Forster’s theory

Bifluorophores consisting of two different fluorescent dyes linked by a flexible spacer containing heteroatoms (oxygen, nitrogen or sulfur atoms) can bind cations. This results in a decrease of the distance between the two fluorophores and, consequently, to an increase in efficiency of photoinduced energy transfer between the two moieties (Figure 2.13) provided that the emission spectrum of the donor (D) overlaps the absorption spectrum of the acceptor (A).(36) The transfer efficiency depends on the distance according to Forster s theory ... 

Fluorescein is an energy acceptor for chromophores such as naphthalene and anthracene and acts as energy donor toward Eosin and Rhodamine, so derivatives have been used for singlet-singlet energy transfer studies. According to Forster s theory [68] the rate constant for energy transfer increases... 

Based on the experimental evidences discussed in sect. 3.6.4 of an effect of the ligand onto the lifetime, numerous publications have appeared that refer to the Forster s theory (De Sa et al., 1993 Beeby et al., 1999 Supkowski and Horrocks, 1999 An et al., 2000). However, this theory is not applied in order to derive the transfer rate constant or the mean interaction distance value but only to justify the search for relationships between the observed decay rate and the number of OH, CH or NH bonds of the ligand, plus a global parameter for the solvent. Thus, although based on a very different theoretical approach, one deals with equations similar to eq. (11), with more terms, as in the following example (Beeby et al., 1999) ... 

It may appear very tempting to apply the Forster s formalism to the question of electrolyte effects onto the lifetime. However, some features of this effect render the use of the Forster s theory difficult experiments with Eu have shown that the observed variations cannot be reproduced solely on the basis of the refractive index changes, a term included in the Forster s... 

Forster s theory [1], has enabled the efficiency of EET to be predicted and analyzed. The significance of Forster s formulation is evinced by the numerous and diverse areas of study that have been impacted by his paper. This predictive theory was turned on its head by Stryer and Haugland [17], who showed that distances in the range of 2-50 nm between molecular tags in a protein could be measured by a spectroscopic ruler known as fluorescence resonance energy transfer (FRET). Similar kinds of experiments have been employed to analyze the structure and dynamics of interfaces in blends of polymers. 

They found that Forster s theory of resonance energy transfer was applicable to such systems if the Interchromophoric distance and orientation, the fluorescence efficiency of the donor, the extinction of the acceptor, and the overlap between the emission of the donor and the absorption of the acceptor are of magnitudes which produce a transfer rate constant of less than 10 s and a transfer efficiency which is not too close to 0 or 1. 

An experimental value of R0 can be obtained by plotting f as a function of the logarithm of the acceptor concentration and fitting the theoretical curve calculated according to Forster s theory to the experimental results. An experimental value larger than the calculated one may be considered as evidence for migration of excitation prior to the transfer. Agreement was obtained between the experimental results and Forster s theory for the system polystyrene—tetraphenylbutadiene [165]. 

R0 is a critical transfer distance as defined in Forster s theory ... 

Mechanism of CL enhancement. According to Forster s theory, energy transfer is a distance dependent interaction between the different electronic excited states of molecules in which excitation energy is transferred from one molecule (donor) to another molecule (acceptor). Fig. 3 shows that fluorescence of HSA at 348nm decreased with increasing FCLA concentration. The energy from excited-state HSA maybe be transferred to FCLA or be lost in a non-radiative manner. 

Underlying Principles Forster s Theory of Dipole-Dipole Interaction... 

Forster s theory is behind a very nsefnl method for determining the absorption spectrum of a collection of identical chromophores within a separation distance of less than 100 A, placed in a protein, DNA, or some other scaffold. One example is the indole groups in a protein, where the interaction causes a broadening of the absorption spectrum. 

Forster s theory is also behind the FRET method (Forster resonance energy transfer or fluorescence resonance energy transfer). In this case, excitation takes place with a narrow laser pulse, corresponding to the lowest excited state of a chromo-phore. The rate of EET is determined by time-resolved fluorescence. 

According to Forster s theory [13], the efficiency of the resonance energy transfer ( ret) is inversely proportional to the sixth-power of the distance (r) between donor and acceptor (2). In (2), Rq is the so-called Forster distance at which the transfer efficiency is 50%. Forster RET is therefore a very sensitive process and can transduce small conformational changes into large intensity modulations. Rq is characteristic for a particular donor-acceptor pair and depends on the overlap integral J between >ret emission and Aret absorption, the PLQY of >ret in its unperturbed state < d and the mutual orientation of the two partners expressed as geometry factor which equals 2/3 for random orientation of the partners (3). For a more detailed discussion of the mechanistics of RET, the reader is referred to the literature [12]. 

The distance between the donor and the acceptor r is described by Forster s theory. Forster derived an equation for the rate of energy transfer from a specific donor to a spcific acceptro kj ... 

According to Forster s theory, this definition of E, combined with Equation (6.43), gives [39,a] ... 

Forster s theory of resonance energy transfer depends implicitly on thermal equilibration to trap the excitation on the acceptor. But the Forster theory is silent concerning the oscillations predicted by Eqs. (10.4a-10.5), and it does not address how rapidly the system equilibrates with the surroundings it simply assumes that equilibration occurs rapidly compared to the rate at which the excitation can return to the donor. 

---