Self-Propelled Dipolar Colloids

• Self-propelled dipolar colloids are active particles that couple autonomous motion with fixed transverse magnetic dipoles, driving anisotropic self-assembly.
• They form dynamic chains and clusters that sweep and capture passive colloids, with capture efficiency enhanced by optimal dipolar interactions and activity levels.
• Simulations reveal that tuning the λ/Pe ratio controls chain stability and trapping performance, guiding the design of responsive microscale trapping platforms.

Self-propelled dipolar colloids are a class of active colloidal systems in which each particle combines autonomous motion (“activity”) with embedded dipole moments, typically magnetic, leading to long-range anisotropic interactions. Of particular recent interest is the interplay between self-organization, dipolar aggregation, and driven dynamics, enabling emergent functions such as efficient trapping of passive colloids in mixed suspensions. This capability arises from the spontaneous formation of dynamic chains and clusters by the active dipolar colloids, which, through their motile and interactive properties, capture and confine passive Brownian particles far from equilibrium. The system’s behavior is governed by the competition between activity and dipolar couplings and can be manipulated by external fields, offering strategies for designing microscale trapping platforms.

1. Model Architecture: Active Brownian Dipoles, Perpendicular Alignment, and Interaction Topology

Self-propelled dipolar colloids are modeled as active Brownian disks each carrying a permanent magnetic dipole moment. Distinctively, the dipole orientation $\vec{\mu}$ is constrained perpendicular to the self-propulsion direction. This fixed orthogonality ensures that when active particles self-propel, their dipoles are always aligned transversely, leading to an anisotropic self-assembly pathway.

The dynamical evolution combines:

• Translational Brownian motion (diffusive noise and self-propulsion velocity $\vec{v}_0$)
• Rotational diffusion (setting the persistent reorientation timescale $D_R^{-1}$)
• Long-range dipole–dipole interactions (pairwise force $U_{\mathrm{dd}}$ favors chain-like alignment for antiparallel neighbors perpendicular to the propulsion direction)
• Interactions with passive colloids via hard-core exclusion and collisions

Key experimental and simulation signatures include the rapid formation of dynamic chains and mobile clusters, which sweep through the medium and engage passive colloidal particles that otherwise undergo Brownian motion.

2. Trapping Mechanism: Chain Formation, Sweeping, and Cluster Collapse

The trapping of passive colloids is achieved through a multi-step process:

• Dipole–dipole interactions drive active particles to align and assemble into flexible, motile chains.
• As these chains traverse the environment (propelled by their self-propulsion), encounters with passive colloids result in the latter being swept up or “captured” by the active chain.
• Chain–chain collisions and further aggregation lead to large, stable clusters that envelop and trap passive colloids, forming dense mixed phases even at low global densities.

This process occurs spontaneously but is highly sensitive to system parameters. Notably, the mechanism exploits dynamical pathways forbidden in thermodynamic equilibrium, relying on both dissipative activity and directional, programmable dipolar assembly.

3. Simulation Insights: Dependence on Péclet Number and Dipolar Coupling

Extensive Brownian dynamics simulations establish that trapping efficiency is controlled by two dimensionless parameters:

Parameter	Definition	Physical Role
$\mathrm{Pe}$	$\mathrm{Pe} = (2v_0)/(\sigma D_R)$	Activity to rotational diffusion ratio
$\lambda$	$\lambda = (\mu_0/4\pi)(\mu^2/(\pi \sigma^3 k_B T))$	Dipolar interaction strength

• Increasing dipolar strength ($\lambda$) increases chain stability, thereby enhancing trap rates, while excessive activity ($\mathrm{Pe}$) disrupts chain cohesion, dispersing actives before they can capture passive particles.
• Simulations without external fields yield maximal passive capture rates of $\sim$25% under optimal conditions.

An explicit stability criterion for chain pushers is provided for a chain propelling $n$ layers of passive colloids:

$$\lambda > \frac{\sqrt{3}}{12} \cdot \frac{n}{n+2} \cdot \mathrm{Pe}$$

This linear $\lambda$–$\mathrm{Pe}$ relationship prescribes the minimum dipolar interactions required to counteract the destabilizing influence of motility, enabling chain persistence sufficient to trap passives.

4. Role of Transient External Magnetic Fields: Alignment and Efficiency Enhancement

Application of a transient external magnetic field ($\vec{B} = B_0 \mathbf{e}_x$ for time $t_B$) aligns all active dipoles instantaneously. This pre-alignment causes all actives to self-propel in a coherent direction, greatly enhancing the formation of extended, coherent chains and their collective sweeping ability. After field removal, the aligned chains undergo spontaneous bending, rotation, and fusion, further stabilizing clusters around trapped passives.

• Capture efficiency in these conditions exceeds 50% for optimal parameters, an enhancement nearly double that achievable without external field intervention.
• The duration of the aligning field should match the scaling $t_B \sim \sigma/v_0$, ensuring sufficient time for particles, even at low motility, to assemble into coherent structures.

5. Quantitative Capture Efficiency: Scaling with $\lambda$/Pe

The competition between activity (Pe) and dipolar stabilization ($\lambda$) is captured by the dimensionless ratio $\lambda/\mathrm{Pe}$, which serves as the organizing parameter for system behavior. Both trapping stability and final capture fraction $C$ scale with this ratio according to:

$$C(\lambda/\mathrm{Pe}) = C_s \left[1 - \exp\left(-r_s \cdot \frac{\lambda}{\mathrm{Pe}}\right)\right]$$

with empirical fit constants $C_s = 0.441$, $r_s = 1.853$.

• For $\lambda/\mathrm{Pe} \ll 1$, trapping is weak: activity dominates, chains rapidly disassemble and passives remain largely untrapped.
• For $\lambda/\mathrm{Pe} \gg 1$, nearly all passives in the swept zone are efficiently captured as dipolar forces stabilize sweeping chains.
• This scaling function provides a robust predictive principle for tuning the system: increase $\lambda$ or reduce $\mathrm{Pe}$ to enhance capture; optimize near the saturation threshold for best resource efficiency.

6. Applications and Design Strategies

Insights into the interplay between activity and dipolar coupling guide the rational design of trapping systems:

• Perpendicular alignment of dipole and propulsion is essential to promote sweeping chain morphology, as opposed to irreversible immobilization or isotropic clustering.
• Transient alignment using magnetic fields enables one-shot or on-demand switching between “free gas,” “sweeping,” and “trapping” operational phases.
• For environmental remediation (e.g., microplastic collection), choosing actives and field strengths to target $\lambda/\mathrm{Pe}$ near the saturation threshold provides maximum capture with minimal active material density.

7. Outlook and Controlling Competing Dynamics

The observed trapping dynamics reflect a general principle: in motile, anisotropically interacting colloidal systems, emergent assembly and function are controlled by the ratio of dissipative to conservative forces ($\mathrm{Pe}$ vs. $\lambda$). External stimuli—magnetic, electric, or optical—provide an effective lever for programming collective behavior, allowing the same system to operate in gas-like, chain-sweeping, or dense cluster-trapping regimes depending on the application. This design flexibility could be extended to multi-component trapping, programmable release, or dynamic environmental response in future research and applications (Compagnie et al., 17 Sep 2025).