Rate constants sintering

D = the metal dispersion at sintering time t D0 = the initial metal dispersion k = the activated kinetic rate constant of sintering n = the sintering order... 

Second Order Sintering Rate Constants and Activation Energies for Pt Catalysts... 

The first or second order rate constant ks is in principle a kinetic parameter that provides a direct quantitative measure of sintering rate and is a function only of temperature. However, it is clear from first principles that rate constants for different experiments or catalysts can be compared with validity only for the same value of m or sintering order. Moreover, it follows from a careful analysis of the data of this study that rate constants of the... 

A similar comparison of rate constants for 0.6 and 5% Pt/alumina and 1,8% Ag/alumina catalysts at 673 K in oxygen atmosphere reveals that sintering rates for the Ag catalyst are roughly 40-50 times higher than for either Pt catalyst. Thus, Pt is clearly much more thermally stable than Ag under oxidizing conditions. These results are consistent with those from a model catalyst study [44] of sintering of Pt and Ag on alumina in vacuum in which it was observed that Pt/alumina was thermally stable in vacuum to about 873 K, above which temperature liquid-like particle migration was observed, while Ag/alumina was stable to only 723 K, above which temperature evaporation of the metal was observed. This latter result is... 

Second order sintering rate constant from General Power Law Expression (GPLE). 

On the other hand, rate constants for 0.6 and 5% Pt/alumina catalysts sintered in H2 at 973 K (see Table 1) of 0.53 and 0.84 h 1 are not substantially different. This result is not altogether unreasonable, as the number of crystallites per unit area of support surface and the metal surface area would be about the same in both 0.6 and 5% catalysts because of the much lower dispersion of the 5% catalyst. Nevertheless, it is fascinating that these two catalysts sinter at much different relative rates in air (see discussion above), a fact suggesting that different mechanisms (i.e., atomic migration vs. crystallite migration) may be involved in air versus H2 atmospheres as proposed by Wynblatt and Ahn [5J. 

FIGURE 16S0 Sintering rate constant fw the (a) initial stage and (b) intermediate stage as a function of the log-normal size distribution width param r, lattice diffusion, g-b.d. giain-boundetiy difiiision, v. viscous flow). Taken from Chappell et al. [47]. 

Samples of catalyst were removed from the pilot-plant reactor at various times during Run >3. Physical and chemical analyses were carried out on these samples and the results were compared with measurements on freshly-reduced catalyst, prior to exposure to synthesis gas. The analyses included BET surface area, S. Cl, Fe and Ni concentration on the catalyst. Cu and ZnO crystallite sizes, and Cu/Zn and Cu VCu ratios on the catalyst surface. The only strong correlation between the rate constant and any of these parameters is shown in Fig. 2, which reveals a striking dependence of the rate constant on the BET surface area. This relationship suggests that sintering of the overall catalyst surface is responsible for a large part of the observed deactivation. 

Fig. 8 is a plot of the normalized rate constant for Run E-7 versus the normalized BET surface area, analogous to Fig. 2 for Run E-3. The strong correlation once again suggests that sintering of the overall catalyst surface was responsible for the majority of the catalyst deactivation observed. 

Table 3 Second-order sintering rate constants, normalized dispersions and activation energies for Ni/alumina catalysts ...

Second-order sintering rate constant from GPLE. 

In principle, (he first- or second-order rate constant k provides a direct quantitative measure of sintering rate that is a functiem only of temperature, although it is shown elsewhere that rate constants should be ccxnpared fix the same order and the same approximate experimental timefi ame. ... 

This type of deactivation mechanism often applies catalyst sintering and coke deactivation. The deactivation rate constant is expected to have an Arrhenius dependence on temperature. 

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