Stem-Volmer equation quenching

The Stem-Volmer(52) equation relates fluorescence intensity and the quenching rate constant, kq ... 

In this equation, F0 and F are the fluorescence intensities in the absence and presence of the quencher, t0 and x are the lifetimes of the fluorophore in the absence and presence of the quencher, kq is the biomolecular quenching constant, and [Q] is the concentration of the quencher (in this case, molecular oxygen). The Stem-Volmer quenching constant is Kn, and is calculated as the product of kq and r0. The Smoluchowski equation describes the biomolecular quenching constant, kq, and is given by... 

This expression for the intensity ratio or quantum yield is a modified form of the Stem-Volmer expression (Equation (6.19)) for the case where there is concurrent static quenching. It contains a term in [Q], like Equation (6.19), but also a term in [QJ, which predicts an upward curvature of the Stem-Volmer plot. The separate values of K and 3Tq can be obtained from the slope and intercept of a linear plot of [(/o//[Q]) — 1 ]/[Q] against [Q]. 

The Eq. (7) is known as the Stem-Volmer equation [33] and /sTsv = qTo as the Stem-Volmer quenching constant. Plotting the tq/t ratio as a function of [Q] thus... 

Equation (33) is the well-known Stem-Volmer equation and SV - ( q is the Stem-Volmer quenching constant. In practice, the ratio of lifetime without to that with quencher is plotted against [B] (figure 12) and k is obtained by dividing the slope by 1. ... 

Quite different kinds of results are found when these experiments are repeated on the core-labelled particles, Figure 5. Here the Stem-Volmer plot [equation (4)] is curved in a way that suggests that some Phe groups are harder to quench than others. These data fit a model, previously applied to proteins, which assumes that only a fraction fa of the chromophores are accessible to quenching, the rest being buried. Plotting our data according to eq. 5, we find fa = 0.5. 

In order to clear up the mechanism of inactivation of excited states, we examined the processes of quenching of fluorescence and phosphorescence in PCSs by the additives of the donor and acceptor type253,2S5,2S6 Within the concentration range of 1 x 1CT4 — 1 x 10"3 mol/1, a linear relationship between the efficiency of fluorescence quenching [(/0//) — 1] and the quencher concentration was found. For the determination of quenching constants, the Stem-Volmer equation was used, viz. 

Fluorescence quenching may be dynamic, if the photochemical process is the result of a collision between the photoexcited indicator dye and the quencher species, or static, when the luminophore and the quencher are preassociated before photoexcitation of the former20. It may be easily demonstrated that dynamic quenching in isotropic 3-D medium obeys the so-called Stem-Volmer equation (2)21 ... 

It may also happen that an association equilibrium exists between the luminescent indicator and the quencher. Non-associated indicator molecules will be quenched by a dynamic process however, the paired indicator dye will be instantaneously deactivated after absorption of light (static quenching). Equation 2 still holds provided static quenching is the only luminescence deactivation mechanism (i.e. no simultaneous dynamic quenching occurs) but, in this case, Ksv equals their association constant (Kas). However, if both mechanisms operate simultaneously (a common situation), the Stem-Volmer equation adopts more complicated forms, depending on the stoichiometry of the fluorophore quencher adduct, the occurrence of different complexes, and their different association constants. For instance, if the adduct has a 1 1 composition (the simplest case), the Stem-Volmer equation is given by equation 3 ... 

The commercialization of inexpensive robust LED and laser diode sources down to the uv region (370 nm) and cheaper fast electronics has boosted the application of luminescence lifetime-based sensors, using both the pump-and-probe and phase-sensitive techniques. The latter has found wider application in marketed optosensors since cheaper and more simple acquisition and data processing electronics are required due to the limited bandwidth of the sinusoidal tone(s) used for the luminophore excitation. Advantages of luminescence lifetime sensing also include the linearity of the Stem-Volmer plot, regardless the static or dynamic nature of the quenching mechanism (equation 10) ... 

In another approach, a fluorescent conjugated polymer was used as the material for the preparation of a chemosensor to detect 2,4,6-trinitrotoluene (TNT) and its related nitroaromatic compounds. To this end, microparticles, made of three-dimensionally cross-linked poly(l,4-phenylene vinylene) (PPV) via emulsion polymerization, were synthesized [61]. This material was chosen due to its high fluorescence intensity and sensitivity to changes in its microenvironment. The chemosensor was exposed to vapour containing different amounts of TNT and quenching of the polymer luminescence at 560 nm was observed after excitation at 430 nm. The dependence of the fluorescence signal in response to the analyte was described by a modified Stem-Volmer equation that assumes the existence of two different cavity types. The authors proposed the modified Stem-Volmer equation as follows ... 

To understand the origin of such a difference in photocatalytic activity, the reaction rate constants were calculated for the quenching of the phosphorescence of VS-1 and V/Si02 catalysts by NO and C3H3 (Anpo, 2000 Anpo et al., 2003 Higashimoto et al., 2001a) by using the Stem-Volmer equation expressed as follows ... 

A representative plot is shown in Figure 1.15 this is known as a Stem-Volmer plot, and (1.16) as a Stern-Volmer equation. This method for obtaining reaction rate constants is again a comparative one, since there is competition between the primary reaction step and the quenching process. A value for the quenching rate constant needs to be known, but in many cases this is independent of the substrate and quencher because triplet quenching is controlled by diftusional collision of the two species. So for a particular solvent at a given temperature kf values are available in the literature as an... 

In the static quenching mechanism (Scheme 23B), the Stem-Volmer equation based on emission intensity is given by Eq. (20), where / and /0 mean the emission intensities in the presence and the absence of quencher, respectively. 

The rate constants for collisional (dynamic) quenching can be determined experimentally from the dependence of excited state lifetime or luminescence intensity using the Stem-Volmer equation (Eq. 7),... 

A second nonlinear fluorescence quenching data treatment method developed by Ventry and Ryan may also be used to extract conditional stability constants, and ligand concentrations from titrations of FA with Cu (23). The model designed is a modification of the original Stem-Volmer theory defined by equation 7 which accounts for either static or dynamic quenching of fluorescent species. 

Careful examination reveals that the modified Stem-Volmer equation is mathematically identical to the original nonlinear model developed by Ryan and Weber (22). Fluorescence quenching curves for Cu -FA and application of the modified Stem-Volmer data treatment to the experimental information are shown in figure 2. Since the nonlinear data treatment and the modified Stem-Volmer equations are algebraically identical, their ability to fit experimental data and provide meaningful parameters is the same. 

Modeling of Multisite Fluorescence Quenching. A traditional multisite fluorescence quenching model using a Stem-Volmer approach has been developed and applied to quenching curves involving residual protein fluorescence (32). More recently, however, the multiple site model has been used to describe structural characteristics in diverse polymer environments (33-3f). The multisite Stem-Volmer model shown in equation 13 may be used to define multiple fluorescent binding sites present under one emission peak... 

Example The quenching rate constant can be calculated using the Stem-Volmer equation ... 

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