Stern-Volmer mechanism

It is of interest to calculate the variation of delayed fluorescence efficiencies of donor and acceptor as a function of acceptor concentration as follows. The donor triplet will be quenched by the normal Stern-Volmer mechanism and its lifetime will therefore be given by ... 

The concept of the Stern-Volmer mechanism and the resolution of that mechanism can also be applied to the donor. In Figure 6, the mechanistic quantum yield for the emission step 41 is given by... 

STERN-VOLMER MECHANISM a simple set of steps describing the deactivation of an excited-state molecule by first-order (and pseudo-first-order) steps and by quenching steps. 

It should be noted that this expression is a general one that can be used for any photochemical reaction that can be quenched. It is commonly called the Stern-Volmer equation. This equation predicts that if the proposed mechanism is correct, the data, when plotted as 4>a0/4>a vs. [Q], should be linear with an intercept equal to unity and a slope equal to kqr. Linear plots were indeed observed out to large d>°/d> values. Assuming a value of 5 x 10 M 1 sec-1 for the quenching rate constant,(7) the data presented in Table 4.1 were obtained. 

An important class of luminescence sensors are those based on the decrease of luminescence intensity and lifetime of the probes as function of analyte concentration. Assume that the probe intensity decays by a single exponential with an unquenched lifetime tq. If quenching occurs only by a dynamic (collisional) mechanism, then the ratio to/t is equal to Fq/F and is described by the classic Stern-Volmer equation... 

The yield determined in a certain type of experiment usually strongly depends on the assumptions made about the formation mechanism. In the older literature, the excited molecules were often assumed to be produced solely in neutral excitations [127,139-143] and energy-transfer experiments with Stern-Volmer-type extrapolation (linear concentration dependence) were used to derive G(5 i). For instance, by sensitization of benzene fiuorescence, Baxendale and Mayer established G(5 i) = 0.3 for cyclohexane [141]. Later Busi [140] corrected this value to G(5 i) = 0.51 on the basis that in the transfer, in addition to the fiuorescing benzene state S, the S2 and S3 states also form and the 82- 81 and 83 81 conversion efficiencies are smaller than 1. Johnson and Lipsky [144] reported an efficiency factor of 0.26 0.02 per encounter for sensitization of benzene fluorescence via energy transfer from cyclohexane. Using this efficiency factor the corrected yield is G(5 i) = 1.15. Based on energy-transfer measurements Beck and Thomas estimated G(5 i) = 1 for cyclohexane [145]. Relatively small G(5 i) values were determined in energy-transfer experiments for some other alkanes as well -hexane 1.4, -heptane 1.1 [140], cyclopentane 0.07 [142] and 0.12 [140], cyclooctane 0.07 [142] and 1.46 [140], methylcyclohexane 0.95, cifi-decalin 0.26 [140], and cis/trans-decalin mixture 0.15 [142]. 

A Stern-Volmer plot obtained in the presence of donors for the stilbene isomerization has both curved and linear components. Two minimal mechanistic schemes were proposed to explain this unforeseen complexity they differ as to whether the adsorption of the quencher on the surface competes with that of the reactant or whether each species has a preferred site and is adsorbed independently. In either mechanism, quenching of a surface adsorbed radical cation by a quencher in solution is required In an analogous study on ZnS with simple alkenes, high turnover numbers were observed at active sites where trapped holes derived from surface states (sulfur radicals from zinc vacancies or interstitial sulfur) play a decisive role... 

This expression is known as the Stern-Volmer equation and Ksv as Stern-Volmer constant. Ksv is the ratio of bimolecular quenching constant to unimolecular decay constant and has the dimension of litre/mole. It implies a competition between the two decay pathways and has the ch".acter of an equilibrium constant. The Stern-Volmer expression is linear in quencher concentration and Ksv is obtained as the slope of the plot of 4>f°If vs [Q], if the assumed mechanism of quenching is operative. Here, t is the actual lifetime of the fluorescer molecule in absence of bimolecular quenching and is expressed as... 

As with other quantitative photochemical studies, it is important to design Stern-Volmer experiments carefully the quencher should be chosen to ensure that it interacts only with the excited state that is of interest, the extent of reaction should be small enough to ensure that substrate depletion does not affect the intensity of light absorbed, and the concentration of quencher should not be so small that it is significantly depleted by its sensitized reaction. Stern-Volmer plots may turn out to be non-linear, for example because the quencher interacts with more than one excited state on the reaction pathway, or because two different excited states lead to the same chemical. product, and such results are of value in unravelling the mechanism. 

The relative linearity of a Stern-Volmer plot of 1/< > versus 1/[A] for the photoreaction of cyclohexenone supports this mechanism and suggests that only one excited state is involved (30). The [2+2] addition of the triplet to a ground state molecule is not concerted, and there is a large solvent polarity effect on the regioselectivity for the head-to-head (HH) versus head-to-tail (HT) photodimers, with the more polar head-to-head isomer being favored in polar media. The polarity effect is attributed to the large difference in the dipole moments of the transition states leading to the products. 

Figure 3.13. The Stern-Volmer quenching constant Ko obtained in Ref. 53 versus the free energy of ionization AG . The open circles are the data borrowed from another work [106], The free-energy dependence shown by the solid line represents the theoretical expectation of Rehm and Weller deduced from their original approach to the simplest reaction mechanism of quenching [53], (From Ref. 107.)...

Such a concentration dependence would te consistent either with a Foster or Dexter transfer mechanism whose rate is such that Stern-Volmer kinetic behaviour is obeyed or would be consistent with the alternative suggestion of scheme (3) where the excited state naphthalene chromophore experiences intramolecular diffusion controlled self quenching. 

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