Tunable colloids: control of colloidal phase transitions with tunable interactions

Refractive-index and density-matched emulsions with programmable DNA interactions

Emulsion droplets on the colloidal length scale are a model system of frictionless compliant spheres. Direct imaging studies of the microscopic structure and dynamics of emulsions offer valuable insights into fundamental processes, such as gelation, jamming, and self-assembly. A microscope, however, can only resolve the individual droplets in a densely packed emulsion if the droplets are closely index-matched to their fluid medium. Mitigating perturbations due to gravity additionally requires the droplets to be density-matched to the medium. Creating droplets that are simultaneously index-matched and density-matched has been a long-standing challenge for the soft-matter community. The present study introduces a method for synthesizing monodisperse micrometer-sized siloxane droplets whose density and refractive index can be precisely and independently tuned by adjusting the volume fraction of three silane precursors. A systematic optimization protocol yields fluorescently labeled ternary droplets whose densities and refractive indexes match, to the fourth decimal place, those of aqueous solutions of glycerol or dimethylsiloxane. Because all of the materials in this system are biocompatible, we functionalize the droplets with DNA strands to endow them with programmed inter-droplet interactions. Confocal microscopy then reveals both the three-dimensional structure and the network of droplet-droplet contacts in a class of self-assembled droplet gels, free from gravitational effects. This experimental toolbox creates opportunities for studying the microscopic mechanisms that govern viscoelastic properties and self-assembly in soft materials.

Unifying Atoms and Colloids near the Glass Transition through Bond-Order Topology

In this combined experimental and simulation study, we utilize bond-order topology to quantitatively match particle volume fraction in mechanically uniformly compressed colloidal suspensions with temperature in atomistic simulations. The obtained mapping temperature is above the dynamical glass transition temperature, indicating that the colloidal systems examined are structurally most like simulated undercooled liquids. Furthermore, the structural mapping procedure offers a unifying framework for quantifying relaxation in arrested colloidal systems.

Porous crystals in charged sphere suspensions by aggregate-driven phase separation

The kinetics of phase transition processes often governs the resulting material microstructure. Using optical microscopy, we here investigate the formation and stabilization of a porous crystalline microstructure forming in low-salt suspensions of charged colloidal spheres containing aggregates comprising some 5-10 of these colloids. We observe the transformation of an initially crystalline colloidal solid with homogeneously incorporated aggregates to individual, compositionally refined crystallites of perforated morphology coexisting with an aggregate-enriched fluid phase filling the holes and separating individual crystallites. A preliminary kinetic characterization suggests that the involved processes follow power laws. We show that this route to porous materials is neither restricted to nominally single component systems nor to a particular microstructure to start from. However, it necessitates an early rapid solidification stage during which the aggregates become trapped in the bulk of the host-crystals. The thermodynamic stability of the reconstructed crystalline scaffold against melting under increased salinity was found comparable to that of pure phase crystallites grown very slowly from a melt. Future implications of this novel route to porous colloidal crystals are discussed.

Active Colloids as Models, Materials, and Machines

Active colloids use energy input at the particle level to propel persistent motion and direct dynamic assemblies. We consider three types of colloids animated by chemical reactions, time-varying magnetic fields, and electric currents. For each type, we review the basic propulsion mechanisms at the particle level and discuss their consequences for collective behaviors in particle ensembles. These microscopic systems provide useful experimental models of nonequilibrium many-body physics in which dissipative currents break time-reversal symmetry. Freed from the constraints of thermodynamic equilibrium, active colloids assemble to form materials that move, reconfigure, heal, and adapt. Colloidal machines based on engineered particles and their assemblies provide a basis for mobile robots with increasing levels of autonomy. This review provides a conceptual framework for understanding and applying active colloids to create material systems that mimic the functions of living matter. We highlight opportunities for chemical engineers to contribute to this growing field.

Internal-stress-induced solid-solid transition involving orientational domains of anisotropic particles

Colloidal particles with anisotropic interaction, such as Janus particles, are important model systems for anisotropic atoms and molecules. Janus particles in a single crystal can rotate collectively and form polycrystalline orientational domains as the temperature increases, while the lattice structure in the translational degree of freedom is preserved. Such an unusual solid-solid transition preserves the long-range translational order but loses the orientational order, and its mechanism is unclear. We find that the transition is induced by internal strains and the orientation-position coupling plays an essential role in the transition. We explain the mechanism using the anisotropic elasticity theory and derive the transition condition and the directions of the domain boundaries by analyzing the strain energy and the stress. The results of the molecular dynamics simulation are consistent with the theoretical analysis. Such a transition mechanism can exist in other anisotropic particle systems.

Feasibility of Control of Particle Assembly by Dielectrophoresis in Liquid-Cell Transmission Electron Microscopy

Liquid-cell transmission electron microscopy (LC-TEM) is a useful technique for observing phenomena in liquid samples with spatial and temporal resolutions similar to those of conventional transmission electron microscopy (TEM). This method is therefore expected to permit the visualization of phenomena previously inaccessible to conventional optical microscopy. However, dynamic processes such as nucleation are difficult to observe by this method because of difficulties in controlling the condition of the sample liquid in the observation area. To approach this problem, we focused on dielectrophoresis, in which electrodes are used to assemble particles, and we investigated the phenomena that occurred when an alternating-current signal was applied to an electrode in an existing liquid cell by using a phase-contrast optical microscope (PCM) and TEM. In PCM, we observed that colloidal particles in a solution were attracted to the electrodes to form assemblies, that the particles aligned along the electric field to form pearl chains and that the pearl chains accumulated to form colloidal crystals. However, these phenomena were not observed in the TEM study because of differences in the design of the relevant holders. The results of our study imply that the particle assembly by using dielectrophoretic forces in LC-TEM should be possible, but further studies, including electric device development, will be required to realize this in practice.

