Nonequilibrium ordering dynamics of confined soft alginate hydrogel colloids driven by time-evolving electrostatic interactions

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. © The Author(s) 2026.