Interfacial and Confined Colloidal Rod Diffusion

Field-Directed Motion, Cargo Capture, and Closed-Loop Controlled Navigation of Microellipsoids

Microrobots have the potential for diverse applications, including targeted drug delivery and minimally invasive surgery. Despite advancements in microrobot design and actuation strategies, achieving precise control over their motion remains challenging due to the dominance of viscous drag, system disturbances, physicochemical heterogeneities, and stochastic Brownian forces. Here, a precise control over the interfacial motion of model microellipsoids is demonstrated using time-varying rotating magnetic fields. The impacts of microellipsoid aspect ratio, field characteristics, and magnetic properties of the medium and the particle on the motion are investigated. The role of mobile micro-vortices generated is highlighted by rotating microellipsoids in capturing, transporting, and releasing cargo objects. Furthermore, an approach is presented for controlled navigation through mazes based on real-time particle and obstacle sensing, path planning, and magnetic field actuation without human intervention. The study introduces a mechanism of directing motion of microparticles using rotating magnetic fields, and a control scheme for precise navigation and delivery of micron-sized cargo using simple microellipsoids as microbots.

Design rules for 2D field mediated assembly of different shaped colloids into diverse microstructures

Assembling different shaped particles into ordered microstructures is an open challenge in creating multifunctional particle-based materials and devices. Here, we report the two-dimensional (2D) AC electric field mediated assembly of different shaped colloidal particles into amorphous, liquid crystalline, and crystalline microstructures. Particle shapes investigated include disks, ellipses, squares, and rectangles, which show how systematic variations in anisotropy and corner curvature determine the number and type of resulting microstructures. AC electric fields induce dipolar interactions to control particle positional and orientational order. Microstructural states are determined via particle tracking to compute order parameters, which agree with computer simulations and show how particle packing and dipolar interactions together produce each structure. Results demonstrate how choice of particle shape and field conditions enable kinetically viable routes to assemble nematic, tetratic, and smectic liquid crystal structures as well as crystals with stretched 4- and 6-fold symmetry. Results show it is possible to assemble all corresponding hard particle phases, but also show how dipolar interactions influence and produce additional microstructures. Our findings provide design rules for the assembly of diverse microstructures of different shaped particles in AC electric fields, which could enable scalable and reconfigurable particle-based materials, displays, and printing technologies.

Single-walled carbon nanotube reptation dynamics in submicron sized pores from randomly packed mono-sized colloids

Studying the Brownian motion of fibers and semi-flexible filaments in porous media is the key to understanding the transport and mechanical properties in a variety of systems. The motion of semi-flexible filaments in gel-like porous media including polymer networks and cell cytoskeleton has been studied theoretically and experimentally, whereas the motion of these materials in packed-colloid porous media, advanced foams, and rock-like systems has not been thoroughly studied. Here we use video microscopy to directly visualize the reptation and transport of intrinsically fluorescent, semiflexible, semiconducting single-walled carbon nanotubes (SWCNTs) in the sub-micron pores of packed colloids as fixed obstacles of packed-colloid porous media. By visualizing the filament motion and Brownian diffusion at different locations in the pore structures, we study how the properties of the environment, like the pore shape and pore structure of the porous media, affect SWCNT mobility. These results show that the porous media structure controls SWCNT reorientation during Brownian diffusion. In packed-colloid pores, SWCNTs diffuse along straight pores and bend across pores; conversely, in gel pores, SWCNTs consistently diffuse into curved pores, displaying a faster parallel motion. In both gel and packed-colloid porous media, SWCNT finite stiffness enhances SWCNT rotational diffusion and prevents jamming, allowing for inter-pore diffusion.

Anisotropic colloidal interactions & assembly in AC electric fields

We match experimental and simulated configurations of anisotropic epoxy colloidal particles in high frequency AC electric fields by identifying analytical potentials for dipole-field and dipole-dipole interactions. We report an inverse Monte Carlo simulation algorithm to determine optimal fits of analytical potentials by matching simulated and experimental distribution functions for non-uniform liquid, liquid crystal, and crystal microstructures in varying amplitude electric fields. Two potentials that include accurate particle volume and dimensions along with a concentration dependent prefactor quantitatively capture experimental observations. At low concentrations, an effective ellipsoidal point dipole potential works well, whereas a novel stretched point dipole potential is found to be suitable at all concentrations, field amplitudes, and degrees of ordering. The simplicity, accuracy, and adjustability of the stretched point dipole potential suggest it can be applied to model field mediated microstructures and assembly of systematically varying anisotropic particle shapes.

The Curvature Effect on the Diffusion of Single Brownian Squares on a Cylindrical Surface in the Presence of Depletion Attractions

The diffusion of single micron-sized Brownian square platelets on cylindrical surfaces with different radii of curvature in the presence of depletion attractions was studied experimentally by video microscopy. The translational motion of a square is found to be diffusive along the axial direction of the cylinder but sub-diffusive along the circumferential direction due to the confinement induced by gravity, while its rotational motion displays a sub-diffusive behavior due to the confinement induced by orientation-dependent depletion attractions. Such a confinement effect decreases as the radius of curvature increases and can be tuned both through surface curvatures and/or depletion attractions. Our work provides a new way to control the translational and rotational dynamics of anisotropic particles through curved surfaces in the presence of depletion attractions.

Rod separation by sawtooth channel

By applying entropic barriers, we present a rod separation mechanism that induces the movement of rods of different sizes in the opposite directions. This mechanism is based on the combination of the saw-tooth channel, a static force, and an oscillating driving force. The asymmetric shape of the channel and the elongated shape of the rod causesa complicated interaction effect between the rods and the channel walls which reduces the accessible configuration space for the rods and leads to entropic free-energy effects.

