Measurement of the hard-sphere equation of state using screened charged polystyrene colloids

Anisotropic particle multiphase equilibria in nonuniform fields

We report a method to predict equilibrium concentration profiles of hard ellipses in nonuniform fields, including multiphase equilibria of fluid, nematic, and crystal phases. Our model is based on a balance of osmotic pressure and field mediated forces by employing the local density approximation. Implementation of this model requires development of accurate equations of state for each phase as a function of hard ellipse aspect ratio in the range k = 1-9. The predicted density profiles display overall good agreement with Monte Carlo simulations for hard ellipse aspect ratios k = 2, 4, and 6 in gravitational and electric fields with fluid-nematic, fluid-crystal, and fluid-nematic-crystal multiphase equilibria. The profiles of local order parameters for positional and orientational order display good agreement with values expected for bulk homogeneous hard ellipses in the same density ranges. Small discrepancies between predictions and simulations are observed at crystal-nematic and crystal-fluid interfaces due to limitations of the local density approximation, finite system sizes, and uniform periodic boundary conditions. The ability of the model to capture multiphase equilibria of hard ellipses in nonuniform fields as a function of particle aspect ratio provides a basis to control anisotropic particle microstructure on interfacial energy landscapes in diverse materials and applications.

Characterization and Optimization of Fluorescent Organosilica Colloids for 3D Confocal Microscopy Prepared Under "Zero-Flow" Conditions

We optimize and characterize the preparation of 3-trimethoxysilyl propyl methacrylate (TPM) colloidal suspensions for three-dimensional confocal microscopy. We revisit a simple synthesis of TPM microspheres by nucleation of droplets from prehydrolyzed TPM oil in a "zero-flow" regime and demonstrate how precise and reproducible control of particle size may be achieved via single-step nucleation with a focus on how the reagents are mixed. We also revamp the conventional dyeing method for TPM particles to achieve uniform transfer of a fluorophore to the organosilica droplets, improving particle identification. Finally, we illustrate how a ternary mixture of tetralin, trichloroethylene, and tetrachloroethylene may be used as a suspension medium which matches the refractive index of these particles while allowing independent control of the density mismatch between particle and solvent.

Computer simulations of self-assembly of anisotropic colloids

Computer simulations have played a significant role in understanding the physics of colloidal self-assembly, interpreting experimental observations, and predicting novel mesoscopic and crystalline structures. Recent advances in computer simulations of colloidal self-assembly driven by anisotropic or orientation-dependent inter-particle interactions are highlighted in this review. These interactions are broadly classified into two classes: entropic and enthalpic interactions. They mainly arise due to shape anisotropy, surface heterogeneity, compositional heterogeneity, external field, interfaces, and confinements. Key challenges and opportunities in the field are discussed.

Phonon eigenfunctions of inhomogeneous lattices: Can you hear the shape of a cone?

We study the phonon modes of interacting particles on the surface of a truncated cone resting on a plane subject to gravity, inspired by recent colloidal experiments. We derive the ground-state configuration of the particles under gravitational pressure in the small-cone-angle limit and find an inhomogeneous triangular lattice with spatially varying density but robust local order. The inhomogeneity has striking effects on the normal modes such that an important feature of the cone geometry, namely its apex angle, can be extracted from the lattice excitations. The shape of the cone leads to energy crossings at long wavelengths and frequency-dependent quasilocalization at short wavelengths. We analytically derive the localization domain boundaries of the phonons in the limit of small cone angle and check our results with numerical results for eigenfunctions.

Surveying the free energy landscape of clusters of attractive colloidal spheres

Controlling the assembly of colloidal particles into specific structures has been a long-term goal of the soft materials community. Much can be learned about the process of self-assembly by examining the early stage assembly into clusters. For the simple case of hard spheres with short-range attractions, the rigid clusters of N particles (where N is small) have been enumerated theoretically and tested experimentally. Less is known, however, about how the free energy landscapes are altered when the inter-particle potential is long-ranged. In this work, we demonstrate how adaptive biasing in molecular simulations may be used to pinpoint shifts in the stability of colloidal clusters as the inter-particle potential is varied. We also discuss the generality of our techniques and strategies for application to related molecular systems.

