Sphere of effective quenching

When M and Q cannot change their positions in space relative to one another during the excited-state lifetime of M (i.e. in viscous media or rigid matrices), Perrin proposed a model in which quenching of a fluorophore is assumed to be complete if a quencher molecule Q is located inside a sphere (called the sphere of effective quenching, active sphere or quenching sphere) of volume Vq surrounding the fluorophore M. If a quencher is outside the active sphere, it has no effect at all on M. Therefore, the fluorescence intensity of the solution is decreased by addition of Q, but the fluorescence decay after pulse excitation is unaffected. 

The probability that n quenchers reside within this volume is assumed to obey a Poisson distribution  

Therefore, because the emission intensity is proportional to P0, Perrin s model 

2 Overview of the intermolecular de-excitation processes of excited molecules I 85 

In contrast to the Stern-Volmer equation (4.10), the ratio Io/I is not linear and shows an upward curvature at high quencher concentrations. At low concentrations, exp(VqNa[Q]) 1 + VqNa[Q], so that the concentration dependence is almost linear (as in the case of the Stern-Volmer plot). 

A plot of ln(Io/l) versus [Q] yields Vq. The values of VqNa are often found to be in the range of 1-3 L mol-1. This corresponds to a quenching sphere radius of about 10 A, which is somewhat larger than the van der Waals contact distance between M and Q. 

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The term static quenching implies either the existence of a sphere of effective quenching or the formation of a ground-state non-fluorescent complex (Figure 4.1) (Case A of Section 4.2.1). 

Alternatively, using the sphere of effective quenching model, we obtain the following relation instead of Eq. (4.29)... 

It is well known, that in aqueous solutions the water molecules, which are in the inner coordination sphere of the complex, quench the lanthanide (Ln) luminescence in result of vibrations of the OH-groups (OH-oscillators). The use of D O instead of H O, the freezing of solution as well as the introduction of a second ligand to obtain a mixed-ligand complex leads to either partial or complete elimination of the H O influence. The same effect may be achieved by water molecules replacement from the inner and outer coordination sphere at the addition of organic solvents or when the molecule of Ln complex is introduced into the micelle of the surfactant. 

In some cases, evidence for the formation of a complex can be obtained (e.g. changes in the absorption spectrum upon complexation), but in the absence of such evidence, the interaction is likely to be non-specific and the model of an effective sphere of quenching is more appropriate. A nonlinear variation of Io/I is predicted in the latter case, but at low quencher concentration, exp(VqNa[Q]) 1 + VqNa[Q]. 

Both AP and Ga have a tightly bound hydrate shell in aqueous solution and both are prone to hydrolysis. In terms of the Hertz electrostatic model for quadrupolar relaxation of ionic nuclei in electrolyte solution (see Section III.C) one therefore expects effective quenching of the electric field gradient caused by the surrounding water dipoles, due to a nearly perfect coordination symmetry. Any contribution to the e.f.g. should therefore arise from outer-sphere solvent dipoles. In terms of the fully orientated solvation (FOS) model this would correspond to a distribution width parameter approaching zero (/. -> 0) with the first term in equation (4) vanishing. This is indeed what Hertz (24) found for both AF" and Ga ", and the experimental infinite dilution relaxation rates ( AP" 7-5 s Ga 350 s ) are remarkably well matched by the computed ones... 

However, the role of the N—H vibration modes of en could also be considered to explain the less efficient quenching of the S—(CH2)2NH2 group. Furthermore, it can also be inferred that the progressive substitution of water molecules for S atoms on the coordination sphere of Eu(fod)3.2H20 exerts a significant effect resulting in the observed phenomena. 

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