Free Volume Distribution and Local Environment of a Polymer with Photo-reactive Probe Technique

Yamashita, Takashi; Ishii, Kuniyoshi; Hasegawa, Mayu

doi:10.2494/photopolymer.20.763

Cited by 3 publications

(1 citation statement)

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“…Further progress in the analysis is still limited. 10,11 Therefore, the development of a novel methodology for solving the distribution function of the components for given data of the convolution of complex phenomena without any assumptions is very important in material science.…”

Section: Introductionmentioning

confidence: 99%

Mathematical optimization approach for estimating the quantum yield distribution of a photochromic reaction in a polymer

et al. 2017

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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 optimization problem to minimize the difference between the input data and a model. This optimization problem involves a differential equation constrained on a functional space as the variable lies in the space of probability distribution functions and the constraints arise from reaction rate equations. This problem can be reformulated as a convex quadratic optimization problem and can be efficiently solved by discretization. Numerical results are also reported here, and they verify the effectiveness of our approach.

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Section: Introductionmentioning

confidence: 99%