Surface reaction coefficients

The plasma-wall interaction of the neutral particles is described by a so-called sticking model [136, 137]. In this model only the radicals react with the surface, while nonradical neutrals (H2, SiHa, and Si H2 +2) are reflected into the discharge. The surface reaction and sticking probability of each radical must be specified. The nature (material, roughness) and the temperature of the surface will influence the surface reaction probabilities. Perrin et al. [136] and Matsuda et al. [137] have shown that the surface reaction coefficient of SiH3 is temperature-independent at a value of = 0.26 0.05 at a growing a-Si H surface in a... 

Information about the surface reaction coefficients of radicals Si H2 +i where n > 1 is scarce. Because the structure of these radicals is similar to that of SiH3, the same surface reaction coefficients are used. It is assumed that if Si H2 i+1 radicals recombine at the surface with a hydrogen atom, a Si H2,+2 neutral is formed and is reflected into the discharge. Another possibility is the surface recombination of Si,H2 +i radicals with physisorbed Si ,H2m + i radicals at the surface. Matsuda et al. [137] have shown that the probability of surface recombination of SiHs with physisorbed SiH3 decreases with increasing substrate temperature. Doyle et al. [204] concluded that at a typical substrate temperature of 550 K, SiH3 radicals mainly recombine with physisorbed H atoms. 

For the SiH2 radicals the surface reaction coefficients have been taken as 5 = P = 0.8 [192]. This sticking coefficient is large because there is no barrier for insertion of this species into the a-Si H surface. Kae-Nune et al. [217] specify a surface recombination probability of about 1 for atomic hydrogen on an a-Si H surface during deposition that results mainly in recombination of H with an H-atom bounded to the surface. 

A possible explanation for the difference in tendencies of the deposition rate between experiment and model is that in the model the surface reaction and sticking coefficients of the radicals are taken to be independent of the discharge characteristics. In fact, these surface reaction coefficients may be influenced by the ions impinging on the surface [251]. An impinging ion may create an active site (or dangling bond) at the surface, which enhances the sticking coefficient. Recent experiments by Hamers et al. [163] corroborate this the ion flux increases with the RF frequency. However, Sansonnens et al. [252] show that the increase of deposition rate cannot be explained by the influence of ions only. 

Nienhuis [189] has used a fitting procedure for the seven most sensitive elementary parameters (reactions SiH4 -t- SiH2 and Si2H6 -I- SiHi, dissociation branching ratio of SiH4, surface reaction coefficient and sticking probability of SiHa, and diffusion coefficients of SiH and H). In order to reduce the discrep-... 

A sticking model is used for the plasma-wall interaction [137]. In this model each neutral particle has a certain surface reaction coefficient, which specifies the probability that the neutral reacts at the surface when hitting it. In case of a surface reaction two events may occur. The first event is sticking, which in the case of a silicon-containing neutral leads to deposition. The second event is recombination, in which the radical recombines with a hydrogen atom at the wall and is reflected back into the discharge. 

It might be thought possible that the diffusional and surface reaction coefficients could be quantified by making certain assumptions. For example, if it is assumed that the diffusional mass transfer coefficient, k, in the crystallization... 

When the mass-transfer coefficient ky is very large, the surface reaction is controlling and 1/k is negligible. Conversely, when the mass-transfer coefficient is very small, diffusional resistance is controlling. Surface reaction coefficients and overall transfer coefficients have been measured and reported on a number of systems (B4, H2, P3, V1). Much of the information in the literature is not directly applicable, because the conditions of measurement differ greatly from those in a commercial crystallizer. Also, the velocities and the level of supersaturation in a system are difficult to determine, and vary with position of the circulating magma in the crystallizer. 

Fleig J, Maier J (2004) The polarization of mixed conducting SOFC cathodes Effects of surface reaction coefficient, ionic conductivity and geometry. J Eur Ceram Soc 24 1343... 

Very recently, considerable effort has been devoted to the simulation of the oscillatory behavior which has been observed experimentally in various surface reactions. So far, the most studied reaction is the catalytic oxidation of carbon monoxide, where it is well known that oscillations are coupled to reversible reconstructions of the surface via structure-sensitive sticking coefficients of the reactants. A careful evaluation of the simulation results is necessary in order to ensure that oscillations remain in the thermodynamic limit. The roles of surface diffusion of the reactants versus direct adsorption from the gas phase, at the onset of selforganization and synchronized behavior, is a topic which merits further investigation. 

From the results of this kinetic study and from the values of the adsorption coefficients listed in Table IX, it can be judged that both reactions of crotonaldehyde as well as the reaction of butyraldehyde proceed on identical sites of the catalytic surface. The hydrogenation of crotyl alcohol and its isomerization, which follow different kinetics, most likely proceed on other sites of the surface. From the form of the integral experimental dependences in Fig. 9 it may be assumed, for similar reasons as in the hy-drodemethylation of xylenes (p. 31) or in the hydrogenation of phenol, that the adsorption or desorption of the reaction components are most likely faster processes than surface reactions. 