Experimental Evidence of Thermal-Like Behavior in Dense Granular Suspensions

We experimentally investigate the statistical behavior of a model two-dimensional granular system undergoing stationary sedimentation. Buoyant cylindrical particles are rotated in a liquid-filled drum, thus confined in a harmonic centripetal potential with tunable curvature, which competes with gravity to produce various stationary states: though heterogeneous, the packing fraction of the system can be tuned from fully dispersed to crystallized as the rotation rate is increased. We show that this dynamical system is in mechanical equilibrium in the confining potential and exhibits a thermal-like behavior, where the granular pressure and the packing fraction are related through an equation of state. We obtain an expression of the equation of state allowing us to probe the nature of the hydrodynamic interactions between the particles. This description is valid in the whole range of the physical parameters we investigated and reveals a buoyant energy scale that we interpret as an effective temperature. We finally discuss the behavior of our system at high packing fractions and the relevance of the equation of state to the liquid-solid phase transition.

Inhomogeneous assembly of driven nematic colloids

We present a quantitative analysis of the nonequilibrium assembly of colloidal particles dispersed in a nematic liquid crystal. The driven particles assemble into reconfigurable circular clusters by liquid-crystal-enabled electrokinetic phenomena generated by an AC electric field that provides propulsion along the local director. We identify the coexistence of different aggregation states, including a central, jammed core, where short-range elastic attraction dominates, surrounded by a liquid-like corona where particles retain their mobility but reach a mechanical equilibrium that we rationalize in terms of a balance between centripetal phoretic drive and pairwise repulsion. An analysis of the compressible liquid-like region reveals a linear density profile that can be tuned with the field frequency, and a bond-orientational order that reaches a maximum at intermediate packing densities, where elastic effects are minimized. Since the phoretic propulsion force acts also on assembled particles, we compute the mechanical pressure and show that a hard-disk equation of state can be used to describe the assembly of this driven system.

Assembly of colloidal particles in solution

Advances in both top-down and bottom-up syntheses of a wide variety of complex colloidal building blocks and also in methods of controlling their assembly in solution have led to new and interesting forms of highly controlled soft matter. In particular, top-down lithographic methods of producing monodisperse colloids now provide precise human-designed control over their sub-particle features, opening up a wide range of new possibilities for assembly structures that had been previously limited by the range of shapes available through bottom-up methods. Moreover, an increasing level of control over anisotropic interactions between these colloidal building blocks, which can be tailored through local geometries of sub-particle features as well as site-specific surface modifications, is giving rise to new demonstrations of massively parallel off-chip self-assembly of specific target structures with low defect rates. In particular, new experimental realizations of hierarchical self-assembly and control over the chiral purity of resulting assembly structures have been achieved. Increasingly, shape-dependent, shape-complementary, and roughness-controlled depletion attractions between non-spherical colloids are being used in novel ways to create assemblies that go far beyond early examples, such as fractal clusters formed by diffusion-limited and reaction-limited aggregation of spheres. As self-assembly methods have progressed, a wide variety of advanced directed assembly methods have also been developed; approaches based on microfluidic control and applying structured electromagnetic fields are particularly promising.

Phase diagram of Janus particles: The missing dimension of pressure anisotropy

Brownian dynamics simulations of single-patch Janus particles under sedimentation equilibrium reveal that the phases found at fixed temperature and volume fraction are extremely sensitive to small changes in lateral box dimension. We trace this sensitivity to an uncontrolled parameter, namely, the pressure component parallel to the hexagonally ordered layers formed through sedimentation. We employ a flexible-cell constant-pressure scheme to achieve explicit control over this usually overlooked parameter, enabling the estimation of phase behavior under given pressure anisotropy. Our results show an increase in the stability range of an orientationally ordered lamellar phase with lateral layer compression and suggest a novel mechanism to control solid-solid phase transitions with negligible change in system volume, thus showing prospect for design of novel structures and switchable crystals from anisotropic building blocks.

