Recombination, activation barriers

Schroeder J and Troe J 1993 Soivent effects in the dynamics of dissociation, recombination and isomerization reactions Activated Barrier Crossing ed G R Fieming and P Hanggi (Singapore Worid Scientific) p 206... 

Thus, in order to reproduce the effect of an experimentally existing activation barrier for the scission/recombination process, one may introduce into the MC simulation the notion of frequency , lo, with which, every so many MC steps, an attempt for scission and/or recombination is undertaken. Clearly, as uj is reduced to zero, the average lifetime of the chains, which is proportional by detailed balance to Tbreak) will grow to infinity until the limit of conventional dead polymers is reached. In a computer experiment Lo can be easily controlled and various transport properties such as mean-square displacements (MSQ) and diffusion constants, which essentially depend on Tbreak) can be studied. 

Whereas the adsorption energies of the adsorbed molecules and fragment atoms only slightly change, the activation barriers at step sites are substantially reduced compared to those at the terrace. Different from activation of a-type bonds, activation of tt bonds at different sites proceeds through elementary reaction steps for which there is no relation between reaction energy and activation barrier. The activation barrier for the forward dissociation barrier as weU as for the reverse recombination barrier is reduced for step-edge sites. 

Class 111-type behavior is the consequence of this impossibihty to create step-edge-type sites on smaller particles. Larger particles wiU also support the step-edge sites. Details may vary. Surface step directions can have a different orientation and so does the coordinative unsaturation of the atoms that participate in the ensemble of atoms that form the reactive center. This wiU enhance the activation barrier compared to that on the smaller clusters. Recombination as well as dissociation reactions of tt molecular bonds will show Class 111-type behavior. 

Since the recombination step (c) does not principally differ from a recombination of two H or D atoms to the respective hcmonuclear imole-cule there is no reason to assume a special activation barrier for a H and a D atom to recombine to the HD molecule. Therefore the rate of the HD production is solely determined by the rates of adsorption of H and D, respectively (as long as the reaction is adsorption-controlled, i.e., at hi enou tenperatures), or by the rate of desorption of HD (provided the reaction is desorpticai-oontrolled, i.e., at low temperatures). If wie deal with the first case only we may w/rite ... 

A second likely error source in the experimental determination of the appearance energy has also a kinetic origin. As shown in figure 4.4, recombination of the products A+ and B may involve an activation barrier (Etec). Therefore, even if Akin = 0, when Eiec is not negligible the measured appearance energy will be an upper limit of the true (thermodynamic) value. 

It is known that on transition metals, dissociation of H2 occurs readily, producing hydrogen adatoms that recombine and desorb as H2 at temperature between 300 and 900 K [9] On the other hand, a substantial activation barrier for H-H bond cleavage makes difficult the dissociation of H2 on noble-metal surfaces [9]. The effect of Pt or Pd catalysts is known to increase activity through the reduction of the activation energy [10,11]. Therefore, strategic addition of a catalyst has the potential to reduce the peak desorption temperature. 

In this section we discuss the accuracy of the BOC-MP projections concerning the activation barriers of dissociation and recombination surface reactions. We shall begin with diatomic adsorbates AB A + B. 

Tables XI and XII list total bond energies in the gas phase (D) and chemisorbed (D + Q) states for all C2HX species (x = 0-6). The calculated activation barriers AE for C—C and C—H bond cleavage and recombination for chemisorbed C2H species are summarized in Table XIII. All the discussion below will refer to chemisorbed species if not stated otherwise.

Thus, we project that hydrogenation of carbidic carbon to form CH species, polymerization of the CH species leading to C-C chain growth, and chain termination leading to the products (followed by their desorption) will occur on carbided iron surfaces where the reaction energetics resembles that on metallic Pd or Pt surfaces. Table XIII clearly shows that the activation barriers for all processes of recombination and desorption are much smaller on Pt than on Fe. Moreover, from Table XIII it follows that on a pure Fe surface such as Fe(110), the desorption energies for... 

The activation barriers AE for dissociation and recombination belong to the same realm of relative energies as AQAB. For this reason, we shall not discuss here purely numerical calculations of AE. Remarkably, many authors tried to conceptualize their computational results in terms of simple analytic models, which have no direct relation to the computations. For example, the effective medium theory (EMT) is a band-structure model with a complex and elaborated formalism including many parameters (154). Nevertheless, while reviewing the numerical EMT applications to surface reactions, Norskov and Stoltze (155) discussed the calculated trends in the activation energies for AB dissociation in terms of a one-parameter model (unfortunately, no details were provided) projecting A b to vary as NJ, 10 - Nd), where Nd is the d band occupancy [cf. Eqs. (21a)—(21c) of the BOC-MP theory]. 

In view of the many important applications in semiconductor technology, the interaction of hydrogen with silicon surfaces has been intensively studied. Recombinative H2 desorption from Si(100)-2 x 1 follows first-order kinetics89, unusual when compared with the second-order kinetics observed for H2 desorption from Si(lll)-7 x 7. The measured activation barriers for the desorption of H2 on Si(100) range from 45 to 66 kcalmol-189 90. 

Summarizing, one can say that 75-90 % of the strain enthalpy released in the dissociation process is found as a reduction in AG or AH. The missing 10-25 % is either a tribute to inadequacies of the compensation effect discussed before or also the recombinations of alkyl radicals pass, in contradiction to Fig. 1, a small activation barrier which is equal to 10-25 % of the strain enthalpy of the dimer 9). 

---