Colloids in rotating electric and magnetic fields: designing tunable interactions with spatial field hodographs

Tunable colloidal spinners: Active chirality and hydrodynamic interactions governed by rotating external electric fields

The rotational dynamics of microparticles in liquids have a wide range of applications, including chemical microreactors, biotechnologies, microfluidic devices, tunable heat and mass transfer, and fundamental understanding of chiral active soft matter which refers to systems composed of particles that exhibit a handedness in their rotation, breaking mirror symmetry at the microscopic level. Here, we report on the study of two effects in colloids in rotating electric fields: (i) the rotation of individual colloidal particles in rotating electric field and related to that (ii) precession of pairs of particles. We show that the mechanism responsible for the rotation of individual particles is related to the time lag between the external field applied to the particle and the particle polarization. Using numerical simulations and experiments with silica particles in a water-based solvent, we prove that the observed rotation of particle pairs and triplets is governed by the tunable rotation of individual particles and can be explained and described by the action of hydrodynamic forces. Our findings demonstrate that colloidal suspensions in rotating electric fields, under some conditions, represent a novel class of chiral soft active matter-tunable colloidal spinners. The experiments and the corresponding theoretical framework we developed open novel prospects for future studies of these systems and for their potential applications.

Droplet Rolling Transport on Hydrophobic Surfaces Under Rotating Electric Fields: A Molecular Dynamics Study

Driving droplets by electric fields is usually achieved by controlling their wettability, and realizing a flexible operation requires complex electrode designs. Here, we show by molecular dynamics methods the droplet transport on hydrophobic surfaces in a rolling manner under a rotating electric field, which provides a simpler and promising way to manipulate droplets. The droplet internal velocity field shows the rolling mode. When the contact angle on the solid surface is 144.4°, the droplet can be transported steadily at a high velocity under the rotating electric field (E = 0.5 V nm-1, ω = π/20 ps-1). The droplet center-of-mass velocities and trajectories, deformation degrees, dynamic contact angles, and surface energies were analyzed regarding the electric field strength and rotational angular frequency. Droplet transport with a complex trajectory on a two-dimensional surface is achieved by setting the electric field, which reflects the programmability of the driving method. Nonuniform wettability stripes can assist in controlling droplet trajectories. The droplet transport on the three-dimensional surface is studied, and the critical conditions for the droplet passing through the surface corners and the motion law on the curved surface are obtained. Droplet coalescence has been achieved by surface designs.

Diffusion mobility increases linearly on liquid binodals above triple point

Self-diffusion in fluids has been thoroughly studied numerically, but even for simple liquids just a few scaling relationships are known. Relations between diffusion, excitation spectra, and character of the interparticle interactions remain poorly understood. Here, we show that diffusion mobility of particles in simple fluids increases linearly on the liquid branch of the liquid-gas binodal, from the triple point almost up to the critical point. With molecular dynamics simulations, we considered bulk systems of particles interacting via a generalised Lennard-Jones potential, as well as ethane. Using a two-oscillator model for the analysis of excitations, we observed that the mobility (inverse diffusion) coefficient on the liquid-gas binodal increases linearly above the triple point until the dispersion of high-frequency spectra has a solid-like (oscillating) shape. In terms of a separate mode analysis (of longitudinal and transverse modes), this corresponds to crossed modes in the intermediate range of wavenumbers q, between the hydrodynamic regime (small q) and the regime of individual particle motion (large q). The results should be interesting for a broad community in physics and chemistry of fluids, since self-diffusion is among the most fundamental transport phenomena, important for prospective chemical technologies, micro-, nanofluidics, and biotechnologies.

Lattice Induced Short-Range Attraction between Like-Charged Colloidal Particles

We perform experiments and computer simulations to study the effective interactions between like-charged colloidal tracers moving in a two-dimensional fluctuating background of colloidal crystal. By a counting method that properly accounts for the configurational degeneracy of tracer pairs, we extract the relative probability of finding a tracer pair in neighboring triangular cells formed by background particles. We find that this probability at the nearest neighbor cell is remarkably greater than those at cells with larger separations, implying an effective attraction between the tracers. This effective attraction weakens sharply as the background lattice constant increases. Furthermore, we clarify that the lattice-mediated effective attraction originates from the minimization of free energy increase from deformation of the crystalline background due to the presence of diffusing tracers.

Grain boundary dynamics driven by magnetically induced circulation at the void interface of 2D colloidal crystals

The complexity of shear-induced grain boundary dynamics has been historically difficult to view at the atomic scale. Meanwhile, two-dimensional (2D) colloidal crystals have gained prominence as model systems to easily explore grain boundary dynamics at single-particle resolution but have fallen short at exploring these dynamics under shear. Here, we demonstrate how an inherent interfacial shear in 2D colloidal crystals drives microstructural evolution. By assembling paramagnetic particles into polycrystalline sheets using a rotating magnetic field, we generate a particle circulation at the interface of particle-free voids. This circulation shears the crystalline bulk, operating as both a source and sink for grain boundaries. Furthermore, we show that the Read-Shockley theory for hard-condensed matter predicts the misorientation angle and energy of shear-induced low-angle grain boundaries based on their regular defect spacing. Model systems containing shear provide an ideal platform to elucidate shear-induced grain boundary dynamics for use in engineering improved/advanced materials.