Local rotational symmetry in the packing of uniform spheres

Local rotational symmetry (LRS) of a particulate system is important for understanding its structure and phase transition. However, how to properly characterize LRS for this system is still a challenge as the system normally includes both ordered and disordered local structures. Herein, based on the so-called common neighbour subcluster (CNS), we proposed a method to characterize the LRS of uniform spheres packings with the packing fraction ρ ranging within 0.20 and 0.74. It was found that different fold LRSs coexist in most packings, and their maximum degree increases at ρ < 0.64, except for the 2-fold LRS held by 6-sphere CNS that continuously increases to form the fcc crystal at ρ = 0.74. The overall LRS involving all the CNSs monotonically increases with two critical changes at ρ = (0.35-0.40) and 0.64; the evolution of individual LRSs held by specific CNS groups critically changes at ρ ≈ (0.35-0.40), 0.50, 0.55-0.60, and 0.64. The physics corresponding to these critical changes has also been discussed. The findings will significantly enrich the understanding of the structural symmetry of materials including atoms and particles.

Sedimentation stacking diagrams of binary mixtures of thick and thin hard rods

We use Onsager theory and the local density approximation to study sedimentation-diffusion equilibrium density profiles of binary mixtures of thick and thin hard rods. We construct stacking diagrams for three diameter ratios, and find that even a simple spindle-shaped phase diagram with only isotropic-nematic demixing can lead to counter-intuitive stacking sequences such as an isotropic phase sandwiched between two nematic phases. For the most complex phase diagram considered here, we find sixteen distinct stacking sequences, including several with five sedimented layers. By adding sedimentation paths to composition-pressure and density-density phase diagrams and calculating density and composition profiles, we show that conclusions about bulk phase diagrams of binary mixtures on the basis of sedimentation-diffusion equilibria should be drawn warily.

Dynamic, Directed Self-Assembly of Nanoparticles via Toggled Interactions

Crystals self-assembled from nanoparticles have useful properties such as optical activity and sensing capability. During fabrication, however, gelation and glassification often leave these materials arrested in defective or disordered metastable states. This is a key difficulty preventing adoption of self-assembled nanoparticle materials at scale. Processes which suppress kinetic arrest and defect formation while accelerating growth of ordered materials are essential for bottom-up approaches to creating nanomaterials. Dynamic, directed self-assembly processes in which the interactions between self-assembling components are actuated temporally offer one promising methodology for accelerating and controlling bottom-up growth of nanostructures. In this article, we show through simulation and theory how time-dependent, periodically toggled interparticle attractions can avoid kinetic barriers and yield well-ordered crystalline domains for a dispersion of nanoparticles interacting via a short-ranged, isotropic potential. The growth mechanism and terminal structure of the dispersion are controlled by parameters of the toggling protocol. This control allows for selection of processes that yield rapid self-assembled, low defect crystals. Although self-assembly via periodically toggled attractions is inherently unsteady and out-of-equilibrium, its outcome is predicted by a first-principles theory of nonequilibrium thermodynamics. The theory necessitates equality of the time average of pressure and chemical potential in coexisting phases of the dispersion. These quantities are evaluated using well known equations of state. The phase behavior predicted by this theory agrees well with measurements made in Brownian dynamics simulations of sedimentation equilibrium and homogeneous nucleation. The theory can easily be extended to model dynamic self-assembly directed by other toggled conservative force fields.

Depletion, melting and reentrant solidification in mixtures of soft and hard colloids

We present extensive experimental and theoretical investigations on the structure, phase behavior, dynamics and rheology of model soft-hard colloidal mixtures realized with large, multiarm star polymers as the soft component and smaller, compact stars as the hard one. The number and length of the arms in star polymers control their softness, whereas the size ratio, the overall density and the composition are additional parameters varied for the mixtures. A coarse-grained theoretical strategy is employed to predict the structure of the systems as well as their ergodicity properties on the basis of mode coupling theory, for comparison with rheological measurements on the samples. We discovered that dynamically arrested star-polymer solutions recover their ergodicity upon addition of colloidal additives. At the same time the system displays demixing instability, and the binodal of the latter meets the glass line in a way that leads, upon addition of a sufficient amount of colloidal particles, to an arrested phase separation and reentrant solidification. We present evidence for a subsequent solid-to-solid transition well within the region of arrested phase separation, attributed to a hard-sphere-mixture type of glass, due to osmotic shrinkage of the stars at high colloidal particle concentrations. We systematically investigated the interplay of star functionality and size ratio with glass melting and demixing, and rationalized our findings by the depletion of the big stars due to the smaller colloids. This new depletion potential in which, contrary to the classic colloid-polymer case, the hard component depletes the soft one, has unique and novel characteristics and allows the calculation of phase diagrams for such mixtures. This work covers a broad range of soft-hard colloidal mixture compositions in which the soft component exceeds the hard one in size and provides general guidelines for controlling the properties of such complex mixtures.

