Stem Volmer equation

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 Stem-Volmer equations discussed so far apply to solutions of the luminophore and the quencher, where both species are homogeneously distributed and Fick diffusion laws in a 3-D space apply. Nevertheless, this is a quite unusual situation in fluorescent dye-based chemical sensors where a number of factors provoke strong departure from the linearity given by equation 2. A detailed discussion of such situations is beyond the scope of this chapter however, the optosensor researcher must take into account the following effects (where applicable) ... 

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) ... 

Equation 1 cannot be used to extract k0 for carbenic rearrangements in the region of A. There, however, a Stem-Volmer analysis can be applied wherein the optical yield of ylide as a function of pyridine concentration is used to obtain ko.4 The optical yield of ylide formation, Ay, is defined in Eq. 3,... 

Figure 13.10 shows the calibration curve of the LED-based optical oxygen sensor compared with the calibration curve of a commercially available Clark-type sensor (Ingold Electrodes, Wilmington, Massachusetts). While the Clark-type shows a linear calibration, the optical sensor allows a hyperbolic response as predicted by the Stem-Volmer-type equation 72 ... 

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

The interaction of an extrinsic membrane protein with a lipid bilayer can also be investigated by energy transfer. The interaction of cytochrome c has attracted much attention, and in an early study by Shaklai et al.(()5> the number of binding sites per red cell was determined. It was shown that an equation analogous to the Stem-Volmer relationship could be derived ... 

In the presence of a quencher, Q, there is an additional rate process for relaxation. The ratio of the fluorescence efficiency in the absence of (( )f0) and the presence of a quencher is given by the Stem-Volmer equation.7 140... 

If A is a thexi state, its reactions should obey conventional chemical kinetics, and we can examine several simple, important cases. Suppose firstly that A is produced by a flash or laser pulse technique in a time short compared to the time scale of the other processes. The produced A will disappear with a rate constant k which is the sum of the rate constants for all applicable processes. In the absence of quencher, we write k° = knr + kT + kcr the time for [A ] to decrease by a factor of e, r°, is just jk°. With quencher present, we have k = knr + kT + kCT + fcq[Q] and i = 1 jk. The ratio of lifetimes in the absence and presence of quencher is given by equation (10). A plot of t°/t versus [Q] should thus be linear, with slope kqr° this product is often designated as Kgy and called the Stem—Volmer constant. 

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 ... 

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... 

In the above sections, nothing was said about the type of reaction between M and Q. This is because the Stem-Volmer equation is model independent, as explained above and also because eqs. (20)-(22) are for a diffusion-controlled reaction. Some information can be obtained regarding an electron transfer from various quenchers of similar chemical structures towards M. In this case, one may derive a relationship between ksv (as obtained from eq. (17)) and the ionization potential of these inhibitors. This is the Rehm-Weller equation, which is schematically depicted in fig. 4. In this plot, the plateau value corresponds to fcdin. For a general overview of problems related to electron transfers, see Pouliquen and Wintgens (1988) (in French). 

Equation (3) is the well-known Stern-Volmer equation and kgv = kq r° is the Stern-Volmer quenching constant. In practice, the ratio of lifetime without to that with quencher is plotted against [B] and kq is obtained by dividing the slope by r°. Analogous Stem-Volmer equations can be obtained for the emission intensity and the reaction quantum yield... 

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... 

Henderson-Hasselbalch equation lahn-Teller effect Lee-Yang-Parr method Lineweaver-Burk method Mark-Houwink plot Meerwein-Ponndorf theory Michaelis-Menten kinetics Stem-Volmer plot van t Hoff-Le Bel theory Wolff-Kishner theory Young-Laplace equation Ziegler-Natta-type catalyst... 

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. 

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