Abstract
The convolution of a series of events is often observed for a variety of phenomena such as the oscillation of a string. A photochemical reaction of a molecule is characterized by a time constant, but materials in the real world contain several molecules with different time constants. Therefore, the kinetics of photochemical reactions of the materials are usually observed with a complexity comparable with those of theoretical kinetic equations. Analysis of the components of the kinetics is quite important for the development of advanced materials. However, with a limited number of exceptions, deconvolution of the observed kinetics has not yet been mathematically solved. In this study, we propose a mathematical optimization approach for estimating the quantum yield distribution of a photochromic reaction in a polymer. In the proposed approach, time-series data of absorbances are acquired and an estimate of the quantum yield distribution is obtained. To estimate the distribution, we solve a mathematical opti...
Highlights
Photochromism is a chemical reaction between two isomers of a molecule
We propose a technique for obtaining the quantum yield distribution of a photochromic reaction based on the time-dependent change in absorbance of a sample
We report our numerical results that verify the effectiveness of our approach
Summary
To express the inhomogeneity of the time constant, a reaction in viscous media may be analyzed with an extended exponential equation introducing another parameter in addition to the original time constant.8 Another approach to the analysis of multicomponent kinetics is the deconvolution method, which is usually performed for fluorescence lifetime measurements.. We propose a technique for obtaining the quantum yield distribution of a photochromic reaction based on the time-dependent change in absorbance of a sample. This change in absorbance is described in theory as a convex combination of decaying curves with their respective quantum yields.
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