Clusters in sedimentation equilibrium for an experimental hard-sphere-plus-dipolar Brownian colloidal system

In this work, we use structure and dynamics in sedimentation equilibrium, in the presence of gravity, to examine, via confocal microscopy, a Brownian colloidal system in the presence of an external electric field. The zero field equation of state (EOS) is hard sphere without any re-scaling of particle size, and the hydrodynamic corrections to the long-time self-diffusion coefficient are quantitatively consistent with the expected value for hard spheres. Care is taken to ensure that both the dimensionless gravitational energy, which is equivalent to a Peclet number Peg, and dipolar strength Λ are of order unity. In the presence of an external electric field, anisotropic chain-chain clusters form; this cluster formation manifests itself with the appearance of a plateau in the diffusion coefficient when the dimensionless dipolar strength Λ ~ 1. The structure and dynamics of this chain-chain cluster state is examined for a monodisperse system for two particle sizes.

Solidification of a Charged Colloidal Dispersion Investigated Using Microfluidic Pervaporation

We investigate the dynamics of solidification of a charged colloidal dispersion using an original microfluidic technique referred to as micropervaporation. This technique exploits pervaporation within a microfluidic channel to extract the solvent of a dilute colloidal dispersion. Pervaporation concentrates the colloids in a controlled way up to the tip of the channel until a wet solid made of closely packed colloids grows and invades the microfluidic channel. For the charged dispersion under study, we however evidence a liquid to solid transition (LST) preceding the formation of the solid, owing to the presence of long-range electrostatic interactions. This LST is associated with the nucleation and growth of domains confined in the channel. These domains are then compacted anisotropically up to forming a wet solid of closely packed colloids. This solid then invades the whole channel as in directional drying with a growth rate which depends on the microfluidic geometry. In the final steps of the solidification, we observed the occurrence of cracks and shear bands, the delamination of the wet solid from the channel walls, and its invasion by a receding air front. Interestingly, this air front follows specific patterns within the solid which reveal different microscopic colloidal organizations.

Directing assembly of DNA-coated colloids with magnetic fields to generate rigid, semiflexible, and flexible chains

We report the formation of colloidal macromolecules consisting of chains of micron-sized paramagnetic particles assembled using a magnetic field and linked with DNA. The interparticle spacing and chain flexibility were controlled by varying the magnetic field strength and the linker spring constant. Variations in the DNA lengths allowed for the generation of chains with an improved range of flexibility as compared to previous studies. These chains adopted the rigid-rod, semiflexible, and flexible conformations that are characteristic of linear polymer systems. These assembly techniques were investigated to determine the effects of the nanoscale DNA linker properties on the properties of the microscale colloidal chains. With stiff DNA linkers (564 base pairs) the chains were only stable at moderate to high field strengths and produced rigid chains. For flexible DNA linkers (8000 base pairs), high magnetic field strengths caused the linkers to be excluded from the gap between the particles, leading to a transition from very flexible chains at low field strengths to semiflexible chains at high field strengths. In the intermediate range of linker sizes, the chains exhibited predictable behavior, demonstrating increased flexibility with longer DNA linker length or smaller linking field strengths. This study provides insight into the process of directed assembly using magnetic fields and DNA by precisely tuning the components to generate colloidal analogues of linear macromolecular chains.

Phase behavior of Janus colloids determined by sedimentation equilibrium

We investigate the phase behavior of short-range interacting isotropic particles and single-patch Janus particles via simulations of sedimentation equilibrium, which allows for a rapid assessment of the equation of state and phase behavior directly from simulation. The methodology is tested against results by traditional methods and is found to yield good agreement for isotropic interactions. The method is then used to study single-patch Janus particles with different interaction strengths and patch sizes with particle area coverage greater than ∼0.63. Our results show an interplay between translational and orientational order. We observe a lamellar phase, a fluid phase and a rotator close-packed structure. The lamellar phase is shown to have a different range of stability than previously observed in simulation studies for systems of similar and longer-ranged interactions.

