Evaluation of integrated time laws

As demonstrated in previous shapters the time laws for photoreactions can only be integrated in a closed form for a few special mechanisms. To avoid this problem one can make use of a time transformation as demonstrated in Section 3.3.11. Thus for many applications the concentrations can be calculated as an analytical function of the transformed time 0. 

Example 5.8 Physically sensitised photoisomerisation and use of time transformation 

The physically sensitised photoisomerisation which had been discussed in Example 3.9 in Section 3.1.1.4 yields a differential equation according to eqs. (3.6) and (3.35) 

According to Section 3.2.2 one obtains for the A th partial step in the case of a simple geometry 

10) represents a system of linear differential equations with constant coefficients, if the quantum yield does not depend on the concentrations. Any photoreaction, which can be rewritten by the transformation eq. (5.9) to such a system, is called a quasi-linear photoreaction in the following. All the relationships derived in Section 2.2 can be used, if the real reaction time is substituted by the transformed time 0. 

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