Abstract
Elucidating how repulsive interactions evolve to generate ordered structures in nonequilibrium colloidal systems remains a central challenge, partly because few experimental platforms provide particle-resolved access to their structural evolution. Here we show that alginate hydrogel colloids confined within cyclohexyl bromide (CHB) emulsion droplets form a controllable model system in which electrostatic interactions evolve in time and drive ordering. Ba2+ ions diffusing from the surrounding aqueous phase progressively crosslink the alginate droplets, increasing their surface charge, while buoyancy compacts them into locally quasi-two-dimensional layers within the CHB phase. As electrostatic repulsion strengthens, the assembly evolves from a disordered state to a hexagonally ordered structure. By calibrating Brownian dynamics simulations to the experimentally measured lattice spring constant, we constrain the effective Debye screening length to ≈2.5–3 μm. Quantitative imaging further shows that ordering emerges once a dimensionless interaction parameter—defined as the ratio of electrostatic interaction energy to thermal energy—reaches values of ≈117–149. The ordered state exhibits reversible disordered–order behavior under mechanical and magnetic perturbations, demonstrating a robust nonequilibrium platform for probing charge-regulated colloidal ordering under confinement.
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The data that support the findings of this study are available from the corresponding authors upon request. Unprocessed raw data are provided as Supplementary Data 1. Source data are provided with this paper.
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Acknowledgements
This study was supported by the National Research Foundation (NRF) of Korea (RS-2025-00516792 to B.J.P., RS-2024-00406741 to B.J.P., and RS-2025−16063688 to H.H). The research was conducted with the support of the equipment and facilities provided by the ACE Center at Kyung Hee University.
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B.J.P. conceived and supervised the project. I.H.J. C.C.R. and H.S.L. performed the microfluidic preparation and measured the behaviors of colloidal ordering. C.C.R. measured the zeta-potential of alginate hydrogel particles. I.H.J. and H.A. performed the image analysis. B.J.P. performed the BD simulations. H.H., H.A., and B.J.P. wrote the first draft. All authors contributed to the interpretation of experimental data and read, edited, commented on this manuscript.
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Jung, I.H., Revadekar, C.C., Lee, H.S. et al. Nonequilibrium ordering dynamics of confined soft alginate hydrogel colloids driven by time-evolving electrostatic interactions. Nat Commun (2026). https://doi.org/10.1038/s41467-026-70266-w
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DOI: https://doi.org/10.1038/s41467-026-70266-w
