Activation-deactivation processes equilibrium constant

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. 

At low cM, the rate-determining step is the second-order rate of activation by collision, since there is sufficient time between collisions that virtually every activated molecule reacts only the rate constant K appears in the rate law (equation 6.4-22). At high cM, the rate-determining step is the first-order disruption of A molecules, since both activation and deactivation are relatively rapid and at virtual equilibrium. Hence, we have the additional concept of a rapidly established equilibrium in which an elementary process and its reverse are assumed to be at equilibrium, enabling the introduction of an equilibrium constant to replace the ratio of two rate constants. 

ATRA/ATRP process is typically determined by measuring the activation ka), deactivation (kd) and overall equilibrium constant for atom transfer Katra/atrp) (Scheme 4) 7 38,41,43 46 complexes that have similar halidophilicities ... 

The system Co-imidazole-aminoacid is active for many cycles (more than 100) and is one of the most effective carriers of both gases. Moreover it is characterized by a favourable temperature range (0-50°C) which determines the existence of the free and oxygenated species at 1 atmosphere of oxygen pressure, as indicated by the values of the equilibrium constants (14). Oxygenated species of these complexes are also relatively resistant (especially in the case of proline and sarcosine) to the spontaneous deactivating intramolecular oxidation processes. 

Detailed balance relates the rates of a particular activation and deactivation energy transfer process. Detailed balance thus provides a quantitative exact relation between rate constants that correspond to the same gap. This is unlike the principle of exponential gap tiiat provides an estimate of how the rate constants vary when the gap changes. The quahtative implication of detailed balance is that on a quantum state-to-quantum state basis, the rate constant for the activation process is always smaller than the rate constant for the reverse deactivation process. Take as an example the V—T process that we started this section with, A -I- BC(v = 0) A -I- BC(v = 1) and the reverse deactivation process, A -I- BC(v = 1) A -I- BC(v = 0). Detailed balance states that at equilibrium the rates of these two detailed ways of transferring populations between BC(v = 1) and BC(v = 0) must be equal. This is to be so even though there may be other processes that can transfer populations, such as transitions in the IR. Therefore, using the subscript eq to designate concentrations at equilibrium,... 

The ATRP process is characterized by the ATRP equilibrium constant, which can be defined as either the ratio of the rate constants of activation and deactivation or as the ratio of concentrations of all involved species. 

Logically, this section should discuss the other rate constant characterizing the ATRP process, namely the deactivation rate constant, kdeact- However, the values of kdeact are typically rather large and difficult to determine experimentally. They are often calculated as the ratio kdeact = kact/KAXRP of the much easier to determine rate constant of activation and equilibrium constant of ATRP. This is why this section is dedicated to the experimental determination of Katrp as well as to the factors (initiator and catalyst structure, solvent, etc.) that influence its values. As seen from eqn (2), the rate of polymerization under classical ATRP conditions depends on the value of the equilibrium constant. 

In complete equilibrium, the ratio of the population of an atomic or molecular species in an excited electronic state to the population in the groun d state is given by Boltzmann factor e — and the statistical weight term. Under these equilibrium conditions the process of electronic excitation by absorption of radiation will be in balance with electronic deactivation by emission of radiation, and collision activation will be balanced by collision deactivation excitation by chemical reaction will be balanced by the reverse reaction in which the electronically excited species supplies the excitation energy. However, this perfect equilibrium is attained only in a constant-temperature inclosure such as the ideal black-body furnace, and the radiation must then give -a continuous spectrum with unit emissivity. In practice we are more familiar with hot gases emitting dis-... 

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