General Kinetic Equation for Reactions Governed by Dual Fluorescence Absorption and Emission Spectroscopy

Abstract

Two conformers are assumed to exist in the Franck-Condon excited state species of dual fluorescing molecules. Kinetic equations for the steady state condition of the equilibrium of the S*A and S*B excited state conformers have been derived. The equations for the quantum yield and the quantum yield ratio have also been mathematically formulated. This derivation of the equations for the existence of dual fluorescence conformers following Franck-Condon's theory has further explained in mathematical terms the basis for the assumptions used in the development of equipment and methods applied in spectroscopy for dual fluorescent molecules or conformers in spectroscopic detection and measurements of the equilibrium concentrations of the dual fluorescing molecules, e.g., the development of probes (sensors) and ratiometric methods. These mathematical equations also explain the versatility of the ratio metric method in the measurement of the equilibrium concentrations of conformers, as shown in the mathematical expressions for the equilibrium concentrations of the steady state quantum yields ΦA and ΦB and the quantum yield ratio ΦA / ΦB.