Time-dependent kinetic behavior

These equations can be solved numerically with a computer, without making any approximations. Naturally all the involved kinetic parameters need to be either known or estimated to give a complete solution capable of describing the transient (time dependent) kinetic behavior of the reaction. However, as with any numerical solution we should anticipate that stability problems may arise and, if we are only interested in steady state situations (i.e. time independent), the complete solution is not the route to pursue. 

Focusing on the shorter time-scale component, the characteristic recovery time shows a strong dependence on the pump-laser power or, equivalently, the number of electrons injected The higher the power, the shorter the recovery time. Similar behavior has been noted by Ford et al. [40]. If 1>app is plotted versus the number of electrons injected per particle (Fig. 4), a linear correlation is obtained. In other words, the reaction appears to be first order in electrons (and first order in the oxidized dye). What does this mean mechanistically The simplest interpretation—sketched in Scheme 1—is that the injected electrons are free to return to any available dye molecule, not just the molecule from which they originated. This would be the case if injected electrons avoided surface states (at least at these shorter times) and remained in the conduction band. (Notably, the power-dependent kinetic behavior persists in a rigid glass matrix. Consequently, possible... 

As is evident from the preceding discussion, the retention behavior of a polypeptide or protein P- expressed in terms of the capacity factor k is governed by thermodynamic considerations. Peak dispersion, on the other hand, arises from time-dependent kinetic phenomena, which are most conveniently expressed in terms of the reduced plate height he, . When no secondary effects, i.e., when no temperature effects, conformational changes, slow chemical equilibrium, pH effects, etc. occur as part of the chromatographic distribution process, then the resolution Rs, that can be achieved between adjacent components separated under these equilibrium or nearequilibrium conditions can be expressed as... 

The diffusive kinetics of geminate pairs have been predicted to show a time-dependent decaying behavior [117-122]. Early experiments showed, in contrast, a decay, with a being dependent on the proton concentration [123]. Experiments on longer time ranges with improved sensitivity are prerequisites for an accurate determination of the asymptotic behavior [124]. In fact, recent measurements on HPTS have demonstrated the validity of the theoretically predicted decay law (see Fig. 14.4) [125]. For 5-(methanesulfonyl)-l-naphthol a kinetic transition from power law to exponential has been reported due to a short photobase lifetime [126]. 

The simplest model of time-dependent behavior of a neutron population in a reactor consists of the point kinetics differential equations, where the space-dependence of neutrons is disregarded. The safety of reactors is greatly enhanced inherently by the existence of delayed neutrons, which come from radioactive decay rather than fission. The differential equations for the neutron population, n, and delayed neutron emitters, are... 

It is possible to distinguish between direct and indirect nOes from their kinetic behavior. The direct nOes grow immediately upon irradiation of the neighboring nucleus, with a first-order rate constant, and their kinetics depend initially only on the intemuclear distance r" indirect nOes are observable only after a certain time lag. We can thus suppress or enhance the indirect nOe s (e.g., at He) by short or long irradiations, respectively, of Ha- a long irradiation time of Ha allows the buildup of indirect negative nOe at He, while a short irradiation time of Ha allows only the direct positive nOe effects of Ha on He to be recorded. 

The time-dependent, rapid freeze-quench Mossbauer experiments with M. capsulatus (Bath) (51) indicate that decay of the peroxo species proceeds with the concomitant formation of another intermediate, named compound Q. This intermediate, observed in both the M. tri-chosporium OB3b (69, 70) and M. capsulatus (Bath) (51, 71) MMO systems by Mossbauer and optical spectroscopy, decays faster in the presence of substrates. Such behavior indicates that this intermediate is probably on the kinetic reaction pathway for hydroxylation (51, 70). 

The time-resolved, chemical behavior of FL depends on the solvent. Irradiation of DAF in cyclohexane gives FLH The lifetime of FL in cyclohexane is 1.4 ns, and the ratio of products obtained (26) indicates that both direct insertion and abstraction-recombination mechanisms are operating (Griller et al., 1984b). Replacement of the cyclohexane by its deuteriated counterpart reveals a kinetic isotope effect of ca 2 (Table 5). 

This section mainly builds upon classic biochemistry to define the essential building blocks of metabolic networks and to describe their interactions in terms of enzyme-kinetic rate equations. Following the rationale described in the previous section, the construction of a model is the organization of the individual rate equations into a coherent whole the dynamic system that describes the time-dependent behavior of each metabolite. We proceed according to the scheme suggested by Wiechert and Takors [97], namely, (i) to define the elementary units of the system (Section III. A) (ii) to characterize the connectivity and interactions between the units, as given by the stoichiometry and regulatory interactions (Sections in.B and II1.C) and (iii) to express each interaction quantitatively by... 

We can apply classical germination laws to this supersaturated system thus, the Avrami-Mempel laws confirm the unidimensional growth of the solid-like gel network. Induction times can also be studied in this framework 11). Here, we are interested first by the different kinetic behaviors which are dependent upon the location in the phase diagram of the initial solution defined by its supersaturation degree. 

The kinetics data of the geminate ion recombination in irradiated liquid hydrocarbons obtained by the subpicosecond pulse radiolysis was analyzed by Monte Carlo simulation based on the diffusion in an electric field [77,81,82], The simulation data were convoluted by the response function and fitted to the experimental data. By transforming the time-dependent behavior of cation radicals to the distribution function of cation radical-electron distance, the time-dependent distribution was obtained. Subsequently, the relationship between the space resolution and the space distribution of ionic species was discussed. The space distribution of reactive intermediates produced by radiation is very important for advanced science and technology using ionizing radiation such as nanolithography and nanotechnology [77,82]. 

Kinetic Considerations. The reaction kinetics are masked by a desorption process as shown below and are further complicated by rate deactivation. The independence of the 400-sec rate on reactant mole ratio is not indicative of zero-order kinetics but results because of the nature of the particular kinetic, desorption, and rate decay relationships under these conditions. It would not be expected to be more generally observed under widely varying conditions. The initial rate behavior is considered more indicative of the intrinsic kinetics of the system and is consistent with a model involving competitive adsorption between the two reactants with the olefin being more strongly adsorbed. Such kinetic behavior is consistent with that reported by Venuto (16). Kinetic analysis depends on the assumption that quasi-steady state behavior holds for the rate during rate decay and that the exponential decay extrapolation is valid as time approaches zero. Detailed quantification of the intrinsic kinetics was not attempted in this work. 

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