Forster transfer rate

Energy transfer from the fluorescent dimer to a nonfluorescent aggregate would also shorten the singlet lifetime. The rate of energy transfer is very sensitive to concentration however, the lifetime at any given temperature appeared to be free of any concentration effects. Moreover, an estimate of the Forster transfer rate at 10 M for even the most favorable conditions indicated that transfer would occur at a much slower rate than the observed quenching. 

Expressing the transition moments in terms of measurable quantities allows the Forster transfer rate to be written in the form ... 

We also notice that, unlike the case of coherent transfer - where the transfer rate is oc Jda and hence Rda - for incoherent transfer the rate is oc Jda and hence Rj3 . It is customary to define a Forster radius, Rp,aX which the Forster transfer rate is equal to the radiative emission rate, kp = /tr. Then,... 

E)ue to its dependence on r the Forster transfer rate (Eq. (25.14)) depends heavily on the separation between the donor and acceptor fluorophores/mole-cules, and efficient transfer only occurs if this separation is less than the Forster transfer radius (Rq). Typical values of Rq are on the order of only a few nanometers, and therefore FRET is very sensitive to distances of this magnitude. 

We first consider numerical calculations for an ideal Gaussian chain at infinite dilution with the isotropic Forster transfer rate [10]. The three-body Fade is given by... 

The latent heat transport accounts for only 2% of the total heat flux in this case. However, it was observed by several investigators that the total heat transfer rate is proportional to this value, <7, lenl, because it is proportional to the bubble volume and the number of bubbles that cause intense agitation of the liquid layer close to the surface. This agitation, termed microconvection, together with the liquid-vapor exchange, were considered to be the key to excellent characteristics of boiling heat transfer (Forster and Greif, 1959). 

Forster derived the following expression for the transfer rate ... 

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... 

Another major energy transfer process, the so-called Forster transfer mechanism is based on a dipole-dipole interaction between the host excited state and the guest ground state (Figure 4.2) [24], It does not include the transfer of electrons and may occur over significantly larger distances. The rate constant of the Forster energy transfer is inversely proportional to the sixth power of the distance R between the molecules ... 

Wong KF, Bagchi B, Rossky PJ (2004) Distance and orientation dependence of excitation transfer rates in conjugated systems beyond the Forster theory. J Phys Chem A 108 5752-5763... 

Forster s formulation of long-range dipole-dipole transfer (very weak coupling) Forster derived the following expression for the transfer rate constant from classical considerations as well as on quantum-mechanical grounds ... 

Fig. 4.16. Transfer rates predicted by Forster for strong, weak and very weak coupling.

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... 

Triplet decay in the [Mg, Fe " (H20)] and [Zn, Fe (H20)] hybrids monitored at 415 nm, the Fe " / P isosbestic point, or at 475 nm, where contributions from the charge-separated intermediate are minimal, remains exponential, but the decay rate is increased to kp = 55(5) s for M = Mg and kp = 138(7) s for M = Zn. Two quenching processes in addition to the intrinsic decay process (k ) can contribute to deactivation of MP when the iron containing-chain of the hybrid is oxidized to the Fe P state electron transfer quenching as in Eq. (1) (rate constant kj, and Forster energy transfer (rate constant kj. The triplet decay in oxidized hybrids thus is characterized by kp, the net rate of triplet disappearance (kp = k -I- ki -I- kj. The difference in triplet decay rate constants for the oxidized and reduced hybrids gives the quenching rate constant, k = kp — kj, = k, -I- k , which is thus an upper bound to k(. 

Rice [147] has noted the similarity of form between the time-dependent rate coefficients from the Smoluchowski, eqn. (19), Debye— Smoluchowski, eqn. (53), diffusion and Forster transfer equations,... 

Forster and Keyes prepared the tetrazine containing [Os(II)(BL)Os(III)] dimer (see below) and examined light induced intramolecular electron transfer in the system. They also measured heterogeneous electron transfer rate constants for oxidation of the complex at a Pt electrode [38]. The work is... 

A mixed quantum classical description of EET does not represent a unique approach. On the one hand side, as already indicated, one may solve the time-dependent Schrodinger equation responsible for the electronic states of the system and couple it to the classical nuclear dynamics. Alternatively, one may also start from the full quantum theory and derive rate equations where, in a second step, the transfer rates are transformed in a mixed description (this is the standard procedure when considering linear or nonlinear optical response functions). Such alternative ways have been already studied in discussing the linear absorbance of a CC in [9] and the computation of the Forster-rate in [10]. 

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