Stern-Volmer expression

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... 

Similarly, the fluorescence quantum yield in the presence of a quencher (F) is given by another Stern-Volmer expression,... 

This is known as the Stern-Volmer expression. A plot of () versus [Q gives a straight line with an intercept equal to 1.0 and a slope equal... 

Triplet sensitization (Section 2.2.2) can be used to determine 3A v for the quenching of a triplet reactant. A complete reaction scheme for sensitization of a reactant A yielding product B from the triplet state would lead to a rather complex Stern Volmer expression, if all steps are treated explicitly. However, if ISC of the sensitizer is very fast and efficient (< >T= 1) and if the concentration of A is chosen to be much higher than that of the quencher added, then we may assume that triplet energy transfer from the sensitizer to A is fast and efficient at all quencher concentrations, so that a plot of versus cq will... 

Finally, Fig. 36 describes as an example the quenching of p-naphthylamine vapour by oxygen and nitrogen dioxide [117]. It is seen that, just as for atoms and simpler molecules, fluorescence quenching obe3 s a linear expression (the Stern-Volmer-expression). 

Inhomogeneous systems can give Stem-Volmer plots that curve downward with increasing [Q], as shown by the dashed curve in Fig. 5.7B. In this situation, a modified Stern-Volmer expression is useful [40]. Consider a protein in which a fraction da of the tryptophan residues is accessible to quenchers in the solvent and a fraction di is inaccessible. In the absence of external quenchers, the overall fluorescence yield will be... 

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. 

For weak quenching, the expression reduces to the Stern-Volmer type relation,... 

The final expression is in the form of the Stern-Volmer equation, where tj, is the monomer lifetime in dilute solution and te is assumed to be excimer lifetime in infinitely dilute solution. 

The quenching of fluorescence by added substance Q at concentrated [Q] is expressed by the Stern-Volmer equation,... 

It is probably appropriate to note at this point that Stern-Volmer type of analysis of luminescence data obtained using modern gated spectrometers (such as the Perkin-Elmer LS5) follows different mathematical expressions than those used for data obtained under continuous irradiation conditions. This is true even for homogeneous systems where the excited state decays with simple monoexponential behaviour. 

We note that the expressions above have been derived for a homogeneous system, where only one triplet lifetime is involved even here a Stern-Volmer type plot based on data from gated spectrometers is not expected to follow "conventional" Stern-Volmer behaviour. 

Stern-Volmer equation may be introduced by the transient component of dynamic quenching. If the quencher molecules are present near the fluorescent molecule at the moment of excitation, the initial quenching before a steady state is achieved, leads to the non-steady state term in the quenching expression. A sphere of transient quenching of volume r, may be defined as... 

A Stern-Volmer type expression is obtained. At constant [B], a plot of 4>r/Ar vi [Q] will be linear and the slope is equal to Kq. 

By substituting this expression into Eq. (3.13), we obtain the ideal Stern-Volmer constant for contact quenching [25,64]. 

At weak quenching (cfc T 1) the expression (3.31) can be subjected to concentration expansion that brings the Stern-Volmer constant to the form... 

Using this expression in Eq. (3.4) for R(t) and integrating the latter in Eq. (3.10), one can get the general contact q and the corresponding Stern-Volmer constant, which is an increasing function of quencher concentration c. There are also a number of competing contact theories that do the same but with slightly different results. They were compared in Ref. 46, reviewed in Section XII. 

Both of these equations can be universally expressed through the Stern-Volmer constant k. The latter one has been used already in Section XII.B as a standard for comparison between the different theories of irreversible quenching. In the case of the reversible reaction (3.703), the problem is more difficult, especially at high concentrations of B molecules. After the dissociation, other B molecules can be involved in the reaction with A. This many-particle competition for the partner couples the motion of the molecules, making the problem unsolvable analytically. Thus only approximate solutions were obtained by means of different methods and assumptions whose validity very often remains unclear. 

It is in the nature of steady-state kinetic calculations that ratios of rate constants are obtained for example, the expressions for the intensity in Eq. 25, or the parameters extracted from the Stern-Volmer treatment, involve ratios of rate constants to the Einstein A factor for emission. Individual rate constants can often be determined from a comparison of kinetic data obtained under stationary conditions with those obtained under nonstationary conditions. For the present purposes, the nonstationary experiment often involves determination of fluorescence or phosphorescence lifetimes (tf, rp). If a process follows first-order kinetics described by a rate constant k, the mean lifetime, r (the time taken for the reactant concentration to fall to 1/e of its initial value), is given by... 

In equation (1) K y is referred to as the Stern-Volmer constant Equation (1) applies when a quencher inhibits either a photochemical reaction or a photophysical process by a single reaction. <1>° and M° are the quantum yield and emission intensity (radiant exitance), respectively, in the absence of the quencher Q, while <1> and M are the same quantities in the presence of the different concentrations of Q. In the case of dynamic quenching the constant K y is the product of the true quenching constant kq and the excited state lifetime, t°, in the absence of quencher, kq is the bimolecular reaction rate constant for the elementary reaction of the excited state with the particular quencher Q. Equation (1) can therefore be replaced by the expression (2)... 

Fredrickson3 has formulated expressions for the concentration depolarization of fluorescence in the presence of molecular rotation. A theoretical examination of diffusion influenced fluorescence quenching by nearest possible quenching neighbours in liquids has been made35. A modified version of Smoluchowski - Collins - Kimball formulation of the Stern - Volmer equations has been matched with experimental data for quenching of anthraquinone derivatives by N,N-dimethyl- -toluidine. Another paper discusses this work on the basis of the kinetics of partly diffusion controlled reactions3 . 

Following a similar approach to that of pyrene exclmer formation, activation energies for pyrene- 4. exciplex formation can be obtained from expression of Eqn. 9 in an Arrhenius form and differentiation by 1/T. ki+k2 are obtained from data taken in eyelohexane (32), and A3 and E3 from the lifetime taken at f CA1 - 0. E3 can also be obtained from the slope of the phase dependent dynamic Stern-Volmer plots. As seen in Table 1 the data from each method are in good agreement. The small differences in activation parameters measured in the cholesteric and isotropic phases probably reflect changes in viscosity that accompany phase transitions. 

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