A bottom-up design strategy for controllable self-assembly based on the isotropic double-well potential

Controllable self-assembly of particles or atoms is still challenging in the synthesis of materials with desirable properties that are highly relevant to the microscopic structures determined by the interparticle interactions. To gain insight into how the interactions affect the self-assembly, we designed various kinds of isotropic double-well potentials and simulated the motion of the particles. By controlling the depth and location of the potential wells and the height of the barriers, we studied their effects on the aggregation structures and the related microscopic kinetic processes. We identified five aggregation patterns at different temperatures and eight kinds of crystals, including Frank-Kasper phases, and observed the expansion or contraction of crystals. We found that the system usually stays in a sparse configuration at very low or very high temperatures. The particles typically assemble into a loosely packed cluster at medium temperatures and then deplete into a tightly packed state with a specific pattern. These phenomena can be explained from the perspective of energy. In contrast, very few structures could be obtained for the system guided by a single-well potential under the same simulation conditions. Thus, the interparticle interactions driven by the double-well potential greatly enrich the possible packing morphology of the system. The information obtained from this work helps us to understand how to achieve a specific self-assembled architecture through a reasonable selection of materials.

Reentrant melting of lanes of rough circular disks

We consider binary suspension of rough, circular particles in two dimensions under athermal conditions. The suspension is subject to a time-independent external drive in response to which half of the particles are pulled along the field direction, whereas the other half is pushed in the opposite direction. Simulating the system with different magnitude of external drive in steady state, we obtain oppositely moving macroscopic lanes only for a moderate range of external drive. Below as well as above the range we obtain states with no lane. Hence we find that the no-lane state reenters along the axis of the external drive in the nonequilibrium phase diagram corresponding to the laning transition, with varying roughness of individual particles and external drive. Interparticle friction (contact dissipation) due to the roughness of the individual particle is the main player behind the reentrance of the no-lane state at high external drives.

First-passage statistics of colloids on fractals: Theory and experimental realization

In nature and technology, particle dynamics frequently occur in complex environments, for example in restricted geometries or crowded media. These dynamics have often been modeled invoking a fractal structure of the medium although the fractal structure was only indirectly inferred through the dynamics. Moreover, systematic studies have not yet been performed. Here, colloidal particles moving in a laser speckle pattern are used as a model system. In this case, the experimental observations can be reliably traced to the fractal structure of the underlying medium with an adjustable fractal dimension. First-passage time statistics reveal that the particles explore the speckle in a self-similar, fractal manner at least over four decades in time and on length scales up to 20 times the particle radius. The requirements for fractal diffusion to be applicable are laid out, and methods to extract the fractal dimension are established.

Rigidity Dictates Spontaneous Helix Formation of Thermoresponsive Colloidal Chains in Poor Solvent

The formation of helical motifs typically requires specific directional interactions. Here, we demonstrate that isotropic interparticle attraction can drive self-assembly of colloidal chains into thermo-reversible helices, for chains with a critical level of backbone rigidity. We prepare thermoresponsive colloidal chains by cross-linking PNIPAM microgel-coated polystyrene colloids ("monomers"), aligned in an AC electric field. We control the chain rigidity by varying cross-linking time. Above the LCST of PNIPAM, there is an effective attraction between monomers so that the colloidal chains are in a bad solvent. On heating, the chains decrease in size. For the most rigid chains, the decrease is modest and is not accompanied by a change in shape. Much less rigid chains form relatively compact structures, resulting in a large increase in the local monomer density. Unusually, chains with intermediate rigidity spontaneously assemble into helical structures. The chain helicity increases with temperature and plateaus above the collapse transition temperature of the microgel particles. We simulate a minimal model that captures the spontaneous emergence of the helical conformations of the polymeric chain and provides insight into this shape transition. Our work suggests that a purely mechanical instability for semiflexible filaments can drive helix formation, without the need to invoke directional interactions.

Depletion Induced Demixing and Crystallization in Binary Colloids Subjected to an External Potential Barrier

Depletion interaction plays an important role in determining the structural and dynamical properties of binary colloidal mixtures. We have investigated the effect of the attractive depletion interaction between an external potential barrier and larger species in the binary mixture on the phase behavior of a binary colloidal mixture using canonical-isokinetic ensemble molecular dynamics simulations. The demixing of the binary mixture due to this depletion interaction increases as the volume fraction increases, and a pure phase of larger particles forms in the region of the potential barrier. The local density of this pure phase is high enough that a face centered cubic crystalline domain is formed at this region. This crystalline phase diffuses perpendicular to the external potential barrier, indicating that moving crystals can be obtained in an equilibrium system. The temperature dependence of diffusivity of larger particles is non-Arrhenius and changes from sub-Arrhenius to super-Arrhenius as the volume fraction increases. This crossover from sub-Arrhenius to super-Arrhenius diffusion coincides with the crystalline formation near the potential barrier.

