Transfer rate constants

After some straightforward manipulations of A3.8.22. the PI-QTST estimate of the proton transfer rate constant can be shown to be given by 48... 

A transfer rate constant can be obtained by applying a Boltzmann distribution, and by writing the concentration of reactant present as... 

Van der Spoel,D., Berendsen, H.J.C. Determination of proton transfer rate constants using ab initio, molecular dynamics and density matrix evolution calculations. Pacific Symposium on Biocomputing, World Scientific, Singapore (1996) 1-14. 

The thiol ( -dodecyl mercaptan) used ia this recipe played a prominent role ia the quaUty control of the product. Such thiols are known as chain-transfer agents and help control the molecular weight of the SBR by means of the foUowiag reaction where M = monomer, eg, butadiene or styrene R(M) = growing free-radical chain k = propagation-rate constant = transfer-rate constant and k = initiation-rate constant. 

The first type of interaction, associated with the overlap of wavefunctions localized at different centers in the initial and final states, determines the electron-transfer rate constant. The other two are crucial for vibronic relaxation of excited electronic states. The rate constant in the first order of the perturbation theory in the unaccounted interaction is described by the statistically averaged Fermi golden-rule formula... 

In the strong-coupling limit at high temperatures the electron transfer rate constant is given by the Marcus formula [Marcus 1964]... 

As an illustration of these considerations, the Arrhenius plot of the electron-transfer rate constant, observed by DeVault and Chance [1966] (see also DeVault [1984]), is shown in fig. 13. 

The exponent in this formula is readily obtained by calculating the difference of quasiclassical actions between the turning and crossing points for each term. The most remarkable difference between (2.65) and (2.66) is that the electron-transfer rate constant grows with increasing AE, while the RLT rate constant decreases. This exponential dependence k AE) [Siebrand 1967] known as the energy gap law, is exemplified in fig. 14 for ST conversion. 

Thus the greater the transfer rate constant and the concentration of the transfer agent the lower will be the molecular weight Figure 2.19). 

This means that the PMC signal will, apart from the generation rate of minority carriers and a proportionality constant, be determined by the interfacial charge transfer rate constant kr and the interfacial charge recombination rate sr... 

The interfacial charge-transfer rate constant can be determined when the PMC signal and the photocurrent are measured simultaneously. When the interfacial charge transfer is, on the other hand, very large and Aps negligible, the PMC value becomes... 

M] = monomer concentration [l] = initiator concentration [R ] = radical concentration f = initiator efficiency k-j g = chain transfer rate "constant" ktr = termination (combination or disproportionation) rate constant... 

EPR studies on electron transfer systems where neighboring centers are coupled by spin-spin interactions can yield useful data for analyzing the electron transfer kinetics. In the framework of the Condon approximation, the electron transfer rate constant predicted by electron transfer theories can be expressed as the product of an electronic factor Tab by a nuclear factor that depends explicitly on temperature (258). On the one hand, since iron-sulfur clusters are spatially extended redox centers, the electronic factor strongly depends on how the various sites of the cluster are affected by the variation in the electronic structure between the oxidized and reduced forms. Theoret-... 

Figure 15. Relationship between electron transfer rate constant ke and hydrogen generation rate constant. (Reprinted from Ref [194], 2000, with permission from lUPAC.)...

Early studies of ET dynamics at externally biased interfaces were based on conventional cyclic voltammetry employing four-electrode potentiostats [62,67 70,79]. The formal pseudo-first-order electron-transfer rate constants [ket(cms )] were measured on the basis of the Nicholson method [99] and convolution potential sweep voltammetry [79,100] in the presence of an excess of one of the reactant species. The constant composition approximation allows expression of the ET rate constant with the same units as in heterogeneous reaction on solid electrodes. However, any comparison with the expression described in Section II.B requires the transformation to bimolecular units, i.e., M cms . Values of of the order of 1-2 x lO cms (0.05 to O.IM cms ) were reported for Fe(CN)g in the aqueous phase and the redox species Lu(PC)2, Sn(PC)2, TCNQ, and RuTPP(Py)2 in DCE [62,70]. Despite the fact that large potential perturbations across the interface introduce interferences in kinetic analysis [101], these early estimations allowed some preliminary comparisons to established ET models in heterogeneous media. 

