On the Question of Defining the Association Constants by the Method of Fluorescence Quenching

American Journal of Analytical Chemistry, 24, 5, 65-68 Published Online November 24 in SciRes. http://www.scirp.org/journal/ajac http://dx.doi.org/.4236/ajac.24.563 On the Question of Defining the Association Constants by the Method of Fluorescence Quenching Nikolay L. Lavrik, Nikolay M. Bazhin Voevodsky nstitute of Chemical inetics and Combustion SB RAS, Novosibirsk, Russian Federation Email: lavrik@kinetics.nsc.ru Received 5 September 24; revised 2 October 24; accepted 5 November 24 Copyright 24 by authors and Scientific Research Publishing nc. This work is licensed under the Creative Commons Attribution nternational License (CC BY). http://creativecommons.org/licenses/by/4./ Abstract A study is made on the previously ignored problem of the dependence of a static fluorescence quenching Stern-Volmer constant on the initial concentration of [ F ] fluorophore F. This correlation is shown to exist. t is concluded that the Stern-Volmer quenching constant may be used as association constant only with [ F]. eywords Fluorescence Quenching, Association Constants, Stern-Volmer Constant. ntroduction Determination of the association constants is one of the most common tasks of physical chemistry, biochemistry, chemistry, etc. The constant in Equation () is taken as the association constant F + Q FQ, () = [ FQ ] ( F FQ )([ Q] [ FQ] ). (2) n () and (2), F and Q are the complexing reagents; FQ is the complex of reagents; [ F ] and [ Q ] are the initial concentrations of F and Q according to preparation. From Equation (2) it easily follows [] that the relative concentration (y) of complex FQ can be calculated How to cite this paper: Lavrik, N.L. and Bazhin, N.M. (24) On the Question of Defining the Association Constants by the Method of Fluorescence Quenching. American Journal of Analytical Chemistry, 5, 65-68. http://dx.doi.org/.4236/ajac.24.563

from the equation where ( + + ) FQ p q 4 p y = = F 2 ( + p+ q) 2 ( ) [ Q] [ F ], [ F] p = q =. (4) One of the numerous methods to determine the value of 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 = + Q. (5) n (3), and 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 value [2] =. (6) 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 the case of static fluorescence quenching under continuous illumination. 2. Fluorescence Quenching under the Conditions of Nonfluorescent Complex Formation (3) for Consider now luminescence quenching in the presence of complex formation under stationary excitation. The following scheme holds for this case: F + Q FQ, F ν F α, + h ex (7) F hν F k, + (8) F F k2. (9) n (7)-(9), α is the coefficient depending on experimental conditions and molar absorption coefficient of fluorofor, ex is the intensity of exciting illumination, k and k 2 are the radiative and non-radiative constants of the excited electronic states of fluorophore F, respectively, and the value is the same as that in (). From (7)-(9), we get d F = α ex ( k + k ) = dt F 2 F Thus, in general, from () the fluorescence intensity is of the form k = k F = α + ( ) [ F ] k k ex 2 However, for a particular case of [ Q] =, the fluorescence intensity is. (). () 66

n fluorescence quenching the Taking into account that we get either or For the small values of р, we have = k F = α To determine the Stern-Volmer constants, on [ Q ] ). For this dependence with small ( ) [ F ] k k ex + 2 value is used. From ()-(2) we obtain [ F] [ F] k. (2) =. (3) [ F] [ F] y[ F] = (4) [ F] [ F] = = (5) y = ( + p+ q) 4 p 2 p q ( + p+ q) 2. (6) + +. (7) is measured as a function of Q values, we get [ Q] p + = + + q + F Q (the dependence of. (8) Comparing (8) with (6) indicates that in the case of complex formation, the Stern-Volmer quenching constant is not equal to, Thus, =. (9) + F + [ F] constant. This correction to unity in the denominator of Equation (9), equal to [ F] takes into account the rather than is measured experimentally. The latter is usually associated with a complex fact that the concentration of molecules F is less than [ F ] because of complex formation. Thus, the generally accepted equating of the experimental quenching constant valid only if [ F]. The value of can be estimated from the dependence of to the equilibrium one (complexing) [2] is on [ F ] = + F. (2) The value and then, respectively, that of are determined from the cut on the Y-axis. 3. Conclusion t is concluded then that introducing the above correction may be a key moment in obtaining the true values of the association constants. The relation [ F] may fail in the case of reagents (fluorophores) with a low 67

quantum yield. n this case, the high concentrations of [ F ] 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. References [] De Weert, M. and Stella, L. (2) Fluorescence Quenching and Ligand Binding: A Critical Discussion of a Popular Methodology. Journal of Molecular Structure, 998, 44-5. http://dx.doi.org/.6/j.molstruc.2.5.23 [2] Lakovicz, J. (2) Principles of Fluorescence Spectroscopy. 3rd Edition, Springer, Berlin. 68