Influence of Brownian Rotations and Energy Transfer upon the Measurements of Fluorescence Lifetime

Abstract

The depolarization of the fluorescence of solutions by either Brownian rotations or intermolecular energy transfer may be simply described by a system of first‐order linear differential equations containing as only parameters the rate of fluorescence emission and the rate of transport of the excitation from one orthogonal component of the emission to another. The steady‐state solution has the form of Perrin's equation describing the depolarization by Brownian rotations, and the time‐dependent depolarization following a unit light impulse is that originally described by Jablonski. The solution for sinusoidal excitation is novel in that: 1. It shows the difference in lifetime between the polarized components of the emission to be a sensitive function of the ratio of the modulation frequency $\omega$ to the emission rate $\lambda$ . For $\text{ω/λ\hspace{0.17em}>\hspace{0.17em}1}$ the difference between the polarized lifetimes may become many times greater than that observed after a unit light impulse. 2. It permits the determination of both the rate of transport of the excitation and the limiting polarization of the fluorescence from observations at one fixed temperature and viscosity. 3. It allows the definition of conditions under which the true or exponential decay of the fluorescence may be measured. Experimental tests of the theory by phase fluorometry are described: These include observations upon dilute solutions in media of limited viscosity where Brownian motion is the only cause of depolarization and observations upon concentrated frozen solutions where depolarization is due to energy transfer alone.