Mass transport kinetic factor

The magnitude of the response current of the amperometric glucose biosensor shown in Figure 7.1 depends on four main factors. First, mass-transport kinetics determine the rates at which substrates can be supplied to, and products removed from, the reaction layer in which enzyme is trapped. Second, enzyme kinetics... 

The intrinsic activity depends on the chemical and physical properties of the active component. For unsupported catalysts, the most important properties are the composition and structure of the catalyst surface and the presence, or absence, of special sites such as Br0nsted or Lewis acid centers, anion or cation defects, and sites of high coordination. For supported catalysts, the size and morphology of the dispersed phase are of additional importance. If intraparticle transport of reactants occurs with a characteristic time that is short compared to that of the reaction, then the observed and intrinsic rates of reaction will be identical. When the characteristic time for intraparticle mass transport is less than that for reaction, the observed rate of reaction per unit mass of catalyst becomes less than the intrinsic value, and the reaction kinetics are dominated by the effects of intraparticle mass transport. The factors governing intraparticle transport are the diffusivities of the reactants and products and the characteristic distance for diffusion. 

The key point is that, in general, the phase behavior of a given reaction system wiU not be known prior to the development of that process. Moreover, in those cases where data are available in the literature, they often refer to mixtures far more dilute than would be used in a commercial process. In such a process, energy and plant costs will clearly dictate that the reaction mixture should contain the minimum amount of SCF (see Beckman s constraint 2 e). This contrasts with SCF extraction, where the concentration of the extract dissolved in the SCF is determined, at least in part, by the mass-transport kinetics on the matrix material. All of these factors mean that the phase behavior of the reaction mixture wiU usuaUy have to be determined by experimental methods. 

PEM fuel cell characteristics are generally described with polarization curves. The thermodynamic equilibrium potential of the hydrogen/oxygen reaction is reduced by various overvoltage terms that depend on mass transport, kinetic, and ohmic phenomena within cell. In other words, the output voltage of a single cell is attributable to different current, temperature, and pressure dependant factors [1]. 

Influence of the Kinetics of Electron Transfer on the Faradaic Current The rate of mass transport is one factor influencing the current in a voltammetric experiment. The ease with which electrons are transferred between the electrode and the reactants and products in solution also affects the current. When electron transfer kinetics are fast, the redox reaction is at equilibrium, and the concentrations of reactants and products at the electrode are those specified by the Nernst equation. Such systems are considered electrochemically reversible. In other systems, when electron transfer kinetics are sufficiently slow, the concentration of reactants and products at the electrode surface, and thus the current, differ from that predicted by the Nernst equation. In this case the system is electrochemically irreversible. 

Figure 10 shows that Tj is a unique function of the Thiele modulus. When the modulus ( ) is small (- SdSl), the effectiveness factor is unity, which means that there is no effect of mass transport on the rate of the catalytic reaction. When ( ) is greater than about 1, the effectiveness factor is less than unity and the reaction rate is influenced by mass transport in the pores. When the modulus is large (- 10), the effectiveness factor is inversely proportional to the modulus, and the reaction rate (eq. 19) is proportional to k ( ), which, from the definition of ( ), implies that the rate and the observed reaction rate constant are proportional to (1 /R)(f9This result shows that both the rate constant, ie, a measure of the intrinsic activity of the catalyst, and the effective diffusion coefficient, ie, a measure of the resistance to transport of the reactant offered by the pore stmcture, influence the rate. It is not appropriate to say that the reaction is diffusion controlled it depends on both the diffusion and the chemical kinetics. In contrast, as shown by equation 3, a reaction in solution can be diffusion controlled, depending on D but not on k. 

Mass transfer and chemical kinetic factors in CVD include the flow of initial substances and gaseous products through the system, the transport of reactants from the gas phase to the substrate surface, the transport of the gaseous products from the substrate surface to the bulk gas, as well as the reactions taking place at the substrate surface . ... 

