Diffusion of reactants

The sequence of events in a surface-catalyzed reaction comprises (1) diffusion of reactants to the surface (usually considered to be fast) (2) adsorption of the reactants on the surface (slow if activated) (3) surface diffusion of reactants to active sites (if the adsorption is mobile) (4) reaction of the adsorbed species (often rate-determining) (5) desorption of the reaction products (often slow) and (6) diffusion of the products away from the surface. Processes 1 and 6 may be rate-determining where one is dealing with a porous catalyst [197]. The situation is illustrated in Fig. XVIII-22 (see also Ref. 198 notice in the figure the variety of processes that may be present). 

For weU-defined reaction zones and irreversible, first-order reactions, the relative reaction and transport rates are expressed as the Hatta number, Ha (16). Ha equals (k- / l ) where k- = reaction rate constant, = molecular diffusivity of reactant, and k- = mass-transfer coefficient. Reaction... 

Pore diameter and distribution are important factors. Small pores limit the accessibihty of internal surface because of increased resistance to diffusion of reactants inwards. Diffusion of products outwards also is slowed, and degradation of those produces may result. 

Diffusion of reactants and products within the pores of the catalyst... 

In contrast to the influence of velocity, whose primary effect is to increase the corrosion rates of electrode processes that are controlled by the diffusion of reactants, temperature changes have the greatest effect when the rate determining step is the activation process. In general, if diffusion rates are doubled for a certain increase in temperature, activation processes may be increased by 10-100 times, depending on the magnitude of the activation energy. 

Active-passive transition It has been shown that /p, the current required to maintain a passive film, increases with temperature at a much greater rate than the critical current for passivation as a result of an activation-controlled process. At some temperature /p will exceed /pri,. and no active-passive transition will be observed, and more important no protection by a passive film is possible because of the high rate of dissolution. At this stage the slow process becomes the diffusion of reactants and control of the rate is... 

Many high-pressure reactions are done neat, but if a solvent is used, the influence of pressure on that solvent is important. The melting point generally increases at elevated pressures, which influences the viscosity of the medium (viscosity of liquids increases approximately two times per kilobar increase in pressure). Controlling the rate of diffusion of reactants in the medium is also important. In most reactions, pressure is applied (5-20kbar) at room temperature, and then the temperature is increased until reaction takes place. 

Step 7. Product species diffuse outward through the pores, the governing equations being similar to those used for the inward diffusion of reactants ... 

The stability of catalyst is one of the most important criteria to evaluate its quality. The influence of time on stream on the conversion of n-heptane at SSO C is shown in Fig. 5. The conversion of n-heptane decreases faster on HYl than on FIYs with time, so the question is Could the formation of coke on the catalyst inhibit diffusion of reactant into the caves and pores of zeolite and decrease the conversion According to Hollander [8], coke was mainly formed at the beginning of the reaction, and the reaction time did not affect the yield of coke. Hence, this decrease might be caused by some impurities introduced during the catalyst synthesis. These impurities could be sintered and cover active sites to make the conversion of n-heptane on HYl decrease faster. 

Shape selective catalysis as typically demonstrated by zeolites is of great interest from scientific as well as industrial viewpoint [17], However, the application of zeolites to organic reactions in a liquid-solid system is very limited, because of insufficient acid strength and slow diffusion of reactant molecules in small pores. We reported preliminarily that the microporous Cs salts of H3PW12O40 exhibit shape selectivity in a liquid-solid system [18]. Here we studied in more detail the acidity, micropore structure and catal3rtic activity of the Cs salts and wish to report that the acidic Cs salts exhibit efficient shape selective catalysis toward decomposition of esters, dehydration of alcohol, and alkylation of aromatic compound in liquid-solid system. The results were discussed in relation to the shape selective adsorption and the acidic properties. 

For catalytic reactions carried out in the presence of a heterogeneous catalyst, the observed reaction rate could be determined by the rate of mass transfer from the bulk of the reaction mixture and the outer surface of the catalyst particles or the rate of diffusion of reactants within the catalyst pores. Consider a simple first order reaction its rate must be related to the concentration of species S at the outer surface of the catalyst as follows ... 

If diffusion of reactants to the active sites in pores is slower than the chemical reaction, internal mass transfer is at least partly limiting and the reactant concentration decreases along the pores. This reduces the reaction rate compared to the rate at external surface conditions. A measure of the reaction rate decrease is the effectiveness factor, r, which has been defined as ... 

The selectivity in a system of parallel reactions does not depend much on the catalyst size if effective diffusivities of reactants, intermediates, and products are similar. The same applies to consecutive reactions with the product desired being the final product in the series. In contrast with this, for consecutive reactions in which the intermediate is the desired product, the selectivity much depends on the catalyst size. This was proven by Edvinsson and Cybulski (1994, 1995) for. selective hydrogenations and also by Colen et al. (1988) for the hydrogenation of unsaturated fats. Diffusion limitations can also affect catalyst deactivation. Poisoning by deposition of impurities in the feed is usually slower for larger particles. However, if carbonaceous depositions are formed on the catalyst internal surface, ageing might not depend very much on the catalyst size. 

