From Global to Localized Illumination: Tunable Photo-induced Patterns in a Ternary Reaction-diffusion System

Zhuo-Hang Cai; Chang-Hao Li; Jian-Feng Li

doi:10.1007/s10118-026-3753-z

Your Location：

Home >

Browse articles >

From Global to Localized Illumination: Tunable Photo-induced Patterns in a Ternary Reaction-diffusion System

RESEARCH ARTICLE | Updated：2026-09-23

- From Global to Localized Illumination: Tunable Photo-induced Patterns in a Ternary Reaction-diffusion System
- Chinese Journal of Polymer Science Vol. 44, Issue 10, Pages: 3586-3596(2026)
- Affiliations：
  
  a.The State Key Laboratory of Molecular Engineering of Polymers, Department of Macromolecular Science, Fudan University, Shanghai 200433, China
  b.College of Energy Engineering and State Key Laboratory of Clean Energy Utilization, Zhejiang University, Hangzhou 310003, China
  c.Joint Research Centre on Medicine, Xiangshan Hospital of Wenzhou Medical University, Ningbo 315700, China
- Author bio：
  
  changhao.li@zju.edu.cn (C.H.L.)
  lijf@fudan.edu.cn (J.F.L.)
- Funds：
- DOI：10.1007/s10118-026-3753-z
  CLC：
- Received：03 April 2026，
  
  Accepted：19 May 2026，
  
  Online First：24 July 2026，
  
  Published：05 October 2026
- Accepted：
Scan QR Code
Cai, Z. H.; Li, C. H.; Li, J. F. From global to localized illumination: tunable photo-induced patterns in a ternary reaction-diffusion system. Chinese J. Polym. Sci. 2026, 44, 3586–3596

Zhuo-Hang Cai, Chang-Hao Li, Jian-Feng Li. From Global to Localized Illumination: Tunable Photo-induced Patterns in a Ternary Reaction-diffusion System[J]. Chinese Journal of Polymer Science, 2026, 44(10): 3586-3596.
Cai, Z. H.; Li, C. H.; Li, J. F. From global to localized illumination: tunable photo-induced patterns in a ternary reaction-diffusion system. Chinese J. Polym. Sci. 2026, 44, 3586–3596 DOI： 10.1007/s10118-026-3753-z.

Zhuo-Hang Cai, Chang-Hao Li, Jian-Feng Li. From Global to Localized Illumination: Tunable Photo-induced Patterns in a Ternary Reaction-diffusion System[J]. Chinese Journal of Polymer Science, 2026, 44(10): 3586-3596. DOI： 10.1007/s10118-026-3753-z.

摘要

Photo-induced multicomponent reaction-diffusion systems provide a valuable theoretical framework for exploring nonequilibrium self-organization under external energy input. Illumination can induce tunable nonequilibrium periodic structures whose characteristic length scale satisfies

$${\mathrm{ln}} \xi\sim \dfrac{s \Delta E}{k_{\mathrm{B}} T_b} $$

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=118966539&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=118966539&type=small

http://notExist.jpg

. Furthermore

distinct spatial morphologies can also be observed under local illumination and a theoretical phase diagram for pattern formation is constructed.

Abstract

Photo-induced reaction-diffusion systems provide a valuable theoretical framework for exploring nonequilibrium self-organization under external energy input. Most existing studies have focused on binary mixtures subjected to globally uniform driving

whereas realistic chemical and biological systems are typically multicomponent and experience strongly localized energy supply. In this work

we extend photo-induced reaction-diffusion models to a multicomponent setting and systematically investigate pattern formation in a minimal three-component system. By combining numerical simulations with linear stability analysis

we find illumination can induce periodic nonequilibrium structures

whose characteristic length scales can be tuned by the input energy density and intrinsic molecular energetic parameters. We further introduce localized illumination to capture the effects of spatially heterogeneous energy input. Under such conditions

a theoretical phase diagram for pattern formation is constructed

revealing distinct spatial morphologies

including dot patterns and target-like structures. In addition

we explicitly examine the nonnegativity of entropy production for both globally and locally illuminated systems. These results provide a unified and physically consistent framework for understanding photo-induced pattern formation in multicomponent nonequilibrium systems and are also applicable to photoexcitation-controlled supramolecular systems such as persulfurated-arene/block-copolymer assemblies.

关键词

Keywords

references

Witzany, G. Crucial steps to life: from chemical reactions to code using agents. Biosystems 2016 , 140 , 49−57..

Goldbeter, A. Dissipative structures in biological systems: bistability, oscillations, spatial patterns and waves. Philos. Trans. R. Soc. A 2018 , 376 , 20170376..

Zwicker, D.; Seyboldt, R.; Weber, C. A.; Hyman, A. A.; Jülicher, F. Growth and division of active droplets provides a model for protocells. Nat. Phys. 2017 , 13 , 408−413..

