Time‐dependent concentration depolarization of fluorescence

A theory of the time course of fluorescence anisotropy (polarization) after impulsive excitation is presented for viscous solutions of identical molecules. In a point‐dipole model of the molecular oscillators, it is shown that the relative anisotropy is a universal function A of the quantity T = c2t/τ, where c is solute concentration (in units of the usual critical concentration), t is time, and τ is actual fluorescence lifetime. The function A(T) is expressed as a contribution A0 from the initially excited dipole plus one from all other dipoles, with the latter shown to be quite small in the region of interest. It is also shown that the representation, A0=Σk=0∞αk Tk/2, is useful for calculations except when T ≫ 1. The kth term in the series corresponds to energy transfer pathways involving k + 1 dipoles. The αk alternate in sign, with α0 = 1 and α1 = − 1.06004 derived analytically; numerically derived values of α2 through α6 are also given. We show that A(T) is the Laplace transform of c2 A(c), where A(c...