The HTE characteristics that apply for gas-phase reactions (i.e., measurement under nondiffusion-limited conditions, equal distribution of gas flows and temperature, avoidance of crosscontamination, etc.) also apply for catalytic reactions in the liquid-phase. In addition, in liquid phase reactions mass-transport phenomena of the reactants are a vital point, especially if one of the reactants is a gas. It is worth spending some time to reflect on the topic of mass transfer related to liquid-gas-phase reactions. As we discussed before, for gas-phase catalysis, a crucial point is the measurement of catalysts under conditions where mass transport is not limiting the reaction and yields true microkinetic data. As an additional factor for mass transport in liquid-gas-phase reactions, the rate of reaction gas saturation of the liquid can also determine the kinetics of the reaction [81], In order to avoid mass-transport limitations with regard to gas/liquid mass transport, the transfer rate of the gas into the liquid (saturation of the liquid with gas) must be higher than the consumption of the reactant gas by the reaction. Otherwise, it is not possible to obtain true kinetic data of the catalytic reaction, which allow a comparison of the different catalyst candidates on a microkinetic basis, as only the gas uptake of the liquid will govern the result of the experiment (see Figure 11.32a). In three-phase reactions (gas-liquid-solid), the transport of the reactants to the surface of the solid (and the transport from the resulting products from this surface) will also... 

The published values for the activation energies and pre-exponential factors of transesterification and glycolysis vary significantly. Catalysts and stabilizers influence the overall reaction rate markedly, and investigations using different additives cannot be compared directly. Most investigations are affected by mass transport and without knowledge of the respective mass transport parameters, kinetic results cannot be transferred to other systems. 

It was assumed that there were no limitations on the rates of oxidation due to mass transport as discussed in detail by Schwartz and Freiberg (1981), this assumption is justified except for very large droplets (> 10 yarn) and high pollutant concentrations (e.g., 03 at 0.5 ppm) where the aqueous-phase reactions are very fast. It was also assumed that the aqueous phase present in the atmosphere was a cloud with a liquid water content (V) of 1 g m-3 of air. As seen earlier, the latter factor is important in the aqueous-phase rates of conversion of S(IV) thus the actual concentrations of iron, manganese, and so on in the liquid phase and hence the kinetics of the reactions depend on the liquid water content. 

As pointed out earlier, CVD is a steady-state, but rarely equilibrium, process. It can thus be rate-limited by either mass transport (steps 2, 4, and 7) or chemical kinetics (steps 1 and 5 also steps 3 and 6, which can be described with kinetic-like expressions). What we seek from this model is an expression for the deposition rate, or growth rate of the thin film, on the substrate. The ideal deposition expression would be derived via analysis of all possible sequential and competing reactions in the reaction mechanism. This is typically not possible, however, due to the lack of activation or adsorption energies and preexponential factors. The most practical approach is to obtain deposition rate data as a function of deposition conditions such as temperature, concentration, and flow rate and fit these to suspected rate-limiting reactions. 

In this article, the authors have attempted to supply a reference to the majority of pertinent papers on gas-carbon reactions. Reasons for the large amount of apparently conflicting data on orders and activation energies for the reactions are advanced. A detailed quantitative discussion of the role which inherent chemical reactivity of the carbon and mass transport of the reactants and products can play in affecting the kinetics of gas-carbon reactions is presented. The possibilities of using bulk-density and surface-area profile data on reacted carbons for better understanding of reaction mechanisms is discussed. Finally, some factors, other than mass transport, affecting gas-carbon reactions are reviewed. 

Note, however, that EM is not determined by the thermodynamic equilibrium potentials Ef and E2 but by the kinetics of the respective reactions, i.e. by the respective anodic and cathodic component curves in Fig. 13(a) with the condition indicated by eqn. (190). These curves may be altered by mass transport conditions, surface area and, specific properties and consequently the mixed potential EM may be susceptible to those kinetic factors, unlike the equilibrium potential of each partial electrode reaction which is fixed by thermodynamics and the activities in the bulk solution. 

Equation (6) is valid only if it is justly assumed that the equilibrium values of qM and E are established infinitely quickly. This is not the case at low electrolyte concentrations since then the diffusion of the ions composing the double-layer becomes a rate-determining factor. In other words, mass transport complicates the charging process. For practical reasons, studies of electrode kinetics are usually made in well-conducting solutions, so that this effect can be ignored. 