Inter-particle correlations in a hard-sphere colloidal suspension with polymer additives investigated by Spin Echo Small Angle Neutron Scattering (SESANS)

Using a neutron scattering technique that measures a statistically-averaged density correlation function in real space rather than the conventional reciprocal-space structure factor, we have measured correlations between poly(methyl-methacrylate) (PMMA) colloidal particles of several sizes suspended in decalin. The new method, called Spin Echo Small Angle Neutron Scattering (SESANS) provides accurate information about particle composition, including the degree of solvent penetration into the polymer brush grafted on to the PMMA spheres to prevent aggregation. It confirms for particles, between 85 nm and 150 nm in radius that inter-particle correlations closely follow the Percus-Yevick hard-sphere model when the colloidal volume-fraction is between 30% and 50% provided the volume-fraction is used as a fitted parameter. No particle aggregation occurs in these systems. When small amounts of polystyrene are added as a depletant to a concentrated suspension of PMMA particles, short-range clustering of the particles occurs and there is an increase in the frequency of near-neighbor contacts. Within a small range of depletant concentration, near-neighbor correlations saturate and large aggregates with power law density correlations are formed. SESANS clearly separates the short- and long-range correlations and shows that, in this case, the power-law correlations are visible for inter-particle distances larger than roughly two particle diameters. In some cases, aggregate sizes are within our measurement window, which can extend out to 16 microns in favorable cases. We discuss the advantages of SESANS for measurements of the structure of concentrated colloidal systems and conclude that the method offers several important advantages.

Settled and unsettled issues in particle settling

Colloid sedimentation has played a seminal role in the development of statistical physics thanks to the celebrated experiments by Perrin, which provided a concrete demonstration of molecular reality and gave strong support to Einstein's theory of Brownian motion. This review, which mostly focuses on settling at low Peclét number, where Brownian fluctuations are dominant, aims to show that a lot more can be learnt both from the sedimentation equilibrium and from the particle settling dynamics of a wide class of systems, ranging from simple colloids to mesogenic suspensions, from soft solids to active particles and living organisms. At the same time, the occurrence of unexpected and surprising effects brings about challenging questions in statistical and fluid mechanics that make sedimentation an exciting field of research.

Sedimentation dynamics and equilibrium profiles in multicomponent mixtures of colloidal particles

In this paper we give a general theoretical framework that describes the sedimentation of multicomponent mixtures of particles with sizes ranging from molecules to macroscopic bodies. Both equilibrium sedimentation profiles and the dynamic process of settling, or its converse, creaming, are modeled. Equilibrium profiles are found to be in perfect agreement with experiments. Our model reconciles two apparently contradicting points of view about buoyancy, thereby resolving a long-lived paradox about the correct choice of the buoyant density. On the one hand, the buoyancy force follows necessarily from the suspension density, as it relates to the hydrostatic pressure gradient. On the other hand, sedimentation profiles of colloidal suspensions can be calculated directly using the fluid density as apparent buoyant density in colloidal systems in sedimentation-diffusion equilibrium (SDE) as a result of balancing gravitational and thermodynamic forces. Surprisingly, this balance also holds in multicomponent mixtures. This analysis resolves the ongoing debate of the correct choice of buoyant density (fluid or suspension): both approaches can be used in their own domain. We present calculations of equilibrium sedimentation profiles and dynamic sedimentation that show the consequences of these insights. In bidisperse mixtures of colloids, particles with a lower mass density than the homogeneous suspension will first cream and then settle, whereas particles with a suspension-matched mass density form transient, bimodal particle distributions during sedimentation, which disappear when equilibrium is reached. In all these cases, the centers of the distributions of the particles with the lowest mass density of the two, regardless of their actual mass, will be located in equilibrium above the so-called isopycnic point, a natural consequence of their hard-sphere interactions. We include these interactions using the Boublik-Mansoori-Carnahan-Starling-Leland (BMCSL) equation of state. Finally, we demonstrate that our model is not limited to hard spheres, by extending it to charged spherical particles, and to dumbbells, trimers and short chains of connected beads.

