General Kinetics Considerations

A. General Kinetic Considerations For an electron transfer reaction of the type represented by Eq. (2),... 

Copolymerization involves the simultaneous chain polymerization of a mixture of two or more monomers (Hillmyer, 2012 Ham and Alfrey, 1964 Odian, 2004a Tirrell, 1986). Aside from the general kinetic considerations which govern these chain reactions, as described earlier, there is imposed an additional... 

Copolymerization involves the simultaneous chain polymerization of a mixture of two or more monomers [89-92], Aside from the general kinetic considerations which govern these chain reactions, as described earlier, there is imposed an additional feature, i.e., the relative participation of the different monomers during the growth of the chain. This new parameter is most important, since it controls the composition of the copolymer. Systems involving more than two monomers are difficult to resolve in this respect, but it has been found possible to treat the case of a pair of monomers with relative ease [91,93-95]. 

General Kinetic Considerations in Chemical Laser Operation at Short Wavelengths... 

There are two general theories of the stabUity of lyophobic coUoids, or, more precisely, two general mechanisms controlling the dispersion and flocculation of these coUoids. Both theories regard adsorption of dissolved species as a key process in stabilization. However, one theory is based on a consideration of ionic forces near the interface, whereas the other is based on steric forces. The two theories complement each other and are in no sense contradictory. In some systems, one mechanism may be predominant, and in others both mechanisms may operate simultaneously. The fundamental kinetic considerations common to both theories are based on Smoluchowski s classical theory of the coagulation of coUoids. 

Studies with other glycosidases " " showed, however, that effective inhibition by glycals is not a general phenomenon, and that inhibition does not correlate well with hydration to 2-deoxy-o-hexoses. Based on kinetic considerations, the interaction of glycosidases with D-glycals (A) can be described by the following scheme ... 

In fact, most reports of substantial rate enhancements by MW in open vessels are in reactions performed under dry-media conditions, in which the reactants are absorbed on inert solid supports [11-16] Since one or more of the reactants is usually a liquid at the reaction temperature [44], these reactions are performed under heterogeneous conditions. Although it is difficult to perform kinetic studies on these reactions, there is little doubt that they generally occur considerably faster than similar conventionally heated reactions. 

I have discussed two cases of chain microstructure determination in SO2 copolymers. First, the styrene-S02 system, which exhibits the general kinetic and compositional behavior of such systems, particularly as a function of polymerization temperature. Second, and considerably more complicated, is the chloroprene-S02 system. This one represents the limit of what can be handled and more or less completely solved at the present time. To do so requires about all o ir resources at superconducting frequen-... 

In general, carbides, nitrides, and borides are manufactured in the vapor phase in order to form high-purity powders. This procedure is fundamentally different than a strict CVD process, since in powder synthesis reactors, deposition on seed particles may be desirable, but deposition on the reactor walls represents a loss of product material. As we will see, in CVD, heterogeneous deposition on a surface will be sought. Aside from this issue of deposition, many of the thermodynamic and kinetic considerations regarding gas phase reactions are similar. 

Let us now turn to some kinetic considerations of NAC reduction. As an example, consider the time courses of nitrobenzene (NB) concentration in 5 mM aqueous hydrogen sulfide (H2S) solution in the absence and presence of natural organic matter (Fig. 14.7). As is evident, although reduction of NB by H2S to nitrosobenzene and further to aniline (Eq. 14-31) is very favorable from a thermodynamic point of view (see Fig. 14.4), it seems to be an extremely slow process. However, when DOM is added to the solution, reduction occurs at an appreciable rate (Fig. 14.7). In order to understand these findings, some general kinetic aspects of redox reactions involving NACs should be recognized. 

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. 

Studies undertaken with petroleum feedstocks to elucidate an understanding of hydrodemetallation reactions have yielded ambiguous and in some cases conflicting results. Comparison of kinetic phenomena from one study to the next is often complicated. Formulation of a generalized kinetic and mechanistic theory of residuum demetallation requires consideration of competitive rate processes which may be unique to a particular feedstock. Catalyst activity is affected by catalyst size, shape, and pore size distribution and intrinsic activity of the catalytic metals. Feedstock reactivity reflects the composition of the crude source and the molecular size distribution of the metal-bearing species. 

Generally, sorption estimates are based on equilibrium conditions only however, incorporation of kinetic considerations into sorption estimation techniques is likely to be an important area of future work. For example, the assumption of equilibrium sorption in dynamic field systems may result in calculating too much pesticide in the sorbed state. 

A general kinetic model should accommodate all chemical processes known to affect the dechlorination process. These include (1) reductive dechlorination takes place on the iron surface, rather than in the aqueous phase, so adsorption must occur (2) other components in the system may affect the dechlorination reaction by competing for the reaction sites (3) surface sites for reduction and for sorption may not be the same, as for the system with PCE and TCE where dechlorination takes place on the reactive sites, but most of the adsorption is clearly on the nonreactive sites (Burris et al., 1995). In the following section we will first discuss a single-site model similar to the one used by Johnson et al. (1998), which has accounted for the first two observations, then develop a two-site model that will also take the third observation into consideration. We aim to illustrate how coadsorbates in the iron system will affect adsorption and reduction of chlorinated solvents. TCE will be used as an example since relevant adsorption and reduction data are available, from which the required parameters for simulation could be estimated. 

The preceding introduction might lead one to believe that this chapter could simply be divided into two basic parts—thermochemical considerations and kinetic considerations—which would cover all the relevant subject matter. However, in the last decade, first-principles (ab initio) computations have become commonplace and their results have often confirmed predictions based on thermochemical approaches, sometimes even surpassing them in accuracy. Hence, there is a need to encompass both thermochemical and ab initio treatments. We group the latter under the heading structural energetics and explore this topic further in Section 2.2. We also talk about the relevant thermodynamic and kinetic factors for specific systems in their respective chapters. For now, we discuss thermodynamics and kinetics in the most general terms. 

The original derivation of the BET equation was an extension and generalization of Langmuir s treatment of monolayer adsorption. This derivation is based on kinetic considerations—in particular on the fact that at equilibrium the rate of condensation of... 

Calculations of copolymer composition are based on kinetic considerations and procedures. In spite of this, less attention has been paid to the copropagation rate than to other copolymerization problems. Today a single concise theory is available, solving the rate of the simplest radical binary copolymerization. Other cases described have not been generalized so far they treat the kinetic behaviour of specific monomer pairs or triplets in specific polymerization circumstances. 

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