Modulation of Non-equilibrium Structures of Active Dipolar Particles by an External Field

TL;DR

This work addresses how an external alignment field modulates non-equilibrium structure formation and polarization in low-density 3D active dipolar particles. Using Brownian dynamics simulations with long-range dipolar interactions and a uniform field, the study maps steady states across dipolar strength $\lambda$, field coupling $\eta$, and activity $f^{a*}$. It finds that in active systems weak fields can stabilize percolated networks and promote polymerization, while strong fields produce polarized columnar states; notably, activity can induce a non-monotonic polarization response and, at intermediate activity, enhance connectivity beyond passive levels. Overall, the field-activity interplay yields richer behavior than in passive systems, with implications for designing reconfigurable active materials and guiding experiments on magnetotactic bacteria and magnetically driven colloids.

Abstract

We study the impact of an external alignment field on the structure formation and polarization behavior of low-density dipolar active particles in three dimensions. Performing extensive Brownian dynamics simulations, we characterize the interplay between long-range dipolar interactions, field alignment, and self-propulsion. We find that the competition between activity (favoring bond breaking) and the field's orientational constraint (promoting bond formation) gives rise to a rich variety of self-assembled, actuated structures. At low to intermediate field strengths, disordered fluids composed of active chains and active percolated networks can emerge, whereas strong fields drive the formation of polarized columnar clusters. Counterintuitively, low activity levels significantly extend the range of field strengths over which percolated networks persist. This structural evolution manifests in the polarization response of strongly dipolar systems, which exhibit a transition from super-Langevin to sub-Langevin behavior with increasing activity, as a result of the coupling between structure formation and activity-induced bond breaking.

Figures (21)

• Figure 1: Schematic of the model system showing two interacting spherical active dipolar particles of diameter $\sigma$. Each particle experiences a self-propulsion force $f^a \hat{\mathbf{e}}_i$ aligned with its dipole moment $\mu \hat{\mathbf{e}}_i$, and interacts with an external alignment field $\mathbf{B}$.
• Figure 2: Representative snapshots of the passive ($f^{a*}$= 0) systems at density $\rho^*$= 0.02 for dipolar coupling strengths $\lambda$ = 4, 6.25, 9, and 12.25, and field coupling strengths $\eta$ = 0, 5, and 10. The external field $\mathbf{B}$ is indicated by the black arrows on the upper panels.
• Figure 3: (a) Mean normalized polarization $P$ [Eq. \ref{['eq:normalized_polarization']}], as a function of the field coupling strength $\eta$ at $f^{a*}$= 0, and (b) angular probability distribution $\psi(\theta)$ at $f^{a*}$= 0 and $\eta = 5$, for all investigated dipolar coupling strengths $\lambda$. Dashed lines correspond to (a) the Langevin function $P_L$ [Eq.\ref{['eq:langevin_polarization']}], and (b) the Langevin distribution $\psi_L$ [Eq. \ref{['eq:langevin_distribution']}].
• Figure 4: Phase diagram of 3D passive ($f^{a*}$= 0) dipolar particles at $\rho^*$= 0.02, as a function of $\lambda$ and $\eta$. Symbols indicate different structural states based on Tab. \ref{['tab:orderparameters']}: gas ($\bm{\times}$), polarized gas ($+$), string-fluid ($\diamond$), polarized string-fluid ($\lozenge$), percolated network ($\circ$), and polarized percolated network ($\star$). The color bar shows the normalized polarization $P$ [Eq. \ref{['eq:normalized_polarization']}]. Dashed lines show the $P\geq0.5$ limit.
• Figure 5: Representative snapshots of the active ($f^{a*}$= 20) systems at density $\rho^*$= 0.02 for dipolar coupling strengths $\lambda$ = 4, 6.25, 9, and 12.25, and field coupling strengths $\eta=$ 0, 5, and 10. The external field $\mathbf{B}$ is indicated by the black arrows on the upper panels.