De Domenico, M. Decoding the architecture of living systems. Rep. Prog. Phys. 2026 , 89 , 014601..

Zampetaki, A. V.; Liebchen, B.; Ivlev, A. V.; Löwen, H. Collective self-optimization of communicating active particles. Proc. Natl. Acad. Sci. U.S.A. 2021 , 118 , e2111142118..

Volpert, V.; Petrovskii, S. Reaction-diffusion waves in biology: new trends, recent developments. Phys. Life Rev. 2025 , 52 , 1−20..

Kondo, S.; Asai, R. A reaction-diffusion wave on the skin of the marine angelfish pomacanthus. Nature 1995 , 376 , 765−768..

Sick, S.; Reinker, S.; Timmer, J.; Schlake, T. WNT and Dkk determine hair follicle spacing through a reaction-diffusion mechanism. Science 2006 , 314 , 1447−1450..

Ait Mahiout, L.; Bessonov, N.; Kazmierczak, B.; Sadaka, G.; Volpert, V. Infection spreading in cell culture as a reaction-diffusion wave. ESAIM: Math. Model. Numer. Anal. 2022 , 56 , 791−814..

El Hajj, W.; El Khatib, N.; Volpert, V. Inflammation propagation modeled as a reaction–diffusion wave. Math. Biosci. 2023 , 365 , 109074..

Potts, J. R.; Petrovskii, S. V. Fortune favours the brave: movement responses shape demographic dynamics in strongly competing populations. J. Theor. Biol. 2017 , 420 , 190−199..

Glotzer, S. C.; Di Marzio, E. A.; Muthukumar, M. Reaction-controlled morphology of phase-separating mixtures. Phys. Rev. Lett. 1995 , 74 , 2034..

Carati, D.; Lefever, R. Chemical freezing of phase separation in immiscible binary mixtures. Phys. Rev. E 1997 , 56 , 3127..

Longo, T. J.; Shumovskyi, N. A.; Asadov, S. M.; Buldryev, S. V.; Anisimov, M. A. Structure factor of a phase separating binary mixture with natural and forceful interconversion of species. J. Non-Cryst. Solids: X 2022 , 13 , 100082..

Aslyamov, T.; Avanzini, F.; Fodor, É.; Esposito, M. Nonideal reaction-diffusion systems: multiple routes to instability. Phys. Rev. Lett. 2023 , 131 , 138301..

Manz, N.; Davydov, V. A.; Zykov, V. S.; Müller, S. C. Excitation fronts in a spatially modulated light-sensitive Belousov-Zhabotinsky system. Phys. Rev. E 2002 , 66 , 036207..

Hildebrand, M.; Skødt, H.; Showalter, K. Spatial symmetry breaking in the Belousov-Zhabotinsky reaction with light-induced remote communication. Phys. Rev. Lett. 2001 , 87 , 088303..

Li, C.; Li, J.; Zhang, H.; Yang, Y. A systematic study on immiscible binary systems undergoing thermal/photo reversible chemical reactions. Phys. Chem. Chem. Phys. 2023 , 25 , 1642−1648..

Yue, B.; Jia, X.; Baryshnikov, G. V.; Jin, X.; Feng, X.; Lu, Y.; Luo, M.; Zhang, M.; Shen, S.; Ågren, H.; et al. Photoexcitation-based supramolecular access to full-scale phase-diagram structures through in situ phase-volume ratio phototuning. Angew. Chem. Int. Ed. 2022 , 61 , e202209777..

Krause, A. L.; Klika, V.; Woolley, T. E.; Gaffney, E. A. From one pattern into another: analysis of Turing patterns in heterogeneous domains via WKBJ. J. R. Soc. Interface 2020 , 17 , 20190621..

Van Gorder, R. A. Pattern formation from spatially heterogeneous reaction–diffusion systems. Philos. Trans. R. Soc. A 2021 , 379 , 20210001..

Penocchio, E.; Rao, R.; Esposito, M. Nonequilibrium thermodynamics of light-induced reactions. J. Chem. Phys. 2021 , 155 , 114101..

Tran-Cong, Q.; Ohta, T.; Urakawa, O. Soft-mode suppression in the phase separation of binary polymer mixtures driven by a reversible chemical reaction. Phys. Rev. E 1997 , 56 , R59−R62..

Tran-Cong, Q.; Harada, A.; Kataoka, K.; Ohta, T.; Urakawa, O. Positive feedback driven by concentration fluctuations in asymmetrically photo-cross-linked polymer mixtures. Phys. Rev. E 1997 , 55 , R6340−R6343..

Zhang, Y.; Liang, X.; Yang, C.; Tang, Y.; Yan, Q. Light-fueled non-photoisomerized dissipative self-assembly system through transient radical-radical interactions. Angew. Chem. Int. Ed. 2025 , 64 , e202512915..

[Landau, L. D.; Lifshitz, E. M. Statistical Physics ; Elsevier, 2013 ; Vol. 5. p. 187..