Salt-concentration-dependent nucleation rates in low-metastability colloidal charged sphere melts containing small amounts of doublets

We determined bulk crystal nucleation rates in aqueous suspensions of charged spheres at low metastability. Experiments were performed in dependence on electrolyte concentration and for two different particle number densities. The time-dependent nucleation rate shows a pronounced initial peak, while postsolidification crystal size distributions are skewed towards larger crystallite sizes. At each concentration, the nucleation rate density initially drops exponentially with increasing salt concentration. The full data set, however, shows an unexpected scaling of the nucleation rate densities with metastability times the number density of particles. Parameterization of our results in terms of classical nucleation theory reveals unusually low interfacial free energies of the nucleus surfaces and nucleation barriers well below the thermal energy. We tentatively attribute our observations to the presence of doublets introduced by the employed conditioning technique. We discuss the conditions under which such small seeds may induce nucleation.

Directed Assembly of Particles for Additive Manufacturing of Particle-Polymer Composites

Particle-polymer dispersions are ubiquitous in additive manufacturing (AM), where they are used as inks to create composite materials with applications to wearable sensors, energy storage materials, and actuation elements. It has been observed that directional alignment of the particle phase in the polymer dispersion can imbue the resulting composite material with enhanced mechanical, electrical, thermal or optical properties. Thus, external field-driven particle alignment during the AM process is one approach to tailoring the properties of composites for end-use applications. This review article provides an overview of externally directed field mechanisms (e.g., electric, magnetic, and acoustic) that are used for particle alignment. Illustrative examples from the AM literature show how these mechanisms are used to create structured composites with unique properties that can only be achieved through alignment. This article closes with a discussion of how particle distribution (i.e., microstructure) affects mechanical properties. A fundamental description of particle phase transport in polymers could lead to the development of AM process control for particle-polymer composite fabrication. This would ultimately create opportunities to explore the fundamental impact that alignment has on particle-polymer composite properties, which opens up the possibility of tailoring these materials for specific applications.

Accelerated annealing of colloidal crystal monolayers by means of cyclically applied electric fields

External fields are commonly applied to accelerate colloidal crystallization; however, accelerated self-assembly kinetics can negatively impact the quality of crystal structures. We show that cyclically applied electric fields can produce high quality colloidal crystals by annealing local disorder. We find that the optimal off-duration for maximum annealing is approximately one-half of the characteristic melting half lifetime of the crystalline phase. Local six-fold bond orientational order grows more rapidly than global scattering peaks, indicating that local restructuring leads global annealing. Molecular dynamics simulations of cyclically activated systems show that the ratio of optimal off-duration for maximum annealing and crystal melting time is insensitive to particle interaction details. This research provides a quantitative relationship describing how the cyclic application of fields produces high quality colloidal crystals by cycling at the fundamental time scale for local defect rearrangements; such understanding of dynamics and kinetics can be applied for reconfigurable colloidal assembly.

Nucleation and Post-Nucleation Growth in Diffusion-Controlled and Hydrodynamic Theory of Solidification

Two-step nucleation and subsequent growth processes were investigated in the framework of the single mode phase-field crystal model combined with diffusive dynamics (corresponding to colloid suspensions) and hydrodynamical density relaxation (simple liquids). It is found that independently of dynamics, nucleation starts with the formation of solid precursor clusters that consist of domains with noncrystalline ordering (ringlike projections are seen from certain angles), and regions that have amorphous structure. Using the average bond order parameter q¯6, we distinguished amorphous, medium range crystallike order (MRCO), and crystalline local orders. We show that crystallization to the stable body-centered cubic phase is preceded by the formation of a mixture of amorphous and MRCO structures. We have determined the time dependence of the phase composition of the forming solid state. We also investigated the time/size dependence of the growth rate for solidification. The bond order analysis indicates similar structural transitions during solidification in the case of diffusive and hydrodynamic density relaxation.

Evaporative self-assembly of the binary mixture of soft colloids

We have reported experimental studies on the self-assembly and degree of ordering of a binary mixture of soft colloids in monolayer deposits obtained by controlled evaporation. A sessile drop containing soft colloids is evaporated on a solid surface to achieve a loosely-packed two-dimensional deposit with a hexagonal arrangement. The soft microgel particles possess a hard core with a compliant corona, which plays a crucial role in retaining the crystallinity of the binary particle monolayer. The ordered arrangement of the binary mixture is observed even when the bulk diameter of one type of particle is 25% higher than the other, irrespective of their mixing ratio (1 : 3, 1 : 1, and 3 : 1). The microgel particles of both sizes are found to be homogeneously distributed throughout the deposit, completely suppressing the size-dependent particle segregation. Furthermore, in contrast to the self-assembly of bidisperse hard colloids, wherein the lattice distorts to accommodate particles of disparate sizes, in soft colloids, the particles deform at the interface to preserve the crystalline lattice. Moreover, unlike the gradual order-to-disorder transition observed in the deposits consisting of monodisperse microgel particles, the deposits of a binary mixture of microgels exhibit no noticeable trend. The areal disorder parameter, pair correlation function and the shape factor which quantifies the local ordering of particles in the deposit indicate the absence of a distinct order-to-disorder transition for the binary mixtures.

