Activation-controlled rate constants

As mentioned in the very beginning, at low free energies of the electron transfer reaction (AH < 0.6 eV), activation-controlled rate constants... 

DELAIRE - I agree with you. The above-defined "activation-controlled rate constant", which is the expression of the "true" reactivity of species, may depend on distance, but is time-independent. However, the experimental rate constant has generally a contribution due to diffusion (see equation (26) ), and, due to the fact that a time interval is needed to establish steady-state profiles for the local concentrations of reactants, the experimental rate constant is time dependent. 

When the quenching reactions are rapid, the observed rate constant must be corrected for the effect of diffusion in order to obtain the activation controlled rate constant. The correction is made by applying... 

Where k 1 and k301 are forward and reverse activation-controlled rate cosntants, kd is the ate constant for the diffusion of the fragments out of the solvent cage, and dif is the bimolecular diffusion-limited rate constant. 

Since the reaction of Inh with the radicals has a low activation energy, is a diffusion-controlled rate constant for the reaction (about 10 lmol s depending on the viscosity of the melt) and thus, even for low concentrations of inhibitor, v 1. The oxidation rate, given by rp, will be very low until [Inh] < Ap[RH]/ ki and thereafter the oxidation will proceed as if there were no additive. This is shown schematically in Figure 1.41(a), and it may be seen that the induction period increases with the concentration, C, of inhibitor. If... 

The flux of an elementary heterogeneous reaction of B at a reactive surface Z is described by equation (7.10), where x is the activation-control (lux constant (heterogeneous rate constant) and I Bill is the concentration of B in solution at Z ( V = 0). 

Transition metal complexes functioning as redox catalysts are perhaps the most important components of an ATRP system. (It is, however, possible that some catalytic systems reported for ATRP may lead not only to formation of free radical polymer chains but also to ionic and/or coordination polymerization.) As mentioned previously, the transition metal center of the catalyst should undergo an electron transfer reaction coupled with halogen abstraction and accompanied by expansion of the coordination sphere. In addition, to induce a controlled polymerization process, the oxidized transition metal should rapidly deactivate the propagating polymer chains to form dormant species (Fig. 11.16). The ideal catalyst for ATRP should be highly selective for atom transfer, should not participate in other reactions, and should deactivate extremely fast with diffusion-controlled rate constants. Finther, it should have easily tunable activation rate constants to meet sped c requirements for ATRP monomers. For example, very active catalysts with equilibrium constants K > 10 for styrenes and acrylates are not suitable for methacrylates. 

Table 6.3 Rate constants for some donor-acceptor reactions of aromatic hydrocarbons with amine bases in acetonitrile, 3 is rate constant (M s ) at temperature T for reaction A - - D A + D+ /to s theoretical diffusion-controlled rate constant io = 4RT/r] (M s ). 3, Eq are the Arrhenius activation energies corre-...

Figure 10 shows that Tj is a unique function of the Thiele modulus. When the modulus ( ) is small (- SdSl), the effectiveness factor is unity, which means that there is no effect of mass transport on the rate of the catalytic reaction. When ( ) is greater than about 1, the effectiveness factor is less than unity and the reaction rate is influenced by mass transport in the pores. When the modulus is large (- 10), the effectiveness factor is inversely proportional to the modulus, and the reaction rate (eq. 19) is proportional to k ( ), which, from the definition of ( ), implies that the rate and the observed reaction rate constant are proportional to (1 /R)(f9This result shows that both the rate constant, ie, a measure of the intrinsic activity of the catalyst, and the effective diffusion coefficient, ie, a measure of the resistance to transport of the reactant offered by the pore stmcture, influence the rate. It is not appropriate to say that the reaction is diffusion controlled it depends on both the diffusion and the chemical kinetics. In contrast, as shown by equation 3, a reaction in solution can be diffusion controlled, depending on D but not on k. 

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