Support diffusion limitations

Adsorption on solid matrices, which improves (at optimal protein/support ratios) enzyme dispersion, reduces diffusion limitations and favors substrate access to individual enzyme molecules. Immobilized lipases with excellent activity and stability were obtained by entrapping the enzymes in hydrophobic sol-gel materials [20]. Finally, in order to minimize substrate diffusion limitations and maximize enzyme dispersion, various approaches have been attempted to solubilize the biocatalysts in organic solvents. The most widespread method is the one based on the covalent linking of the amphiphilic polymer polyethylene glycol (PEG) to enzyme molecules [21]. 

The surface concentration Cq Ajc in general depends on the electrode potential, and this can affect significantly the form of the i E) curves. In some situations this dependence can be eliminated and the potential dependence of the probability of the elementary reaction act can be studied (called corrected Tafel plots). This is, for example, in the presence of excess concentration of supporting electrolyte when the /i potential is very small and the surface concentration is practically independent of E. However, the current is then rather high and the measurements in a broad potential range are impossible due to diffusion limitations. One of the possibilities to overcome this difficulty consists of the attachment of the reactants to a spacer film adsorbed at the electrode surface. The measurements in a broad potential range give dependences of the type shown in Fig. 34.4. 

Zeolites have ordered micropores smaller than 2nm in diameter and are widely used as catalysts and supports in many practical reactions. Some zeolites have solid acidity and show shape-selectivity, which gives crucial effects in the processes of oil refining and petrochemistry. Metal nanoclusters and complexes can be synthesized in zeolites by the ship-in-a-bottle technique (Figure 1) [1,2], and the composite materials have also been applied to catalytic reactions. However, the decline of catalytic activity was often observed due to the diffusion-limitation of substrates or products in the micropores of zeolites. To overcome this drawback, newly developed mesoporous silicas such as FSM-16 [3,4], MCM-41 [5], and SBA-15 [6] have been used as catalyst supports, because they have large pores (2-10 nm) and high surface area (500-1000 m g ) [7,8]. The internal surface of the channels accounts for more than 90% of the surface area of mesoporous silicas. With the help of the new incredible materials, template synthesis of metal nanoclusters inside mesoporous channels is achieved and the nanoclusters give stupendous performances in various applications [9]. In this chapter, nanoclusters include nanoparticles and nanowires, and we focus on the synthesis and catalytic application of noble-metal nanoclusters in mesoporous silicas. 

The studies of Thomas and Raja [28] showed a remarkable effect of pore size on enantioselectivity (Table 42.3). The immobilized catalysts were more active than the homogeneous ones, but their enantioselectivity increased dramatically on supports which had smaller-diameter pores. This effect was ascribed to more steric confinement of the catalyst-substrate complex in the narrower pores. This confinement will lead to a larger influence of the chiral directing group on the orientation of the substrate. Although pore diffusion limitation can lead to lower hydrogen concentrations in narrow pores with a possible effect on enantioselectivity (see Section 42.2), this seems not to be the case here, because the immobilized catalyst with the smallest pores is the most active one. 

Electron transfer [Eq. (1)] would occur at a rate near the diffusion limit if it were exothermic. However, a close estimate of the energetics including solvation effects has not been made yet. Recent support of the intermediacy of a charge transfer complex such as [Ph—NOf, CP] comes from the observation of a transient (Amax f 440 nm, t =2.7 0.5 ms) upon flashing (80 J, 40 ps pulse) a degassed solution (50% 2-propanol in water, 4 X 10 4 M in nitrobenzene, 6 moles 1 HCl) 15). The absorption spectrum of the transient is in satisfactory agreement with that of Ph—NO2H, which in turn arises from rapid protonation of Ph—NOf under the reaction conditions ... 

There are a number of examples of tube waU reactors, the most important being the automotive catalytic converter (ACC), which was described in the previous section. These reactors are made by coating an extruded ceramic monolith with noble metals supported on a thin wash coat of y-alumina. This reactor is used to oxidize hydrocarbons and CO to CO2 and H2O and also reduce NO to N2. The rates of these reactions are very fast after warmup, and the effectiveness factor within the porous wash coat is therefore very smaU. The reactions are also eternal mass transfer limited within the monohth after warmup. We wUl consider three limiting cases of this reactor, surface reaction limiting, external mass transfer limiting, and wash coat diffusion limiting. In each case we wiU assume a first-order irreversible reaction. 

The rate of reaction of methyl radicals is in excellent agreement with the predictions of the Smoluchowski theory (see Chap. 2, Sect. 2.6). Consequently, it appears that geminate radicals move towards and away from each other at a diffusion-limited rate. Once an encounter pair is formed, reaction is very rapid (primary recombination). Furthermore, the encounter pair is held together for a considerable time (< 0.1ns in mobile solvents) because the surrounding solvent molecules hinder their separation (solvent caging). There is much evidence which lends some support for this view the most important influences on the recombination probability are listed below. 

Returning to the survival probability, in Fig. 57, the kinetic theory and diffusion equation [cf. eqn. (132)] predictions are compared. Three values of the activation rate coefficient are used, being 0.5, 1.0 and 2.0 times the Smoluehowski rate coefficient for a purely diffusion-limited homogeneous reaction, 4ttoabD. With a diffusion coefficient of 5x 10 9 m2 s1 and encounter distance of 0.5 nm, significant differences are noted between the kinetic theory and diffusion equation approaches [286]. In all cases, the diffusion equation leads to a faster rate of reaction. In their measurements of the recombination rate of iodine atoms in hydrocarbon solvents, Langhoff et al. [293] have noted that the diffusion equation analysis consistently predicts a faster rate of iodine atom recombination than is actually measured. Thus there is already some experimental support for the value of the kinetic theory approach compared with the diffusion equation analysis. Further developments cannot fail to be exciting. 

So far, the CO2 consumption was kept constant and was the limiting factor for efficiency, and a step-wise increase of the quantity of CO2 employed was investigated. To simulate natural conditions, contaminated rice samples at different levels were stored for 6 days at 20°C to support diffusion and adsorption of the diverse pesticides into and onto the rice. The concentrations of individual pesticides were adjusted to about 500/1,000 and 2,000 ppb. The results, as displayed in Fig. 9.6-16, show that the removal of pesticides above 90% is possible under given conditions (100 bar, 40°C). 

For the synthesis, diffusion limitation occurred rather than crystal formation limitation. Stirring resulted in more uniform, but thinner coatings. Pretreatment of the stainless-steel support with dilute template solution improved the crystal growth in the upper part of the channels. 

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