A simple derivation of the luminescence anisotropy decay from randomly distributed cylinders rotating about a single axis.

A simple derivation is given of the expression describing the anisotropy decay of luminescence for a solution of molecules that can only undergo rotational diffusion about a single cylindrical axis. The usual derivations of the anisotropy decay for this cylindrical model have simply taken limiting cases of the equations resulting from the general treatment of the anisotropy decay of a completely anisotropic rotator or the rotation of an ellipsoid. The arguments presented here can be understood without the mathematical sophistication required to follow the general derivations for the rotational diffusion of a completely anisotropic rotator or ellipsoids. The underlying physical mechanisms leading to a multiple exponential decay of the fluorescence anisotropy signal from a single axis rotating cylinder are clearly shown by following this derivation. The resulting expression for the anisotropy decay is not new. However, the derivation is easily understood, and this article is meant as an introduction to the more advanced treatments of anisotropy decay by rotational diffusion. After presenting the derivation of the rotating cylinder, the corresponding steps of these general treatments and this simple model are indicated. The model is of special interest for describing the anisotropy decay resulting from rotations of proteins within membranes.