Deactivation constant

A jj = Catalyst microactivity at anytime Aq = Catalyst inicroactivity at starting time t = Time after changing catalyst or makeup rate S = Daily fractional replacement rate = addition rate/inventory K = Deactivation constant = fn(A, - A )/-t... 

The experimental results for hybridoma and protozoa cells given as examples in Fig. 25 indicate that much higher stress (4 to 30 times) is required under laminar flow conditions of viscosimeters than in stirred vessels to achieve the same death rate k. Here the death rate k is defined as first order deactivation constant k = 1/t In (Nq/N), where N, is the initial and N the time-dependent number of living cells in special deactivation experiments under otherwise optimal living conditions. The stress in Fig. 25 was calculated with Eq. (28) for stirred vessels and with Eq. (1) for the viscosimeter. Our own results for hybri-... 

When the enzyme is incubated at 4 °C with aqueous buffer, a very small deactivation constant is found. In the presence of a second phase of MTBE, deactivation is 30% higher (4 °C). The highest increase in enzyme deactivation is due to the temperature the deactivation constants are 22-fold (1.3 x 17) or 255-fold (15 X 17) higher when incubating the enzyme at 20 °C in pure buffer or in a two-phase system respectively. In the presence of the substrate benzaldehyde almost the entire enzyme is deactivated within 1 h. This deactivation in a two-phase system is to some extent dependent on the size of the phase boundary and can... 

Rdes deactivation constant (assuming first-order exponential decay)... 

If the deactivation constant, kd, remains constant over the reaction time, equation (5.4-2) can be integrated and Eqn. 5.4-3 results. 

Regardless of whether it is the observed deactivation constant kd obs or the intrinsic deactivation constant kd, that is being analyzed, when running a biocatalytic process it is often of great importance to keep deactivation over time as small as possible. In this context, readers are reminded of the difference between resting stability and operational or process stability as already discussed in Chapter 5, Section... 

To ascertain the upper limit of protein thermostability and to evaluate the effect of additional disulfide bridges on the enhancement of protein thermostability, additional cysteine residues were introduced into several unrelated proteins by site-directed mutagenesis and deactivation behavior tested at 100°C (Volkin, 1987). All the proteins investigated underwent heat-induced beta-elimination of cystine residues in the pH 4—8 range with first-order kinetics and similar deactivation constants kj that just depended on pH 0.8 0.3 h-1 at pH 8.0 and 0.06 0.02 h 1 at pH 6.0. These results indicate that beta-elimination is independent of both primary amino acid sequence and the presence of secondary structure elements. Elimination of disulfides produces free thiols that cause yet another deleterious reaction in proteins, heat-induced disulfide interchange, which can be much faster than beta-elimination. 

The first-order dependence of the deactivation constant was found to be proportional not only to the power imparted by the impeller but also to the area between the liquid and the glass wall, air surface, or poly(tetrafluoroethylene) (PTFE) surface (Colombie, 2001). Hydrophobic PTFE and air interfaces increased lysozyme inactivation fourfold over glass. In addition, the number and thus the molecular surface of inactivated enzymes, which are more hydrophobic than native enzymes, enhanced lysozyme inactivation and aggregation. 

The deactivation functions for the isomerisation reactions of n-hexane were shown to be exponential functions of the coke content. The deactivation constant, the parameter of these functions, did not differ significantly for the various isomerisation reactions leading to tertiary carbenium ions. The deactivation constant for the isomerisation to 2,2-di-Me-butane, formed out of a secondary carbenium ion, was larger. 

The deactivation constant, obtained by fitting the data to a first order law equation (8), decreases with the reduction temperature for all cases, and is especially low for the impregnated alumina-titania catalyst. These results suggest the formation of carbon deposits and deactivation of catalysts occurs due to the metal activity, The contribution of the acid sites to deactivation seems to be negligible, despite the fact that alumina-titania supports present higher acidity than alumina or titania single oxides (9). 

Table 3. Operation conditions of the extended time test for measuring the deactivation constants 531...

The former corresponds to low rates of deactivation,while for high deactivation rates,travelling wave deactivation occurs. For the standing wave deactivation,the hot spot temperature decreases during deactivation, while for the travelling wave deactivation, constant pattern profiles exist and the hot spot temperature increases. 

Table 3. This is not simply a problem with the absolute magnitudes of the rate constants. The flow tube data were simulated using rate constant ratios that are clearly not reflected in the vibrational relaxation data. It is possible that the inconsistencies arise because we are not comparing equivalent properties. Thus far we have assumed that Heidner et al. deactivation rate constants are for vibrational deactivation. However, it is possible that electronically excited states of I2 also play an important role in the dissociation process [e.g. the neglected reactions (11), (12), and (13)]. If this was the case, the deactivation constants would be trying to represent a combination of vibrational relaxation and electronic quenching effects. Further studies of the dissociation mechanism will be needed to unravel this convoluted problem.

The mathematical approach of the Levenspiel model (ref. 12) was employed by accepting the hypothesis of independence. Thus, for the side by side poisoning the rate at which the active sites are poisoned is given by -da /dt = kp C a . The data were most satisfactorily correlated by the deactivation order d = 1. Thus, the deactivation constant, k, and the order of reaction of thiophene, m, were determined from the linear plots of In ac against time obtained for different Cp values. The values of k and m are given in Table 3. The greatest k constants and the lowest m values were found for Pt-Re/Al O catalysts. 

The resulting reaction rate constants with their 95% reliability interval are given in table 4. Based on the criteria for discrimination that have been mentioned above, it is not possible to discriminate between the two models. The values of the calculated reaction rate constants are almost the same, and the deactivation constant kj is negligibly small. From the data in table 4 it can be concluded that the deactivation of the catalyst with this hydrowax feedstock after 0.15 s is negligible. Because the model without deactivation describes the data with the same accuracy and less parameters, this model is selected for the optimal description of the data. 

Activity and deactivation constants of Pt/AbOa and Pt-Au/AbOs catalysts for the hydrogenolysis of methylcyclopentane at 623 K. 

The deactivation constant for the sulfured catalysts are reported in Table 4. It can be observed that the specific activity (kh) of the sulfured catalysts is lower than that shown by the non sulfured catalysts (Table 1). However, the deactivation constants k d of the sulfured catalysts are lower, implying that the bimetallic Pt-Au are the less affected by sulfur poisoning. 

Burguet et al. investigated the catalyst decay accompanying the reaction of cyclohexanone oxime over ultrastable H-Y zeolite [58]. The basic compounds present during the reaction i. e. oxime, -caprolactam, methylpyridine, 5-cyano-pent-l-ene, hydroxylamine, and aniline were considered to be the catalyst poisons. Hydroxylamine is more basic than the other products and might be more poisonous. Hydroxylamine selectivity decreased with temperature, which could explain qualitatively the apparent decrease in the deactivation constant (k with increasing temperature. 

Estimate of the deactivation constant can be graphically carried out from Equation 7 plotting In [[Sf - S(t)]/r - dS(t)/dt] vs t (Figure 7.4). A straight line is thus obtained whose slope is given by ( - Kd) and the line intersects the vertical axis at the point of coordinate (In V axo). 

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