Surface reaction resistance

Finally, when the surface reaction resistance controls the global rate, k Cso mA and k Cso Dqa/ s, Eq. (11) becomes... 

The surface reaction resistance is most likely to be important at lower reaction temperatures and is the only resistance that can truly be rate controlling throughout the entire reaction. 

Such characteristic horizontal bands, as shown in Figure 5.43, might be termed adsorption multiplicity since they arise primarily from the interactions of external film heat and mass transfer resistances with the adsorption resistance. For smaller adsorption resistance, the horizontal bands disappear giving way to the more familiar multiplicity regions, arising from the interactions of physical transport and surface reaction resistances. 

Reaction spraying is also being widely explored. In this case new compositions or particle surface reactions providing enhanced coating properties, eg, nitrides for wear resistance, are achieved while the particle is in transit. 

Thermodynamic data suggest that P -alumina is stable in sulfur and that Na20-rich //"-alumina maybe unstable to some degree. In the latter event, depletion of Na20 from / " -alumina according to Eq. (5) would result in a surface layer resistant to further corrosion. A significant corrosion reaction does occur be-... 

As our first approach to the model, we considered the controlling step to be the mass transfer from gas to liquid, the mass transfer from liquid to catalyst, or the catalytic surface reaction step. The other steps were eliminated since convective transport with small catalyst particles and high local mixing should offer virtually no resistance to the overall reaction scheme. Mathematical models were constructed for each of these three steps. 

The model postulates two significant resistances in series diffusion through the growing shell ( R.jyp) and polymerization at the catalyst surface (R(jat catalytic reaction resistance,... 

As discussed in Chapter 7, this form can provide a good fit of the data if the reaction is not too close to equilibrium. However, most reaction engineers prefer a mechanistically based rate expression. This section describes how to obtain plausible functional forms for based on simple models of the surface reactions and on the observation that aU the rates in Steps 2 through 8 must be equal at steady state. Thus, the rate of transfer across the film resistance equals the rate of diffusion into a pore equals the rate of adsorption equals the rate of reaction equals the rate of desorption, and so on. This rate is the pseudohomo-geneous rate shown in Steps 1 and 9. 

Equation (1) consists of various resistance terms. l/Kj a is the gas absorption resistance, while 1/ K,a corresponds to the maleic anhydride diffusion resistance and l/i k represents the chemical reaction resistance. The reaction rate data obtained under the reaction conditions of 250°C and 70 atm were plotted according to equation (1). Although catalytic reaction data with respect to time on stream were not shown here, a linear correlation between reaction rate data and catalyst loading was observed as shown in Fig. 2. The gas absorption resistance (1/ a) was -1.26 h, while the combined reaction-diffusion resistance (lJK,a + 1 T]k) was determined to be 5.57 h. The small negative value of gas absorption resistance indicates that the gas-liquid diffusion resistance was very small and had several orders of magnitude less than the chanical reaction resistance, as similarly observed for the isobutene hydration over Amberlyst-15 in a slurry reactor [6]. This indicates that absorption of malei c anhydride in solvent was a rapid process compared to the reaction rate on the catalyst surface. 

The presence (or absence) of pore-diffusion resistance in catalyst particles can be readily determined by evaluation of the Thiele modulus and subsequently the effectiveness factor, if the intrinsic kinetics of the surface reaction are known. When the intrinsic rate law is not known completely, so that the Thiele modulus cannot be calculated, there are two methods available. One method is based upon measurement of the rate for differing particle sizes and does not require any knowledge of the kinetics. The other method requires only a single measurement of rate for a particle size of interest, but requires knowledge of the order of reaction. We describe these in turn. 

The rate is independent of particle size. This is an indication of neghgible pore-diffusion resistance, as might be expected for either very porous particles or sufficiently small particles such that the diffusional path-length is very small. In either case, i -> 1, and ( rA)obs = ( rA)inl for the surface reaction. 

Weisz-Prater criterion. The relative significance of pore-diffusion resistance can be assessed by a criterion, known as the Weisz-Prater (1954) criterion, which requires only a single measurement of the rate, together with knowledge of De, Le, and the order of the surface reaction (but not of the rate constant). 

Consider an nth-order surface reaction, represented by A(g) — product(s), occurring in a catalyst particle, with negligible external resistance to mass transfer so that cAs cAg- Then the observed rate of reaction is... 