Direct measurement of the free energy of aging hard sphere colloidal glasses

The nature of the glass transition is one of the most important unsolved problems in condensed matter physics. The difference between glasses and liquids is believed to be caused by very large free energy barriers for particle rearrangements; however, so far it has not been possible to confirm this experimentally. We provide the first quantitative determination of the free energy for an aging hard sphere colloidal glass. The determination of the free energy allows for a number of new insights in the glass transition, notably the quantification of the strong spatial and temporal heterogeneity in the free energy. A study of the local minima of the free energy reveals that the observed variations are directly related to the rearrangements of the particles. Our main finding is that the probability of particle rearrangements shows a power law dependence on the free energy changes associated with the rearrangements similar to the Gutenberg-Richter law in seismology.

Structure and dynamics studies of concentrated micrometer-sized colloidal suspensions

We present an experimental study of the structural and dynamical properties of concentrated suspensions of different sized polystyrene microspheres dispersed in glycerol for volume fraction concentrations between 10% and 20%. The static structure, probed with ultrasmall-angle X-ray scattering, shows a behavior very similar to that of hard spheres. The equilibrium dynamics is probed with ultrasmall-angle X-ray scattering-X-ray photon correlation spectroscopy, a new technique that overcomes the limits of visible light-scattering techniques imposed by multiple scattering and is suitable for studies of optically opaque materials containing micrometer-sized structures. We found that the intensity autocorrelation functions are better described by a stretched exponential function and microspheres in a concentrated suspension move collectively. We also found that the inverse of the effective diffusion coefficients displays a peak with respect to the scattering vector that resembles the peaks in the static structure factors, which indicates that a long-lived, low free-energy state exists. The relaxation time is approximately inversely related to scattering vector, a behavior consistent with models that describe the dynamics in terms of random, local structural arrangements in disordered media.

Nanosphere templated continuous PEDOT:PSS films with low percolation threshold for application in efficient polymer solar cells

Nanometer-sized monodisperse polystyrene nanospheres (PS NS) were designed as an opal template for the formation of three-dimensionally continuous poly(3,4-ethylenedioxythiophene):poly(styrene sulfonate) (PEDOT:PSS) films. The resultant films were successfully applied as the anode buffer layer (ABL) to produce highly efficient polymer solar cells (PSCs) with enhanced stability. The conductivity of the PS NS-PEDOT:PSS films was maintained up to ø(PS) = 0.75-0.80, indicating that the formation of continuous PEDOT:PSS films using PS NS templates was successful. To demonstrate the applicability of the PS NS-PEDOT:PSS film for organic electronics, the PS NS-PEDOT:PSS films were used as ABLs in two different PSCs: P3HT:PCBM and P3HT:OXCBA. The photovoltaic performances of both PSCs were maintained up to ø(PS) = 0.8. In particular, the power conversion efficiency of the P3HT:OXCBA PSC with a PS NS-PEDOT:PSS ABL (ø(PS) = 0.8) was greater than 5% and the air stability of the device was significantly enhanced.

The unbearable heaviness of colloids: facts, surprises, and puzzles in sedimentation

Sedimentation has played a key role in the development of colloid science. In fact, it is because of the celebrated experiments by Perrin, yielding a concrete demonstration of molecular reality and giving strong support to Einstein's theory of Brownian motion, that colloids enter the realm of basic physics. Subsequent investigations have shown that a lot more can be learnt both from sedimentation equilibrium and from particle settling dynamics. These advances, together with new experimental approaches, will be reviewed in this paper. Yet, we shall also show that inquiring about gravity settling is far from being a closed matter: for instance, the concept of buoyancy for a settling colloidal mixture is far from being obvious. Moreover, sedimentation holds novel surprises, such as colloidal inflations and settling disasters, showing that a simple external field like gravity may induce mind-boggling, and theoretically challenging effects.

