On the rotational diffusion-controlled photo-reaction and reaction-induced birefringence

We have treated photo-induced intramolecular reactions where the reactant molecule in liquids or in solids has a photo-active group which is assumed to react with another group whose rate is proportional to the product of the strength of the electric field of an external light and an induced dipole moment on the former group, which is equivalent to the interaction energy between the field and the dipole. When the reactant is subject to a linearly polarized light, the reaction rate becomes dependent upon the orientation of the former group relative to the direction of the light and the system becomes optically birefringent. Since the reaction redistributes the orientation of the reactant inhomogeneously, the diffusion tries to average out the distribution. The dynamics of the reaction is considered theoretically taking into account these two opposing factors with the reference to the dichroism using a model for the rotational diffusion-controlled reaction based on the Smoluchowski equation modified with a sink term arising from the reaction. We treated two typical cases of the slow and fast reactions, and obtained the following quantities exactly in terms of continued fractions as a function of the rotational diffusion constant D and the rate constant with application of the natural light: the relaxation time for the time-dependent dichroism and the stationary dichroism for the former case, and the reaction constant r for the reactant for the latter case which is found to be r ∝ D14 for intermediate values of D. Also, it is shown that theoretical results agree satisfactorily with those of experiments.