Kinetic species

For any chemical reaction, whether inorganic or organic, we must choose which kinetic species to include in the elementary reactions that make up the overall process ideally, molecular or chemical information is available to guide this choice. In general, for an elementary (irreversible) reaction among species A and B, to give species C and D, in relative amounts a, b, c, and d, respectively. 

It is generally agreed that there is a common sequence of mechanistic pathways for all PASCs as shown earlier in Scheme 1. Though the partially hydrogenated thiophene intermediate is illustrated in that scheme as a tetrahydro derivative, it has been shown that this intermediate is, in reality, an equilibrium mixture of the tetra- and hexahydrodibenzothiophenes. The rate of equilibration is at least 10 times greater than the other associated rates. Thus, the pair can be treated as a single kinetic species (26). 

In Eq. 1.3, i A = -1 for any A and uB = +1 for any B. Since Eq. 1.3 is an overall reaction, the assumption of constant stoichiometry underlying the definition of is not trivial, as discussed in Section 1.1. For example, at high pH, Eq. 1.28 would not always be applicable because of the influence of the reactions in Eqs. 1.1 and 1.5. On the other hand, at equilibrium, when the hydration reaction is described by Eq. 1.10, the application of Eq. 1.28 is possible. This fact serves to emphasize the difference between equilibrium chemical species that figure in thermodynamic parameters (e.g., Eq. 1.11) and kinetic species that figure in the mechanism of a reaction. The set of kinetic species is in general larger than the set of equilibrium species for any overall chemical reaction. 

The mechanistic significance of Eq. 3.1, despite its great utility in mineral solubility studies, is, on the other hand, almost nil. No implication of reaction pathways, other than the postulate of stoichiometric control of aqueous-phase products, can be made on the basis of an overall reaction alone, since it features only enough species to satisfy minimal equilibrium criteria. Any number of additional kinetic species can intervene to govern the reaction pathways, which may be parallel, sequential, or a combination of these two, and the detailed interactions of the solid phase with the aqueous phase are often unlikely to be represented accurately by a spontaneous decomposition reaction like Eq. 3.1. As a case in point, the dissolution reaction of calcite (the forward reaction in Eq. 3.14) may be considered. Given the existence of protons and carbonate species in the aqueous-solution phase, at least three overall reactions more specific than Eq. 3.14 can be postulated to epitomize the detailed interactions of calcite with aqueous species 7,33,34... 

Strictly speaking, any multi-step kinetic scheme will involve a lag. However, realistically observing hysteresis in enzyme kinetics is always associated with the existence of one of several slow step(s) prior to the final step. This is because if all the steps prior to the final step were fast, then there would be a rapid pre-equilibriation and the rapid steps could be lumped into a single kinetic species (see Section 4.2.1). 

Time-resolved fluorescence studies of fluorene-fluorenone copolymers in dilute toluene solution, enable us to identify different time regimes in the photoluminescence (PL) decay. Figure 18 shows the results of a maximum entropy method (MEM) analysis of the PL decays of fluorene-fluorenone copolymers [58] collected at the fluorene emission wavelength [66]. The different time regimes of the PL decay are associated with different kinetic species which migrate to the defects, most typically these are the CTS defects... 

Analysis of receptor/ligand interactions is made much more complicated by explicit consideration of these physical features. Without such considerations, we are often able to model receptor phenomena with first-order ordinary differential equations based on straightforward mass-action kinetic species balances. When diffusion and probabilistic effects are taken into account, the models can easily give rise to partial differential equations, second-order ordinary differential equations, extremely large sets of first-order ordinary differential equations, and/or probabilistic differential equations. 

Fe, liver and kidney for cobalt nuclides, liver and prostate for Zn, skeletal muscle for Cs, and GI tract for Zr. The persistence of radionuclides in mammals varies with the chemical form, kinetics, species, and other variables. Thus, the time for 50% persistence of selected radionuclides in whole-animal studies ranges from 19 h to 14 days for 4 to 35 days for Cs 5 to 12h for the short-lived component of Co, 5 to 21 days for the long-lived component 25 to 593 days for Sr and 4 to 26 days for... 

The above results highlight the important role that can be played in the self-assembly process by the different conformations of the L2-type ligands. The reaction between L2(x=2) and Ag was reinvestigated, with a special emphasis on the kinetic species that may or may not be direct intermediates toward the thermodynamically stable [3 x 3] grid. The [3 x 3]-Ag9 grid forms immediately, as the only reaction product, when the two components are mixed in the correct stoichiometric ratio... 

Polymerization to equilibrium occurs without termination or transfer and with only one kinetic species. When polymerization begins, all the growing ends P should already exist (infinitely fast start reaction). This case is found, for example, in the polymerization of lauryl lactam,... 

Um and Wang [63] used a three-dimensional model to study the effects an interdigitated flow field. The model accounted for mass transport, eleetroohemieal kinetics, species profiles and ciurent density distribution within the eell. Interdigitated flow fields result in foreed convection of gases, which aids in liquid water removal at the cathode. This would help improve performance at high current densities when transport limitations due to exeessive... 

The analysis of time-resolved fluorescence decay curves, using a sum of discrete exponential functions to fit the experimental data, is based on a simple assumption the number of different exponential terms used has to be equal to the number of kinetically different excited state species present in the molecular system. While this assumption has the advantage of providing a clear physical meaning for the fitting parameters, decay times and pre-exponential coefficients, the identification of the different kinetic species is frequently not evident, particularly in more complex systems like polymers and proteins, and this approach has been questioned [85]. 

Interestingly, these authors observed a different kinetic behavior of this system in the two solvents this phenomenon was explained by a two-step mechanism involving distinct kinetic species as a function of the... 

The traditional approach to understanding both the steady-state and transient behavior of battery systems is based on the porous electrode models of Newman and Tobias (22), and Newman and Tiedermann (23). This is a macroscopic approach, in that no attempt is made to describe the microscopic details of the geometry. Volume-averaged properties are used to describe the electrode kinetics, species concentrations, etc. One-dimensional expressions are written for the fluxes of electroactive species in terms of concentration gradients, preferably using the concentrated solution theory of Newman (24). Expressions are also written for the species continuity conditions, which relate the time dependence of concentrations to interfacial current density and the spatial variation of the flux. These equations are combined with expressions for the interfacial current density (heterogeneous rate equation), electroneutrality condition, potential drop in the electrode, and potential drop in the electrolyte (which includes spatial variation of the electrolyte concentration). These coupled equations are linearized using finite-difference techniques and then solved numerically. 

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