Kinetics of the photoisomisation
When it is assumed that intrinsic kinetics is obeyed and that the photoreaction follows the first order kinetics, the photoisomerization of cis -cyclooctene to trans -cyclooctene is represented in scheme 1:
Scheme 1. Photo isomerisation of trans fromcis-cyclooctene
For a first order reversible reaction [37], the concentration of thecis -cyclooctene \(C_{\text{cis}}\) as a function of time obeys Eq 3.1. For a batch process, the conversion time histories have been monitored:
\begin{equation} \frac{C_{cis,(\tau)}\ }{C_{cis,(0)}\ }=\left[\frac{1}{k_{1}+k_{-1}}\left(k_{1}e^{-\tau\left(k_{1}+k_{-1}\right)}+k_{-1}\right)\right]\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (3.1)\nonumber \\ \end{equation}
In this equation \(C_{cis,(0)}\) represents the concentration ofcis at the start of reaction. See supplementary material S1 for the derivation.