The role of attraction in the phase diagrams and melting scenarios of generalized 2D Lennard-Jones systems

Monolayer and two-dimensional (2D) systems exhibit rich phase behavior, compared with 3D systems, in particular, due to the hexatic phase playing a central role in melting scenarios. The attraction range is known to affect critical gas–liquid behavior (liquid–liquid in protein and colloidal systems), but the effect of attraction on melting in 2D systems remains unstudied systematically. Here, we have revealed how the attraction range affects the phase diagrams and melting scenarios in a 2D system. Using molecular dynamics simulations, we have considered the generalized Lennard-Jones system with a fixed repulsion branch and different power indices of attraction from long-range dipolar to short-range sticky-sphere-like. A drop in the attraction range has been found to reduce the temperature of the gas–liquid critical point, bringing it closer to the gas–liquid–solid triple point. At high temperatures, attraction does not affect the melting scenario that proceeds through the cascade of solid–hexatic (Berezinskii–Kosterlitz–Thouless) and hexatic–liquid (first-order) phase transitions. In the case of dipolar attraction, we have observed two triple points inherent in a 2D system: hexatic–liquid–gas and crystal–hexatic–gas, the temperature of the crystal–hexatic–gas triple point is below the hexatic–liquid–gas triple point. This observation may have far-reaching consequences for future studies, since phase diagrams determine possible routes of self-assembly in molecular, protein, and colloidal systems, whereas the attraction range can be adjusted with complex solvents and external electric or magnetic fields. The results obtained may be widely used in condensed matter, chemical physics, materials science, and soft matter.

2D colloids in rotating electric fields: A laboratory of strong tunable three-body interactions

Many-body forces play a prominent role in structure and dynamics of matter, but their role is not well understood in many cases due to experimental challenges. Here, we demonstrate that a novel experimental system based on rotating electric fields can be utilised to deliver unprecedented degree of control over many-body interactions between colloidal silica particles in water. We further show that we can decompose interparticle interactions explicitly into the leading terms and study their specific effects on phase behaviour. We found that three-body interactions exert critical influence over the phase diagram domain boundaries, including liquid-gas binodal, critical and triple points. Phase transitions are shown to be reversible and fully controlled by the magnitude of external rotating electric field governing the tunable interactions. Our results demonstrate that colloidal systems in rotating electric fields are a unique laboratory to study the role of many-body interactions in physics of phase transitions and in applications, such as self-assembly, offering exciting opportunities for studying generic phenomena inherent to liquids and solids, from atomic to protein and colloidal systems.

Diagrammatics of tunable interactions in anisotropic colloids in rotating electric or magnetic fields: New kind of dipole-like interactions

Anisotropic particles are widely presented in nature, from colloidal to bacterial systems, and control over their interactions is of crucial importance for many applications, from self-assembly of novel materials to microfluidics. Placed in rapidly rotating external electric fields, colloidal particles attain a tunable long-range and many-body part in their interactions. For spherical colloids, this approach has been shown to offer rich capabilities to construct the tunable interactions via designing the internal structure of particles and spatial hodographs of external rotating fields, but in the case of anisotropic particles, the interactions remain poorly understood. Here, we show that tunable interactions between anisotropic rod-like and spheroidal colloidal particles in rotating electric or magnetic fields can be calculated and analyzed with the diagrammatic technique we developed in the present work. With this technique, we considered an in-plane rotating electric field, obtained the long-range asymptotics of the anisotropic interactions, calculated the tunable interactions between particles rotating synchronously, and found conditions for rotator repulsion. We compared the mechanisms providing tunable interactions to those for orientational (Keesom), induction (Debye), and dispersion (London) interactions in molecular systems and found that the tunable interactions between anisotropic particles represent a novel kind of dipole-like interaction. The method can be directly generalized for magnetically induced interactions, 3D systems, and fields with spatial hodographs. The results provide significant advance in theoretical methods for tunable interactions in colloids and, therefore, are of broad interest in condensed matter, chemical physics, physical chemistry, materials science, and soft matter.

