Critical overlap radius

For the design of complexing bifluorophores, much attention should be paid to the Forster critical radius of the donor-acceptor pair as compared to the interchromophoric distance (Figure 2.13). This critical radius depends on the donor quantum yield and on the spectral overlap between donor emission and acceptor emission. Complex-... 

The only recent example of Forster transfer of photochemical importance is the demonstration by Saltiel163 that the ability of azulene to increase the photostationary transjcis ratio in direct photoisomerization of the stilbenes is due entirely to radiationless transfer of excitation from traw.y-stilbene singlets to azulene. As expected for Forster transfer, this azulene effect did not depend upon solvent viscosity. The experimental value of R0, the critical radius of transfer in Forster s formula,181 was 18 A, in good agreement with the value calculated from the overlap of stilbene emission and azulene absorption. 

The case of transverse field overlapping is far more complicated than that of longitudinal overlapping. According to the previous analysis, the field energy is limited mainly within a well-defined radius r. As long as the ratio 0 exceeds the critical value 0 c, the photon wavepackets of the beam will not overlap and will have hardly any mutual interaction. The beam then behaves as a stream of individual photon particles, that is, when representing each photon as an axisymmetric wavepacket. 

The tris-bipyridine complexes on the other hand are encapsulated by the oxalate network. Thus in the co-doped systems a [Cr(bpy)3]3+ complex happening to sit in the first acceptor shell of a given donor is much closer to this donor than a [Cr(bpy)3]3+ complex sitting in the second shell, n-n overlap between ligand orbitals of the donor and an acceptor in the first shell ensure efficient energy transfer on the sub-microsecond timescale mediated by exchange interaction. Additionally, the relative orientation of donor and acceptor plays an important role for the n-n overlap. For acceptors further away, for which there is no exchange pathway, dipole-dipole interaction takes over. With a critical radius of the order of 11 A, this is much less efficient and the overall quantum efficiency is thus less than unity. 

Here p is a critical density of the solution per polymer corresponding to the starting of the polymeric chains conformational volumes overlapping having into diluted solution j the conformation of Flory ball by the radius ... 

De Gennes and Adam and Delsanti have discussed the properties of solutions in the concentration range of coil overlap in terms of a critical concentration c which is defined as M/Aoi where s is the radius of gyration and A o is Avogadro s number. This is similar in magnitude to the concentration defined by c[r)] = 3. Above the c, the solution is termed semidilute. 

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