Activation energy coverage dependence

At high coverages, adsorbate interactions will always be present, implying that preexponential factors and activation energies are dependent on coverage. In the following we shall assume that the mean-field approximation is valid, but one should be aware that it may be a source of error. The alternative to this approximation is to perform Monte Carlo simulations (see Chapter 7). 

The applications of this simple measure of surface adsorbate coverage have been quite widespread and diverse. It has been possible, for example, to measure adsorption isothemis in many systems. From these measurements, one may obtain important infomiation such as the adsorption free energy, A G° = -RTln(K ) [21]. One can also monitor tire kinetics of adsorption and desorption to obtain rates. In conjunction with temperature-dependent data, one may frirther infer activation energies and pre-exponential factors [73, 74]. Knowledge of such kinetic parameters is useful for teclmological applications, such as semiconductor growth and synthesis of chemical compounds [75]. Second-order nonlinear optics may also play a role in the investigation of physical kinetics, such as the rates and mechanisms of transport processes across interfaces [76]. 

With the aid of (B1.25.4), it is possible to detennine the activation energy of desorption (usually equal to the adsorption energy) and the preexponential factor of desorption [21, 24]. Attractive or repulsive interactions between the adsorbate molecules make the desorption parameters and v dependent on coverage [22]- hr the case of TPRS one obtains infonnation on surface reactions if the latter is rate detennming for the desorption. 

We again assume that the pre-exponential factor and the entropy contributions do not depend on temperature. This assumption is not strictly correct but, as we shall see in Chapter 3, the latter dependence is much weaker than that of the energy in the exponential terms. The normalized activation energy is also shown in Fig. 2.11 as a function of mole fraction. Notice that the activation energy is not just that of the rate-limiting step. It also depends on the adsorption enthalpies of the steps prior to the rate-limiting step and the coverages. 

How do we derive the activation energy of desorption from TPD Data Unfortunately, the differential equation in (12) can not be solved analytically. Hence, analyzing TPD curves can be a cumbersome task, in particular because the kinetic parameters usually depend on surface coverage. 

Figure 7.8. The compensation effect in the desorption ofAg from a ruthenium surface activation energy and pre-exponential factor depend in the same way on coverage. The...

Hence, the activation energy contains coverage-dependent, second-order terras, which are usually ignored. This is only allowed in three cases. The trivial cases are when the kinetic parameters are constant, or when the coverage does not change... 

Because the Arrhenius plots of both TPD experiments are straight lines over a large portion of the data points, the reaction between CO and O is, most likely, an elementary step, with an activation energy of 103 5 kj mol and a pre-exponential factor of s . This analysis is again only valid if coverage dependencies play... 

Figure 5 summarises results for the CO2, N2 and N2O formation rates for the dependence of apparent activation energies on catalyst potential. Although there is a notable increase in activation energy with increased Na coverage in each case, the variation is not as abrupt at that characteristic of EP CO oxidation [24] and NO+CO reactions. 

We have measured the kinetics of ethylidyne formation from chemisorbed ethylene over Pt(lll) surfaces. The rates of reaction display a first order dependence on the ethylene coverage. There is an isotope effect, since the reaction for CjH is about twice as fast as for CjD. We obtain values for the activation energy of 15.0 and 16.7 Kcal/mole for the normal and deuterated ethylene, respectively. These values are lower than those obtained from TDS experiments, but the differences can be reconciled by taking into account the hydrogen recombination when analyzing the thermal desorption data. 

The simultaneous desorption peaks observed at 560-580 K in TPR are of reaction-limited desorption. The peak temperatures of these peaks do not depend on the coverage of methoxy species, indicating that the desorption rate (reaction rate) on both surfaces has a first-order relation to the coverage of methoxy species. Activation energy (Ea) and the preexponential factor (v) for a first-order process are given by the following Redhead equation [12] ... 

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