Transition state desorption

Carboxylates, which are chiral in the a-position totally lose their optical activity in mixed Kolbe electrolyses [93, 94]. This racemization supports either a free radical or its fast dynamic desorption-adsorption at the electrode. A clearer distinction can be made by looking at the diastereoselectivity of the coupling reaction. Adsorbed radicals should be stabilized and thus react via a more product like transition state... 

Figure 3.14. Microscopic pictures of the desorption of atoms and molecules via mobile and immobile transition states. Ifthe transition state resembles the ground state, we expect a prefactor of desorption of the order of 10 s h Ifthe adsorbates are mobile in the transition state, the prefactor increases by one or two orders of magnitude. For desorbing...

By applying the machinery of statistical thermodynamics we have derived expressions for the adsorption, reaction, and desorption of molecules on and from a surface. The rate constants can in each case be described as a ratio between partition functions of the transition state and the reactants. Below, we summarize the most important results for elementary surface reactions. In principle, all the important constants involved (prefactors and activation energies) can be calculated from the partitions functions. These are, however, not easily obtainable and, where possible, experimentally determined values are used. 

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 . ... 

Sketch plausible transition states for (a) the dissociation of a molecule in the gas phase (b) the reaction of cyclopropane to give propene (c) the isomerization of CH3CN to CH3NC (d) the desorption of an atom from a surface (e) the dissociation of an adsorbed molecule such as CO on a metal surface. 

Suggest a transition state for the desorption of a molecule when the preexponential factor is 10 s . Do the same for a desorption when the prefac-... 

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]. 

The classical approach for discussing adsorption states was through Lennard-Jones potential energy diagrams and for their desorption through the application of transition state theory. The essential assumption of this is that the reactants follow a potential energy surface where the products are separated from the reactants by a transition state. The concentration of the activated complex associated with the transition state is assumed to be in equilibrium... 

From the point of view of associative desorption, this reaction is an early barrier reaction. That is, the transition state resembles the reactants.46 Early barrier reactions are well known to channel large amounts of the reaction exoergicity into product vibration. For example, the famous chemical-laser reaction, F + H2 — HF(u) + H, is such a reaction producing a highly inverted HF vibrational distribution.47-50 Luntz and co-workers carried out classical trajectory calculation on the Born-Oppenheimer potential energy surface of Fig. 3(c) and found indeed that the properties of this early barrier reaction do include an inverted N2 vibrational distribution that peaks near v = 6 and extends to v = 11 (see Fig. 3(a)). In marked contrast to these theoretical predictions, the experimentally observed N2 vibrational distribution shown in Fig. 3(d) is skewed towards low values of v. The authors of Ref. 44 also employed the electronic friction theory of Tully and Head-Gordon35 in an attempt to model electronically nonadiabatic influences to the reaction. The results of these calculations are shown in... 

Temperature programmed desorption (TPD) or thermal desorption spectroscopy (TDS), as it is also called, can be used on technical catalysts, but is particularly useful in surface science, where one studies the desorption of gases from single crystals and polycrystalline foils into vacuum [2]. Figure 2.9 shows a set of desorption spectra of CO from two rhodium surfaces [14]. Because TDS offers interesting opportunities to interpret desorption in terms of reaction kinetic theories, such as the transition state formalism, we will discuss TDS in somewhat more detail than would be justified from the point of view of practical catalyst characterization alone. 

Expression (2-16) is approximately correct for first-order desorption and for values of vt[ between 108 and 1013 K l. It is very often applied to determine from a single TDS spectrum. The critical point however is that one must choose a value for v, the general choice being 1013 s, independent of coverage. As we explain below, this choice is only valid when there is little difference between the entropy of the molecule in the ground state and that in its transition state 125, 27], The Redhead formula should only be used if a reliable value for the prefactor is available ... 

The transition state theory of reaction rates [21] provides the link between macroscopic reaction rates and molecular properties of the reactants, such as translational, vibrational, and rotational degrees of freedom. For an extensive discussion of transition state theory applied to surface reactions we refer to books by Zhdanov [25] and by Van Santen and Niemantsverdriet [27]. The desorption of a molecule M proceeds as follows ... 

MadS is the adsorbed molecule, the superscript referring to the transition state for desorption... 

One degree of freedom of the adsorbed molecule serves as the reaction coordinate. For desorption, the reaction coordinate is the vibration of the molecule with respect to the substrate. In the transition state this vibration is highly excited and the chance that the adsorption bond breaks is given by the factor kT/h. All other degrees of freedom of the excited molecule are in equilibrium with those of the molecule in the ground state and are accounted for by their partition functions. 

The expression for the rate constant of desorption in the transition state theory is ... 

We use this knowledge to derive preexponential factors from (2-20) for a few desorption pathways (see Fig. 2.15). The simplest case arises if the partition functions Q and Q in (2-20) are about equal. This corresponds to a transition state that resembles the ground state of the adsorbed molecule. In order to compare (2-20) with the Arrhenius expression (2-15) we need to apply the definition of the activation energy ... 

The desorption flux is so low under these conditions that no gas phase collisions occurred between molecular desorption and LIF probing. Phase space treatments " of final-state distributions for dissociation processes where exit channel barriers do not complicate the ensuing dynamics often result in nominally thermal distributions. In the phase space treatment a loose transition state is assumed (e.g. one resembling the products) and the conserved quantities are total energy and angular momentum the probability of forming a particular flnal state of ( , J) is obtained by analyzing the number of ways to statistically distribute the available (E, J). 

Budde et have recently observed the ultraviolet laser-induced desorption of NO from oxidized Ni(lOO). The 193 nm excitation wavelength used was resonant with gas phase NO transitions to a predissociative upper state. Desorption yields of NO from clean Ni(lOO) were essentially zero. Comparison of TPD results from clean and oxidized nickel surfaces indicated that an oxidized nickel surface could support a weakly bound NO state not found on clean Ni(100). 

In the absence of transport limitations, the processes of adsorption, surface diffusion, surface reaction, and desorption can be treated via the transition state theory (Baetzold and Somorjai, 1976 Zhdanov et al, 1988). For example, the application of the TST to a single site adsorption process,... 

Thirdly, the rates of adsorption and desorption could be calculated by means of the transition state method and be equalized. But, bo... 

If we know that the desorption follows first order kinetics (n=l) and we have an educated guess on the value of A (e.g from transition state theory), Redheads equation makes it easy to determine E from a measurement of the peak temperature, T. 

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