Compartmental Analysis Approach to Fluorescence Anisotropy: Perylene in Viscous Solvents

The fluorescence and polarization anisotropy decays of perylene in viscous solvents are investigated at several temperatures between -20 and 35 OC by using the technique of multifrequency phase and modulation fluorometry. The anisotropy decay data are globally analyzed over all temperatures studied and fit directly to physical quantities by using a compartmental model. We present a generalized compartmental model that can be used to calculate anisotropy decay arising from any type of interconversion that introduces a change in the fluorescence polarization. This generalized model provides a simple method to calculate the anisotropy decay for systems undergoing different kinds of interconversions such as excited-state reactions, rotational diffusion, “jump” motions, or any combination which can be treated in a compartmental form. The basic idea is to consider a rotation as an interconversion between compartments which represent different geometries with respect to the laboratory frame. Compartments due to other processes can be added to these rotational compartments. A matrix is constructed by using the decay rates of each compartment and the rates of interconversion between these compartments. The polarization of each compartment and initial conditions are contained in vectors. Using this formalism, the fluorescence anisotropy decay can be represented as a standard eigenvector-eigenvalue problem which may be solved analytically or numerically. As a simple example, this compartmental model is applied to the perylene molecule undergoing only rotational diffusional motions, and is used to globally fit the anisotropy decay data at various temperatures and viscosities. We fit directly to the physical quantities needed to define the compartments, using only three fitting parameters, two rotational diffusion constants, and the average angle between the absorption and emission dipoles. In previous studies, four parameters were used to fit the anisotropy decay of perylene, that is, two rotational correlation times and two preexponentials. The results of this study are shown to be in agreement with previous measurements.