Experimental Evidence for Algebraic Double-Layer Forces.

According to conventional wisdom, electric double-layer forces normally decay exponentially with separation distance. Here, we present experimental evidence of algebraically decaying double-layer interactions. We show that algebraic interactions arise in both strongly overlapping as well as counterion-only regimes, albeit the evidence is less clear for the former regime. In both of these cases, the disjoining pressure profile assumes an inverse square distance dependence. At small separation distances, another algebraic regime is recovered. In this regime, the pressure decays as the inverse of separation distance.

Self-assembly of charged colloidal cubes.

In this work, we show how and why the interactions between charged cubic colloids range from radially isotropic to strongly directionally anisotropic, depending on tuneable factors. Using molecular dynamics simulations, we illustrate the effects of typical solvents to complement experimental investigations of cube assembly. We find that in low-salinity water solutions, where cube self-assembly is observed, the colloidal shape anisotropy leads to the strongest attraction along the corner-to-corner line, followed by edge-to-edge, with a face-to-face configuration of the cubes only becoming energetically favorable after the colloids have collapsed into the van der Waals attraction minimum. Analysing the potential of mean force between colloids with varied cubicity, we identify the origin of the asymmetric microstructures seen in experiment.

Convectively Assembled Monolayers of Colloidal Cubes: Evidence of Optimal Packings.

We employ a system of cubic colloids with rounded corners to study the close-packed monolayers that form via convective assembly. We show that by controlled solvent evaporation large densely packed monolayers of colloidal cubes are obtained. Using scanning electron microscopy and particle-tracking algorithms, we investigate the local order in detail and show that the obtained monolayers possess their predicted close-packed optimal packings, the Λ0-lattice and the Λ1-lattice, as well as the simple square-lattice and disordered packings. We further show that shape details of the cube corners are important for the final packing symmetry, where the frequency of the Λ1-lattice increases with decreasing roundness of the corners, whereas the frequency of the Λ0-lattice is unaffected. The formation of both optimal packings is found to be a consequence of the out-of-equilibrium formation process, which leads to small shifts in rows of cubes, thereby transforming the Λ1-lattice into the Λ0-lattice.

Interactions between amphoteric surfaces with strongly overlapping double layers.

The entropic repulsion between strongly overlapping electrical double-layers from two parallel amphoteric plates is described via the Donnan equilibrium in the limit of zero electric field. The plates feature charge-regulation and the inter-plate solution is in equilibrium with a reservoir of a monovalent electrolyte solution. A finite electric potential and disjoining pressure is found at contact between the plates, due to a complete discharging of the plates. For low potentials, the decay of potential and pressure is fully governed by a characteristic length scale and the contact potential. Additionally, for large separations we find a universal inverse square decay of disjoining pressure, irrespective of the contact potential. The results of the Donnan theory show quantitative agreement with self-consistent field computations that solve the full Poisson equation.

Self-organization in dipolar cube fluids constrained by competing anisotropies.

For magnetite spherical nanoparticles, the orientation of the dipole moment in the crystal does not affect the morphology of either zero field or field induced structures. For non-spherical particles however, an interplay between particle shape and direction of the magnetic moment can give rise to unusual behaviors, in particular when the moment is not aligned along a particle symmetry axis. Here we disclose for the first time the unique magnetic properties of hematite cubic particles and show the exact orientation of the cubes' dipole moment. Using a combination of experiments and computer simulations, we show that dipolar hematite cubes self-organize into dipolar chains with morphologies remarkably different from those of spheres, and demonstrate that the emergence of these structures is driven by competing anisotropic interactions caused by the particles' shape anisotropy and their fixed dipole moment. Furthermore, we have analytically identified a specific interplay between energy, and entropy at the microscopic level and found that an unorthodox entropic contribution mediates the organization of particles into the kinked nature of the dipolar chains.

Shape-sensitive crystallization in colloidal superball fluids.

Guiding the self-assembly of materials by controlling the shape of the individual particle constituents is a powerful approach to material design. We show that colloidal silica superballs crystallize into canted phases in the presence of depletants. Some of these phases are consistent with the so-called "Λ1" lattice that was recently predicted as the densest packing of superdisks. As the size of the depletant is reduced, however, we observe a transition to a square phase. The differences in these entropically stabilized phases result from an interplay between the size of the depletants and the fine structure of the superball shape. We find qualitative agreement of our experimental results both with a phase diagram computed on the basis of the volume accessible to the depletants and with simulations. By using a mixture of depletants, one of which is thermosensitive, we induce solid-to-solid phase transitions between square and canted structures. The use of depletant size to leverage fine features of the shape of particles in driving their self-assembly demonstrates a general and powerful mechanism for engineering novel materials.

