Exploring Conductivity Enhancement through Lining Transitions: Insights from Non-equilibrium Large-Scale Brownian Dynamics Simulations of Macroions

We investigate laning transitions in concentrated macroions using large-scale Brownian Dynamics simulations coupled with Poisson's equation and stress let constrained hydrodynamic interactions. In dense regimes, particle-based simulations reveal structural dynamics inaccessible to analytical models. We link the non-equilibrium field-dependent conductivity, beyond the Wien effect, to particle alignment, with ionic motion under applied fields resulting in dramatic shifts in local structure. Laning transitions, commonly observed in lattice models of binary systems, occur when species segregate into aligned lanes under high fields. To quantify this transition, we analyze the charge structure factor orthogonal to the field, and propose an order parameter based on real and imaginary contributions to the correlation length as a robust indicator of the transition. We capture the critical scaling from both sides of the transition, shedding light on the interplay between microscopic structure and macroscopic transport. These findings offer valuable insights for understanding electrochemical systems and optimizing applications in energy storage and biological processes.