Mathematical modeling of morphological changes in photochromic crystals by catastrophe theory

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 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 at the nanoscale and lead to the realization of important functions as 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 the hyperbolic operating curves in the model, intrinsic properties of the photochromic crystals are represented. The induced morphogenesis, such as bending, cracking, and photosalient, are systematically classified by the proposed catastrophe model, which even implies 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.