Rate constants, for transfers

Inhibitors are characterized by inhibition constants which are defined as the ratio of the rate constant for transfer to inhibitor to the propagation constant for the monomer in analogy with Eq. (6.87) for chain transfer constants. For styrene at 50°C the inhibition constant of p-benzoquinone is 518, and that for O2 is 1.5 X 10. The Polymer Handbook (Ref. 3) is an excellent source for these and most other rate constants discussed in this chapter. 

Dexter s formulation of exchange energy transfer (very weak coupling) In contrast to the inverse sixth power dependence on distance for the dipole-dipole mechanism, an exponential dependence is to be expected from the exchange mechanism. The rate constant for transfer can be written as... 

Because this chapter will be mainly concerned with the Forster mechanism of transfer, the results of the Forster theory, given in Section 4.6.3, are recalled here for convenience. The rate constant for transfer between a donor and an acceptor at... 

For an ensemble of donor and acceptor molecules distributed at random in an infinite volume, it is easy to calculate the sum of the rate constants for transfer from donor to all acceptors because all donors of this ensemble are identical in the rapid diffusion limit ... 

A 0f is the standard potential difference between phases a and p for this ion, kf is the standard rate constant for transfer of ion / and a is the charge-transfer coefficient. Concentrations c (a) and c (/3) correspond to the immediate vicinity of the phase boundary and are functions of the potential differences in the diffuse double layers according to the Boltzmann relationship... 

Case Relative Rate Constants for Transfer, Propagation, and Reinitiation Type of Effect Effect on Rp Effect on X ... 

The expression for rate constant for transfer is similar to the one derived for nonradiative processes within a molecule... 

Ki, K2, and K3 are composite constants involving a variety of rate constants, and K is the ratio of the rate constants for transfer to modifier, k, and for propagation (6). When K is large, (1— )K diminishes rapidly as a increases. Figure 5 shows plots of a number of curves derived from Equation 6. Apart from K, all other parameters are... 

First-order rate constant for transfer from pool A to pool B (day 1)... 

For many energy transfer processes, the interaction takes place when the partners are separated by more than the sum of the gas-kinetic collision radii. For example, energy transfer between excited singlet states of hydrocarbons occurs as fast as spontaneous decay at concentrations in benzene corresponding to a distance, r, between exchanging molecules of about 5 nm, or about 10 times the collision diameter. The measured rate constants for transfer of excitation in the hydrocarbons also seem greatly to exceed the diffusion-limited rate, and do not depend on solvent viscosity. 

Intermolecular electron transfer seems normally to require virtually direct contact between the donor and acceptor molecules. According to a widely accepted theory, the rate constant for transfer decreases exponentially with the separation of the donor and acceptor species. In fluids, the internu-clear separation fluctuates with time, so that transfer is dominated by the short-distance events. Under such circumstances, the transfer process can be regarded as a normal bimolecular reaction, for which in a transition-state formulation the rate coefficient, kt, is characterized by a free energy of activation, A G, equated somewhat arbitrarily with the activation energy, a, of the conventional Arrhenius expression ... 

Rate constant for transfer out of the initial vibrational level to all other vibrational states. Estimated error limits, 40%. 

Rate constants for transfer between the hyperflne levels of I P3/2 have not been measured. Yukov provided a theoretical estimate of 2.3 x 10 cm s for transfer induced by collisions with He, while Okunevich... 

Analogous results were obtained for the uncomplexed CD-St heptachromophoric cyclodextrin discussed in Section 7.2.4.2. In this case however, and owing to the larger Forster radius for homotransfer (22 A), the leveling of the anisotropy occurs in ca. 100 ps, and the average reciprocal rate constant for transfer is only 2.4 ps [14]. Nevertheless, a similar nearest neighbor distance (7 A) is recovered. 

The rate constants for transfer of hydride ion from l-alkyl-3-cyano-... 

Figure 4.3 Relative rate constants for transfer of trapped electrons to various organic acceptors in glassy MTHF at 77 K, From Beitz and Miller (1979).

We have a rate constant for transferring tritium from the enzyme-coenzyme complex to the product. The next thing to find out is how hot the enzyme-coenzyme complex gets during the course of the reaction. Then, with that rate constant, we should predict how hot the products can get. 

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