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.

Effect of prenucleation clusters arising from liquid-liquid phase transition on nucleation in a one-component charged colloidal suspension

It is generally thought that liquid-liquid phase transition (LLPT) in a one-component suspension never or only very rarely happens. If this were true, it would contradict the two nonclassical nucleation models building on either liquid droplets or prenucleation clusters (PNCs). One way out of this paradox is to suppose that LLPT occurs in pathway to nucleation. This study specifies the physical parameters of charged colloids which can bring out LLPT according to the consistent prediction of the DLVO (Derjaguin-Landau-Verwey-Overbeek) potential and the Sogami potential about long-range attraction, and reveals that surface charge is not the only factor to affect attraction, size also plays an essential role. For the first time, we follow exactly the evolution from LLPT to nucleation in which PNCs participate, and characterize pre-ordered liquid-like property of the PNCs and their particle-like and template effect by optical microscopy and light scattering. Furthermore, it is found that when the configuration of the PNCs is changed by a little salt, the pathway to nucleation is altered significantly. Our results demystify LLPT in a one-component suspension and dissolve the paradox, thus extending the range of applicability of the nonclassical nucleation models.

Tunable and Cooperative Thermomechanical Properties of Protein-Metal-Organic Frameworks

We recently introduced protein-metal-organic frameworks (protein-MOFs) as chemically designed protein crystals, composed of ferritin nodes that predictably assemble into 3D lattices upon coordination of various metal ions and ditopic, hydroxamate-based linkers. Owing to their unique tripartite construction, protein-MOFs possess extremely sparse lattice connectivity, suggesting that they might display unusual thermomechanical properties. Leveraging the synthetic modularity of ferritin-MOFs, we investigated the temperature-dependent structural dynamics of six distinct frameworks. Our results show that the thermostabilities of ferritin-MOFs can be tuned through the metal component or the presence of crowding agents. Our studies also reveal a framework that undergoes a reversible and isotropic first-order phase transition near-room temperature, corresponding to a 4% volumetric change within 1 °C and a hysteresis window of ∼10 °C. This highly cooperative crystal-to-crystal transformation, which stems from the soft crystallinity of ferritin-MOFs, illustrates the advantage of modular construction strategies in discovering tunable-and unpredictable-material properties.

Crystallization in Confinement

Many crystallization processes of great importance, including frost heave, biomineralization, the synthesis of nanomaterials, and scale formation, occur in small volumes rather than bulk solution. Here, the influence of confinement on crystallization processes is described, drawing together information from fields as diverse as bioinspired mineralization, templating, pharmaceuticals, colloidal crystallization, and geochemistry. Experiments are principally conducted within confining systems that offer well-defined environments, varying from droplets in microfluidic devices, to cylindrical pores in filtration membranes, to nanoporous glasses and carbon nanotubes. Dramatic effects are observed, including a stabilization of metastable polymorphs, a depression of freezing points, and the formation of crystals with preferred orientations, modified morphologies, and even structures not seen in bulk. Confinement is also shown to influence crystallization processes over length scales ranging from the atomic to hundreds of micrometers, and to originate from a wide range of mechanisms. The development of an enhanced understanding of the influence of confinement on crystal nucleation and growth will not only provide superior insight into crystallization processes in many real-world environments, but will also enable this phenomenon to be used to control crystallization in applications including nanomaterial synthesis, heavy metal remediation, and the prevention of weathering.

Kinetics-controlled design principles for two-dimensional open lattices using atom-mimicking patchy particles

The design and discovery of new two-dimensional materials with desired structures and properties are always one of the most fundamental goals in materials science. Here we present an atom-mimicking design concept to achieve direct self-assembly of two-dimensional low-coordinated open lattices using three-dimensional patchy particle systems. Besides honeycomb lattices, a new type of two-dimensional square-octagon lattice is obtained through rational design of the patch configuration of soft three-patch particles. However, unexpectedly the building blocks with thermodynamically favoured patch configuration cannot form square-octagon lattices in our simulations. We further reveal the kinetic mechanisms controlling the formation of the honeycomb and square-octagon lattices. The results indicate that the kinetically favoured intermediates play a critical role in determining the structure of obtained open lattices. This kinetics-controlled design principle provides a particularly effective and extendable framework to construct other novel open lattice structures.

Understanding the Phase and Morphological Behavior of Dispersions of Synergistic Dual-Stimuli-Responsive Poly(N-isopropylacrylamide) Nanogels

