Substrate transport limitations

This paper addresses the general subject of substrate transport in polymer-immobilized catalyst systems. The equations needed to interpret reaction rate data for polymer systems are developed and their applicability is discussed. The effects of experimental variables on observed reaction rates in the presence of substrate transport limitations are discussed. A simple method for estimating substrate diffusion coefficients is presented. Methods for testing reaction rate data to determine if substrate transport is affecting the observed reaction rates are developed and the limitations of these methods are discussed. Finally, examples of recent studies are reviewed and discussed within the framework of the mathematical formalism to demonstrate application of the formalism and to show that carefully designed experiments are required to establish the presence of substrate limitations. 

In the absence of substrate transport limitations, the substrate concentration is Independent of radial position in the polymer. The rate measured under these circumstances would be an intrinsic reaction rate. The substrate material balance is greatly simplified because Equation 8 no longer needs to be solved. A specific example of this can be found in the literature (16). 

The results in Equations 35, 36 and 37 can be used to test for substrate transport limitations. Examples from the literature using these simple tests will be presented later. Caution must be exercised in applying the simple tests individually because they are written for a situation where all other factors are equal, and this may not be the case for polymer-immobilized catalysts. 

There are a number of factors which may influence the activity or selectivity of a polymer-immobilized catalyst. Substrate diffusion is but one. This article has reviewed the mathematical formalism for interpreting reaction rate data. The same approach that has been employed extensively in heterogeneous systems is applicable to polymer-immobilized systems. The formalism requires an understanding of the extent of substrate partitioning, the appropriate intrinsic kinetic expression and a value for the substrate s diffusion coefficient. A simple method for estimating diffusion coefficients was discussed as were general criteria for establishing the presence of substrate transport limitations. Application of these principles should permit one to identify experimental conditions which will result in the intrinsic reaction rate data needed to probe the catalytic properties of immobilized catalysts. 

Ebrahimi S, Picioreanu C, Xavier JB, et al. 2(X)5. Biofilm growth pattern in honeycomb monolith packings Effect of shear rate and substrate transport limitations. Catal Today 105(3 ) 448-454. 

The specificity of several of the enzymes identified in the 4S pathway of different organisms has been studied. In case of the DBT desulfurizing enzymes, little difference is expected in the specificity of the enzymes, say DszA, from different Rhodococcus strains found to date. This is essentially because the DNA sequence for the enzymes investigated so far has been the same. The difference in the specificity observed with whole cell assays is essentially due to the differences in substrate intake via the cell membrane and not necessarily due to a difference in the intrinsic enzyme specificity. It has been found that while isolated enzyme DszC (from KA2-5-1) can desulfurize up to 4,6 dipropyl DBT, whole cells cannot, indicating substrate transport as limiting factor. 

Remarkably, the use of a fluorous biphasic solvent system in combination with a [Rh(NBD)(DPPE)]+-type catalyst (NBD = norbornadiene) copolymerized into a porous nonfluorous ethylene dimethacrylate polymer, resulted in an increased activity of the catalyst relative to a situation when only toluene was used as solvent [30]. The results were explained by assuming that fluorophobicity of the substrate (methyl-trans-cinnamate) leads to a relatively higher local substrate concentration inside the cavities of the polymer when the fluorous solvent is used. That is, the polymer could be viewed as a better solvent than the fluorous solvent system. This interpretation was supported by the observations that (i) the increase in activity correlates linearly with the volume fraction of fluorous solvent (PFMCH) and (ii) the porous ethylene dimethacrylate polymer by itself lowers the concentration of decane in PFMCH from 75 mM to 50 mM, corresponding to a 600 mM local concentration of decane in the polymer. Gas to liquid mass transport limitation of dihydrogen could be mled out as a possible cause. 

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. 

Additional experiments in a loop reactor where a significant mass transport limitation was observed allowed us to investigate the interplay between hydrodynamics and mass transport rates as a function of mixer geometry, the ratio of the volume hold-up of the phases and the flow rate of the catalyst phase. From further kinetic studies on the influence of substrate and catalyst concentrations on the overall reaction rate, the Hatta number was estimated to be 0.3-3, based on film theory. 

