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

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.