In FPTRMS, transport of the reactive species of interest from the reactor to the detector can make a contribution to the observed time dependence such that the chemical kinetics becomes convoluted with mass transport rates. This will have to be accounted for in data analysis if reliable rate coefficients are to be obtained. If the physical rate processes are sufficiently fast they will make a negligible contribution to the kinetics. In this section we examine the above four factors to see when they influence the chemical kinetics. The first, third, and fourth items put an upper limit on the rate at which decays and growths can be reliably determined, and the second one sets a lower limit on the decay rate. 

This expression of the current-potential relationship is totally general. For each particular situation, the expressions of the rate constants (through a given kinetic model) and of the limiting currents and mass transport coefficients should be provided to analyze the influence of the different factors that can control the global rate. 

We have used CO oxidation on Pt to illustrate the evolution of models applied to interpret critical effects in catalytic oxidation reactions. All the above models use concepts concerning the complex detailed mechanism. But, as has been shown previously, critical. effects in oxidation reactions were studied as early as the 1930s. For their interpretation primary attention is paid to the interaction of kinetic dependences with the heat-and-mass transfer law [146], It is likely that in these cases there is still more variety in dynamic behaviour than when we deal with purely kinetic factors. A theory for the non-isothermal continuous stirred tank reactor for first-order reactions was suggested in refs. 152-155. The dynamics of CO oxidation in non-isothermal, in particular adiabatic, reactors has been studied [77-80, 155]. A sufficiently complex dynamic behaviour is also observed in isothermal reactors for CO oxidation by taking into account the diffusion both in pores [71, 147-149] and on the surfaces of catalyst [201, 202]. The simplest model accounting for the combination of kinetic and transport processes is an isothermal continuously stirred tank reactor (CSTR). It was Matsuura and Kato [157] who first showed that if the kinetic curve has a maximum peak (this curve is also obtained for CO oxidation [158]), then the isothermal CSTR can have several steady states (see also ref. 203). Recently several authors [3, 76, 118, 156, 159, 160] have applied CSTR models corresponding to the detailed mechanism of catalytic reactions. 

Kinetics of Immobilized Enzymes. Another major factor in the performance of immobilized enzymes is the effect of the matrix on mass transport of substrates and products. Hindered access to the active site of an immobilized enzyme can affect the kinetic parameters in several ways. The effective concentration of substrates and products is also affected by the chemistry of the matrix especially with regard to the respective partition coefficients between the bulk solution and the matrix. In order to understand the effects of immobilization upon the rate of an enzyme-catalyzed reaction one must first consider the relationship between the velocity of an enzyme-catalyzed reaction and the... 

With continuing increase in anode potential, the current-potential relationship deviates from the linear relationship. As the potential continues to increase, the increase in the current slows down until it reaches a maximum and then decreases to a minimum point, and finally increases to the limiting current plateau. This is a transition from kinetics of electrochemical reaction domain to mass transport domain. This region may have a very different shape depending on electrolytes, potential scan rate, and other factors. Details of this region are discussed elsewhere [7,8]. 

Numerous studies on the kinetics and mechanisms of CVD reactions have been made. These studies provide useful information such as activation energy and limiting steps of deposition reactions which are important for the understanding of deposition processes. The main problem in the CVD kinetics studies is the complexity of the deposition process. The difficulty arises not only from the various steps of the CVD process but also from the temperature and concentration gradient, geometric effects, and gas flow patterns in the reaction zones. Exact kinetic analysis is therefore usually not possible as the kinetic data are reactor dependent. There are several possible rate-limiting factors but mass transport and surface kinetics control are the most... 

The mass-transport-limited current density for oxygen reduction is independent of the kinetic parameters for this reaction rather it depends on factors such as the concentration and the diffusion coefficient of oxygen in the medium. It depends oh the rate of flow of the liquid in a pipe or around a sailing ship or a structure immersed in a river. 

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