Simplified Kinetic Scheme

It is clear from the above discussions that deriving a general kinetic scheme for cationic polymerizations is rather unrealistic. Nevertheless, we shall postulate here a conventional polymerization reaction scheme based upon the chemistry given in the earlier sections and show where the implied assumptions are not realistic enough. Using an ideal reaction scheme, we may depict a cationic polymerization by the following set of elementary reactions  

To proceed further, we may now assume a steady state in the concentration of the active species d = 0). An assumption that this occurs due to i ,- = Rt 

Problem 8.19 Derive expressions for cationic polymerization rate for the following three cases (a) an added chain transfer agent terminates the kinetic chain [Eq. (8.117)] (b) 

How would the order dependence of the polymerization rate change if either monomer or any of the components of the initiating system is involved in solvating the propagating 

The expressions given above can be employed only if the steady-state conditions exist, at least over some part of the overall reaction. Steady-state is implied if Rp is constant with conversion. However, many, if not most, cationic polymerizations proceed so rapidly that the steady-state is not achieved and even in slower polymerizations, the steady-state may not be achieved if Ri Rt. 

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Sharma et al. (2005) developed a ID two-phase model for the analysis of periodic NOx storage and reduction by C3H6 in a catalytic monolith, based on a simplified kinetic scheme. They focused on the evaluation of temperature and reaction fronts along the monolith and their effect on NOx conversion. Kim et al. (2003) proposed a phenomenological control-oriented lean NOx trap model. 

In the last two cases, we would still expect a behavior of the short-wavelength FB band similar to that of DMABN There, the kBA channel toward the TICT state leads to efficient fluorescence quenching of FB. This can be seen directly in the low-temperature range, for example, in Fig. 2.1 (Section II.A), below 180 K, where the quantum yield of FB fluorescence increases upon cooling because the horizontal radiationless transition kBA is slowed down. The simplified Kinetic Scheme II, also valid for any other monomolecular quenching process, describes this... 

Scheme 2. Simplified kinetic scheme without photochemical processes.

Figure 6 Simplified kinetic scheme for the interaction between a substrate and an effector molecule for an enzyme with two binding sites within the active site. Source From Ref. 17.

Scheme 3.3 Simplified kinetic scheme for flavour generation by the Maillard reaction130...

F. Jousse, T. Jongen, W. Agterof, S. Russell, and P. Braat, Simplified kinetic scheme of flavor formation by the Maillard reaction, J. Food Sci., 2002, 67, 2534-2542. 

In Minero s Case 2, the concentration of the substrate is high or it is very hydrophobic, although it should be borne in mind that such a scenario may result in the oxidised substrate behaving as an extrinsic recombination centre. A direct consequence of this is that Minero s model is no longer applicable as his simplified kinetic scheme did not consider this reaction. Thus, the utility of the resultant expressions is limited to mainly very hydrophobic or poor water soluble compounds at low concentrations. Under these conditions, equation (9.59) simplifies to... 

Note that in the simplified kinetics scheme that is discussed here, the rate of CO dissociation equals the rate of "Ci" production. In Figure 3a, the relationship between rate of "Ci" production and product selectivity is sketched. 

The final kinetic scheme describing the propylene-NOa photooxidation is quite complex, and the qualitative, determining characteristics of the system become obscured in the computational detail. A simplified kinetic scheme is given below that provides a framework for the overall description. 

Figure 7.34. A simplified kinetic scheme for the diastereoselective oxetane formation in the Patemo-BQchi reaction (kj and 2 as well as k, and kj include intersystem crossing steps) (by permission from Buschmann et al., 1989).

From this simplified kinetics scheme, one obtains23 ... 

The observed monomer and excimer fluorescence decays of Py on Si-C g can be understood within the context of a simplified kinetic scheme comprising two groups of kinetically distinct pyrene molecules, Py(1) and Py(2), see Scheme (IV). In the octadecyl layer, these two sets of molecules are assumed to reside in regions of... 

