Determination of the association constants K is one of the most common tasks of physical chemistry, biochemistry, chemistry, etc. The constant K in equation (1) is taken as the association constant

In (1) and (2), F and Q are the complexing reagents; FQ is the complex of reagents; and are the

initial concentrations of F and Q according to preparation.

From equation (2) it easily follows [1] that the relative concentration (y) of complex FQ can be calculated from the equation

where

One of the numerous methods to determine the value of K is the fluorescence one [2] . The basis of the described method is the assumption that the complexes FQ do not fluoresce (static quenching) and that the dynamic quenching of excited molecules F is absent.

The essence of this approach is that the fluorescence quenching constant is estimated from the Stern-Volmer equation

In (3), I₀ and I are the fluorescence intensities of the fluorophore F in the absence and in the presence of quencher Q. The resulting constant is taken as the K value [2]

However, in the case of static quenching, the constant depends on the initial concentration of the fluorophore. This factor does not take into account usually [2] . The cause of such dependence is the formation of complexes FQ, which leads to a decrease in the concentration of free molecules F in contrast to the usual practice of using Stern-Volmer equation in the systems in which the concentration of the fluorophore does not depend on the concentration of the quencher.

The present work is devoted to the extent of correction to the experimental Stern-Volmer constant for the case of static fluorescence quenching under continuous illumination.

Consider now luminescence quenching in the presence of complex formation under stationary excitation. The following scheme holds for this case:

In (7)-(9), is the coefficient depending on experimental conditions and molar absorption coefficient of fluorofor, I_ex is the intensity of exciting illumination, k₁ and k₂ are the radiative and non-radiative constants of the excited electronic states of fluorophore F^*, respectively, and the K value is the same as that in (1). From (7)-(9), we get

Thus, in general, from (10) the fluorescence intensity I is of the form

However, for a particular case of, the fluorescence intensity is

In fluorescence quenching the value is used. From (10)-(12) we obtain

Taking into account that

we get either

or

For the small values of р, we have

To determine the Stern-Volmer constants, is measured as a function of (the dependence of

on). For this dependence with small values, we get

Comparing (18) with (6) indicates that in the case of complex formation, the Stern-Volmer quenching constant is not equal to K,

Thus, rather than K is measured experimentally. The latter is usually associated with a complex

constant. This correction to unity in the denominator of Equation (19), equal to takes into account the fact that the concentration of molecules F is less than because of complex formation. Thus, the generally

accepted equating of the experimental quenching constant to the equilibrium one (complexing) K [2] is

valid only if.

The value of K can be estimated from the dependence of on

The value and then, respectively, that of K are determined from the cut on the Y-axis.

It is concluded then that introducing the above correction may be a key moment in obtaining the true values of

the association constants. The relation may fail in the case of reagents (fluorophores) with a low

quantum yield. In this case, the high concentrations of are used to provide reliable observations. This

necessitates the introduction of a corrective factor which is also obligatory for the case of large complexing constants.