Cotton, M. W.; Golestanian, R.; Agudo-Canalejo, J. Catalysis-induced phase separation and autoregulation of enzymatic activity. Phys. Rev. Lett. 2022 , 129 , 158101..

Liu, B.; Tong, C.; Yang, Y. The kinetics and phase patterns in a ternary mixture coupled with chemical reaction of A + B $$\rightleftharpoons $$ https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=118967080&type= https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=118967080&type=small http://notExist.jpg C. J. Phys. Chem. B 2001 , 105 , 10091−10100..

Tong, C.; Zhang, H.; Yang, Y. Phase separation dynamics and reaction kinetics of ternary mixture coupled with interfacial chemical reaction. J. Phys. Chem. B 2002 , 106 , 7869−7877..

Tomé, T.; de Oliveira, M. J. Entropy production in nonequilibrium systems at stationary states. Phys. Rev. Lett. 2012 , 108 , 020601..

Li, C.; Li, J.; Yang, Y. First-principle derivation of single-photon entropy and Maxwell–Jüttner velocity distribution. Entropy 2022 , 24 , 1609..

Mahato, R. R.; Adikessavane, N.; Ettikkan, N. K.; Maiti, S. A chemoenzymatic reaction-diffusion system with local inhibition and distal activation. Nat. Commun. 2025 , 16 , 9885..

Eisenmann, I.; L’homme, A.; Lahlou, A.; Bujaldon, S.; Le Saux, T.; Bailleul, B.; Desprat, N.; Jeanneret, R. Light-induced phase separation with finite wavelength selection in photophobic microalgae. Phys. Rev. Lett. 2025 , 135 , 148401..

Torra, J.; Campelo, F.; Garcia-Parajo, M. F. Tensing flipper: photosensitized manipulation of membrane tension, lipid phase separation, and raft protein sorting in biological membranes. J. Am. Chem. Soc. 2024 , 146 , 24114−24124..

Li, J.; Li, T.; Ma, X.; Su, Z.; Yin, J.; Jiang, X. Light-induced programmable 2D ordered patterns based on a hyperbranched poly(ether amine)(HPEA)-functionalized graphene film. ACS Appl. Mater. Interfaces 2020 , 13 , 1704−1713..

Zheng, J.; Chen, J.; Jin, Y.; Wen, Y.; Mu, Y.; Wu, C.; Wang, Y.; Tong, P.; Li, Z.; Hou, X.; Tang, J. Photochromism from wavelength-selective colloidal phase segregation. Nature 2023 , 617 , 499−506..

Barrett, J. W.; Blowey, J. F.; Garcke, H. Finite element approximation of the Cahn–Hilliard equation with degenerate mobility. SIAM J. Numer. Anal. 1999 , 37 , 286−318..

Barrett, J. W.; Blowey, J. F.; Garcke, H. On fully practical finite element approximations of degenerate Cahn-Hilliard systems. ESAIM: Math. Model. Numer. Anal. 2001 , 35 , 713−748..

Müller, M. Z.; Bernero, M.; Xie, C.; Qiu, W.; Oggianu, E.; Rabut, L.; Michaels, T. C. T.; Style, R. W.; Müller, R.; Qin, X. H. Cell-guiding microporous hydrogels by photopolymerization-induced phase separation. Nat. Commun. 2025 , 16 , 4923..

Biria, S.; Hosein, I. D. Control of morphology in polymer blends through light self-trapping: an in situ study of structure evolution, reaction kinetics, and phase separation. Macromolecules 2017 , 50 , 3617−3626..

Views

Downloads

CSCD

Alert me when the article has been cited

Submit

Tools

Publicity Resources

Enhanced Mechanical Properties and Prolonged Recovery Onset Period of Timed Shape Memory Hydrogels via Hydrophobic Interaction

Phase Separation Enabled Functional Ionogels

A Transparent Acoustic Damping Hydrogel with Dual-scale Bicontinuous Microphase Separation

Enhancing Processability of Phenylethynyl-terminated Imide Oligomers and Properties of Cured Polyimides via ―CF3 Incorporation

One-handed Helical Poly(m-terphenyl acetylene)s with Broad Optical Activity Range from Ultraviolet-Visible to Near-infrared Regions

Related Author

Xiao-Ting Jia

Yi-Ting Sun

Chu-Jun Ni

Qian Zhao

Xue Wang

Xin Fu

Lie Chen

Ming-Jie Liu

Related Institution

Eye Center, Affiliated Second Hospital, School of Medicine, Zhejiang University

State Key Laboratory of Chemical Engineering, College of Chemical and Biological Engineering, Zhejiang University

International Research Institute for Multidisciplinary Science, Beihang University

Key Laboratory of Bio-Inspired Smart Interfacial Science and Technology of Ministry of Education, School of Chemistry, Beihang University

Department of Applied Chemistry, College of Science, China Agricultural University

⁰