Theory of Rotational Motion of Prolate Luminescent Molecules in Solution * R. Alicki**, M. Alicka, and A. Kawski Luminescence Research Group, Institute of Physics, University of Gdansk, Poland Z. Naturforsch. 86a, 1158-1162 (1981); received May 16, 1981 On the ground of a generalized equation for rotational diffusion which takes the inertial effect into account, an expression for the steady-state fluorescence depolarization for prolate molecules with the emission transition moment parallel to the long axis, has been derived. The present theoretical results differ from those of previous studies and are in good agreement with the ex- perimental results. 1. Introduction The effect of the Brownian rotational motion upon the fluorescence anisotropy (FA) 1 , r, of mol- ecules has been so far an object of numerous ex- perimental and theoretical investigations [1,2]. For asymmetric molecules, the generalized Perrin theo- ries predict extremely complex relations between parameters which are characteristic of the lumines- cent molecule itself (limiting fluorescence anisotropy, ro, molecular volume of a molecule together with its solvent shell, V, mean fluorescence lifetime, r) and the environment (solvent viscosity and tem- perature, 7] and T, respectively) in which the mol- ecule is located [3—9]. It was found, however, that the theories of fluorescence depolarization based on the approximation of rotational diffusion do not satisfactorily describe the experimental results ob- served, in particular for prolate ellipsoid-of-revolu- tion-shaped molecules for which the emission tran- sition moment is parallel to the long molecular axis [10—12]. In such case, the complex relation men- tioned above is simplified yielding the Perrin equa- 1 The FA is determined by r ~ 2 J 2 ' where J = J|| + 2J_L is the total fluorescence intensity; J\\ and «/ x designate the components of the fluorescence intensity parallel and perpendicular to the direction of the electric vector of the exciting light. * This work was supported within the project MR.I.5.2.01. ** Mathematical Physics Group, Institute of Physics, Uni- versity of Gdansk. Reprint requests to Prof. Dr. A. Kawski, Uniwersytet Gdanski, Instytut Fizyki, ul. Wita Stwosza 57, 80-952 Gdansk, Poland. tion for a spherical rotator (ro/r = 1 -f r/0, where 0= Vrj/kT) [13], which does not reflect properly 1/r versus Tjrj in the whole viscosity range. In order to explain this discrepancy (i.e. the non- linear dependence of 1/r upon T/r) for a prolate molecule the emission transition moment of which lies along its longer axis), the libration motions were assumed to play the predominant role in thermal motions of prolate molecules [10]. Final expression obtained with such assumption describes properly the behaviour of 1/r as a function of Tjrj, neverthe- less, the limitations assumed which were set upon the rotational motions of molecules in solutions raises certain doubts. The assumption as to the limited rotational motion is surely proper when the lumines- cent molecules are in anisotropic environment (e.g. in biological membranes, liquid crystals, etc.) [14, 15]. We shall show hereafter that the mentioned dis- crepancies between the experimental results and the existing theoretical studies result from the fact that the inertial effects have not been taken into account when considering rotational diffusion of molecules in liquid solutions. These effects turn out to influence substantially the decay of the fluorescence aniso- tropy for short lifetimes of a molecule after the excitation. 2. Theory Let us consider in detail the rotational motion of ellipsoid of revolution (Fig. 1), axes 1, 2 und 3 of which are the main ones of a friction tensor (£**), being simultaneously those of the inertia tensor (/tl). We assume moreover that £i = £2 = £ and Ii = 12 = I, and that the direction of the emission 0340-4811 / 81 / 0900-0967 $ 01.00/0. — Please order a reprint rather than making your own copy.