The rate of desorption

Desorption is always activated because the particles have to be lifted from the foot of a potential well. A physisorbed particle vibrates in its shallow potential well, and might shake itself off the surface after a short time. The temperature dependence of the first-order rate of departure can be expected to be Arrhenius-like, with an activation energy for desorption, Ed, comparable to the enthalpy of physisorption:

kd =Ae^−Ed/RT

Therefore, the half-life for remaining on the surface has a temperature dependence

t_1/2 ==τ₀e^Ed/RT τ0=

(Note the positive sign in the exponent.) If we suppose that 1/τ0 is approximately the same as the vibrational frequency of the weak particle–surface bond (about 10¹² Hz) and Ed ≈25 kJ mol⁻¹, then residence half-lives of around 10 ns are predicted at room temperature. Lifetimes close to 1 s are obtained only by lowering the temperature to about 100 K. For chemisorption, with Ed = 100 kJ mol⁻¹ and guessing that τ0 = 10⁻¹⁴ s (because the adsorbate–substrate bond is quite stiff), we expect a residence half-life of about 3 × 10³ s (about an hour) at room temperature, decreasing to 1 s at about 350 K. The desorption activation energy can be measured in several ways. However, we must be guarded in its interpretation because it often depends on the fractional cover age, and so may change as desorption proceeds. Moreover, the transfer of concepts such as ‘reaction order’ and ‘rate constant’ from bulk studies to surfaces is hazardous, and there are few examples of strictly first-order or second-order desorption kinetics ( just as there are few integral-order reactions in the gas phase too). If we disregard these complications, one way of measuring the desorption activation energy is to monitor the rate of increase in pressure when the sample is maintained at a series of temperatures, and to attempt to make an Arrhenius plot. A more sophisticated technique is temperature programmed desorption (TPD) or thermal desorption spectroscopy (TDS). The basic observation is a surge in desorption rate (as monitored by a mass spectrometer) when the temperature is raised linearly to the temperature at which desorption occurs rapidly, but once the desorption has occurred there is no more adsorbate to escape from the surface, so the desorption flux falls again as the temperature continues to rise. The TPD spectrum, the plot of desorption flux against temperature, therefore shows a peak, the location of which depends on the desorption activation energy. There are three maxima in the example shown in Fig. 25.23, indicating the presence of three sites with different activation energies. In many cases only a single activation energy (and a single peak in the TPD spectrum) is observed. When several peaks are observed they might correspond to adsorption on different crystal planes or to multilayer adsorption. For instance, Cd atoms on tungsten show two activation energies, one of 18 kJ mol⁻¹ and the other of 90 kJ mol⁻¹. The explanation is that the more tightly bound Cd atoms are attached directly to the substrate, and the less strongly bound are in a layer (or layers) above the primary overlayer. Another example of a system showing two desorption activation energies is CO on tungsten, the values being 120 kJ mol⁻¹ and 300 kJ mol⁻¹. The explanation is believed to be the existence of two types of metal–adsorbate binding site, one involving a simple M-CO bond, the other adsorption with dissociation into individually adsorbed C and O atoms.

Fig. 25.23 The flash desorption spectrum of H2on the (100) face of tungsten. The three peaks indicate the presence of three sites with different adsorption enthalpies and therefore different desorption activation energies. (P.W. Tamm and L.D. Schmidt, J. Chem. Phys. 51, 5352 (1969).)

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مواضيع ذات صلة

Units

Names of quantities

Working galvanic cells

Electrolysis

Experimental techniques

The rate laws

The electric potential at the interface

The structure of the interface

Catalytic activity at surfaces

Mechanisms of heterogeneous catalysis

Mobility on surfaces

The rate of adsorption