Effectiveness factor, substrate

Finally we learned that if we analyze the first factor (substrate), we will find two effects at play electroiucs and sterics. We saw that Sn2 reactions require primary or secondary substrates because of sterics—it is too crowded for the nucleophile to attack a tertiary substrate. On the other hand, SnI reactions did not have a problem with sterics, but electronics was a bigger issue. Tertiary was the best, because the alkyl groups were needed to stabilize the carbocation. 

Intraparticle Mass Transfer. One way biofilm growth alters bioreactor performance is by changing the effectiveness factor, defined as the actual substrate conversion divided by the maximum possible conversion in the volume occupied by the particle without mass transfer limitation. An optimal biofilm thickness exists for a given particle, above or below which the particle effectiveness factor and reactor productivity decrease. As the particle size increases, the maximum effectiveness factor possible decreases (Andrews and Przezdziecki, 1986). If sufficient kinetic and physical data are available, the optimal biofilm thickness for optimal effectiveness can be determined through various models for a given particle size (Andrews, 1988 Ruggeri et al., 1994), and biofilm erosion can be controlled to maintain this thickness. The determination of the effectiveness factor for various sized particles with changing biofilm thickness is well-described in the literature (Fan, 1989 Andrews, 1988)... 

There is no analytical solution for the effectiveness factor in the case of Michaelis-Menten kinetics. However, at very low substrate concentrations, the kinetics are known to become first-order. For this particular case, an analytical solution for q can be found ... 

The expression for the effectiveness factor q in the case of zero-order kinetics, described by the Michaelis-Menten equation (Eq. 8) at high substrate concentration, can also be analytically solved. Two solutions were combined by Kobayashi et al. to give an approximate empirical expression for the effectiveness factor q [9]. A more detailed discussion on the effects of internal and external mass transfer resistance on the enzyme kinetics of a Michaelis-Menten type can be found elsewhere [10,11]. 

Figure 11.19 Plots of the external effectiveness factor as a function of the substrate modulus Da for different values of the dimensionless bulk substrate concentration is the limiting first-order effectiveness factor attained at sufficiently low concentrations. Adapted from C.Horvath and J.M.Engasser. Biotechnol.Bioeng., 16, 909 (1974).

This equation cannot be integrated immediately as f is a function of the substrate concentration C. A possible procedure is calculation of the overall effectiveness factor... 

This equation, again, cannot be integrated immediately as t is a function of the substrate concentration C., which changes when going from the entrace to the exit of the plug-flow reactor. The procedure to solve this equation is the calculation of the overall effectiveness factor at n substrate concentration in the interval C to Through this n (... 

The rate of cell growth is influenced by temperature, pH, composition of medium, rate of air supply, and other factors. In the case that all other conditions are kept constant, the specific growth rate may be affected by the concentration of a certain specific substrate (the limiting substrate). The simplest empirical expression for the effect ofthe substrate concentration on the specific growth rate is the following Monod equation, which is similar in form to the Michaelis-Menten equation for enzyme reactions ... 

Determine the effectiveness factor and the initial reaction rate, when the substrate concentration is 0.6 kmol m . ... 

In the case of gel entrapped biocatalysts, or where the biocatalyst has been immobilised in the pores of the carrier, then the reaction is unlikely to occur solely at the surface. Similarly, the consumption of substrate by a microbial film or floe would be expected to occur at some depth into the microbial mass. The situation is more complex than in the case of surface immobilisation since, in this case, transport and reaction occur in parallel. By analogy with the case of heterogeneous catalysis, which is discussed in Chapter 3, the flux of substrate is related to the rate of reaction by the use of an effectiveness factor rj. The rate of reaction is itself expressed in terms of the surface substrate concentration which in many instances will be very close to the bulk substrate concentration. In general, the flux of substrate will be given by ... 

For spherical particle geometry, as in the case of a microbial floe, a pellet of mould or a bead of gel-entrapped enzyme, the expression for the effectiveness factor can again be derived by a procedure similar to that used in Chapter 3 for a spherical pellet of conventional catalyst. A material balance for the substrate across an elementary shell of radius r and thickness dr within the pellet will yield ... 

Figure 3.4 shows the substrate concentration profile when = 5. The effectiveness factor when the reaction rate is expressed by the Michaelis-Menten equation can be calculated as... 

After immobilizing this enzyme on the surface of insoluble matrix by physical adsorption, it was found that the Ka% value was increased to 0.08 mol/L whereas the rfl ax value stayed the same as rmax. What is the effectiveness factor of the immobilized enzyme when the substrate concentration is 1 mol/L ... 

Fig. 5 shows the effect of substrate concentration and agitation on substrate/EPS factor, YP/S. Figure 6 shows the correlation between experimental results and values predicted by the mathematical model generated by S tatistica, indicating a good correlation between experimental and predicted values. 

From the analysis of surface graphs, it canbe observed that the conversion factor substrate/EPS (YP/S) changed from 3.9 to 15.9%, representing an increase of 24.5% in the efficiency of the process. Smaller values of substrate concentration (X,) increased in the conversion factor, YP/S, whereas aeration did not represent a significant effect. 

A classic non-competitive inhibitor has no effect on substrate binding and vice-versa. Inhibitor and substrate molecules adsorb independently on different sites but, while the inhibitor does not affect the adsorption of the substrate it does inhibit the further reaction of the adsorbed species. On a metal catalyst this type of inhibition could arise when the substrate is adsorbed on a comer atom and the inhibitor on face atoms near the comer. The resulting steric or electronic factors could prevent further reaction of the adsorbed substrate. 

On the other hand, approximate calculations of ti can also be used [85].In this way, cumbersome solutions of the differential equations are not required if one merely wishes to obtain a general idea of substrate-related diffusional restrictions. A profound insight into effectiveness factors is given by Kasche [86] where a good correlation between calculated and experimental data is demonstrated. 

Ruckenstein [96] has calculated the resulting diffusion-restricted enzyme activities at high substrate concentrations. He teaches us in simple terms that pH-shifts and resulting reductions in activity occur even at substrate concentrations high enough to exclude any substrate-related diffusional restrictions, i.e. at effectiveness factors close to 1. 

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