Active adaptolates: motility-induced percolating structures with an adaptive packing geometry

TL;DR

This paper investigates how external periodic potentials influence active matter, specifically overdamped active Brownian particles, revealing a novel intermediate phase called active adaptolates. Using a 2D ABP model with a cosine-based lattice potential, the authors show that at intermediate lattice heights the system forms a system-spanning, square-ordered, dynamically active network, distinct from motility-induced phase separation and trapped states. The transition to active adaptolates is sharp, evidenced by peaks in susceptibility and finite-size scaling consistent with 2D percolation universality, and requires sufficient activity (critical Pe). Practically, the work provides a framework to design and control the intrinsic structure of active materials via external fields without quenching their dynamics, with potential applications in tunable optical and mechanical properties of active systems.

Abstract

It is well known that periodic potentials can be used to induce freezing and melting in colloids. Here, we transfer this concept to active systems and find the emergence of a so-far unknown active matter phase in between the frozen solid-like phase and the molten phase. This phase of "active adaptolates" adopts the geometry of the underlying lattice like the frozen phase, maintains ballistic dynamics like the molten phase, and percolates. In particular, this finding creates a route to use external fields for designing the intrinsic structure of active systems without qualitatively affecting their dynamics.

Figures (4)

• Figure 1: Lattice-induced freezing and melting in active systems lead to active adaptolates. Upper panel: Steady-state snapshots for (a-e) increasing values of the dimensionless barrier height $V$. Each colored disc denotes an ABP with the color indicating their cluster-ID, i.e. the index of the cluster they belong to. Middle panel: Zoomed snapshots (indicated by the black squares in the upper panel) show the local packing geometry. Lower panel: Zoomed snapshots showing the particle speed, averaged over 100 frames in the steady-state. Parameters: $Pe=300r_c$, $\phi=0.5$, $L=r_c$ and $\epsilon=300r_c^2$.
• Figure 2: (a) Distribution $P(\rho)$ of the local density $\rho$ of ABPs for different barrier heights $V$. (b) Global bond order parameters $\psi_4$ (orange triangles) and $\psi_6$ (blue circles) as a function of $V$, averaged over different snapshots in the stationary state. The boundaries between MIPS, active adaptolates (AA), and the trapped phase correspond to the peaks of the susceptibility (Fig. \ref{['fig3']}a).
• Figure 3: (a) Susceptibility as a function of the reduced lattice height $V/r_c^2$ showing the three different nonequilibrium phases in the background. The peaks in the susceptibility $\chi$ at $V\approx 65r_c^2$ and $\approx 95r_c^2$ denote the separation of the active adaptolate phase from the MIPS and the trapped phase respectively. Inset: Normalized mean largest cluster size $n_l$ (blue circles) and normalized mean largest cluster extension $d_l$ (orange checks). (b,e) Binder cumulant $U_4$ as a function of $V/r_c^2$ and $Pe/r_c$ respectively for four different system sizes $L_d$. (c,d) Finite-size scaling of $n_l$ and $\chi$ for different $L_d$. The collapse occurs for the critical exponents $\beta\approx 0.16$, $\gamma\approx 2.35$, $\nu\approx 1.25$ and critical lattice height $V_c \approx 96.3r_c^2$, indicating that the transition between the AA and trapped phase is a proper phase transition that belongs to the 2D percolation universality class.
• Figure 4: Mean squared displacement of the ABPs as a function of time $t$ for different $V$. Inset: Late-time diffusion coefficient $D$ of the ABPs, normalized by the diffusion coefficient $D_0$ of passive particles for $V=0$, as a function of $V$. Notice that $D$ decays much slower and smoother than $\psi_6$ (Fig. \ref{['fig2']}b). The figure indicates that the particles in the active adaptolate phase move one to two orders of magnitude faster than free passive Brownian particles.