Laning Transitions in Pattern Forming Driven Binary Systems with Competing Interactions

TL;DR

This work investigates laning transitions in a binary system of oppositely driven particles with SALR (short-range attraction, long-range repulsion) interactions in two dimensions. By simulating overdamped dynamics with half the particles driven in +x and half in -x, the authors map the dynamical phases as functions of drive, density, and the attraction-to-repulsion balance, revealing jammed, moving-liquid, and laned states beyond the purely repulsive case. Key findings include polarized elongated bubbles, striped laned states, and plastic bubble flow, with nonmonotonic unjamming thresholds and clear signatures in velocity-force and differential mobility curves. These results advance understanding of pattern-forming driven systems and have potential relevance for soft matter, vortex matter, and pedestrian-flow analogs where competing interactions shape collective motion.

Abstract

A binary system of particles that move in opposite directions under an applied field can exhibit disordered states as well as laned states where the particles organize into oppositely moving high-mobility lanes to reduce collisions. Previous studies of laning transitions generally focused on particles with purely repulsive interactions. Here, we examine laning transitions for oppositely moving pattern-forming systems of particles with competing attractive and repulsive interactions, which in equilibrium form crystal, stripe, and bubble states. In addition to multiple types of laned states, we find jammed crystals, stripes, and bubbles, and generally observe a much richer variety of phases compared to the purely repulsive system. In the stripe forming regime, the system can dynamically reorder into oppositely moving stripes that are aligned in the direction of the drive. The bubble phase can produce strongly polarized jammed states of elongated bubbles where particles in the individual bubbles segregate to opposite sides of the bubbles. We also find disordered states, segregated laned bubble states where the bubbles pass each other in lanes, and segregated bubbles that move through one another. In the compact bubble regime, we obtain a plastic bubble state in which the oppositely driven particles remain trapped in the bubbles but the bubbles move past each other at a slow velocity due to a net imbalance in the bubble population. At higher drives, individual particles begin to jump from bubble to bubble. We show that the different phases and the transitions between them produce signatures in the velocity-force and differential mobility curves. We demonstrate that the critical force for escaping from the jammed state is nonmonotonic, with stripes exhibiting the lowest unjamming force.

Figures (24)

• Figure 1: (a) Velocity $\langle V \rangle$ vs drive $F_D$ for oppositely driven SALR particles at a density of $\rho = 0.441$ with $B = 0.0$ in the purely repulsive Coulomb interaction regime. Region J is the jammed phase shown in Fig. \ref{['fig:2']}(a), ML is the moving liquid phase shown in Fig. \ref{['fig:2']}(b), and L is the laned phase shown in Fig. \ref{['fig:2']}(c). (b) The $d\langle V \rangle/dF_D$ vs $F_D$ curve more clearly shows the transitions among phases J, ML, and L. (c) The fraction of sixfold-coordinated particles, $P_6$, vs $F_D$ also shows signatures of the three phases.
• Figure 2: Particle positions for the system from Fig. \ref{['fig:1']} at $\rho = 0.441$ and $B = 0.0$, where the particles have only a Coulomb repulsion. Red (blue) particles are driven in the negative (positive) $x$ direction. (a) The jammed phase J at $F_D = 0.05$. (b) The moving liquid ML at $F_D = 0.4$. (c) The segregated laned state L at $F_D = 1.5$. Note that the radius of the circles representing the particles has been chosen for visual clarity here and throughout this work.
• Figure 3: Dynamic phase diagram as a function of $F_D$ vs $\rho$ for the system from Fig. \ref{['fig:1']} with $B = 0.0$. J: jammed state (blue); ML: moving liquid (red); and L: the higher drive laned state (green).
• Figure 4: Particle positions for the system from Fig. \ref{['fig:3']}. Red (blue) particles are driven in the negative (positive) $x$ direction. (a) At $\rho = 0.037$ and $F_D = 0.5$, the system has fully segregated into one-dimensional (1D) lanes. Here the particle trajectories are also plotted as colored lines indicating the direction of drive, with red for $\sigma_i=-1$ and blue for $\sigma_i=+1$. (b) The laned state at $\rho = 0.86$ and $F_D = 1.6$.
• Figure 5: $\langle V \rangle$ vs $F_D$ for the system from Fig. \ref{['fig:4']} with $B=0.0$ at $\rho = 0.037$ (blue) and $\rho = 0.86$ (green). For the higher density $\rho = 0.86$, there is an extended regime of the moving liquid state and a sharper transition into the laned state at higher drives.