This work represents a detailed investigation into the phase and morphological behavior of synergistic dual-stimuli-responsive poly(N-isopropylacrylamide) nanogels, a material that is of considerable interest as a matrix for in situ forming implants. Nanogels were synthesized with four different diameters (65, 160, 310, and 450 nm) as monodispersed particles. These different samples were then prepared and characterized as both dilute (0.1 wt %) and concentrated dispersions (2-22 wt %). In the dilute form, all of the nanogels had the same response to the triggers of the physiological temperature and ionic strength. In water, the nanogels would deswell when heated above 32 °C, while they would aggregate if heated above this temperature at the physiological ionic strength. In the concentrated form, the nanogels exhibited a wide range of morphological changes, with liquid, swollen gel, shrunken gel, and aggregate structures all possible. The occurrence of these structures was dependent on many factors such as the temperature, ionic strength of the solvent, size and ζ-potential of the nanogel, and dispersion concentration. We explored these factors in detail with techniques such as visual studies, rheology, effective volume fraction, and shape factor measurement. The different-sized nanogels displayed differing phase and morphological behavior, but generally higher concentrations of the nanogels (>7 wt %) yielded gels in water with the transitions depending on the temperature. The smallest nanogel (65 nm diameter) exhibited the most unique behavior; it did not form a swollen gel at any concentration tested. Shape factor measurement for the nanogel samples showed that two of the larger three samples (160 and 310 nm) had core-shell structures with denser core cross-linking, while the smallest nanogel sample displayed a homogeneous cross-linked structure. We hypothesize that the smallest nanogels are able to undergo more extensive interpenetration compared to the larger nanogels, which meant that the smallest nanogel was not able to form a swollen gel. In the presence of salt at 12 wt %, all of the nanogels formed aggregates when heated above 35 °C due to the screening of the electrostatic stabilization by the salt. This work revealed unique behavior of the smallest nanogel with a homogeneous cross-linked structure; its phase and morphological behavior were unlike a particle dispersion, rather these were more similar to those of a branched polymer solution. In total, these findings can be used to provide information about the design of poly(N-isopropylacrylamide) nanogel dispersions for different applications where highly specific spatiotemporal control of morphology is required, for example, in the formation of in situ forming implants or for pore blocking behavior.

Thermophoresis of a Colloidal Rod: Contributions of Charge and Grafted Polymers

In this study, we investigated the thermodiffusion behavior of a colloidal model system as a function of the Debye length, λ_DH, which is controlled by the ionic strength. Our system consists of an fd-virus grafted with poly(ethylene glycol) (PEG) with a molecular mass of 5000 g mol^-1. The results are compared with recent measurements on a bare fd-virus and with results of PEG. The diffusion coefficients of both viruses are comparable and increase with the increasing Debye length. The thermal diffusion coefficient, D_T, of the bare virus increases strongly with the Debye length, whereas D_T of the grafted fd-virus shows only a very weak increase. The Debye length dependence of both systems can be described with an expression derived for charged rods using the surface charge density and an offset of D_T as adjustable parameters. It turns out that the ratio of the determined surface charges is inverse to the ratio of the surfaces of the two systems, which means that the total charge remains almost constant. The determined offset of the grafted fd-virus describing the chemical contributions is the sum of D_T of PEG and the offset of the bare fd-virus. At high λ_DH, corresponding to the low ionic strength, the S_T values of both colloidal model systems approach each other. This implies a contribution from the polymer layer, which is strong at short λ_DH and fades out for the longer Debye lengths, when the electric double layer reaches further than the polymer chains and therefore dominates interactions with the surrounding water.

Tunable interactions between particles in conically rotating electric fields

Tunable interactions between colloidal particles in external conically rotating electric fields are calculated, while the (vertical) axis of the field rotation is normal to the (horizontal) particle motion plane. The comparison of different approaches, including the methods of noninteracting, self-consistent dipoles, and the boundary element method, indicates that the last method is the most suitable for tunable interaction analysis. Thorough analysis, performed for interactions in pairs and clusters of colloidal particles, indicate that two- and three-body interactions make the main contributions in the interaction energy, while the effect of high-order terms is negligible. The tunable interactions are determined by the dielectric properties of the particles and solvent and can be changed in a wide range, providing a rich variety for the experimental "design" of different interactions, including repulsion, attraction, combination of short-range repulsion with long-range attraction, barrier-type interactions with short-range attraction and long-range repulsion, and double-scale repulsive (core-shoulder) interactions. These conclusions can be generalized for magnetically induced tunable interactions. The results indicate that tunable interactions can be widely applied in self-assembly and particle-resolved studies of generic phenomena in fluids and crystals, and, therefore, are of broad interest in the fields of chemical physics, physical chemistry, materials science, and soft matter.

Phase Behavior of Bowl-Shaped Colloids: Order and Dynamics in Plastic Crystals and Glasses

Charged fluorescent bowl-shaped colloids consisting of a polystyrene core surrounded by a poly(N-isopropylmethacrylamide) shell are obtained by nanoengineering spherical composite microgels. The phase diagram of these soft bowl-shaped colloids interacting through long-range Yukawa-type interactions is investigated using confocal laser scanning microscopy. The bowl-shaped structure leads to marked differences in phase-behavior compared to their spherical counterpart. With increasing number density, a transition from a fluid to a plastic crystal phase, with freely rotating particles, followed by a glass-like state is observed. It is found that the anisotropic bowl shape frustrates crystallization and slows down crystallization kinetics and causes the glass-like transition to shift to a significantly lower volume fraction than for the spheres. Quantitative analysis of the positional and orientational order demonstrates that the plastic crystal phase exhibits quasi-long range translational order and orientational disorder, while in the disordered glass-like phase the long-range translational order vanishes and short-range rotational order appears, dictated by the specific bowl shape. It is further shown that the different structural transitions are characterized by decoupling of the translational and orientational dynamics.