Real-Time Visualization and Dynamics of Boron Nitride Nanotubes Undergoing Brownian Motion

We report the first real-time imaging of individualized boron nitride nanotubes (BNNTs) via stabilization with a rhodamine surfactant and fluorescence microscopy. We study the rotational and translational diffusion and find them to agree with predictions based on a confined, high-aspect-ratio rigid rod undergoing Brownian motion. We find that the behavior of BNNTs parallels that of individualized carbon nanotubes (CNTs), indicating that BNNTs could also be used as model rigid rods to study soft matter systems, while avoiding the experimental disadvantages of CNTs due to their strong light absorption. The use and further development of our technique and findings will accelerate the application of BNNTs from material engineering to biological studies.

A simulation algorithm for Brownian dynamics on complex curved surfaces

Brownian dynamics of colloidal particles on complex curved surfaces has found important applications in diverse physical, chemical, and biological processes. However, most Brownian dynamics simulation algorithms focus on relatively simple curved surfaces that can be analytically parameterized. In this work, we develop an algorithm to enable Brownian dynamics simulation on extremely complex curved surfaces. We approximate complex curved surfaces with triangle mesh surfaces and employ a novel scheme to perform particle simulation on these triangle mesh surfaces. Our algorithm computes forces and velocities of particles in global coordinates but updates their positions in local coordinates, which combines the strengths from both global and local simulation schemes. We benchmark the proposed algorithm with theory and then simulate Brownian dynamics of both single and multiple particles on torus and knot surfaces. The results show that our method captures well diffusion, transport, and crystallization of colloidal particles on complex surfaces with nontrivial topology. This study offers an efficient strategy for elucidating the impact of curvature, geometry, and topology on particle dynamics and microstructure formation in complex environments.

Non-equilibrium steady-state colloidal assembly dynamics

Simulations and experiments are reported for nonequilibrium steady-state assembly of small colloidal crystal clusters in rotating magnetic fields vs frequency and amplitude. High-dimensional trajectories of particle coordinates from image analysis of experiments and from Stokesian Dynamic computer simulations are fit to low-dimensional reaction coordinate based Fokker-Planck and Langevin equations. The coefficients of these equations are effective energy and diffusivity landscapes that capture configuration-dependent energy and friction for nonequilibrium steady-state dynamics. Two reaction coordinates that capture condensation and anisotropy of dipolar chains folding into crystals are sufficient to capture high-dimensional experimental and simulated dynamics in terms of first passage time distributions. Our findings illustrate how field-mediated nonequilibrium steady-state colloidal assembly dynamics can be modeled to interpret and design pathways toward target microstructures and morphologies.

Diffusion of colloidal rods in corrugated channels

In many natural and artificial devices diffusive transport takes place in confined geometries with corrugated boundaries. Such boundaries cause both entropic and hydrodynamic effects, which have been studied only for the case of spherical particles. Here we experimentally investigate the diffusion of particles of elongated shape confined in a corrugated quasi-two-dimensional channel. The elongated shape causes complex excluded-volume interactions between particles and channel walls which reduce the accessible configuration space and lead to novel entropic free-energy effects. The extra rotational degree of freedom also gives rise to a complex diffusivity matrix that depends on both the particle location and its orientation. We further show how to extend the standard Fick-Jacobs theory to incorporate combined hydrodynamic and entropic effects, so as, for instance, to accurately predict experimentally measured mean first passage times along the channel. Our approach can be used as a generic method to describe translational diffusion of anisotropic particles in corrugated channels.

Optimal Navigation of Self-Propelled Colloids

Controlling the navigation of self-propelled, Brownian colloids in complex microstructured environments ( e.g., porous media and tumor vasculature) is important to emerging applications ( e.g., enhanced oil recovery and drug delivery). Here, we report a feedback control strategy by which to navigate self-propelled colloids through free space and increasingly complex mazes. Colloid rod position and orientation within mazes is sensed in real time, and instantaneous propulsion along the rod long axis can be actuated via light intensity. However, because uncontrolled rod rotational diffusion determines the propulsion direction, feedback control based on a policy is required to decide how to actuate propulsion magnitude versus colloid position and orientation within mazes. By considering stochastic rod dynamics including self-propulsion, translational-rotational diffusion, and rod-maze interactions, a Markov decision process framework is used to determine optimal control policies to navigate between start and end points in minimal time. The free-space navigation optimal policy effectively reduces to a simple heuristic in which propulsion is actuated only when particles point toward the target. The emergent structure of optimal control policies in mazes is based on the practice of globally following the shortest geometric paths; however, locally, propulsion is actuated to either follow paths toward the target or to produce collisions with maze features as part of generating more-favorable positions and orientations. Findings show how the coupled effects of maze size, propulsion speed, control update time, and relative particle translational and rotational diffusivities influence navigation performance.

Measurement of Anisotropic Particle Interactions with Nonuniform ac Electric Fields

Optical microscopy measurements are reported for single anisotropic polymer particles interacting with nonuniform ac electric fields. The present study is limited to conditions where gravity confines particles with their long axis parallel to the substrate such that particles can be treated using quasi-2D analysis. Field parameters are investigated that result in particles residing at either electric field maxima or minima and with long axes oriented either parallel or perpendicular to the electric field direction. By nonintrusively observing thermally sampled positions and orientations at different field frequencies and amplitudes, a Boltzmann inversion of the time-averaged probability of states yields kT-scale energy landscapes (including dipole-field, particle-substrate, and gravitational potentials). The measured energy landscapes show agreement with theoretical potentials using particle conductivity as the sole adjustable material property. Understanding anisotropic particle-field energy landscapes vs field parameters enables quantitative control of local forces and torques on single anisotropic particles to manipulate their position and orientation within nonuniform fields.