Decay types

The most widely accepted model to predict E-cat activity is based on a first-order decay type [7] ... 

The Ni-28Mo alloy provides a special case of selective corrosion analogous to the weld-decay type of attack it may be removed by solution treatment or using an alloy containing 2%... 

Decay Type Reactions Over Rough Sureace... 

For the 1 per cent europium-doped sample, a buildup and decay type of curve similar to that of Chang was found. This, of course, indicates a slow internal conversion to the 5D0 metastable level. From this rise and decay... 

Radioactive decay usually involves one of three basic types of decay, a decay, (3 decay, or y decay in which an unstable nuclide spontaneously changes into a more stable form and emits some radiation. In Table 1.1, we summarize the basic features of these decay types. 

Decay Type Emitted Particle A Z AN AA Typical Energy of Emitted Particle Example Occurrence... 

For example, supported TiCl4/MgCl2 catalysts show a short period of acceleration, followed by a prolonged steady period 92,93). However, in the presence of electron donors, they may show the typical decay rate kinetics observed during propylene polymerization 93). Bulk catalysts prepared by interaction of TiCU with Mg(OR)2 show either a stationary rate, or a non-stationary rate, according to the titanium content 88,94). Bulk catalysts prepared by reduction of TiCl4 with organomagnesium compounds show a decay type rate 92-95>. 

In ethylene polymerization with the catalytic system TicyMgClj—TIBA a progressive change of the kinetic curve from stationary-type of decay-type upon addition... 

Natta and Pasquon [12) were the first to study the effect of the catalyst particle size on the rate of polymerization. For a constant concentration of the monomer, they found that the rate of polymerization changed with time. With ground Ti02 (particle size < 2/i) the rate of propylene polymerization quickly reached a maximum and then decreased gradually to an asymptotic stationary value. In the case of unground particles (size up to 10/i), however, there were no maxima but the rate accelerated to approach the same asymptotic stationary value. The former behavior is referred to as the decay type, whereas the latter is known as the build-up or acceleration type. Figure 9.7 shows typical rate curves of these types and the different zones, termed build-up, decay, and stationary periods, into which they can be classified. 

Figure 9.7 Typical kinetic curves obtained during propylene polymerization by TiClj. (A decay type B build-up or acceleration type I build-up period II decay period III stationary period.)...

The decay type behavior observed in some cases may be due to active site destruction. This can be due to thermal deactivation or further reduction of the transition metal by the group I-III metal component. The decay type kinetics is explained later while discussing the mechanism of polymerization in terms of the deactivation of some of the active sites. 

Kei et al. [22] have used Langmuir-type adsorption to explain the observed rate behavior both during the initial stage (build-up period) and in the stationary state of the polymerization of propylene with TiCls-AlEta which exhibits a decay-type behavior (curve A in Fig. 9.9) (see Problem 9.8). Similarly the observed rate behavior in the build-up period of the acceleration-type curve (curve B in Fig. 9.9) can be explained. 

In the build-up period of the decay-type Ziegler-Natta polymerization of propylene, the rates are found to be different when propylene is introduced after TiCls and AlEts are allowed to equilibrate from the case when AlEts is added after the gas in introduced. The rates in the former case are given by the expression... 

T Nilsson. Defining fungal decay types A proposal for discussion. Intern Res. Group on Wood Preserve Document IRGAVP/1264, 1985. 

First, it is possible to show by using the orthonormality of the eigenvector matrix C that each of the N band types arising from an N-level system has a decay with a unique quantum beat phase distribution. That is, each decay type is different from the others by virtue of its quantum beat phases. 

Finally, Fig. 10 shows the decays of a third group of fluorescence bands in the 61 spectrum. It is apparent from the figure that all four bands decay in a similar manner. Fourier analysis of the decays confirms that this is indeed so. Figure 11 shows the Fourier spectrum of the decay at the top of Fig. 10. One notes that the same three beat components that are present here are present in the other two decay-types. Moreover, one notes (1) two — 1 beat phases and one +1 phase, (2) that the phase behavior in Fig. 11 is different from that in Fig. 9, and (3) that the sum of beat modulation depths is —0.70. 

Figure 13. Representative decay types for fluorescence bands in the = 1420 cm 1 spectrum of anthracene. The wavenumber shifts of the bands from the excitation energy are given in the figure. From top to bottom R - 16.0.1.6, and 1.6 A.

Decay-type and Stable Reaction Dynamics in Flows... 

We will refer to this type of systems as decay-type reaction systems since the stability of the local equilibrium implies that deviations from the stable steady state, in the absence of transport processes, decay in time. When the concentration field is advected by... 

After discussing the effect of the flow on the average concentration, we turn to the analysis of the statistics of the concentration fluctuations in such decay-type reaction systems. Even in the case of linear decay, where the average concentration is not affected by mixing, the fluctuations depend on the advecting flow. The distribution of the fluctuations over different length scales can be characterized by the power spectral density of the concentration field (taken along a one-dimensional section C(x), for simplicity) defined as... 

We note that the above results are not limited to the case of linear decay, but also apply to any kind of decay-type or stable reaction dynamics in a flow with chaotic advection (Chertkov, 1999 Hernandez-Garcfa et ah, 2002). In such systems where the reaction dynamics is nonlinear, the decay rate b should be replaced by the absolute value of the negative Lyapunov exponent of the Lagrangian chemical dynamics given by the second equation in (6.25), that represents the average decay rate of small perturbations in the chemical concentration along the trajectory of a fluid element. 

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