Energy transfer Multipolar interaction

For electric multipolar interactions, the energy transfer mechanism can be classified into several types, according to the character of the involved transitions of the donor (D) and acceptor (A) centers. Electric dipole-dipole (d-d) interactions occur when the transitions in D and A are both of electric dipole character. These processes correspond, in general, to the longest range order and the transfer probability varies with l/R, where R is the separation between D and A. Other electric multipolar interactions are only relevant at shorter distances dipole-quadrupole (d-q) interaction varies as l/R, while quadrupole-quadrupole interaction varies as l/R °. 

Energy transfer probabilities due to multipolar magnetic interactions also behave in a similar way to that previously discussed for multipolar electric interactions. Thus, the transfer probability for a magnetic dipole-dipole interaction also varies with 1 / 7 , and higher order magnetic interactions are only influential at short distances. In any case, the multipolar magnetic interactions are always much less important than the electric ones. 

The decay time of the Cr " band of approximately 150 ns is very short for such emission. Radiative energy transfer may not explain it because in such a case the decay curves of each of the ions are independent of the presence of the other. Thus non-radiative energy transfer may also take part, probably via multipolar or exchange interactions. In such cases the process of luminescence is of an additive nature and the lifetime of the sensitizer from which the energy is transferred is determined, apart from the probability of emission and radiationless transitions, by the probability of the energy transfer to the ion activator. 

Nonradiative energy transfer is due to electric or magnetic multipolar interactions or to exchange interactions. ... 

When acceptor ions are present, the decay of donor ions does not exhibit an exponential behavior. In the absence of energy transfer between donor ions and assnming a random distribntion of acceptor ions, for multipolar interactions the decay is given by... 

Dexter, following the classic work by Forster, considered energy transfer between a donor (or a sensitizer) S and an acceptor (or activator) A in a solid. This process occurs if the energy difference between the ground and excited states of S and A are equal (resonance condition) and if a suitable interaction between both systems exists. The interaction may be either an exchange interaction (if we have wave function overlap) or an electric or magnetic multipolar interaction. In practice the resonance condition can be tested by considering the spectral overlap of the S emission and the A absorption spectra. The Dexter result looks as follows ... 

The microscopic behaviour between the ions in dilute systems results from multipolar interaction. On the other hand in the rate equations which are used for measurement of macroscopic data such as quantum efficiencies of fluorescence, the multipole questions are absent. The macroscopic treatment of energy transfer was performed recently independently by Fong and Diestler (5) and Grant ( >) who conclude that the concentration... 

Resonance energy transfer occurs between a sensitizer (S) and an activator (A) with the same radiative frequency, and the mechanism could be of exchange interaction or electric multipolar interaction. 

Fig. 2.5 Diagrams of the energy-transfer mechanisms of electric multipolar and exchange interactions...

The value of can also be calculated by using the quantitative theories for D-A multipolar energy transfer given by Forster and Dexter. For instance, the transfer rate for dipole -dipole interaction is given by the Dexter equation [2] ... 

Energy transfer between two inorganic ions can occur either by multipolar interaction or an exchange mechanism in dilute systems (Reisfeld and Jorgensen, 1977 Reisfeld, 1973, 1975, 1976a), or by multi-step migration in concentrated systems (Powell and Blasse, 1980). In addition to resonant transfer, phonon-assisted transfer is a quite common phenomenon (Reisfeld, 1976a, 1986). 

Multipolar interaction has been previously discussed in section 4.2, in connection with cross-relaxation, where the general formula for time evolution was presented. The same formula holds for macroscopic cases of energy transfer. When dealing with the microscopic situation, we have for the resonant nonradia-tive energy transfer... 

Forster and Dexter properly identified the microscopic interionic interaction leading to the communication between an excited and an unexcited ion as arising from the multipolar electrostatic fields produced by the excited state. In order to explain transfer in lanthanide doped systems where often there is no direct overlap in the sharp line spectra of acceptor and donor ions, it becomes necessary to invoke phonon assistance to conserve energy which entail the emission and absorption of one or more phonons. As in the case of relaxation, the various phonon mediated transfer processes have characteristic temperature dependences which allow their identification. The microscopic processes have also definite parametric dependences such as on Rj, the distance between interacting centers, on the amount of energy to be taken up or supplemented by... 

The SIBFA model [25, 26] (sum of interactions between fragments ab initio computed) obtains the energy of a system as the contribution of electrostatic multipolar, short-range repulsion, polarization, charge transfer and dispersion. 

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