Transition of Dielectrophoresis-Assembled 2D Crystals to Interlocking Structures under a Magnetic Field

Aspherical cubic hematite colloids with cylindrical arms protruding from each face, referred to as "hexapods", were assembled via negative dielectrophoresis and then manipulated using an applied magnetic field. Upon application of an ac electric field, the hexapods aligned in close-packed linear chains parallel to the field direction. The chains then aggregated to the center of the device, with adjacent chains separated by distances approximately equal to twice the arm length. The resulting open packing structure exhibited cmm plane group symmetry due to the obstruction of arms, with a high density of incorporated defects. Subsequent application of a magnetic field to the dielectrophoresis (DEP)-assembled structure was found to anneal the colloidal crystal by reorienting the hexapods to align their intrinsic magnetic dipoles with the magnetic field direction. During reorganization, the colloidal packing density was found to decrease by more than 10% at both the center and edges of the crystal, accompanied by a significant loss of ordering, prior to redensification of the 2D lattice with fewer defects. Reorganization at the edge was 1.5 times faster than at the center, consistent with the need for cooperative colloidal motion to remove defects at the centers of the crystals.

Thermodynamics of two-dimensional Yukawa systems across coupling regimes

Thermodynamics of two-dimensional Yukawa (screened Coulomb or Debye-Hückel) systems is studied systematically using molecular dynamics (MD) simulations. Simulations cover very broad parameter range spanning from weakly coupled gaseous states to strongly coupled fluid and crystalline states. Important thermodynamic quantities, such as internal energy and pressure, are obtained and accurate physically motivated fits are proposed. This allows us to put forward simple practical expressions to describe thermodynamic properties of two-dimensional Yukawa systems. For crystals, in addition to numerical simulations, the recently developed shortest-graph interpolation method is applied to describe pair correlations and hence thermodynamic properties. It is shown that the finite-temperature effects can be accounted for by using simple correction of peaks in the pair correlation function. The corresponding correction coefficients are evaluated using MD simulation. The relevance of the obtained results in the context of colloidal systems, complex (dusty) plasmas, and ions absorbed to interfaces in electrolytes is pointed out.

Rational design and dynamics of self-propelled colloidal bead chains: from rotators to flagella

The quest for designing new self-propelled colloids is fuelled by the demand for simple experimental models to study the collective behaviour of their more complex natural counterparts. Most synthetic self-propelled particles move by converting the input energy into translational motion. In this work we address the question if simple self-propelled spheres can assemble into more complex structures that exhibit rotational motion, possibly coupled with translational motion as in flagella. We exploit a combination of induced dipolar interactions and a bonding step to create permanent linear bead chains, composed of self-propelled Janus spheres, with a well-controlled internal structure. Next, we study how flexibility between individual swimmers in a chain can affect its swimming behaviour. Permanent rigid chains showed only active rotational or spinning motion, whereas longer semi-flexible chains showed both translational and rotational motion resembling flagella like-motion, in the presence of the fuel. Moreover, we are able to reproduce our experimental results using numerical calculations with a minimal model, which includes full hydrodynamic interactions with the fluid. Our method is general and opens a new way to design novel self-propelled colloids with complex swimming behaviours, using different complex starting building blocks in combination with the flexibility between them.

Interactions in reentrant phase behavior of a charged nanoparticle solution by multivalent ions

The interactions following a reentrant phase transition of charged silica nanoparticles from one phase to two phases and back to one phase by varying the concentration of multivalent counterions have been examined. The observations are far beyond the framework of Debye-Hückel or even nonlinear Poisson-Boltzmann equations and demonstrate the universal behavior of multivalent counterion-driven charge inversion. We show that the interplay of multivalent counterion-induced short-range attraction and long-range electrostatic repulsion between nanoparticles results in reentrant phase behavior.

Tunable hydrodynamics: a field-frequency phase diagram of a non-equilibrium order-to-disorder transition

We present experiments on a model system consisting of dielectric (silicone oil) drops in a "leaky dielectric" (castor oil) carrier fluid that exhibits dynamic non-equilibrium phases as a function of the amplitude and frequency of an external AC electric field. At high frequencies, the dielectric drops are pinned to a periodic lattice by dielectrophoretic forces induced by a patterned bottom electrode. Beginning with this state of imposed order, we examine the processes that take this system from order to disorder, with decreasing frequency corresponding to an increase in the range of the hydrodynamic forces. We find two kinds of disorder, shape- and translational disorder, that occur in frequency-amplitude space. We also find regimes where drop breakup is dominant, and where order/disorder of large drops can be probed without significant drop breakup. With decreasing frequency (i.e., increasing hydrodynamic coupling between drops) and on timescales from seconds to minutes, the drops exhibit motion that resembles Brownian motion of particles in a crystal, with an effective temperature that increases with the strength of the electrohydrodynamic driving force. In this limit, the system behaves like a thermal system and the lattice is seen to melt at an effective Lindemann parameter of L_eff ∼ 0.08. This non-equilibrium thermodynamics, probed on timescales from seconds to minutes, likely arises from the pseudo-random velocity fields in the carrier fluid, as evidenced by the fractional, t^3/2, super-diffusive tracer dynamics at shorter timescales.

