Surface step rate-determining steps

When the surface is completely covered by an oxide film, dissolution becomes independent of the geometric factors such as surface curvature and orientation, which are responsible for the formation and directional growth of pores. Fundamentally, unlike silicon, which does not have an atomic structure identical in different directions, anodic silicon oxides are amorphous in nature and thus have intrinsically identical structure in all orientations. Also, on the oxide covered surface the rate determining step is no longer electrochemical but the chemical dissolution of the oxide.1... 

An ultimate objective of this work is the application to more complicated processes such as ion-molecule reactions and charge exchange. In such processes it is quite clear that relatively long-lived complexes must be involved. Systems of interest will usually involve more than one accessible potential surface. The rate-determining step in a given reaction is likely to be the transfer from one potential surface to another or the decomposition of a collision complex in competition with other possible modes (channels). 

Without a catalyst, the reaction between N2 and H2 occurs only slowly, since the activation barrier for the dissociation of N2 and H2 in the gas phase is very high. In the presence of a suitable catalyst such as Fe, dissociation of N2 and H2 to give adsorbed atoms is facile, with the energy released by the formation of M—N and M—H bonds more than offsetting the energy required for N=N and H—H fission. The adsorbates then readily combine to form NH3 which desorbs from the surface. The rate-determining step is the dissociative adsorption of N2 (equation 26.30) the notation (ad) refers to an adsorbed atom. 

The OH binding effects on ORR on Ag(hkl) surfaces were studied by Markovic et al. [46,47]. Similar to that on Pt surfaces, the rate-determining step (rds) for the... 

Xu et al. used the conical intersection concept applied earlier in computations on aromatic nitration. They maintain that the initial interaction of benzene with a nitronium cation could either involve an initial single-electron transfer or a polar conventional two-electron-transfer electrophilic mechanism, involving a vr-complex, since both intermediates are minima on the potential energy surface. The rate-determining step could be either the formation of the first complex or the ET, depending on the system and experimental conditions. They believe that the latter... 

The measurement of a from the experimental slope of the Tafel equation may help to decide between rate-determining steps in an electrode process. Thus in the reduction water to evolve H2 gas, if the slow step is the reaction of with the metal M to form surface hydrogen atoms, M—H, a is expected to be about If, on the other hand, the slow step is the surface combination of two hydrogen atoms to form H2, a second-order process, then a should be 2 (see Ref. 150). 

Some early observations on the catalytic oxidation of SO2 to SO3 on platinized asbestos catalysts led to the following observations (1) the rate was proportional to the SO2 pressure and was inversely proportional to the SO3 pressure (2) the apparent activation energy was 30 kcal/mol (3) the heats of adsorption for SO2, SO3, and O2 were 20, 25, and 30 kcal/mol, respectively. By using appropriate Langmuir equations, show that a possible explanation of the rate data is that there are two kinds of surfaces present, 5 and S2, and that the rate-determining step is... 

The mechanism of the synthesis reaction remains unclear. Both a molecular mechanism and an atomic mechanism have been proposed. Strong support has been gathered for the atomic mechanism through measurements of adsorbed nitrogen atom concentrations on the surface of model working catalysts where dissociative N2 chemisorption is the rate-determining step (17). The likely mechanism, where (ad) indicates surface-adsorbed species, is as follows ... 

It was found that [5-7] the rate of flocculation of particles produced by the bridging action of polymer is the slower process and, consequently, the rate-determining step. The primary adsorption of polymer is fairly rapid, but the slow attainment of the adsorption equilibrium under agitation arises at least in part from the breakdown of floes offering new surfaces for adsorption. Thus, the bridging step is slow because a polymer adsorbed on one particle must find another particle having a free surface available to complete the bridge. 

If the rate-determining step were not a surface reaction but adsorption of competing reactants, we should obtain from the corresponding equations the expression which is formally identical with Eq. (15), in which, however, the relative reactivity is given by the expression S = fc dsA/ adsB. On the basis of data on competitive reactions only, these two cases cannot there-... 

When the temperature of the analyzed sample is increased continuously and in a known way, the experimental data on desorption can serve to estimate the apparent values of parameters characteristic for the desorption process. To this end, the most simple Arrhenius model for activated processes is usually used, with obvious modifications due to the planar nature of the desorption process. Sometimes, more refined models accounting for the surface mobility of adsorbed species or other specific points are applied. The Arrhenius model is to a large extent merely formal and involves three effective (apparent) parameters the activation energy of desorption, the preexponential factor, and the order of the rate-determining step in desorption. As will be dealt with in Section II. B, the experimental arrangement is usually such that the primary records reproduce essentially either the desorbed amount or the actual rate of desorption. After due correction, the output readings are converted into a desorption curve which may represent either the dependence of the desorbed amount on the temperature or, preferably, the dependence of the desorption rate on the temperature. In principle, there are two approaches to the treatment of the desorption curves. 

Calderbank et al. (C6) studied the Fischer-Tropsch reaction in slurry reactors of 2- and 10-in. diameters, at pressures of 11 and 22 atm, and at a temperature of 265°C. It was assumed that the liquid-film diffusion of hydrogen from the gas-liquid interface is a rate-determining step, whereas the mass transfer of hydrogen from the bulk liquid to the catalyst was believed to be rapid because of the high ratio between catalyst exterior surface area and bubble surface area. The experimental data were not in complete agreement with a theoretical model based on these assumptions. 

Independently of this, chronoabsorptiometric measurements by Genies et al. have proved that PPy films grow in timer linear to t and not to j/t. In the opinion of the authors this implies that the rate-determining step during film growth is a radical ion coupling and not the diffusion of the uncharged monomer towards the electrode surface. The attested phenomenon that PPy polymerizes... 

Rate of Formation of Primary Precursors. A steady state radical balance was used to calculate the concentration of the copolymer oligomer radicals in the aqueous phase. This balance equated the radical generation rate with the sum of the rates of radical termination and of radical entry into the particles and precursors. The calculation of the entry rate coefficients was based on the hypothesis that radical entry is governed by mass transfer through a surface film in parallel with bulk diffusion/electrostatic attraction/repulsion of an oligomer with a latex particle but in series with a limiting rate determining step (Richards, J. R. et al. J. AppI. Polv. Sci.. in press). Initiator efficiency was... 

It is important to realize that the assumption of a rate-determining step limits the scope of our description. As with the steady state approximation, it is not possible to describe transients in the quasi-equilibrium model. In addition, the rate-determining step in the mechanism might shift to a different step if the reaction conditions change, e.g. if the partial pressure of a gas changes markedly. For a surface science study of the reaction A -i- B in an ultrahigh vacuum chamber with a single crystal as the catalyst, the partial pressures of A and B may be so small that the rates of adsorption become smaller than the rate of the surface reaction. 

The partial oxidation of propylene occurs via a similar mechanism, although the surface structure of the bismuth-molybdenum oxide is much more complicated than in Fig. 9.17. As Fig. 9.18 shows, crystallographically different oxygen atoms play different roles. Bridging O atoms between Bi and Mo are believed to be responsible for C-H activation and H abstraction from the methyl group, after which the propylene adsorbs in the form of an allyl group (H2C=CH-CH2). This is most likely the rate-determining step of the mechanism. Terminal O atoms bound to Mo are considered to be those that insert in the hydrocarbon. Sites located on bismuth activate and dissociate the O2 which fills the vacancies left in the coordination of molybdenum after acrolein desorption. 

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