Photokinetic methods: A mathematical analysis of the rate equations in photochromic systems

Abstract

In this article the analytical integration of kinetic equations describing the dynamic behavior of reversible photoreactions has been undertaken. Photochemical systems giving rise to competing thermal and photochemical steps are kinetically analyzed; the rate law is set up and analytical solutions are obtained under precisely defined boundary conditions. More complicated kinetic systems, where several species interact both thermally and photochemically, are also investigated. The kinetic treatment leads to a system of coupled differential equations which are amenable to analytical solutions, under the appropriate experimental and boundary conditions. The usefulness of the equations developed is illustrated by their application to some spirooxazine and chromene photochromic systems: two examples are described in detail. © 1999 John Wiley & Sons, Inc., Int J Chem Kinet 31: 303–313, 1999