General Kinetic Scheme

Many cationic polymerizations are both rapid and heterogeneous, which makes the formulation of a rigorous kinetic scheme extremely difficult. At best, a scheme of general validity can be deduced, but this should not be applied indiscriminately. Following the steady-state approach outlined for radical reactions, the rate of initiation Vj of a cationic reaction is proportional to the catalyst-cocatalyst concentration c and the monomer concentration [M]. 

Termination can be taken as a first-order process in contrast to the free-radical mechanisms, and 

Although not universally applicable, this scheme gives an adequate description of the polymerization of styrene by SnCl4 in ethylene dichloride at 298 K. 

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A general kinetic scheme for mechanism-based inactivators is outlined as follows ... 

In conclusion, several examples of free radical polymerizations under phase transfer conditions have been described in the literature since the initial reports in 1981. In all of these cases it is apparent that transfer of an active species from one phase to a second phase is intimately involved in the initiation step of the polymerization. However, it is also clear that these are complex reactions mechanistically, and one general kinetic scheme may not be sufficient to describe them all. The extent of phase transfer and the exact species transferred will depend to a large extent upon the nature of the two phases, upon the... 

The kinetics of step polymerizations other than polyesterification follow easily from those considered for the latter. The number of different general kinetic schemes encountered in actual polymerization situations is rather small. Polymerizations by reactions between the... 

Although most polymerases conform to the general kinetic scheme, some polymerases have different mechanisms with regard to p/t binding and selection. Other aspects in the polymerase cycle such as dNTP binding, chemistry, and the conformational change will be discussed in later sections. 

After three decades of accumulating experimental results, we should be expected to have an almost complete knowledge of the rate equations that describe the most important thermosetting polymerizations. Unfortunately, the situation seems to be quite different on the one hand, some authors persist in using intrinsically incorrect methodologies to analyze kinetic data on the other hand, even for the most studied systems - e.g., the epoxy-amine reaction - no general kinetic schemes are universally accepted. 

General kinetic scheme 501 6.2. Trace amount determination of other ions 508... 

In order to develop a sound optimization policy, a good understanding of styrene polymerization kinetics is necessary. In the following section the general kinetic scheme of styrene homopolymerization is introduced. 

In order to understand the ORR reaction pathway, considering the general kinetics scheme of oxygen reduction reaction (Scheme... 

The general kinetic scheme (Fig. 7.34) displays two stages of diastereo-selection (1) a preferred formation of that of the two diastereomeric 1,4-... 

The general kinetic scheme shown in Scheme 8 has been developed for alkyl migration in [Mn(R)(CO)s] compounds. Thus, two pathways to the final product are avaUable (i) a second-order pathway (AiMn(R)(CO)5][L]) and (ii) a two-step sequence via the coordinatively unsaturated intermediate [Mn(COR)(CO)4]. In polar solvents, this intermediate may exist as a solvated hexacoordinate species, [Mn(COR)-(CO)4(S)] (S = molecule of solvent). In the absence of a suitably polar solvent, the intermediate is thought to adopt a square-based pyramidal conformation (99,100) with the acetyl ligand occupying a basal position, although a 7r-acyl derivative has also been proposed (101,102). 

Before using kinetic data for mechanistic studies, a general kinetic scheme for skeletal rearrangement should be proposed. Very high negative orders... 

The specificity of the reaction mechanism to the chemistry of the initiator, co-initiator and monomer as well as to the termination mechanism means that a totally general kinetic scheme as has been possible for free-radical addition polymerization is inappropriate. However, the general principles of the steady-state approximation to the reactive intermediate may still be applied (with some limitations) to obtain the rate of polymerization and the kinetic chain length for this living polymerization. Using a simplified set of reactions (Allcock and Lampe, 1981) for a system consisting of the initiator, I, and co-initiator, RX, added to the monomer, M, the following elementary reactions and their rates may be... 

It is clear from the above discussions that deriving a general kinetic scheme for cationic polymerizations is rather unrealistic. Nevertheless, we shall postulate a conventional polymerization reaction scheme based upon the chemistry given in the earlier sections and show where its inherent assumptions are questionable in cationic systems. An ideal reaction scheme is shown below ... 

Polymers usually exhibit fluorescence and phosphorescence emission similar to that of low molecular weight model compounds. A general kinetic scheme can be used to describe the absorption and dissipation of energy in polymer films and solutions (the notation of Birks [3] has been used throughout this section) namely,... 

Influence of Oxygen and RNO Concentrations on G( — RNO)350. The results shown in Figure 2 are difficult to understand on any simple competition scheme and appear to obey one of the possible combinations listed in the followed generalized kinetic scheme represented in the rate determining Equations 3a through 5, where X represents one or more primary or secondary intermediate radicals (or other radiolytic intermediates ). 

Dne might expect that the limits of reactor mixing determine directly the limits of reactor performance for more general kinetic schemes as well as the single convex or concave rate expression of the last section. Unfortunately nature is more subtle. We present next an example that dispels this notion, and then discuss what is known about the limits of reactor performance. This example is based on one presented by dasser, Hildebrandt and Godorr 111]. Levenspiel [17] shows how to find the optimal reactor configuration for this type of example. 

For an understanding of basic kinetic terms which we will frequently employ In this chapter. It Is essential to present a general kinetic scheme of the processes Involved In oxygenations... 

The solution behavior of exciplexes is even more complex, and accounts for the formation of radicals, triplet exciplexes and ordinary triplet states (2j0, 22). The general kinetic scheme for the photophysics of exciplexes has been summarized by Mattes and Farid (201 and is diagrammed below. Some of our results may be reconciled with the processes summarized by this scheme ... 

Scheme 1.1 General kinetics scheme for free-radical polymoization x is the numbo of primary free radicals R formed from one molecule of the initiator I (usually jr = 1 or 2) M represents either a molecule of monomer or a monomer unit in a polymer chain RM and RMp are propagating chain radicals with degrees of polymerization equal to n and p respectively RM , RMp and RM -MpR are terminated ( dead ) polymer chains with degrees of polymerization equal to n, p and n + p respectively T—A represents species which undergo chain transfer, the symbols for the individual rate coefficients are given above the reaction arrows for each process...

SCHEME 2.7 A more general kinetic scheme for the formation of cis- and trawi -P-lactams from monosubstituted ketenes and ( )-imines. 

The analysis of excimer and monomer emission in fluid systems is complex. A general kinetic scheme for excimer formation, including the inter- and intramolecular complex formation in terms of a singlet ground and excited states, and the various photophysical processes occurring in polymers, is given in Table 4.1. The three routes of energy... 

The general kinetic scheme (Scheme 8.2) has thus been proposed as representative of the ROP of lactide. In Scheme 8.2, C is the concentration of catalytic sites, M the concentration of lactide, A the concentration of octanoic acid, R the concentration of active chains with length n (number of lactoyl repeating units), D that of dormant chains with length n, and the different fc s (feai, a2, s> te) indicate the rate con-... 

We now describe the Bartlett model. The general kinetic scheme is shown in Fig. 2.39. The overall reaction sequence is... 

The most general kinetic scheme for a three-state system is the so-called photokinetic triangle (Scheme 15.10), described by Eqs. (15.48-15.50) (these are simple extensions of Eqs. (15.24—15.26). The decays are sums of three exponential terms (Eq. 15.49), and the kinetics involves nine unknowns (six reaction rate-constants and three reciprocal lifetimes). 

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