Core-shell particles in rotating electric and magnetic fields: Designing tunable interactions via particle engineering

Tunable interactions between colloidal particles, governed by external rotating electric or magnetic fields, yield rich capabilities for prospective self-assembly technologies of materials and fundamental particle-resolved studies of phase transitions and transport phenomena in soft matter. However, the role of the internal structure of colloidal particles in the tunable interactions has never been systematically investigated. Here, we study the tunable interactions between composite particles with core-shell structure in a rotating electric field and show that the engineering of their internal structure provides an effective tool for designing the interactions. We generalized an integral theory and studied the tunable interactions between core-shell particles with homogeneous cores (layered particles) and cores with nano-inclusions to reveal the main trends in the interactions influenced by the structure. We found that depending on the materials of the core, shell, and solvent, the interactions with the attractive pairwise part and positive or negative three-body part can be obtained, as well as pairwise repulsion with attractive three-body interactions (for triangular triplets). The latter case is observed for the first time, being unattainable for homogeneous particles but feasible with core-shell particles: Qualitatively similar interactions are inherent to charged colloids (repulsive pairwise and attractive three-body energies), known as a model system of globular proteins. The methods and conclusions of our paper can be generalized for magnetic and 3D colloidal systems. The results make a significant advance in the analysis of tunable interactions in colloidal systems, which are of broad interest in condensed matter, chemical physics, physical chemistry, materials science, and soft matter.

Field-Driven Reversible Alignment and Gelation of Magneto-Responsive Soft Anisotropic Microbeads

Magnetic fields offer untethered control over the assembly, dynamics, and reconfiguration of colloidal particles. However, synthesizing "soft" colloidal particles with switchable magnetic dipole moment remains a challenge, primarily due to strong coupling of the dipoles of the adjacent nanoparticles. In this article, we present a way to overcome this fundamental challenge based on a strategy to synthesize soft microbeads with tunable residual dipole moment. The microbeads are composed of a polydimethylsiloxane (PDMS) matrix with internally embedded magnetic nanoparticles (MNPs). The distribution and orientation of the MNPs within the PDMS bead matrix is controlled by an external magnetic field during the synthesis process, thus allowing for the preparation of anisotropic PDMS microbeads with internal magnetically aligned nanoparticle chains. We study and present the differences in magnetic interactions between microbeads containing magnetically aligned MNPs and microbeads with randomly distributed MNPs. The interparticle interactions in a suspension of microbeads with embedded aligned MNP chains result in the spontaneous formation of percolated networks due to residual magnetization. We proved the tunability of the structure by applying magnetization, demagnetization, and remagnetization cycles that evoke formation, breakup, and reformation of 2D percolated networks. The mechanical response of the microbead suspension was quantified by oscillatory rheology and correlated to the propensity for network formation by the magnetic microbeads. We also experimentally correlated the 2D alignment of the microbeads to the direction of earth's magnetic field. Overall, the results prove that the soft magnetic microbeads enable a rich variety of structures and can serve as an experimental toolbox for modeling interactions in dipolar systems leading to various percolated networks, novel magneto-rheological materials, and smart gels.

Elastic and Stretchable Double Network Hydrogel as Printable Ink for High-Resolution Fabrication of Ionic Skin

A hydrogel that combines both printability and adaptability, high elasticity, and stretchability can provide ideal mechanical properties, and also render complex and accurate construction for ionic skin. However, it is extremely challenging. Here, we propose a colloidal-based double-network (DN) hydrogel as printable inks for high-precision fabrication of ionic skins. Particularly, polyacrylamide (PAAm), as the covalent network that can maintain the long-term material integrity, was combined with gelatin colloidal network to improve the injectability and printability of the resulting DN hydrogels. The DN design cooperatively provides the hydrogels with higher toughness values and deformability than what single colloidal or PAAm network can achieve. Further design of ionic skin based on capacitor microarray was demonstrated to serve as a sensitive and stable capacitor that can respond to external stimuli, thereby allowing to sense the body movements such as finger bending, laugh, and wrist pulse by translating mechanical changes into electric signals. Therefore, this study provides a novel strategy for the design and preparation of high-resolution ionic skins as the wearable sensor.

Hierarchical assemblies of superparamagnetic colloids in time-varying magnetic fields

Magnetically-guided colloidal assembly has proven to be a versatile method for building hierarchical particle assemblies. This review describes the dipolar interactions that govern superparamagnetic colloids in time-varying magnetic fields, and how such interactions have guided colloidal assembly into materials with increasing complexity that display novel dynamics. The assembly process is driven by magnetic dipole-dipole interactions, whose strength can be tuned to be attractive or repulsive. Generally, these interactions are directional in static external magnetic fields. More recently, time-varying magnetic fields have been utilized to generate dipolar interactions that vary in both time and space, allowing particle interactions to be tuned from anisotropic to isotropic. These interactions guide the dynamics of hierarchical assemblies of 1-D chains, 2-D networks, and 2-D clusters in both static and time-varying fields. Specifically, unlinked and chemically-linked colloidal chains exhibit complex dynamics, such as fragmentation, buckling, coiling, and wagging phenomena. 2-D networks exhibit controlled porosity and interesting coarsening dynamics. Finally, 2-D clusters have shown to be an ideal model system for exploring phenomena related to statistical thermodynamics. This review provides recent advances in this fast-growing field with a focus on its scientific potential.