Second-order deactivation

A kinetic model which accounts for a multiplicity of active centres on supported catalysts has recently been developed. Computer simulations have been used to mechanistically validate the model and examine the effects on Its parameters by varying the nature of the distrlbultons, the order of deactivation, and the number of site types. The model adequately represents both first and second order deactivating polymerizations. Simulation results have been used to assist the interpretation of experimental results for the MgCl /EB/TlCl /TEA catalyst suggesting that... 

Second Order Deactivation. All simulations described thus far are based on first order deactivation. As mentioned previously, the model is capable of fitting second order decay data. To assess the effect of second order decay, simulations were carried out with similar distributions of activities and termination rates with the active sites undergoing second order decay. 

A blmodal distribution like that previously described but with second order deactivation was also simulated. As was seen with the first order case, increasing the fraction of HAFD sites lowered However, in this case 6 only reaches a lower limit... 

A blmodal with second order deactivation hybrid... 

Evaluation of F(x) for Second Order Deactivation. As mentioned earlier for the case of second order decay F(x) cannot be derived analytically, however numerical calculation of F(x) or Its evaluation from simulated rate data Indicates that the function defined In Equation 11 provides an excellent approximation. This was also confirmed by the good fit of model form 12 to simulated polymerization data with second order deactivation. Thus for second order deactivation kinetics the rate expression Is Identical to Equation 12 but with 0 replacing 02. 

Computer simulations have been useful for validating a kinetic model that Is not easily tested. The model was equally capable of describing multi-site polymerizations which can undergo either first or second order deactivation. The model parameters provided reasonably accurate kinetic information about the Initial active site distribution. Simulation results were also used as aids for Interpretation of experimental data with encouraging results. 

With the assumptions of second-order deactivation and first-order reaction, the regimes are characterized as follows ([A]solid 0 = initial concentration of solid substrate, [A111ril = substrate solubility) ... 

Plots of various catalysts are shown in Pig. 4-5 Straight lines go through the origin for all catalysts, thus a second-order deactivation which is concentration independent applied in this study The values of k for various catalysts are illustrated in Table 2. For chromium-promoted catalyst, k value increases with increasing Cr/Cu molar ratio. The promoted catalysts with Cr/Cu=l/40 and 1/10 are more stable than the unpromoted one For alkaline earth metal-promoted catalysts, Mg-promoted catalyst is more stable than the unpromoted one however, the Ca-, Sr-, and Ba-promoted catalysts are poor in stabilities The stability of the alkaline earth metal promoted catalyst is in the order Mg> Ca> Sr> Ba. 

Fig. 4 Test for second-order deactivation of Cr-promoted and unpromotsd catalysts ...

Second-order deactivation rate constant of catalyst at 300°C... 

Recent investigations on ethane formation in the photolysis of acetaldehyde indicate that decomposition into methyl and formyl radicals occurs from the triplet state which is also removed by first-order internal conversion and, to some extent, by second-order deactivation. In the mercury-photosensitized reaction methyl radicals are formed by direct dissociation of the excited aldehyde molecules, as well as by collision of excited mercury atoms . 

Example 9.8. Parallel and sequential deactivation in a hypothetical reaction. The principle of mechanistic modeling can be illustrated by the oversimplified example of a single-step isomerization reaction A — P with Langmuir-Hinshelwood kinetics, rate control by the surface reaction, and slow second-order deactivation. 

If second-order deactivation were sequential rather than parallel, its rate would be that of the step ( ) = (f), and the deactivation rate equation would contain KPpf(t) = KP pA — pA(f)] instead of KA pA it) in the numerator. Parallel deactivation is relatively fast at low conversion, sequential deactivation is so at high conversion. 

Currently, second-order deactivation = 2 seems to be the most popular, but = 1 and = 3 have also been used to fit data. 

For Ziegler-Natta polymerization of alkenes, second-order deactivation decay explains much better experimental data than the first-order decay. Such behavior in supported systems was attributed to simultaneous deactivation of adjacent catalytic species on the surface. In homogeneous polymerization with metallocene catalysts (Fig. 9.53), a metallocene complex Cp2ZrCl2 reacts first (kj) with a cocatalyst MAO ([—O—Al—CH (CH3-) ). Subsequently, alkenes molecules are inserted (kpi) into the Zr-C bond of the formed metaUocenium ion Cp2Zr -CH3. A polymer molecule grows in length by numerous insertion reactions (kpi). 

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