Activation rate constants

The exact quantum expression for the activated rate constant was first derived by Yamamoto [6]. The resulting quantum reactive flux correlation fiinction expression is given by... 

Haynes G R, Voth G A and Poliak E 1993 A theory for the thermally activated rate constant in systems with spatially dependent friction Chem. Phys. Lett. 207 309... 

The activity of initiators in ATRP is often judged qualitatively from the dispersity of the polymer product, the precision of molecular weight control and the observed rates of polymerization. Rates of initiator consumption are dependent on the value of the activation-deactivation equilibrium constant (A") and not simply on the activation rate constant ( acl). Rate constants and activation parameters are becoming available and some valuable trends for the dependence of these on initiator structure have been established.292"297... 

Transition metal-catalyzed atom transfer radical addition Atom transfer radical polymerization Equilibrium constant for atom transfer Activation rate constant for atom transfer Deactivation rate constant for atom transfer 2,2 -Bipyridine... 

Activation rate constants (k) in ATRP/ATRA are typically determined from model studies in which copper complex is reacted with alkyl halide in the presence of radical trapping agents such as TEMPO [127,128,129], Rates are determined by monitoring the rate of disappearance of alkyl halide in the presence of large excess of the activator (Cu X/L) and TEMPO. Under such pseudo-first order conditions, the activation rate constant can be calculated ln([RX]0/[RX]() vs.t plots (slope =-k) Cu C/... 

Other investigations include the effect of solvent, counterion, temperature, lig-and/catalyst ratio, and the presence of monomer and copper(II) complexes on the activation rate constant [133,134,135,136,137,138,139],... 

Additionally, deactivation rate constants (kd) for the more active catalysts such as Cu X/Me4CYCLAM have been estimated from the initial degree of polymerization without reactivation, end functionality, and molecular weight distributions [138,141,142], With recent advances in determination of the equilibrium constant for atom transfer (KATRP=kJkd), deactivation rate constants (k =k KX[M,) can now be easily obtained from readily accessible activation rate constants (k) [115],... 

Fig. 11 Correlation of activation rate constants (kac[) and deactivation rate constants with...

Tang W, Matyjaszewski K (2007) Effects of initiator structure on activation rate constants in ATRP. Macromolecules 40 1858-1863... 

Step 18. Fit C7 base condition adsorption constants and real-time activity rate constant fcj by using base case condition data on C6 and C7 charge stocks. 

In RRKM theory, the activation rate constant kact of Eq. 10.146 in QRRK theory is replaced by the more rigorous... 

The activated rate constant of electron transfer, k , is given by... 

The activation rate constant a controlling diffusion within the wells is expressed by the following equation ]84] ... 

The first problem discovered with the Lindemann model is the use of the simple collision theory, Eq. (1) for the activation rate constant. The collision frequency Zam can be calculated simply from collision theory, leaving the activation energy Eq to be determined. The low pressure limit is often difficult to attain experimentally, because collisions with impurities or collisions between... 

Thus, in a general situation, an electron transfer between a donor D and an acceptor A must be considered in terms of, at least, the three successive elementary steps outlined in Scheme 3. This representation may be even more segmented when, for example, different ion pairs are involved, such as [A , solvent, D" or [A , (solvent)n, D". Yet it is sufficient her to consider the simplest situation represented in Scheme 3 [45]. The formation or dissociation of cages in Scheme 3, each a physical process, is normally handled on physicochemical grounds. Yet following a notation by Debye their effects may be represented under the form of pseudo-rate constants k if (reactant pair) and k j. (product pair). Using this notation, it follows [46] that the overall kf and backward rate constant kb are given by Eqs. (48) and (49) as a function of the activation rate constants kp and kb relative to the pairs. 

Apparent forward (or backward) activation rate constant Equilibrium constant Acidity dissociation equilibrium constant Formal acidity dissociation equilibrium constant... 

In total, alkoxyamine systems with large cleavage (activation) rate constants tend to show small coupling (deactivation) rate constants. This provides large equilibrium constants that increase the conversion rates. It must not deteriorate the control since this depends on kd and the product k kc. In comparison, the more recently introduced nitroxides 6, 8, and 9 provide larger equilibrium constants than e.g. 3 (TEMPO). For acrylate-derived radicals, the equilibrium constants are usually smaller than for styryl type radicals, and this may, at least in part, explain the failure of TEMPO-regulated acrylate polymerizations. However, judging from model studies,62-63 this reason does not apply for methacrylates. 

AG, Free Energy of Activation Rate Constant Upper Limit on Concentration Diffusion-Controlled Limit Dropping the AG by 1.36 kcal/mol (5.73 kJ/mol) Increases the Rate of Reaction Tenfold at Room Temperature Reasonable Rate at 25°C Half-Life Lifetime of an intermediate Rate-Determining Step Transition State Position Reactivity vs. Selectivity Thermodynamic vs. Kinetic AG = AH -TAS, Enthalpy of Transition Entropy of Transition Stabilization of Intermediates Stabilization of Reactants... 

B5. Bau man, D. J., and Lytwyn, A., Tbromhin activation rate constant One-stage chro-mogenic assay for the extrinsic system. Thromb. Res. 26, 1-12 (1982). 

The exact quantum mechanical activated rate constant expression can be written as [85, 86]... 

J. D. Doll, J. Chem. Phys. 81, 3536 (1984). In Appendix A of this paper, it was speculated that the quantum-activated rate constant might be computed from classical dynamics on the Feynman-Hibbs effective potential energy surface. 

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