Kinetic characteristics of a solid photochromic film

Analytical or numerical solutions are given for the kinetic equations describing the time behavior of a solid photochromic film for the cases of photocoloration, photobleaching, and thermal bleaching. A procedure to evaluate relative quantum yields and absorption cross sections from the comparison of experimental results with theoretical solutions is demonstrated by an example using 6-nitro-8 piperidinomethyl-1', 3', 3'-trimethylspiro-[1H-benzopyran-2, 2'-indoline] as a photochromic compound. The theoretical results are presented in a suitably normalized form to be applicable to a broad range of experimental situations. The agreement between calculated and measured results is good as long as strictly first-order reaction mechanisms are obeyed.