Unraveling the impact of competing interactions on non-equilibrium colloidal gelation

Abstract: Competing interactions stabilize exotic mesoscopic structures, yet the microscopic mechanisms by which they influence non-equilibrium processes leading to disordered states remain largely unexplored, despite their critical role in self-assembly across a range of nanomaterials and biological systems. Here, we numerically investigate the structural evolution in charged colloidal model systems, where short-range attractions and long-range repulsions compete. We reveal that these two interaction scales drive sequential ordering within clusters, from tetrahedra motifs to linear aggregates with chiral order. This process disrupts early-stage percolated networks, resulting in reentrant behavior -- a dynamic transition from disordered cluster to network to chiral rigid cluster. On the other hand, the cluster-elastic network boundary in the final state is governed by isostatic percolation, which slows structural rearrangements, preserves branching points, and sustains a long-lived network. The resulting structure consist of rigid Bernal spiral-like branches connected through flexible branching points lacking order. These insights advance our microscopic understanding of out-of-equilibrium ordering driven by competing interactions, particularly phenomena like temporally delayed frustration reflecting different length scales of competing interactions. The mechanisms identified here may play a crucial role in mesoscale self-organization across soft materials, from nanoparticle assemblies to biological gels and cytoskeletal networks. Understanding how competing interactions regulate structure and dynamics could guide the design of adaptive materials with tunable mechanical properties and offer new perspectives on biological processes such as cytoplasmic organization and cellular scaffolding.