Triple Junction at the Triple Point Resolved on the Individual Particle Level

At the triple point of a repulsive screened Coulomb system, a fcc crystal, a bcc crystal, and a fluid phase coexist. At their intersection, these three phases form a liquid groove, the triple junction. Using confocal microscopy, we resolve the triple junction on a single-particle level in a model system of charged PMMA colloids in a nonpolar solvent. The groove is found to be extremely deep and the incommensurate solid-solid interface to be very broad. Thermal fluctuations hence appear to dominate the solid-solid interface. This indicates a very low interfacial energy. The fcc-bcc interfacial energy is quantitatively determined based on Young's equation and, indeed, it is only about 1.3 times higher than the fcc-fluid interfacial energy close to the triple point.

Ehrenfest urn model with interaction

We studied the Ehrenfest urn model in which particles in the same urn interact with each other. Depending on the nature of interaction, the system undergoes a first- or second-order phase transition. The relaxation time to the equilibrium state, the Poincaré cycles of the equilibrium state and the most far-from-equilibrium state, and the duration time of the states during first-order phase transition are calculated. It was shown that the scaling behavior the Poincaré cycles could serve as an indication to the nature of phase transition, and the behavior of the ratio of duration time of the states could be strong evidence of the metastability during first-order phase transition.

Self-Assembly of Colloidal Molecules due to Self-Generated Flow

The emergence of structure through aggregation is a fascinating topic and of both fundamental and practical interest. Here we demonstrate that self-generated solvent flow can be used to generate long-range attractions on the colloidal scale, with subpiconewton forces extending into the millimeter range. We observe a rich dynamic behavior with the formation and fusion of small clusters resembling molecules. The dynamics of this assembly is governed by an effective conservative energy that for large separations r decays as 1/r. Breaking the flow symmetry, these clusters can be made active.

Electric-Field Assisted Assembly of Colloidal Particles into Ordered Nonclose-Packed Arrays

Nonclose-packed colloidal arrays have many potential applications ranging from plasmonic sensors, light trapping for photovoltaics, to transparent electrodes. However, scalable fabrication of those structures remains a challenge. In this Article, we investigate the robustness of an electric-field assisted approach systematically. A monolayer of nonclose-packed crystalline array is first created under a low-frequency alternating-current electric field in solution. We then apply a sequence of direct-current pulses to fix the particle array onto the substrate so that it remains intact even after both field removal and solvent evaporation. Key process parameters such as the alternating-current field strength, direct-current magnitude, particle concentration, and solvent-evaporation rate that affect both ordering and fixing of colloidal particles have been studied systematically. We find that direct currents with an intermediate magnitude induce electrophoretic motion of particles toward the substrate and facilitate their permanent adhesion on the substrate due to strong van der Waals attraction. A higher current, however, causes lateral aggregation of particles arising from electroosmotic flow of solvent and destroys the periodic ordering between particles. This approach, in principle, can be conveniently adapted into the continuous convective assembly process, thus making the fabrication of nonclose-packed colloidal arrays scalable.

Frequency-Dependent Solvent Impedance and Colloid Microelectrophoresis Measurements in Partially Polar Solvents

We carry out frequency-dependent solvent impedance measurements and alternating current (ac) colloid microelectrophoresis experiments in partially polar solvents in the low-frequency regime (0.25 Hz ≤ f ≤ 10 Hz). Solvent electrode polarization effects are quantified first in partially polar solvent mixtures containing bromocyclohexane (CHB). We find that the polarization capacitance from electrode polarization exhibits a clear power law behavior C_p = C_p0 f^-m with power law exponent m = 0.25 ± 0.04. Once we account for electrode polarization effects, we are able to obtain quantitative mobilities in the low-frequency regime from our ac microelectrophoresis measurements; for these measurements, we use poly(methyl methacrylate colloids that are gravitationally confined to a plane while suspended in a low-polar solvent mixture of cis-trans decahydronapthalene and CHB. We find that the dimensionless electrophoretic mobility is constant, consistent with expectations for frequencies below the ion-diffusion frequency, and has a value E = 1.6 ± 0.4.

Multiscale directed self-assembly of composite microgels in complex electric fields

This study explored the application of localized electric fields for reversible directed self-assembly of colloidal particles in 3 dimensions. Electric field microgradients, arising from the use of micro-patterned electrodes, were utilized to direct the localization and self-assembly of polarizable (charged) particles resulting from a combination of dielectrophoretic and multipolar forces. Deionized dispersions of spherical and ellipsoidal core-shell microgels were employed for investigating their assembly under an external alternating electric field. We demonstrated that the frequency of the field allowed for an exquisite control over the localization of the particles and their self-assembled structures near the electrodes. We extended this approach to concentrated binary dispersions consisting of polarizable and less polarizable composite microgels. Furthermore, we utilized the thermosensitivity of the microgels to adjust the effective volume fraction and the dynamics of the system, which provided the possibility to dynamically "solidify" the assembly of the field-responsive particles by a temperature quench from their initial fluid state into an arrested crystalline state. Reversible solidification enables us to re-write/reconstruct various 3 dimensional assemblies by varying the applied field frequency.