Figure 4 Simplified kinetic scheme of single-nucleotide incorporation by a DNA polymerase. Step 1, Mg-dNTP binding step 2, N-subdomain closing step 3, catalytic Mg + binding step 4, nucleotidyl transfer (chemistry) step 5, catalytic Mg " dissociation step 6, N-subdomain reopening step 7, pyrophosphate release. E = DNA polymerase in open conformation E = closed conformation D = DNA substrate D + = DNA product elongated by addition of one nucleotide N = Mg dNTP M = catalytic Mg " P = Mg PP. Reproduced with permission from M. Bakhtina S. Lee Y. Wang C. Dunlap B. Lamarche M. D. Tsai, Biochemistry 2005, 44, 5177-5187. Copyright 2005 American Chemical Society.

A SIMPLIFIED KINETIC SCHEME Luclo Fornl and Roberta Mlgllo... 

A simplified kinetic scheme, taking Into account all the mentioned hypotheses, takes the form... 

Comparison of the molar flowrates of C2H6 and C2H4 for the exact solution (solid lines) and the simplified kinetic scheme (dashed lines),. ... 

The simplest possible kinetic scheme is the Uni Uni kinetic scheme (Scheme 8.1), where Uni indicates one substrate and the second Uni indicates the evolution of only a single product. The main feature of this highly simplified kinetic scheme is the presence of an intermediate chemical species designated ES that is a complex (essentially non-covalent) between biocatalyst E and substrate molecule S. This is sometimes referred to as the Michaelis complex for reasons that will become apparent shortly Given such a simple mechanistic scheme, v can be expressed as... 

While being useful exercises, both of these simulations were based on simplified kinetic schemes and physical models of spur dynamics. For some problems (free ion yields) these considerations may be of little importance, for other (product yields) the oversimplification leads to ambiguous results. In particular, this applies to calculations of the "singlet yields" (implicitly identified with the yields of the lowest Si states) where the estimates entirely depend on the kinetic scheme [85,86]. Most of such calculations address only one facet of the problem the relative significance of "geminate" recombination and cross-recombination in multiple-pair spurs. In the recent Monte-Carlo simulations [85], the initial spatial distribution of ionization events was calculated using the same approach that was used in the calculations of the free ion yield (see above). The total yield of singlet recombination for the primary pairs was estimated. 

The example considered here is again the hydrocarbon oxidation process with its simplified kinetic scheme used in Sec. 11. S.b. Suppose the reactor is at a temperature of 362 C and let the gas entering the bed be 362 C. How long will it take to... 

A simplified kinetic scheme of a many-electron process has been proposed which takes into consideration not every but only those of the reactions (1.6) where i = j, that is, N - 1 disproportionation reactions of general kind [16, 20-22]... 

The simplified kinetic scheme in Fig.l illustrates both, the complex nature of the reverse ET from P+H and its connection to the forward ET processes. In quinone-free RCs further ET from H is blocked leading to a lifetime of the radical pair (RP) P+H of = 10 ns at 300K. This is sufficiently long to allow the hyperfine interaction (HFl) to induce transitions between the initially generated singlet and the triplet (P+H") RP states and to open... 

Fomi, L. and MigUo, R., Catalytic synthesis of 2-methylpyrazine over Zn-Cr-O/Pd a simplified kinetic scheme. Heterogeneous Catalysis and Fine Chemicals 111, 329-336,1993. 

In Section 2.1.4, we presented the simplified kinetic scheme for the description of unimolecular reactions for thermal activation. The macroscopic rate constant of the unimolecular reaction kuni depends on the total concentration of the buffer gas [M]. In the limit of low [M] concentration, the rate constant characterizes the activation process, and in the limit of high [M] concentrations the rate constant characterizes the unimolecular reaction. Under the conditions of medium [M] concentrations, the activation rate is comparable with that of unimolecular reactions. Thus, only bears... 

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