Photokinetics in viscous media

As derived in Chapter 3.4 the photokinetic factor depends on the volume 

The concentrations dependent on time and location in the polymer are given by partial differential equations and using nomencalture introduced in eq. (5.131)  

One can integrate eq. (5.175) with respect to time t and can determine the integration constanty(z) at initial conditions for time r = 0, where no gradient of concentration is given  

Integration within the limits 0 and z gives a time-dependent constant g t), which can be determined at initial condition z = 0  

This integral cannot be solved explicitly. A Newton-Raphson iteration is used first to determine 6 values, which are used to calculate the concentrations of a 6) and b(6) according to eq. (5.174). In Fig. 5.70 the result of such an examination is given. One finds a systematic deviation, which can be explained by a diffusion process actually happening for cis- and trans-azobenzene molecules. 

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M. Guther, Software for Photokinetics in Viscous Media, Tubingen, 1987. 

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