Kinetics of chemical reactions at liquid interfaces has often proven difficult to study because they include processes that occur on a variety of time scales [1]. The reactions depend on diffusion of reactants to the interface prior to reaction and diffusion of products away from the interface after the reaction. As a result, relatively little information about the interface dependent kinetic step can be gleaned because this step is usually faster than diffusion. This often leads to diffusion controlled interfacial rates. While often not the rate-determining step in interfacial chemical reactions, the dynamics at the interface still play an important and interesting role in interfacial chemical processes. Chemists interested in interfacial kinetics have devised a variety of complex reaction vessels to eliminate diffusion effects systematically and access the interfacial kinetics. However, deconvolution of two slow bulk diffusion processes to access the desired the fast interfacial kinetics, especially ultrafast processes, is generally not an effective way to measure the fast interfacial dynamics. Thus, methodology to probe the interface specifically has been developed. 

There was therefore a clear need to assess the assumptions inherent in the classical kinetic approach for determining surface-catalysed reaction mechanisms where no account is taken of the individual behaviour of adsorbed reactants, substrate atoms, intermediates and their respective surface mobilities, all of which can contribute to the rate at which reactants reach active sites. The more usual classical approach is to assume thermodynamic equilibrium and that surface diffusion of reactants is fast and not rate determining. 

Scanning electron microscopy and other experimental methods indicate that the void spaces in a typical catalyst particle are not uniform in size, shape, or length. Moreover, they are often highly interconnected. Because of the complexities of most common pore structures, detailed mathematical descriptions of the void structure are not available. Moreover, because of other uncertainties involved in the design of catalytic reactors, the use of elaborate quantitative models of catalyst pore structures is not warranted. What is required, however, is a model that allows one to take into account the rates of diffusion of reactant and product species through the void spaces. Many of the models in common use simulate the void regions as cylindrical pores for such models a knowledge of the distribution of pore radii and the volumes associated therewith is required. 

Now at steady state, the observed rate of reaction within the pore just balances the rate of diffusion of reactant into the pore... 

Under steady-state conditions, the reaction rate is equal to the rate of diffusion of reactant through the poisoned region. The latter may be written as... 

The obvious technological advantage of a heterogeneous catalyst is that it can be easily separated from reactants and products. However, the serious physical problem is diffusion of reactants to active centers on the surface of the catalyst and back diffusion of the formed intermediate and final products from the surface into the solution. This duffusion occurs much more slowly in the liquid phase compared to the gas phase. The problem of effectiveness of the heterogeneous catalyst in comparison with the homogeneous catalyst is closely connected with the problem of diffusion and sorption on the surface in the liquid phase. 

Dioxygen and oxidized substances react on the surface of the catalyst only. The pure heterogeneous reaction occurs only after diffusion of reactants to the catalytic surface and back diffusion of products from the surface into the solution. A combination of a few mechanisms of such types are possible. 

The sulfoxidation of alkanes occurs with heat evolution. This is the basis for rate of oscillation of rapid sulfoxidation at a relatively high pressure when the feedback arises between reaction rate, diffusion of reactants into liquid phase, and heat evolution [27],... 

The addition of dioxygen to sulfonyl radicals occurs very rapidly and is also limited by the diffusion of reactants in the solvent. The rate constant of the reaction... 

Rapid bimolecular reactions are limited by diffusion of reactants in the liquid and solid phases. Diffusion occurs in polymers much more slowly than in liquids. Hence, such rapid reactions as recombination of free radicals occurs in polymers with rate constants of a few order of magnitude more slowly than in solution. For example, the reaction of sterically hindered phenoxyl with the peroxyl radical... 

Reactions described earlier were not limited by rotational diffusion of reactants. It is evident that such bimolecular reactions can occur that are limited not by translational diffusion but by the rate of reactant orientation before forming the TS. We discussed the reactions of sterically hindered phenoxyl recombination in viscous liquids (see Chapter 15). We studied the reaction of the type radical + molecule, which are not limited by translational diffusion in a solution but are limited by the rate of reactant orientation in the polymer matrix [28]. This is the reaction of stable nitroxyl radical addition to the double bond of methylenequinone. 

It should be taken into account that the reaction of chain propagation occurs in polymer more slowly than in the liquid phase also. The ratios of rate constants kjlkq, which are so important for inhibition (see Chapter 14), are close for polymers and model hydrocarbon compounds (see Table 19.7). The effectiveness of the inhibiting action of phenols depends not only on their reactivity, but also on the reactivity of the formed phenoxyls (see Chapter 15). Reaction 8 (In + R02 ) leads to chain termination and occurs rapidly in hydrocarbons (see Chapter 15). Since this reaction is limited by the diffusion of reactants it occurs in polymers much more slowly (see earlier). Quinolide peroxides produced in this reaction in the case of sterically hindered phenoxyls are unstable at elevated temperatures. The rate constants of their decay are described in Chapter 15. The reaction of sterically hindered phenoxyls with hydroperoxide groups occurs more slowly in the polymer matrix in comparison with hydrocarbon (see Table 19.8). 

Photosensitization of diaryliodonium salts by anthracene occurs by a photoredox reaction in which an electron is transferred from an excited singlet or triplet state of the anthracene to the diaryliodonium initiator.13"15,17 The lifetimes of the anthracene singlet and triplet states are on the order of nanoseconds and microseconds respectively, and the bimolecular electron transfer reactions between the anthracene and the initiator are limited by the rate of diffusion of reactants, which in turn depends upon the system viscosity. In this contribution, we have studied the effects of viscosity on the rate of the photosensitization reaction of diaryliodonium salts by anthracene. Using steady-state fluorescence spectroscopy, we have characterized the photosensitization rate in propanol/glycerol solutions of varying viscosities. The results were analyzed using numerical solutions of the photophysical kinetic equations in conjunction with the mathematical relationships provided by the Smoluchowski16 theory for the rate constants of the diffusion-controlled bimolecular reactions. 

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