The catalytic principle of micelles as depicted in Fig. 6.2, is based on the ability to solubilize hydrophobic compounds in the miceUar interior so the micelles can act as reaction vessels on a nanometer scale, as so-called nanoreactors [14, 15]. The catalytic complex is also solubihzed in the hydrophobic part of the micellar core or even bound to it Thus, the substrate (S) and the catalyst (C) are enclosed in an appropriate environment In contrast to biphasic catalysis no transport of the organic starting material to the active catalyst species is necessary and therefore no transport limitation of the reaction wiU be observed. As a consequence, the conversion of very hydrophobic substrates in pure water is feasible and aU the advantages mentioned above, which are associated with the use of water as medium, are given. Often there is an even higher reaction rate observed in miceUar catalysis than in conventional monophasic catalytic systems because of the smaller reaction volume of the miceUar reactor and the higher reactant concentration, respectively. This enhanced reactivity of encapsulated substrates is generally described as micellar catalysis [16, 17]. Due to the similarity to enzyme catalysis, micelle and enzyme catalysis have sometimes been correlated in literature [18]. 

The kinetic modeling of the external transport limitation is successful with aid of a double-substrate-limitation function [61-63] ... 

However, under some circumstances, the rate is not only leveled but it is also inhibited as the substrate concentration increases. In a comprehensive study on 3-chloro-4-hydroxybenzoic acid and chlorophenols, Cunningham and colleagues [35] deduced that the rate can be strongly inhibited in consequence of (1) chemisorption-induced depletions of surface —OH groups, (2) adsorbate-enhanced hole-electron recombination on the TiO2 surfaces, (3) mass transport limitations within the TiOz particle aggregates. They reported that, depending on... 

The objectives of using solvents are diverse, e.g., to dissolve a solid substrate, to limit catalyst deactivation, to improve selectivity, or to enhance mass-transport. The solvents are selected depending on the substrate and the desired effect. Hence, they range from water, alcohols, ethers, or low alkanes, to CO2. The effects of the solvent on phase-behaviour, viscosity, and density at different concentrations, temperatures and pressures can explain much about the effect of the solvent on the reaction. 

To aleviate the dissolution of the enzymatic film during the glucose assay procedure, a covering membrane made by addition of 10 pi of Nafion 0.5% was used. The amperometric current increases until a constant value of 20 pA is reached on the fourth glucose assay (Fig. IB). The addition of Nafion film atop of the AQ-enzyme layer doesn t seem to denaturate the enzyme entrapped in the AQ film because the current reached a similar value as the current observed in absence of Nafion. On the other hand, the use of Nafion as covering membrane gives a thicker film that leads to mass transport limitation of the substrates in the AQ film (20). It results in a longer time to obtain the steady-state current. 

In summary, the steady state and transient performance of the poly(acrylamide) hydrogel with immobilized glucose oxidase and phenol red dye (pAAm/GO/PR) demonstrates phenomena common to all polymer-based sensors and drag delivery systems. The role of the polymer in these systems is to act as a barrier to control the transport of substrates/products and this in turn controls the ultimate signal and the response time. For systems which rely upon the reaction of a substrate for example via an immobilized enzyme, the polymer controls the relative importance of the rate of substrate/analyte delivery and the rate of the reaction. In membrane systems, the thicker the polymer membrane the longer the response time due to substrate diffusion limitations as demonstrated with our pAAm/GO/PR system. However a membrane must not be so thin as to allow convective removal of the substrates before undergoing reaction, or removal of the products before detection. The steady state as well as the transient response of the pAAm/GO/ PR system was used to demonstrate these considerations with the more complicated case in which two substrates are required for the reaction. 

Scanning electrochemical microscopy seeks to overcome the lack of sensitivity and selectivity of the probe tip in STM and AFM to the substrate identity and chemical composition. It does this by using both tip and substrate as independent working electrodes in an electrochemical cell, which therefore also includes auxiliary and reference electrodes. The tip is a metal microelectrode with only the tip active (usually a metal wire in a glass sheath). At large distances from the substrate, in an electrolyte solution containing an electroactive species the mass-transport-limited current is therefore... 

The intrinsic catalytic properties of enzymes are modified either during immobilization or after they were immobilized [25-27], In heterogeneous catalysis such as is carried out by immobilized enzymes, the rate of reaction is determined not simply by pH, temperature and substrate solution, but by the rates of proton, heat and substrate transport, through the support matrix to the immobilized enzyme. In order to estimate this last phenomenon, we have studied the internal mass transfer limitation both in hexane and in SC C02, with different enzymatic support sizes. 

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