FIG. 10 Potential dependence of the electron-transfer rate constant k i) normalized to the value at the potential of zero charge TCNQ reduction by hexacyanoferrate at the water-DCE... 

FIG. 21 Complex IMPS spectra obtained for the photo-oxidation of DFcET by ZnYPPC" at the water-DCE interface (a). The opposite potential dependencies of the phenomenological ET rate constant and the porph5rin coverage (b) are responsible for the maximum on the flux of electron injection obtained from IMPS responses for DFcET and Fc (c). The potential dependence of the back electron-transfer rate constant is also shown in (d). (From Ref. 83. Reproduced by permission of The Royal Society of Chemistry.)... 

The driving force for the transfer process was the enhanced solubility of Br2 in DCE, ca 40 times greater than that in aqueous solution. To probe the transfer processes, Br2 was recollected in the reverse step at the tip UME, by diffusion-limited reduction to Br . The transfer process was found to be controlled exclusively by diffusion in the aqueous phase, but by employing short switching times, tswitch down to 10 ms, it was possible to put a lower limit on the effective interfacial transfer rate constant of 0.5 cm s . Figure 25 shows typical forward and reverse transients from this set of experiments, presented as current (normalized with respect to the steady-state diffusion-limited current, i(oo), for the oxidation of Br ) versus the inverse square-root of time. 

M sulfuric acid to air [34]. As discussed above, for the aqueous-DCE interface, the rate of this irreversible transfer process (with the air phase acting as a sink) was limited only by diffusion of Bt2 in the aqueous phase. A lower limit for the interfacial transfer rate constant of 0.5 cm s was found [34]. 

FIG. 29 Oxygen-transfer rate constants derived from Fig. 28 as a function of the reciprocal of the interfacial area per molecule. (Reprinted from Ref 19. Copyright 1998 American Chemical Society.)... 

Fig. 5. Plot of apparent electron self exchange rate constants kf P, derived from polymer De values for films containing the indicated metals, mixed valent states, and ligands, all in acetonitrile, using Equation 2, vs. literature heterogeneous electron transfer rate constants k° for the corresponding monomers in nitrile solvents. See Ref. 6 for details. (Reproduced from Ref. 6. Copyright 1987 American Chemical Society.)...

The donor-acceptor complexes [Ir(/r-dmpz)(CO)(PPh2 0(CH2)2R )]2 exhibit photo-induced electron-transfer rate constants of 1012s—1 and charge recombination rates slower than 2 x 10los-1 when R = pyridine and 4-phenylpyridine.534 Further studies on these complexes revealed that recombination reactions were temperature dependent and slower for the deuterated acceptors.535... 

Xu Xj = amount of drug in compartment 1 and j, respectively ky, kjt = first-order transfer rate constants from compartment 1 to j and from compartment j to 1, respectively Fi0, kj0 = first-order exit rate constants from compartment 1 and j, respectively... 

FI = continued product where any term is defined as equal to 1 when the index takes a forbidden value, i.e., i = 1 in the numerator or m = j in the denominator X = summation where any term is defined as equal to zero when the index j takes a forbidden value, i.e., j = 1 ky, kji = first-order intercompartmental transfer rate constants Eh Em = sum of exit rate constants from compartments i or m n = number of driving force compartments in the disposition model, i.e., compartments having exit rate constants... 

Disposition rate constants are functions of the intercompartmental transfer rate constants and exit rate constants and can be expressed as such by equating the denominators of Eqs. (5) and (6). Common input functions, in, are as follows. 

The greater the rate constant for chain transfer, the lower the molecular weight of the polymer. One way to affect the rate constants is by changing the temperature. In general, the chain transfer rate constant is much more sensitive to temperature effects, increasing dramatically as the temperature is increased. For these reasons, there is an inverse correlation between temperature and molecular weight of polyvinyl chloride as shown in Fig. 22.3. 

Transfer rate constants are postulated as shown in Table II, following the approach described by Mackay and Paterson (4). The air-water value selected was lower than is generally used since it appears that a low value is necessary to reconcile observed air and water concentration, and mass balances as discussed in a recent review of PCB behavior in the Great Lakes (Mackay et al. U3)). 

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