Photochromic diarylethene is known to exhibit reversible photoisomerization under irradiation with ultraviolet (UV) and visible light. Besides reversible optical properties upon light irradiation, a variety of discontinuous morphological changes of the crystals are reported in the literature, such as sudden crystal bending, cracking, and photosalient effects, which are caused simply by UV and visible light irradiation. These morphological phenomena with discontinuities are micro-scale changes caused by photoisomerization of molecules at the nanoscale and lead to the realization of important functions for optical devices. However, the theoretical models behind these phenomena are not well understood. In this paper, we construct a mathematical model that can treat diverse phenomena in a unified model by using swallow-tail catastrophe, a higher-order catastrophe than cusp catastrophe, from the seven elementary catastrophes that can describe discontinuities in the phenomena. By introducing hyperbolic operating curves in the model, the intrinsic properties of the photochromic crystals are represented. The induced morphogenesis, such as bending, cracking, and photosalient effects, are systematically classified by the proposed catastrophe model, which even implies the possibility of unexplored operating conditions of the crystals and explains known phenomena. The proposed catastrophe-theory-based modeling provides a foundation for understanding and discovering the versatile morphogenesis in photochromic crystals. Furthermore, the proposed approach provides a basis for understanding and discovering various morphological changes in photochromic crystals and similar systems.
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7 February 2023
Research Article|
February 06 2023
Mathematical modeling of morphological changes in photochromic crystals by catastrophe theory
Hirotsugu Suzui
;
Hirotsugu Suzui
a)
(Conceptualization, Data curation, Formal analysis, Visualization, Writing – original draft)
1
Department of Information Physics and Computing, Graduate School of Information Science and Technology, The University of Tokyo
, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
a)Author to whom correspondence should be addressed: [email protected]
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Kazuharu Uchiyama
;
Kazuharu Uchiyama
(Supervision, Writing – review & editing)
2
University of Yamanashi
, 4-3-11 Takeda, Kofu, Yamanashi 400-8511, Japan
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Kingo Uchida
;
Kingo Uchida
(Resources, Supervision, Writing – review & editing)
3
Department of Materials Chemistry, Ryukoku University
, 1-5 Yokotani, Oecho, Seta, Otsu, Shiga 520-2194, Japan
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Ryoichi Horisaki
;
Ryoichi Horisaki
(Supervision, Writing – review & editing)
1
Department of Information Physics and Computing, Graduate School of Information Science and Technology, The University of Tokyo
, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
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Hirokazu Hori
;
Hirokazu Hori
(Supervision, Writing – review & editing)
2
University of Yamanashi
, 4-3-11 Takeda, Kofu, Yamanashi 400-8511, Japan
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Makoto Naruse
Makoto Naruse
(Supervision, Writing – review & editing)
1
Department of Information Physics and Computing, Graduate School of Information Science and Technology, The University of Tokyo
, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
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Hirotsugu Suzui
1,a)
Kazuharu Uchiyama
2
Kingo Uchida
3
Ryoichi Horisaki
1
Hirokazu Hori
2
Makoto Naruse
1
1
Department of Information Physics and Computing, Graduate School of Information Science and Technology, The University of Tokyo
, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
2
University of Yamanashi
, 4-3-11 Takeda, Kofu, Yamanashi 400-8511, Japan
3
Department of Materials Chemistry, Ryukoku University
, 1-5 Yokotani, Oecho, Seta, Otsu, Shiga 520-2194, Japan
a)Author to whom correspondence should be addressed: [email protected]
J. Appl. Phys. 133, 055110 (2023)
Article history
Received:
August 11 2022
Accepted:
January 23 2023
Citation
Hirotsugu Suzui, Kazuharu Uchiyama, Kingo Uchida, Ryoichi Horisaki, Hirokazu Hori, Makoto Naruse; Mathematical modeling of morphological changes in photochromic crystals by catastrophe theory. J. Appl. Phys. 7 February 2023; 133 (5): 055110. https://doi.org/10.1063/5.0119073
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