In situ observation of self-assembly of sugars and surfactants from nanometres to microns.

The hierarchical self-assembly of sugar and surfactant molecules into hollow tubular microstructures was characterized in situ with high resolution small-angle X-ray scattering spanning more than three orders of magnitude of spatial scales. Scattering profiles reveal that aqueous host-guest inclusion complexes self-assemble into multiple equally spaced curved bilayers forming a collection of concentric hollow cylinders. Scattering data can be described by a simple theoretical model of the microtubes. The interlamellar distance was found to be surprisingly large. Moreover, we report that the multi-walled structure of the microtubes swells as the concentration or the temperature is varied.

Depletion controlled surface deposition of uncharged colloidal spheres from stable bulk dispersions.

The competition between surface adsorption and bulk aggregation was investigated for silica colloids dispersed in cyclohexane in contact with hydrophobized silica substrates. Central to this study is that the colloids and surfaces have the same material and surface properties. Colloid-colloid and colloid-surface interactions were controlled by addition of polymers providing depletion interaction. Bulk instability was determined by turbidity and viscosity measurements and surface adsorption by ellipsometry measurements. At increasing polymer concentration, strong surface adsorption occurred at polymer concentrations below that required for bulk phase separation. Complementary Monte Carlo simulations with the use of a new weak depletion theory support quantitatively the experimental observation of the existence of an interval of interaction strength at which aggregation in bulk is negligible while surface adsorption is substantial.

Swelling enhanced remanent magnetization of hydrogels cross-linked with magnetic nanoparticles.

Hydrogels that are pH-sensitive and partially cross-linked by cobalt ferrite nanoparticles exhibit remarkable remanent magnetization behavior. The magnetic fields measured outside our thin disks of ferrogel are weak, but in the steady state, the field dependence on the magnetic content of the gels and the measurement geometry is as expected from theory. In contrast, the time-dependent behavior is surprisingly complicated. During swelling, the remanent field first rapidly increases and then slowly decreases. We ascribe the swelling-induced field enhancement to a change in the average orientation of magnetic dipolar structures, while the subsequent field drop is due to the decreasing concentration of nanoparticles. During shrinking, the field exhibits a much weaker time dependence that does not mirror the values found during swelling. These observations provide original new evidence for the markedly different spatial profiles of the pH during swelling and shrinking of hydrogels.

Reconfigurable assembly of superparamagnetic colloids confined in thermo-reversible microtubes.

Structural transformations of superparamagnetic colloids confined within self-assembled microtubes are studied by systematically varying tube-colloid size ratios and external magnetic field directions. A magnetic field parallel to microtubes may stretch non-linear chains like zigzag chains into linear chains. Non-parallel fields induce new structures including repulsive chains of single colloids, kinked chains and repulsive dimers, which are not observed for unconfined magnetic colloids in the bulk. The formed colloidal structures are confirmed via model calculations which account for tube-colloid size ratio effects and their reconfigurability with the field direction. Furthermore, structures are formed that allow controllable switching between a helical and a non-helical state. All observed field-induced transformations in microtubes are reversible provided the microtubes are not completely filled with colloids. In addition, we demonstrate magnetic field-responsive 2D crystallization by extending control over colloidal configurations in single microtubes to multiple well-aligned microtubes.

Particle shape anisotropy in pickering emulsions: cubes and peanuts.

We have investigated the effect of particle shape in Pickering emulsions by employing, for the first time, cubic and peanut-shaped particles. The interfacial packing and orientation of anisotropic microparticles are revealed at the single-particle level by direct microscopy observations. The uniform anisotropic hematite microparticles adsorb irreversibly at the oil-water interface in monolayers and form solid-stabilized o/w emulsions via the process of limited coalescence. Emulsions were stable against further coalescence for at least 1 year. We found that cubes assembled at the interface in monolayers with a packing intermediate between hexagonal and cubic and average packing densities of up to 90%. Local domains displayed densities even higher than theoretically achievable for spheres. Cubes exclusively orient parallel with one of their flat sides at the oil-water interface, whereas peanuts preferentially attach parallel with their long side. Those peanut-shaped microparticles assemble in locally ordered, interfacial particle stacks that may interlock. Indications for long-range capillary interactions were not found, and we hypothesize that this is related to the observed stable orientations of cubes and peanuts that marginalize deformations of the interface.

