Active diffusing crystals in a 2D non-equilibrium system

Abstract

We investigate a 2D dynamical absorbing state model of monodisperse disks, in which rich phase behavior arises from interactions consisting solely of repulsive displacements between overlapping particles. The phase diagram reveals several unconventional features, including a disordered and static absorbing configuration, where no particles overlap, separated by a second-order phase transition to a continuously evolving active hexagonal crystal with collective ring diffusion, which in turn undergoes a first-order phase transition to an active isotropic liquid. The only driving parameter is $ε$, the maximum size of the random repulsive kicks. Small $ε$ facilitates self-organization into an ordered state, but large $ε$ prevents this organization from occurring. This is very different from typical order-disorder transitions, where there are two competing influences, energy and entropy, that drive the transition.

Figures (5)

• Figure 1: Monodisperse 2D Biased Random Organization (BRO) phase diagram. As a function of the two control parameters, the repulsive kick size $\epsilon/r$ and area fraction $\phi$, BRO configurations evolve from random initial conditions to three steady-state phases: 1) absorbing random, 2) active liquid, and 3) active crystal. These phases are characterized by the fraction of active particles $f_a$ ( A) and the global orientational order $|\langle \Psi_6 \rangle |$ ( B). Global translational order, as measured by the height of the first Bragg peak, looks qualitatively similar to the global orientational order in B. All absorbing states, where particles avoid overlaps, are random. Active states show both disordered (liquid) and ordered (crystalline) structural features, separated by a first-order phase boundary (red dashed line). The boundary between absorbing and active liquid phases in monodisperse BRO exhibits Manna critical exponents and matches that of bi-disperse 2D BRO (green dashed line). The transition from absorbing to active crystal phases also displays Manna exponents, with the densest absorbing state corresponding to the maximum circle packing $\phi(\epsilon \rightarrow 0) = \pi/(2\sqrt{3})$. All simulations contain $N = 1600$ particles and are run until a steady state value of $f_a$ and $|\langle \Psi_6 \rangle |$ is reached.
• Figure 2: Two active configurations. The left panel is in the active disordered phase, the right panel in the active crystalline phase. Defects, particles with either fewer or more than 6 Voronoi neighbors, are indicated. If we wait longer, the number of defects in the crystalline phase will decrease in a way reminiscent of Ostwald ripening.
• Figure 3: Active crystal dynamics. A Trajectories of 2D BRO active defect-free crystals. Particles are largely confined to crystalline cages. However, crystal rearrangements occur when a large number of particles collectively hop lattice sites in a closed ring-like structure. Ring-like lattice diffusion occurs with increasing frequency as the melting boundary is approached $\epsilon_{melt} \approx 0.4125$. Above the melting point, long-range translational and orientational order are lost, and trajectories are isotropic and random. B Mean-squared displacement is plotted for varied kick sizes crossing through the melting point. Liquid phases exhibit diffusive behavior (MSD $\sim t$) for $\epsilon/r \gtrsim \epsilon_{melt}$. Active crystalline phases exhibit long-time diffusive behavior and an intermediate caging plateau that increases with distance from the melting boundary. Colors correspond to the plotted points in C and D. C The diffusion constant $D$, estimated from long-time dynamics, is plotted as a function of epsilon, showing a sharp, two-order-of-magnitude jump crossing through melting. Active crystals exhibit an exponentially decreasing diffusion coefficient away from the phase boundary. D The global orientational order $|\langle \Psi_6 \rangle|$ (black line) and global translational order $S(q_{max})$ (cyan line) both vanish simultaneously with increasing epsilon, indicating there is no hexatic phase. The sharp decrease in order is coincident with the jump in the diffusion coefficient. All simulations run with $N=1600$ particles.
• Figure 4: Sequential trajectory images of a portion of the full system at $\phi = 0.9069$ for three kick sizes $\epsilon$ in the active crystal phase. All $\epsilon$ values show the defect-free exchange of particles in a closed, ring shape. On approach to melting, loop structures grow in size and complexity, but the crystal phase remains stable. Particles are labeled by identity. Trajectories are composed of 20 points recorded at time intervals of $\delta t= [2,4.8,11.8]\cdot 10^3$ cycles for $\epsilon/r = [0.41,0.393,0.377]$, respectively.
• Figure 5: A The long-time diffusion constant (red) and the defect fraction (blue) are plotted as a function of kick size $\epsilon/r$ crossing the melting boundary at constant area fraction $\phi = 0.915$. B The computable information density (CID), blue points, and the defect fraction, green points, are plotted as a function of area fraction for constant $\epsilon/r$ where both second-order, absorbing-active crystal (black dashed line) and first-order active crystal-active liquid (red dashed line) phase boundaries are present. CID and defect fraction both decrease with increasing $\phi$. CID and defect fraction are continuous, but the slope changes sign crossing the absorbing-active boundary. Both then show a discontinuous jump crossing the melting boundary. CID exhibits a stronger signal than the trend in defect density, indicating that structural correlations beyond the presence of defects also contribute to CID.