Section 2.4 , then we get the following expression for the surface residence time
τ = τ_{o} exp ( ΔH_{ads} / RT )
where : 
τ_{o} ( = 1/ν ) corresponds to the period of vibration of the bond between the adsorbed molecule and substrate and is frequently taken to be about 10^{13} s . 