The environmental effect on the fluorescence intensity in solution. An analytical model

In this paper a mathematical model describing the non-specific interactions of the medium surrounding a fluorophore on its fluorescence intensity is proposed. The model, which has been developed for quantitative analytical applications, is based on the following general ideas: (1) the medium affects the fluorescence quantum yield across the non-radiative decay constant (k(nr)); (2) the k(nr) can be simplified to the singlet-to-triplet intersystem crossing (k(ISC)) constants; (3) k(ISC) follows the energy gap law and then depends on the singlet and triplet energy difference, and (4) the medium, due to solvation, changes the energy of both excited levels (singlet and triplet), then the constants and finally the fluorescence intensity. In our model, the strength of the fluorophore solvation by the solvent (represented by its refraction index, n, dielectric constant, epsilon, and electric charge) changes the singlet (excited)-to-fundamental and the singlet-to-triplet energy gaps, thus the k(ISC) and k(IC) (internal conversion constant) values and in consequence the fluorescence quantum yield. The final model relates the fluorescence intensity (F) with the solvent dielectric constant and refraction index. Finally, the model is particularized for the case of a medium composed of a solvent and a solute, obtaining an F-to-solute concentration relationship and enabling this fact to be used for analytical applications. The very first experimental data are shown demonstrating the fulfilment of this model.