Radical concentration, quasi-equilibrium

Fig. 2 shows clearly that the quasi-equilibrium radical concentration sets the rate of fuel consumption and chemical heat release. It also shows the stability. Whatever the initial value of [r] it moves towards [R]e and remains there. It can only increase as [R]e increases with temperature. Thus, though the oxidation of methane is a branching chain reaction, fuel... 

The role of illumination consists in creating electron-hole pairs, which are necessary for the partial reactions. During the reduction of OBr" ions, Br radicals are formed as intermediates (cfr. reaction (55)), which appear to initiate an autocatalytic reaction mechanism surface states are formed, through which holes are injected into the valence band (at least at not too high OBr concentrations). These surface states, which are experimentally detected as a peak in the capacitance-potential plot [24, 81], are believed to be associated with adsorbed OBr. Furthermore, voltammetric experiments demonstrate that these surface states can be annihilated by a sufficiently large concentration of holes at the surface. The latter explains why this induced electroless etching effect is not observed at p-GaP, since in this case the holes are present at the surface in a quasi-equilibrium cloud of majority carriers, in contrast to the case of n-GaP. 

Being kinetically identical, the chains P nad Pm in the polymerization system de ned in Fig. 11.36 may be represented by the same symbol (P) for the termination reactions. Viewed in a relatively short time scale and considering a stationary state in which all reversible reactions are in equilibrium (or in quasi-equilibrium) and the concentrations of all radical species are (approximately) invariant with time, the following two equations should hold in respect of the propagating and intermediate radical concentrations (Kwak et al., 2004) ... 

With a continuous source of new radicals in the system, an equilibrium is achieved instantaneously between radical generation and consumption, such that Rinit = Rurm- This characteristic, proven to be true for almost all FRP conditions [6], is a result of the fast dynamics of radical reactions compared to that of the overall polymerization system. Often referred to as radical stationarity or the quasi-steady-state assumption (QSSA), it leads to the well-known analytical expression for total radical concentration [Eq. (9)]. 

The mentioned work of SFR to adjust the radical concentrations for a high preference of aoss-combination was originally recognized in the chemistry of low-mass compounds and termed the persistent radical effect (PRE). In the field of polymerization, such a work of X" was clearly recognized by Johnson et al. in their computer simulation work, and subsequently by Fukuda et al. and Greszta and Matyjaszewski, and clear experimental evidence for the inequality [X"] [P ] and the quasi-equilibrium in eqn [2] was first presented for a nitroxide-mediated LRP of styrene by Fukuda et al. Subsequently, Fischer made a detailed theoretical analysis of the PRE in polymerization. For more details about PRE, the readers are referred to the review by Fischer. ... 

The existence of the addition-fiagmentation quasi-equilibrium and the steadiness of the radical concentrations led to the following rate equation ... 

However, eqn (4.7) dilfers from the law of mass action in the usual sense since it contains the initial concentration [R R NORjo instead of the momentary concentration [R R NOR]. Moreover, the radical concentrations [R R NO ] and [R ] are time-dependent, even though the time dependence cancels out. For these reasons, the equilibrium (4.7) is often called a quasi-equilibrium. Fukuda et independently derived the eqn (4.4) and (4.5) using the ad hoc... 

In the presence of the RTCP catalysts, Rp is somewhat smaller than in their absence (IMP), as shown in Figure 7.10a (and Figure 7.3a) for the St/PSt I/BPO with and without Gel4 at 80 °C. This is because A undergoes irreversible crosstermination with Polymer (rate constant This mechanism is analogous to the one for the rate retardation in the RAFT polymerization, where the intermediate radical (Polymer-(X )-Polymer) undergoes the relevant crosstermination. In theory, when the quasi-equilibrium of RT holds and the radical concentrations [Polymer ] and [A ] are stationary, Rp is given by eqn (7.3). ... 

We see that the rate of production of products is determined by two quantities, the first a quasi-thermodynamic quantity, the equilibrium concentration of free radicals, and the second a kinetic quantity, namely, the rate at which each radical can go through a chain cycle. When the cycle is made up of two steps of disproportionate speed as in the present case, it is the slower step (in this case Br + H2) which is of importance in determining the over-all rate. It is this feature which explains in this case the specific inhibition by HBr even though the over-all reaction is essentially not reversible. The slow step in a chain will in general (though not always) be endothermic. This implies that its reverse is exothermic and hence of lower activation energy, and so faster. We can thus always expect inhibition by products in chain reactions except in those cases in which the fast steps are of unusual speed. 

---