Spatial distribution of nanocrystals imaged at the liquid-air interface.

The 3D distribution of nanocrystals at the liquid-air interface is imaged for the first time on a single-particle level by cryogenic electron tomography, revealing the equilibrium concentration profile from the interface to the bulk of the liquid. When the surface tension of the liquid is decreased, the interaction of the nanocrystals with the liquid-air interface shifts from adsorption to desorption. Macroscopic surface tension measurements do not detect this transition, due to the presence of surface-active molecular species.

Algebraic repulsions between charged planes with strongly overlapping electrical double layers.

Langmuir's disjoining pressure between two flat, charged planes was calculated analytically for strongly overlapping double layers in the limit of zero electric field between the planes. The resulting repulsion has a long-range algebraic decay that stems from the thermodynamic equilibrium between homogeneously distributed interplate ions and ions in the surrounding electrolyte reservoir. Together with the van der Waals attraction, the repulsion forms the zero-field pendant of the exponentially screened DLVO potential, a pendant that is always repulsive at large plate-plate distances. The experimental occurrence of algebraic repulsions can be simply predicted from surface charge density and ionic strength.

Frequency-dependent magnetic susceptibility of magnetite and cobalt ferrite nanoparticles embedded in PAA hydrogel.

Chemically responsive hydrogels with embedded magnetic nanoparticles are of interest for biosensors that magnetically detect chemical changes. A crucial point is the irreversible linkage of nanoparticles to the hydrogel network, preventing loss of nanoparticles upon repeated swelling and shrinking of the gel. Here, acrylic acid monomers are adsorbed onto ferrite nanoparticles, which subsequently participate in polymerization during synthesis of poly(acrylic acid)-based hydrogels (PAA). To demonstrate the fixation of the nanoparticles to the polymer, our original approach is to measure low-field AC magnetic susceptibility spectra in the 0.1 Hz to 1 MHz range. In the hydrogel, the magnetization dynamics of small iron oxide nanoparticles are comparable to those of the particles dispersed in a liquid, due to fast Néel relaxation inside the particles; this renders the ferrogel useful for chemical sensing at frequencies of several kHz. However, ferrogels holding thermally blocked iron oxide or cobalt ferrite nanoparticles show significant decrease of the magnetic susceptibility resulting from a frozen magnetic structure. This confirms that the nanoparticles are unable to rotate thermally inside the hydrogel, in agreement with their irreversible fixation to the polymer network.

Self-assembly of colloidal cubes via vertical deposition.

The vertical deposition technique for creating crystalline microstructures is applied for the first time to nonspherical colloids in the form of hollow silica cubes. Controlled deposition of the cubes results in large crystalline films with variable symmetry. The microstructures are characterized in detail with scanning electron microscopy and small-angle X-ray scattering. In single layers of cubes, distorted square to hexagonal ordered arrays are formed. For multilayered crystals, the intralayer ordering is predominantly hexagonal with a hollow site stacking, similar to that of the face centered cubic lattice for spheres. Additionally, a distorted square arrangement in the layers is also found to form under certain conditions. These crystalline films are promising for various applications such as photonic materials.

Enthalpy and entropy of nanoparticle association from temperature-dependent cryo-TEM.

Quantum dots form equilibrium structures in liquid dispersions, due to thermodynamic forces that are often hard to quantify. Analysis of these structures, visualized using cryogenic electron microscopy, yields their formation free energy. Here we show that the nanoparticle interaction free energy can be further separated into the enthalpic and entropic contributions, using the temperature dependence of the assembled structures. Monodisperse oleic acid-capped PbSe nanoparticles dispersed in decalin were used as a model system, and the temperature-dependent equilibrium structures were imaged by cryo-TEM, after quenching from different initial temperatures. The interaction enthalpy and entropy follow from van 't Hoff's exact equation for the temperature dependence of thermodynamic equilibria, now applied to associating nanoparticles. The enthalpic component gives the magnitude of the contact interaction, which is crucial information in understanding the energetics of the self-assembly of nanoparticles into ordered structures.

