Dexterity rating

By substituting Eq. (B4.4.5) into Eq. (B4.4.7), we obtain the Forster rate constant kjl (Eq. 4.78 in the text) for energy transfer in the case of long-range dipole-dipole interaction, and substitution of Eq. (B4.4.6) into Eq. (B4.4.7) leads to the Dexter rate constant k fl (Eq. 4.85 in the text) for the short-range exchange interaction. 

The occurrence of energy transfer requires electronic interactions and therefore its rate decreases with increasing distance. Depending on the interaction mechanism, the distance dependence may follow a 1/r (resonance (Forster) mechanism) or e (exchange (Dexter) mechanisms) [ 1 ]. In both cases, energy transfer is favored by overlap between the emission spectrum of the donor and the absorption spectrum of the acceptor. 

Based on cathodic polarization curves, Dexter and Gao concluded that the increase of E for 316 stainless steel exposed to natural seawater was due to an increased rate of the cathodic reduction of oxygen at a given potential. It is not possible from Ecorr or polarization curves to decide whetlier the increase in Ecorr is due to thermodynamic effects, kinetic... 

In contrast to the dipole-dipole interaction, the electron-exchange interaction is short ranged its rate decreases exponentially with the donor-acceptor distance (Dexter, 1953). This is expected since, for the electron exchange between D and A, respective orbital overlap would be needed. If the energy transfer is envisaged via an intermediate collision complex or an exciplex, D + A—(D-------A)- D + A, then Wigner s rule applies there must be a spin com-... 

Developed into a power series in R 1, where R is the intermolecular separation, H exhibits the dipole-dipole, dipole-quadrupole terms in increasing order. When nonvanishing, the dipole-dipole term is the most important, leading to the Forster process. When the dipole transition is forbidden, higher-order transitions come into play (Dexter, 1953). For the Forster process, H is well known, but 0. and 0, are still not known accurately enough to make an a priori calculation with Eq. (4.2). Instead, Forster (1947) makes a simplification based on the relative slowness of the transfer process. Under this condition, energy is transferred between molecules that are thermally equilibriated. The transfer rate then contains the same combination of Franck-Condon factors and vibrational distribution as are involved in the vibrionic transitions for the emission of the donor and the adsorptions of the acceptor. Forster (1947) thus obtains... 

The rate of energy transfer at a very short donor-acceptor separation R by the exchange mechanism has been given by Dexter (1953) as follows ... 

In the Collins-Kimball theory, the rate constant for the reaction was assumed to be distance-independent. Further refinement proposed by Wilemski and Fix-manc) consists of considering that the reaction rate constant has an exponential dependence on distance, which is indeed predicted for electron transfer reactions and energy transfer via electron exchange (see Dexter s formula in Section 4.6.3). The rate constant can thus be written in the following form ... 

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... 

Energy transfer in solution occurs through a dipole-dipole interaction of the emission dipole of an excited molecule (donor) and the absorptive moment of a unexcited molecule (acceptor). Forster<40) treated the interaction quantum mechanically and derived and expression for the rate of transfer between isolated stationary, homogeneously broadened donors and acceptors. Dexter(41) formulated the transfer rate using the Fermi golden rule and extended it to include quadrupole and higher transition moments in either the donor or the acceptor. Following the scheme of Dexter, the transfer rate for a specific transition is... 

An expression for transfer by exchange interaction was derived by Dexter for a vibrationally relaxed system. The rate of transfer is given b>... 

The cross-section of light absorption in processes (71) and (73) can be calculated according to eqns. (68) and (69), assuming d to be the dipole matrix element between the states A and A or B and B. The rate constants of processes (72) and (74) can be calculated with the help of the equations presented in the previous sections of this chapter. The rate constant of process (75) can be calculated using the formula which is the same as the well-known Forster-Dexter formula for electron excitation transfer [30],... 

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