As shown in Example 22-3, for solid particles of the same size in BMF, the form of the reactor model resulting from equation 22.2-13 depends on the kinetics model used for a single particle. For the SCM, this, in turn, depends on particle shape and the relative magnitudes of gas-film mass transfer resistance, ash-layer diffusion resistance and surface reaction rate. In some cases, as illustrated for cylindrical particles in Example 22-3(a) and (b), the reactor model can be expressed in explicit analytical form additional results are given for spherical particles by Levenspiel(1972, pp. 384-5). In other f l cases, it is convenient or even necessary, as in Example 22-3(c), to use a numerical pro-... 

Heterogeneously catalyzed hydrogenation is a three-phase gas-liquid-solid reaction. Hydrogen from the gas phase dissolves in the liquid phase and reacts with the substrate on the external and internal surfaces of the solid catalyst Mass transfer can influence the observed reaction rate, depending on the rate of the surface reaction [15]. Three mass transfer resistances may be present in this system (Fig. 42.1) ... 

In Fig. 7.27, there appears a single capacitive reactance loop in different pH media. The eapacitive reactance loop radius is bigger in the lime medium than that without lime. The reaction resistance increases from 14000 in the absence of lime to 15000 in the presence of lime. EIS exhibits passivation characteristic. The results indicate the formation of surface oxidation products which prevent the transferring of electron, giving rise to the increase of surface resistance and descending of corrosive current. It may be mainly because of the following reactions on the surface of galena in the lime medium besides Eq. (7-12) ... 

The latter authors used anode and cathode symmetrical cells in EIS analysis in order to simplify the complication that often arises from asymmetrical half-cells so that the contributions from anode/ electrolyte and cathode/electrolyte interfaces could be isolated, and consequently, the temperature-dependences of these components could be established. This is an extension of their earlier work, in which the overall impedances of full lithium ion cells were studied and Ret was identified as the controlling factor. As Figure 68 shows, for each of the two interfaces, Ra dominates the overall impedance in the symmetrical cells as in a full lithium ion cell, indicating that, even at room temperature, the electrodic reaction kinetics at both the cathode and anode surfaces dictate the overall lithium ion chemistry. At lower temperature, this determining role of Ra becomes more pronounced, as Figure 69c shows, in which relative resistance , defined as the ratio of a certain resistance at a specific temperature to that at 20 °C, is used to compare the temperature-dependences of bulk resistance (i b), surface layer resistance Rsi), and i ct- For the convenience of comparison, the temperature-dependence of the ion conductivity measured for the bulk electrolyte is also included in Figure 69 as a benchmark. Apparently, both and Rsi vary with temperature at a similar pace to what ion conductivity adopts, as expected, but a significant deviation was observed in the temperature dependence of R below —10 °C. Thus, one... 

Iso-UP has ester bonds only in the main chain where hydrolysis occurs, so a part of reaction products from the main chain dissolves into the solution. While the crosslink formed by styrene remains unaffected because of its stable C-C bonding. As a result, the corroded surface layer resists the diffusion of NaOH solution. This mechanism is just like an oxidation of the metal at high temperature with formation of thick, cohered oxide scale, and can be expressed by similar relation of Wagner s parabolic law as shown in Equation 2. The concept of corrosion in metals can be applied in this case too. 

For ash-free particles which shrink with reaction, only two resistances, gas film and surface reaction, need to be considered. Because these are both based on the changing exterior surface of particles, we may combine them to give at any instant... 

Since no ash is formed at any time during reaction, we have here a case of kinetics of shrinking particles for which two resistances at most, surface reaction and gas film, may play a role. In terms of these, the overall rate constant at any instant from Eq. 35 is... 

Because of the poor oxide, passivation of germanium surfaces is required for practical use of this semiconductor in devices. Although an ideally passivated surface would resist oxidation and degradation perfectly, such complete resistance is not possible in practice. For this discussion, we consider passivated surfaces as those that strengthen resistance to oxidation in both ambient air and aqueous solution. Three different surface terminating layers are reviewed sulfide-, chloride-, and hydride-terminated germanium. To date, sulfide termination creates the most ideal passivating layer, whereas both chloride and hydride termination add limited stability sufficient to alter the surface reactivity in a way that allows for further reaction. 

Here, k can be visualized as the number of successful jumps per unit time across the surface energy barrier eb into the reaction volume (Fig. 5-9). A particularly useful form for k is found if one regards 1/Ar to be a generalized resistivity obtained by adding together the diffusional and the reactional resistivities... 

FIGURE 12.11 Although aluminum has a negative standard potential, signifying that it can be oxidized by hydrogen ions, nitric acid stops reacting with it as soon as an impenetrable layer of aluminum oxide has formed on its surface. This resistance to further reaction is termed passivation of the metal. 

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