The effect of confinement on the electrohydrodynamic behavior of droplets in a microfluidic oil-in-oil emulsion

A two-fluid emulsion (silicone oil drops in the "leaky dielectric", castor oil) with electrohydrodynamically driven flows can serve as a model system for tunable studies of hydrodynamic interactions [Varshney et al., Sci. Rep., 2012, 2, 738]. Flows on multiple length- and time-scales have been observed but the underlying mechanism for these chaotic, multi-scale flows is not understood. In this work, we conducted experiments varying the thickness of the test cell to examine the role of substrate interactions on size distribution, mean square displacement and velocity of the drops as a function of the electric field strength. We find that the electric capillary number, Ca_E, at the threshold of drop breakup is of order unity for cell thicknesses of 100 μm or thicker, but much larger for thinner cells. Above this threshold, there is a clear transition to super-diffusive droplet motions. In addition, we observe that there is a convective instability prior to the onset of chaotic flows, with the lengthscale associated with the convection rolls increasing linearly with an increase in the cell thickness. The fact that the convective instability appears to occur in the leaky dielectric castor oil regardless of whether the second component is liquid drops, solid particles, or dissolved dye has implications on the underlying mechanism for the unsteady flows.

Contact-Free Templating of 3-D Colloidal Structures Using Spatially Nonuniform AC Electric Fields

The formation of ordered and regularly shaped structures of colloidal particles with the aid of spatially nonuniform electric fields is a modern research area of great interest. This work illustrates how alternating current (AC) electrokinetic effects (dielectrophoresis, electroosmosis) can serve as contact-free templates, inside which colloidal microspheres can assemble into a variety of shapes and sizes. We show how three-dimensional colloidal structures of square, circular, and diamond shape of many tens of micrometers in size can be reproducibly formed with a single set of quadrupolar microelectrodes. Numerical simulations performed help to explain the role of AC electroosmosis and AC dielectrophoresis on the shaping of these structures as a function of applied voltage and frequency. We also demonstrate how the templating repertoire is further enhanced with the simultaneous application of a second, individually controlled AC electric field, which enables a variety of asymmetric colloidal structures to be produced using the same set of quadrupolar microelectrodes. As the preservation of shape and size of such electric-field templated structures after medium evaporation still remains a big challenge, here we also report on a novel method that permits the stabilization and isolation of these particle assemblies through medium gelation and subsequent hydrogel removal with a UV/ozone treatment.

A possible four-phase coexistence in a single-component system

For different phases to coexist in equilibrium at constant temperature T and pressure P, the condition of equal chemical potential μ must be satisfied. This condition dictates that, for a single-component system, the maximum number of phases that can coexist is three. Historically this is known as the Gibbs phase rule, and is one of the oldest and venerable rules of thermodynamics. Here we make use of the fact that, by varying model parameters, the Gibbs phase rule can be generalized so that four phases can coexist even in single-component systems. To systematically search for the quadruple point, we use a monoatomic system interacting with a Stillinger-Weber potential with variable tetrahedrality. Our study indicates that the quadruple point provides flexibility in controlling multiple equilibrium phases and may be realized in systems with tunable interactions, which are nowadays feasible in several soft matter systems such as patchy colloids.

Alternating strings and clusters in suspensions of charged colloids

We report the formation of alternating strings and clusters in a binary suspension of repulsive charged colloids with double layers larger than the particle size. Within a binary cell model we include many-body and charge-regulation effects under the assumption of a constant surface potential, and consider their repercussions on the two-particle interaction potential. We find that the formation of induced dipoles close to a charge-reversed state may explain the formation of these structures. Finally, we will touch upon the formation of dumbbells and small clusters in a one-component system, where the effective electrostatic interaction is always repulsive.

Nanoparticle Clusters: Assembly and Control Over Internal Order, Current Capabilities, and Future Potential

The current state of the art in the use of colloidal methods to form nanoparticle assemblies, or clusters (NPCs) is reviewed. The focus is on the two-step approach, which exploits the advantages of bottom-up wet chemical NP synthesis procedures, with subsequent colloidal destabilization to trigger assembly in a controlled manner. Recent successes in the application of functional NPCs with enhanced emergent collective properties for a wide range of applications, including in biomedical detection, surface enhanced Raman scattering (SERS) enhancement, photocatalysis, and light harvesting, are highlighted. The role of the NP-NP interactions in the formation of monodisperse ordered clusters is described and the different assembly processes from a wide range of literature sources are classified according to the nature of the perturbation from the initial equilibrium state (dispersed NPs). Finally, the future for the field and the anticipated role of computational approaches in developing next-generation functional NPCs are briefly discussed.

Interpolation method for pair correlations in classical crystals

Effects of anharmonicity on the pair correlation function of classical crystals are studied. The recently proposed shortest-graph approach using the Gaussian representation of the individual correlation peaks (the peak width is determined by the length of the shortest graph connecting a given pair of particles) is further improved, to account for anharmonic corrections due to finite temperatures and hard-sphere-like interactions. Two major effects are identified, leading to a modification of the correlation peaks at large or short distances: (i) the peaks at large distances, well described by Gaussians, should be calculated from the finite-temperature phonon spectra; (ii) at short distances, the correlation peaks deviate significantly from the Gaussian form due to the lattice discreteness. We propose the analytical interpolation method, based on the shortest-graph approach, which includes both effects. By employing the molecular dynamics simulations, the accuracy of the method is verified for three- and two-dimensional crystals with the Yukawa, inverse-power-law, and pseudo-hard-sphere pair interactions. The capabilities of the method are demonstrated by calculating the phase diagram of a three-dimensional Yukawa system.