The role of filament-packing dynamics in powering amoeboid cell motility.

Although several models have been proposed to account for how cytoskeleton polymerization drives protrusion in cell motility, the precise mechanism remains controversial. Here, we show that, in addition to force exerted directly against the membrane by growing filaments, the way elongating filaments pack also contributes to protrusion by generating an expansion of the cytoskeleton gel. Tomography shows that filament packing in the major sperm protein (MSP) -based nematode sperm-motility machinery resembles that observed with rigid rods. Maximum rod-packing density decreases dramatically as the rods lengthen. Therefore, as filaments elongate, the cytoskeleton gel expands to accommodate their packing less densely. This volume expansion combines with polymerization to drive protrusion. Consistent with this hypothesis, an engineered MSP mutant that generates shorter filaments shows higher filament-packing density and slower movement.

Controlling CaCO3 Particle Size with {Ca2+}:{CO3 2-} Ratios in Aqueous Environments.

The effect of stoichiometry on the new formation and subsequent growth of CaCO3 was investigated over a large range of solution stoichiometries (10-4 < r aq < 104, where r aq = {Ca2+}:{CO3 2-}) at various, initially constant degrees of supersaturation (30 < Ωcal < 200, where Ωcal = {Ca2+}{CO3 2-}/K sp), pH of 10.5 ± 0.27, and ambient temperature and pressure. At r aq = 1 and Ωcal < 150, dynamic light scattering (DLS) showed that ion adsorption onto nuclei (1-10 nm) was the dominant mechanism. At higher supersaturation levels, no continuum of particle sizes is observed with time, suggesting aggregation of prenucleation clusters into larger particles as the dominant growth mechanism. At r aq ≠ 1 (Ωcal = 100), prenucleation particles remained smaller than 10 nm for up to 15 h. Cross-polarized light in optical light microscopy was used to measure the time needed for new particle formation and growth to at least 20 µm. This precipitation time depends strongly and asymmetrically on r aq. Complementary molecular dynamics (MD) simulations confirm that r aq affects CaCO3 nanoparticle formation substantially. At r aq = 1 and Ωcal ≫ 1000, the largest nanoparticle in the system had a 21-68% larger gyration radius after 20 ns of simulation time than in nonstoichiometric systems. Our results imply that, besides Ωcal, stoichiometry affects particle size, persistence, growth time, and ripening time toward micrometer-sized crystals. Our results may help us to improve the understanding, prediction, and formation of CaCO3 in geological, industrial, and geo-engineering settings.

Depletion-Induced Chiral Chain Formation of Magnetic Spheres.

Experimental evidence is presented for the spontaneous formation of chiral configurations in bulk dispersions of magnetized colloids that interact by a combination of anisotropic dipolar interactions and isotropic depletion attractions. The colloids are superparamagnetic silica spheres, magnetized and aligned by a carefully tuned uniform external magnetic field; isotropic attractions are induced by using poly(ethylene oxide) polymers as depleting agents. At specific polymer concentrations, sphere chains wind around each other to form helical structures-of the type that previously have only been observed in simulations on small sets of unconfined dipolar spheres with additional isotropic interactions.

Evidence for a macroscopic electric field in the sedimentation profiles of charged colloids.

The determination of molecular masses from barometric sedimentation profiles, a main topic in ultracentrifugal analysis, is thought to be quantitatively correct for non-interacting particles. Whereas this expectation is justified for uncharged colloids or macromolecules at low volume fractions, early ultracentrifugation studies on charged particles had already indicated that the obtained masses might be much too low. More recently, expanded sedimentation profiles have been observed for charged particles, sometimes inflated by orders of magnitude relative to the barometric prediction, which highlights a shortcoming in our understanding of centrifugation of even very dilute charged species. Theory and simulations, anticipated by various authors, now propose that strongly non-barometric sedimentation profiles might be caused by an internal macroscopic electric field that, even for non-interacting particles, significantly decreases the buoyant particle mass. The existence of this field and its intriguing consequences still lack experimental verification. Here we report ultracentrifugation experiments on charged colloidal silica spheres, showing both the existence of such a macroscopic electric field and its drastic effects on the sedimentation profiles of very dilute dispersions at low ionic strength.