Deactivation constant, Arrhenius

For the temperature dependence of the deactivation constant an Arrhenius relationship is assumed ... 

The dependence of the experimental values of the deactivation constant on temperature is shown in an Arrhenius plot in figure 3. The activation enthalpy of the deactivation reaction is estimated to be 20Si 103 J/mole. This agrees well with earlier results of Fratzke et al. (3), 204xlo3 J/mole andNielsen ( ), 197xlo3 J/mole. 

Figure 3. Arrhenius relationship for deactivation constant. (9) Constant conversion, (A, , O) constant flow.

The operational conditions, that is, the concentration of substrate and enzyme, the temperature range, and the reactor configuration are summarized in Table 13.2. The activation energy of the reaction, E, was typically obtained for a batch reactor and compared with that calculated for a CSMR. The data obtained in the CSMR at steadystate enabled us, by using a semi-log plot of reaction rate versus time, to identify a first-order mechanism of enzyme deactivation and to determine both its first-order deactivation constant, kj, and the reaction rate at time zero, r, for each substrate and temperature. It was thus possible to compare the effect of the operational parameters on the activity and stability of these two enzymes. From the Arrhenius plot of these Tq, the E,-values were determined for each substrate, and were found to match the values obtained in the batch reactors. 

Do not infer from the above discussion that all the catalyst in a fixed bed ages at the same rate. This is not usually true. Instead, the time-dependent effectiveness factor will vary from point to point in the reactor. The deactivation rate constant kj) will be a function of temperature. It is usually fit to an Arrhenius temperature dependence. For chemical deactivation by chemisorption or coking, deactivation will normally be much higher at the inlet to the bed. In extreme cases, a sharp deactivation front will travel down the bed. Behind the front, the catalyst is deactivated so that there is little or no conversion. At the front, the conversion rises sharply and becomes nearly complete over a short distance. The catalyst ahead of the front does nothing, but remains active, until the front advances to it. When the front reaches the end of the bed, the entire catalyst charge is regenerated or replaced. 

The kinetic parameters are listed in Table 1. The linearity of lnAr l/r plot is revealed by the correlation coefficient. For all reactions but the deactivation, the rate constants follow the Arrhenius law satisfactorily, implying catalyst deactivation may involve more than one elementary steps. 

The constant is expected to have an Arrhenius dependence on temperature. Deactivation by coke deposition in cracking operations apparently has this kind of correlation. 

We now consider hydrogen transfer reactions between the excited impurity molecules and the neighboring host molecules in crystals. Prass et al. [1988, 1989] and Steidl et al. [1988] studied the abstraction of an hydrogen atom from fluorene by an impurity acridine molecule in its lowest triplet state. The fluorene molecule is oriented in a favorable position for the transfer (Figure 6.18). The radical pair thus formed is deactivated by the reverse transition. H atom abstraction by acridine molecules competes with the radiative deactivation (phosphorescence) of the 3T state, and the temperature dependence of transfer rate constant is inferred from the kinetic measurements in the range 33-143 K. Below 72 K, k(T) is described by Eq. (2.30) with n = 1, while at T>70K the Arrhenius law holds with the apparent activation energy of 0.33 kcal/mol (120 cm-1). The value of a corresponds to the thermal excitation of the symmetric vibration that is observed in the Raman spectrum of the host crystal. The shift in its frequency after deuteration shows that this is a libration i.e., the tunneling is enhanced by hindered molecular rotation in crystal. 

The Constant—Parameter Arrhenius Plot (CPAP) technique uses in addition the effect of temperature. The observed rate constants are plotted in an Arrhenius form at a constant value of the deactivation parameter, r i.e., one curve for points lepieseuting the fresh catalyst (t = 0), etc. For each curve, a low—temperature asymptote and a high-temperature asymptote can be drawn, and these can be extrapolated to intersect at a point with coordinates 1/T ( r), ta k (ir). Then, as shown in ref. (1), the values of k.. ... 

The setup used to obtain CPAP data was different from that of the last section. Pre-deactivated samples of catalyst are available, and the HT reactions themselves do not (further) deactivate the catalyst. Hence we worked with the pre-deactivated samples, measuring observed rates of an HT reaction as a fiinctimi of temperature, with each sample generating an Arrhenius-type plot at a constant level of deactivation. The samples were from Run 242, using Illinois number 6 coal as the feed solid and Shell 324M as the catalyst. The catalyst pdlet is O.S mm in diameter and 4 mm in length and has a bulk density of 0.78 g/ml, an average pore diameter of llsA. and a specific surface area of 180 m /g. It contains 3.4 percent NiO, 19 percent MoO, and 63 percent AlnO. The HT reaction used... 

If we replace the activity of the catalyst, a , by a", where a is the fraction of the sites that are active (not deactivated) and n is number of sites used by the main reaction and substitute the Arrhenius form for the rate constant in terms of the activation energy into the left-hand side of Equation 12, we get... 

In eqn. 2, e a(T)t j a factor that expresses the extent of catalyst deactivation with time, and may be regarded as a time constant for catalyst activity loss. This form of catalyst deactivation factor derives from the assumption that catalyst activity decays exponentially with time, at constant temperature. A and E are, respectively, the preexponential factor and the activation energy for the rate constant. E can be determined from an Arrhenius plot for k1 under conditions where the quantity e a(T)t is essentially constant. Fig. 4 shows the results of experiments that were conducted at the end of the catalyst life tests at 498°K and 538eK shown in Fig. 3. The greater extent of deactivation at 538°K is clearly evident in Fig. 4, since the data at 538°K fall well below those at 498°K. The activation energies derived from the slopes of the two lines on Fig. 4 average t7.9 kcal/mole and agree to within 0.8 kcal/mole. 

The rate constants, the adsorption equilibrium constants, and the deactivation parameters a, and oto were determined from the measurement of Pa and pj, as a function of time and position (i.e., W/F o) in the bed, through a special sampling device. In addition, the coke profile was measured at the end of the run. The parameters were found to be statistically significant, and the rate coefficients obeyed the Arrhenius temperature dependence. 

Applied in sensors, the complex is usually immobilized in solid polymer matrices. Hence, the first two mechanisms will also play a significant role. Additionally, at higher temperatures the triplet excited state of the ligand can also be deactivated leading to a less efficient energy transfer to the lanthanide irai. The rate constants w of the crossover processes involved can be described approximatively by an Arrhenius-type equation, where the barrier height is expressed by the activation energy a [118, 119] ... 

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