Substrate concentration, bulk phase

Concentration of substrate in bulk phase (mole/vol) Concentration of substrate in resin phase (mole/vol) Time (dimensional)... 

The concentration of the product absorbed in the resin phase and the real rate constant were determined by the measurements of the time dependencies of product formation in the bulk phase and of the quantities adsorbed to the resin of both the product and substrate by assuming the following reaction scheme ... 

Another setup used for the hydrogenation of DMI with Ru-BINAP was equipped with dense PDMS elastomer membranes (Jacobs et al. [48]). The catalyst solution was present in a submerged membrane system, prepared as a sealed PDMS capsule . The catalytically active complex was retained by the membrane while substrate and products, dissolved in the bulk phase, could cross the membrane under the influence of the concentration difference without the need for mechanical pressure. 

Sw = substrate concentration in the bulk water phase (g m-3) ra = biofilm surface flux (g nr2 s-1, g nr2 h 1 or g nr2 d-1) ku2 = 1/2-order rate constant per unit biofilm surface area... 

Raghvan and Srinivasan developed a model, for bimolecular micellar catalysed reactions, which also predict constancy in /cobs values at high detergent concentration and may be used for evaluating the binding constants of reactants. They proposed the distribution of both reactant and nucleophile in aqueous and micellar phases. The product formation is assumed to result from decomposition of ternary complex involving substrate, nucleophile and micelle. After analyzing the data on the basis of this model, they concluded that almost all the nucleophile is present in the bulk phase. 

For a triphasic reaction to work, reactants from a solid phase and two immiscible liquid phases must come together. The rates of reactions conducted under triphasic conditions are therefore very sensitive to mass transport effects. Fast mixing reduces the thickness of the thin, slow moving liquid layer at the surface of the solid (known as the quiet film or Nemst layer), so there is little difference in the concentration between the bulk liquid and the catalyst surface. When the intrinsic reaction rate is so high (or diffusion so slow) that the reaction is mass transport limited, the reaction will occur only at the catalyst surface, and the rate of diffusion into the polymeric matrix becomes irrelevant. Figure 5.17 shows schematic representations of the effect of mixing on the substrate concentration. 

On the basis of the Hatta number, the transformations carried out in biphasic systems can be described as slow (Ha < 0.3), intermediate (with a kinetic-diffusion regime 0.3 < Ha < 3.0), and fast (Ha > 3). These are diffusion limited and take place near the interface (within the diffusion layer). Slow transformations are under kinetic control and occur mostly in a bulk phase, so that the amount of substrate transformed in the boundary layer in negligible. When diffusion and reaction rate are of similar magnitude, the reaction takes place mostly in the diffusion layer, although extracted substrate is also present in the continuous phase, where it is transformed at a rate depending on its concentration [38, 50, 54]. 

Polymer acids or polyanions can catalyze the acid hydrolyss of esters, amides, and ethers. This is because the local proton concentration in the polymer domain is hi r than that in the bulk phase. The rate acceleration caused by this effect is moderate. However, when substrate molecules are attracted to the polymer molecule by electrostatic and hydrophobic forces, the catalytic efficiency increases (up to ca. 100 fold compared with mineral acids). Similar results were obtained for the alkali hydrolysis in the presence of polycations. 

Based partly on anecdotal evidence from culture work, observations in waste water treatment systems with very high particulate loads, the tendency of nitrifiers to grow in aggregates in bioreactor biofilms, and the prevalence of small particles in natural waters, it has been suggested that nitrification occurs mainly on particles and is mediated by particle-attached bacteria (Hagopian and Riley, 1998). Nitrifier sequences were found both associated with particles and in the bulk seawater phase in the northwestern Mediterranean Sea. In the clone library of 16S rRNA sequences, Nitrosomonas-like sequences were preferentially associated with particles and Nitrosospira-]ike sequences dominated in clones from the planktonic phase (PhiUips et al, 1999). This may indicate niche preference by the different groups on the basis of attachment to particles, substrate concentration or other physical/... 

