Theory of Holographic Formation in Multicomponent Photopolymer-Based Nanocomposites
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ANOPHOTONICS
Theory of Holographic Formation in Multicomponent Photopolymer-Based Nanocomposites1 V. N. Borisova, * and V. V. Lesnichiib a
ITMO University, St. Petersburg, 197101 Russia Freiburg, Freiburg, D-79104 Germany * e-mail: [email protected]
b Albert-Ludwigs-Universität
Received January 18, 2020; revised January 18, 2020; accepted April 20, 2020
Abstract—The derivation of the three-component (monomer, chemically neutral component, and polymer) photopolymerization model from general thermodynamic considerations is presented. This model, together with another previously published one, are subject to a numerical solution for the case of a two-component one-dimensional diffusion (polymer component being steady). The divergence of results of work for both models was compared based on the average speed of the root-mean-square deviation in the spatial spectrum domain for relative volume fraction functions for all three components. Such a comparison was performed for 81 pairs of initial relative amount of neutral component and effective diffusion coefficient. The results of the work may serve as a good guide for the choice of parameters of experiments, which are aimed to verify the correctness of the modified theory. Keywords: photopolymerization, photoformer, holographic grating, multicomponent diffusion, polymer, holography DOI: 10.1134/S0030400X20080093
INTRODUCTION The theory of holographic recording in photopolymer materials has been of high interest for the last decades. Initially presented by Zhao [1] and followed by Sheridan [2], it describes the mass transfer process in terms of self-diffusion of one component (monomer) based on Fick’s laws. Such a depiction operates with the effective diffusion coefficient which in common case depends on the environment of each component. Since the diffusion coefficient is the soughtfor parameter in terms of experiments, if the diffusion coefficient depends on its surrounding, the experimentally received coefficient can be used only for the experiment with exactly the same initial conditions. Thus, the theory loses its predicting function, which makes it hard to apply for modeling the parameters of a hologram. Besides that, the counterflux of another component has to be considered. The second generation of the theory, proposed by Karpov [3], modifies the interdiffusion coefficient to derive the new one, which does not depend on the environment of components. Recently, a generalized theory considering multicomponent diffusion was proposed [4]. In this work, we present another depiction of two-component dif1 The 2nd International School-Conference for young researchers
“Smart Nanosystems for Life,” St. Petersburg, Russia, December 10–13, 2019.
fusion processes, in an attempt to obtain those directly from the laws of thermodynamics [5]. THEORY The theory proposed in this article is a modification of the one previously published by Karpov [3]. Both theories consider a model of polymerization in a three-component system, that is, the conversion of monomer to polymer
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