A and E refer to the desorption, dissociation, decomposition or other surface reactions by which the reactant or reactants represented by M are converted into products. If [M] is constant within the temperature interval studied, then the values of A and E measured refer to this process. Alternatively, if the effective magnitude of [M] varies with temperature, the apparent Arrhenius parameters do not specifically refer to the product evolution step. This is demonstrated quantitatively by the following example [36]. When E = 100 kJmole-1 andA [M] = 3.2 X 1030 molecules sec-1, then rate coefficients at 400 and 500 K are 2.4 X 1017 and 1.0 X 1020 molecules sec-1, respectively. If, however, E is again 100 kJ mole-1 and A [M] varies between 3.2 X 1030 molecules sec-1 at 500 K and z X 3.2 X 1030 molecules sec-1 at 400 K, the measured values of A and E vary significantly, as shown in Fig. 7, when z ranges from 10-3 to 103. Thus, the measured value of E is not necessarily identifiable with the rate-limiting step if a concentration of a participant is temperature-dependent. This... 

In the case of control by surface reaction kinetics, the rate is dependent on the amount of reactant gases available. As an example, one can visualize a CVD system where the temperature and the pressure are low. This means that the reaction occurs slowly because of the low temperature and there is a surplus of reactants at the surface since, because of the low pressure, the boundary layer is thin, the diffusion coefficients are large, and the reactants reach the deposition surface with ease as shown in Fig. 2.8a. 

Forward rate constant for reversible surface reaction Exam. 10.2 Reverse rate constant for reversible surface reaction Exam. 10.2 Mass transfer coefficient for a catalyst particle 10.2... 

As described in Chapter 3, v ,/ and so on are the reaction coefficients by which species are made up from the current basis entries. Mass transfer coefficients are not needed for gases in the basis, because no accounting of mass balance is maintained on the external buffer, and the coefficients for the mole numbers Mp of the surface sites are invariably zero, since sites are neither created nor destroyed by a properly balanced reaction. 

Here A(g) and B(g) denote reactant and product in the bulk gas at concentrations CA and Cg, respectively kAg and kBg are mass-transfer coefficients, s is an adsorption site, and A s is a surface-reaction intermediate. In this scheme, it is assumed that B is not adsorbed. In focusing on step (3) as the rate-determining step, we assume kAg and kBg are relatively large, and step (2) represents adsorption-desorption equilibrium. 

Experimental data are shown for the rate of a surface catalyzed reaction, 2A = B. It is expected that the rates of surface reaction and diffsion to the surface both are factors. The diffusional coefficient is kd = 137.5. 

Heterogeneous uptake on surfaces has also been documented for various free radicals (DeMore et al., 1994). Table 3 shows values of the gas/surface reaction probabilities (y) of the species assumed to undergo loss to aerosol surface in the model. Only the species where a reaction probability has been measured at a reasonable boundary layer temperature (i.e. >273 K) and on a suitable surface for the marine boundary layer (NaCl(s) or liquid water) have been included. Unless stated otherwise, values for uptake onto NaCl(s), the most likely aerosol surface in the MBL (Gras and Ayers, 1983), have been used. Where reaction probabilities are unavailable mass accommodation coefficients (a) have been used instead. The experimental values of the reaction probability are expected to be smaller than or equal to the mass accommodation coefficients because a is just the probability that a molecule is taken up on the particle surface, while y takes into account the uptake, the gas phase diffusion and the reaction with other species in the particle (Ravishankara, 1997). 

Model fits of the experimental data show that it is also possible to use simplified first-order elementary reaction kinetics for these catalysts to approximate the WGS reaction as a single reversible surface reaction. Furthermore, the fitted values for the pre-exponential coefficients and the activation energies have been evaluated and are not much different from other data available in the open literature. 

It also follows from analogy to coordination chemistry of solutions that the apparent macroscopic stoichiometric coefficient for [H+] should be affected by pH. For example, the mole-fraction averaged proton release from the two competing surface reactions... 

To what extent is the macroscopic proton release the direct expression of the metal/surface site reactions Table V compares the macroscopic proton coefficients (Xp ) ) with the coefficient expected if only the Cd(II) surface reactions are considered is the proton coefficient determined by considering the mole fraction of Cd(II) surface species and their formation reactions (Figure 14b). For example, when pSOH is 2.84, y = 0.11 x 1 + 0.89 x 2 = 1.89. At high alumina concentrations pSOH 2.14-2.53) the single surface reaction required to fit the data sets a limiting proton release of 2.0. 

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