A rigorous kinetic description of interfacial catalysis has been hampered by the ill-defined physical chemistry of the lipid—water interface (Martinek et ai, 1989). Traditional kinetic assumptions are undermined by the anisotropy and inhomogeneity of the substrate aggregate. For example, the differential partitioning of reactants (enzyme, calcium ion, substrate) and products (lysolecithins, fatty acids) between the two bulk phases prevents direct measurement of enzyme and substrate concentrations. This complicates dissection of the multiple equilibria that contribute to the observed rate constants. Only recently has it become possible to describe clearly the activity of SPLA2S in terms of traditional Michaelis— Menten kinetics. Such a description required the development of methods to reduce experimentally the number of equilibrium states available to the enzyme (Berg etai, 1991). 

A very good initial guess at the structure of a surface alloy may actually be obtained from the bulk phase diagram for the deposited element-substrate system. This is so, simply because, if there are no specific surface effects, the observed structures would have to be those found in the bulk phase diagram. Since the concentration of the deposited element should be considered small (it is actually "almost" zero, but in the case of local equilibria only the substrate atoms close to the surface may participate in the alloy formation, and thus the "effective" concentration of the deposited element could be quite high), the surface alloy will usually have the structure of the first ordered phase in the... 

A special situation may arise if reaction products considerably affect the hydrogen solubility, which then varies during the reaction. Such a phenomenon occurs most often in the hydrogenation of the substrate in bulk, without solvent, mainly where the chemical character of the hydrogenation product markedly differs from that of the initial compound [e.g., hydrogenation of nitrobenzene to aniline and water (72)]. In such a case the hydrogen concentration cannot be drawn into the constant, because its varying concentration in the liquid phase is reflected in the form of the kinetic equation. In many such cases the effect of reaction products is also reflected in the kinetic equation. 

It has been reported in several papers (70, 77,97,98) that in some systems a change in the solvent may importantly affect the selectivity of hydrogenation of two substrates differing in their structure. At the same time, in this case (concentration range) the solvent did not play any role in equations of the Langmuir-Hinshelwood type, because the latter were mostly reduced to equations for pseudo-zero order. Hence, a change in selectivity was most likely caused by interactions of the solvent from the bulk phase with adsorbed molecules of substrates on the catalyst surface. 

When adsorption of the surfactant onto the substrate is strong, however, Fowkes found that the rate of wetting was determined not by the bulk phase concentration of the surfactant, but by the rate of diffusion of the surfactant to the wetting front. In this case the concentration of surfactant present at the advancing liquid front was so depleted by adsorption that the surface tension (or contact angle) there, and... 

A very commonly observed trend is that activity is highest in the least polar solvents. In many of these cases this is an effect of water or substrate availability, as just noted. Hexane is regularly identified as the best medium, because the low solubility of water and most substrates makes them most available to the enzyme, when comparisons are made at equal concentrations. Nevertheless, even when water and substrate availability have been allowed for, non-polar solvents seem to offer the highest activity. The probable explanation involves the tendency for solvent molecules to migrate from the bulk phase into the immediate environment of the enzyme. The picture is simplest when there is a discrete aqueous phase (albeit of very small volume) around the enzyme molecules. The more hydrophobic the bulk solvent, the lower will be the (saturating) concentration in the aqueous phase, which is what is experienced by the enzyme. Even in the absence of an identifiable aqueous... 

So ss - s/sf bulk liquid phase Substrate initial concentration, M L"3 Dimensionless substrate concentration in the catalyst annulus... 

Taking into account that different orders of isomer activity have been previously reported, it can be concluded that antioxidant potential of tocopherols is mainly dependent on the tested lipid system. Indeed, the antioxidant activities of tocopherols have been investigated in various lipid substrates, including vegetable oils, animal fats, emulsions, PUFAs, etc. Huang et al. proposed that the relative antioxidant activity of different tocopherols depends on temperature, lipid composition, physical state (bulk phase, emulsion), and tocopherol concentration. 

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