Non-equilibrium steady-state colloidal assembly dynamics

Coiling of semiflexible paramagnetic colloidal chains

Semiflexible filaments deform into a variety of configurations that dictate different phenomena manifesting at low Reynolds number. Harnessing the elasticity of these filaments to perform transport-related processes at the microfluidic scale requires structures that can be directly manipulated to attain controllable geometric features during their deformation. The configuration of semiflexible chains assembled from paramagnetic colloids can be readily controlled upon the application of external time-varying magnetic fields. In circularly rotating magnetic fields, these chains undergo coiling dynamics in which their ends close into loops that wrap inward, analogous to the curling of long nylon filaments under shear. The coiling is promising for the precise loading and targeted transport of small materials, however effective implementation requires an understanding of the role that field parameters and chain properties play on the coiling features. Here, we investigate the formation of coils in semiflexible paramagnetic chains using numerical simulations. We demonstrate that the size and shape of the initial coils are governed by the Mason and elastoviscous numbers, related to the field parameters and the chain bending stiffness. The size of the initial coil follows a nonmonotonic behavior with Mason number from which two regions are identified: (1) an elasticity-dependent nonlinear regime in which the coil size decreases with increasing field strength and for which loop shape tends to be circular, and (2) an elasticity-independent linear regime where the size increases with field strength and the shape become more elliptical. From the time scales associated to these regimes, we identify distinct coiling mechanisms for each case that relate the coiling dynamics to two other configurational dynamics of paramagnetic chains: wagging and folding behaviors.

Extension of Kelvin's equation to dipolar colloids

Suspensions of colloids driven out-of-equilibrium demonstrate interesting collective behavior, such as organized and directed clustering and swarming. These systems require continuous energy input, yet some of the dynamics of these driven systems resemble the equilibrium-phase behavior of molecular fluids, such as crystallization, condensation, and phase separation. Consequently, there has been significant interest in exploring the applicability of thermodynamic concepts, such as pressure and surface tension, to describe nonequilibrium phenomena. Here, we show how rotating magnetic fields can drive superparamagnetic particles to form steady-state vapor–liquid coexistence that can be analyzed with Kelvin’s equation to determine an “effective vapor pressure” for this active colloidal system. These results illustrate the convergence of statistical physics of simple liquids to nonequilibrium colloidal fluids.

Vapor pressure refers to the pressure exerted by the vapor phase in thermodynamic equilibrium with either its liquid or solid phase. An important class of active matter is field-driven colloids. A suspension of dipolar colloids placed in a high-frequency rotating magnetic field undergoes a nonequilibrium phase transition into a dilute and dense phase, akin to liquid–vapor coexistence in a simple fluid. Here, we compute the vapor pressure of this colloidal fluid. The number of particles that exist as the dilute bulk phase versus condensed cluster phases can be directly visualized. An exponential relationship between vapor pressure and effective temperature is determined as a function of applied field strength, analogous to the thermodynamic expression between vapor pressure and temperature found for pure liquids. Additionally, we demonstrate the applicability of Kelvin’s equation to this field-driven system. In principle, this appears to be in conflict with macroscopic thermodynamic assumptions due to the nonequilibrium and discrete nature of this colloidal system. However, the curvature of the vapor–liquid interface provides a mechanical equilibrium characterized by interfacial tension that connects the condensed clusters observed with these active fluids to classical colligative fluid properties.

Periodic deformation of semiflexible colloidal chains in eccentric time-varying magnetic fields

Elastic filaments driven out of equilibrium display complex phenomena that involve periodic changes in their shape. Here, the periodic deformation dynamics of semiflexible colloidal chains in an eccentric magnetic field are presented. This field changes both its magnitude and direction with time, leading to novel nonequilibrium chain structures. Deformation into S-, Z-, and 4-mode shapes arises via the propagation and growth of bending waves. Transitions between these morphologies are governed by an interplay among magnetic, viscous, and elastic forces. Furthermore, the periodic behavior leading to these structures is described by four distinct stages of motion that include rotation, arrest, bending, and stretching of the chain. These stages correspond to specific intervals of the eccentric field's period. A scaling analysis that considers the relative ratio of viscous to magnetic torques via a critical frequency illustrates how to maximize the bending energy. These results provide new insights into controlling colloidal assemblies by applying complex magnetic fields.

Nonequilibrium self-assembly of multiple stored targets in a dimer-based system

Nonequilibrium self-assembly can be found in various biological processes where chemical potential gradients are exploited to steer the system to a desired organized structure with a particular function. Microtubules, for example, are composed of two globular protein subunits, α-tubulin and β-tubulin, which bind together to form polar dimers that self-assemble a hollow cylinder structure in a process driven by GTPase activity. Inspired by this process, we define a generic self-assembly lattice model containing particles of two subunits, which is driven out-of-equilibrium by a dimer-favoring local driving force. Using Monte Carlo simulations, we characterize the ability of this system to restore pre-encoded target structures as a function of the initial seed size, interaction energy, chemical potential, number of target structures, and strength of the nonequilibrium drive. We demonstrate some intriguing consequences of the drive, such as a smaller critical seed and an improved target assembly stability, compared to the equilibrium scenario. Our results can expand the theoretical basis of nonequilibrium self-assembly and provide deeper understanding of how nonequilibrium driving can overcome equilibrium constraints.

Controlling colloidal crystals via morphing energy landscapes and reinforcement learning

We report a feedback control method to remove grain boundaries and produce circular shaped colloidal crystals using morphing energy landscapes and reinforcement learning-based policies. We demonstrate this approach in optical microscopy and computer simulation experiments for colloidal particles in ac electric fields. First, we discover how tunable energy landscape shapes and orientations enhance grain boundary motion and crystal morphology relaxation. Next, reinforcement learning is used to develop an optimized control policy to actuate morphing energy landscapes to produce defect-free crystals orders of magnitude faster than natural relaxation times. Morphing energy landscapes mechanistically enable rapid crystal repair via anisotropic stresses to control defect and shape relaxation without melting. This method is scalable for up to at least N = 10³ particles with mean process times scaling as N ^0.5 Further scalability is possible by controlling parallel local energy landscapes (e.g., periodic landscapes) to generate large-scale global defect-free hierarchical structures.

Structure of a two-dimensional superparamagnetic system in a quadratic trap

Ground-state structures of a two-dimensional (2D) system composed of superparamagnetic charged particles are investigated by means of molecular dynamics simulation. The charged particles trapped in a quadratic potential interact with each other via the repulsive, attractive, and magnetic dipole-dipole forces. Simulations are performed within two regimes: a one-component system and a two-component system where the charged particles have the identical charge-to-mass ratio. The effects of magnetic dipole-dipole interaction, mixing ratio of the two species and confinement frequency on the ground-state structures are discussed. It is found that as the strength of the magnetic dipole increases, the charged particles tend to self-organize into chainlike structures. The two species particles exhibit different structural features, depending on the competition of electrostatic repulsive interaction, magnetic dipole-dipole interaction and confinement force. The potential lanes are observed through analyzing the global potential of the magnetic particles, which guide the unmagnetic particles aligning themselves in the direction of the potential lanes.