Pre-exponential factor of desorption

In this chapter, we discuss TPR and reduction theory in some detail, and show how TPR provides insight into the mechanism of reduction processes. Next, we present examples of TPO, TP sulfidation (TPS) and TPRS applied on supported catalysts. In the final section we describe how thermal desorption spectroscopy reveals adsorption energies of adsorbates from well-defined surfaces in vacuum. A short treatment of the transition state theory of reaction rates is included to provide the reader with a feeling for what a pre-exponential factor of desorption tells about a desorption mechanism. The chapter is completed with an example of TPRS applied in ultra-high vacuum (UHV), in order to illustrate how this method assists in unraveling complex reaction mechanisms. 

Equations similar to eqns. (5), (6) and (8) were obtained by Zhdanov [104] to describe the monomolecular adsorption and associative desorption and Eley-Rideal s bimolecular reaction. He examined the dependence of the rate constants of these processes on the surface coverages and discussed various approximations applied previously to describe the effect of lateral interaction of adsorbed molecules on the desorption rate constant. He also considered the effect of the lateral interaction on the pre-exponential factor of the rate constants for various processes, and in terms of the "precursor state model, the effect of ordering the adsorbed molecules on the sticking coefficient and the rate constant of monomolecular desorption. 

It has been tentatively suggested that the unusually large pre-exponential factor for desorption over dissociation of the molecular chemisorbed precursor on Pt(l 11) may be a result of the role of defects... 

Fig. 19. The Linear relationship between desorption peak temperature and desorption energy assuming a pre-exponential factor of 1013 s 1 and a heating rate of I K s 1.

Table 1. Compilation of pre-exponential factors and desorption energies for wetting layers and multilayers of p-4P and p-6P on various substrates.

Waugh [26], we thus assume an immobile transition state without rotation for all of the species, which results in a pre-exponential factor of 10 Pa s for adsorption/desorption reactions, and s for surface reactions. The resulting microkinetic model for the WGS reaction is summarized in Table 1. Fine-tuning of some of the pre-exponential factors of the adsorption/desorption reactions, however, was necessary in order to be consistent with the known thermodynamics of the overall reaction, i.e., for a RR, the activation energies of the forward and reverse reactions are related to the enthalpy change via... 

The rate of molecular desorption may vary over a few orders of magnitude, depending on the rotation of the molecule in the transition state. When molecules go from a rigid adsorption state to a rotating transition state, the pre-exponential factor of the desorption rate constant increases by several orders of magnitude. The partition function of the internal vibration of a molecule remains close to one because the molecular frequencies are generally high compared to kT. 

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]. 

On K modified Ni(100) and Ni(lll)62,63 and Pt(lll)64 the dissociative adsorption of hydrogen is almost completely inhibited for potassium coverages above 0.1. This would imply that H behaves as an electron donor. On the other hand the peaks of the hydrogen TPD spectra shift to higher temperatures with increasing alkali coverage, as shown in Fig. 2.22a for K/Ni(lll), which would imply an electron acceptor behaviour for the chemisorbed H. Furthermore, as deduced from analysis of the TPD spectra, both the pre-exponential factor and the activation energy for desorption... 

The effect of electronegative modifiers on the activation energy of CO desorption, Ed, and on the corresponding pre-exponential factor, vd, can be quantified by analysis of the TPD spectra at very low CO coverages. The... 

Unraveling catalytic mechanisms in terms of elementary reactions and determining the kinetic parameters of such steps is at the heart of understanding catalytic reactions at the molecular level. As explained in Chapters 1 and 2, catalysis is a cyclic event that consists of elementary reaction steps. Hence, to determine the kinetics of a catalytic reaction mechanism, we need the kinetic parameters of these individual reaction steps. Unfortunately, these are rarely available. Here we discuss how sticking coefficients, activation energies and pre-exponential factors can be determined for elementary steps as adsorption, desorption, dissociation and recombination. 

Equation (12) also contains a pre-exponential factor. In Section 3.8.4 we treated desorption kinetics in terms of transition state theory (Figure 3.14 summarizes the situations we may encounter). If the transition state of a desorbing molecule resembles the chemisorbed state, we expect pre-exponential factors on the order of ek T/h = 10 s . However, if the molecule is adsorbed in an immobilized state but desorbs via a mobile precursor, the pre-exponential factors may be two to three orders of magnitude higher than the standard value of 10 s . ... 

As the initial coverages of CO and O are known, and the surface is free of CO at the end of the temperature-programmed experiment, the actual coverages of CO and O can be calculated for any point of the TPD curves in Fig. 7.14. Hence, an Arrhenius plot of the rate of desorption divided by the coverages, against the reciprocal temperature yields the activation energy and the pre-exponential factor ... 

Refer to Chapter 3 and summarize the values of pre-exponential factors you may expect for the desorption of gases. 

We now want to estimate the CO coverage when the catalyst is located in a plug-flow reactor with a partial pressure of Pqq = 0-01 bar at T= 1000 K. The desorption energy is estimated to be 147 kj mol and the pre-exponential factor is set to the usual 10 s , while the sticking coefScient is estimated to be 0.2 and independent of temperature. For simplicity we assume that each Ni atom can adsorb a CO molecule. 

A pre-exponential factor and activation energy for each rate constant must be established. All forward rate constants involving alkyne adsorption (ki, k2, and ks) are assumed to have equal pre-exponential factors specified by the collision limit (assuming a sticking coefficient of one). All adsorption steps are assumed to be non-activated. Both desorption constants (k.i and k ) are assumed to have preexponential factors equal to 10 3 sec, as expected from transition-state theory [28]. Both desorption activation energies (26.1 kcal/mol for methyl acetylene and 25.3 kcal/mol for trimethylbenzene) were derived from TPD results [1]. 

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