Polymeric dispersants delay sedimentation in colloidal asphaltene suspensions

Asphaltenes, among the heaviest components of crude oil, can become unstable under a variety of conditions and precipitate and sediment out of solution. In this report, we present sedimentation measurements for a system of colloidal scale asphaltene particles suspended in heptane. Adding dispersants to the suspension can improve the stability of the system and can mediate the transition from a power-law collapse in the sedimentation front to a rising front. Additional dispersant beyond a crossover concentration can cause a significant delay in the dynamics. Dynamic light scattering measurements suggest that the stabilization provided by the dispersants may occur through a reduction of both the size and polydispersity of the asphaltene particles in suspension.

Consolidation of charged colloids during drying

We consider the drying of latex dispersions containing submicrometer-sized particles dispersed in water. It is well known that the consolidation of colloidal particles is influenced by a number of factors such as particle size and shape and interparticle potential. In this work, we focus on the effect of surface charge on the consolidation front. Recent experimental and theoretical investigations on the sedimentation of charged colloidal spheres have shown that the large mass difference between noninteracting colloids and ions sets up a macroscopic electric field, thereby enhancing the diffusivity of the particles and resulting in an inflated sedimentation profile. Our experimental measurements of the concentration profile during drying-induced consolidation also reveal similar charge effects. We present a model for the consolidation of charged particles that accounts for the presence of an induced external electric field. As expected, the predicted particle diffusivity is enhanced by the onset of the electric field at low particle concentration. Fluorescence and bright-field microscopy were used to detect the particle concentration variation in a dispersion dried in a capillary, and the measured profile agrees with the prediction confirming the influence of particle charge on consolidation.

Interfacial colloidal crystallization via tunable hydrogel depletants

We demonstrate an approach using temperature-dependent hydrogel depletants to thermoreversibly tune colloidal attraction and interfacial colloidal crystallization. Total internal reflection and video microscopy are used to measure temperature-dependent depletion potentials between approximately 2 microm silica colloids and surfaces as mediated by approximately 0.2 microm poly-N-isopropylacrylamide (PNIPAM) hydrogel particles. Measured depletion potentials are modeled using the Asakura-Oosawa theory while treating PNIPAM depletants as swellable hard spheres. Monte Carlo simulations using the measured potentials predict reversible, quasi-2D crystallization and melting at approximately 27 degrees C in quantitative agreement with video microscopy images of measured microstructures (i.e., radial distribution functions) over the temperature range of interest (20-29 degrees C). Additional measurements of short-time self-diffusivities display excellent agreement with predicted diffusivities by considering multibody hydrodynamic interactions and using a swellable hard sphere model for the PNIPAM solution viscosity. Our findings demonstrate the ability to quantitatively measure, model, and manipulate kT-scale depletion attraction and phase behavior as a means of formally engineering interfacial colloidal crystallization.

Breakdown of the Yukawa model in de-ionized colloidal suspensions

We study effective colloidal interactions in de-ionized colloidal mixtures through sedimentation-diffusion equilibrium. We derive a coarse-grained effective model (EM) and compare its density profiles with those of the computationally much more expensive primitive model (PM) of colloids and counterions in gravity. The EM, which contains not only standard pairwise screened-Coulomb interactions, but also explicit many-body effects by means of a so-called volume term, can quantitatively account for all observed sedimentation phenomena such as lifting of colloids to high altitudes, segregation into layers in mixtures, and floating of heavy colloids on top of lighter ones. Without the volume term there is no quantitative agreement between the PM and EM, even in the present high-temperature limit of interest, showing that de-ionized colloidal suspensions cannot be described by a pairwise Yukawa model.

Why is random close packing reproducible?

We link the thermodynamics of colloidal suspensions to the statistics of regular and random packings. Random close packing has defied a rigorous definition yet, in three dimensions, there is near universal agreement on the volume fraction at which it occurs. We conjecture that the common value of phi{rcp} approximately 0.64 arises from a divergence in the rate at which accessible states disappear. We relate this rate to the equation of state for a hard-sphere fluid on a metastable, noncrystalline branch.

Tunable colloids: control of colloidal phase transitions with tunable interactions

Systems of spherical colloidal particles mimic the thermodynamics of atomic crystals. Control of interparticle interactions in colloids, which has recently begun to be extensively exploited, gives rise to rich phase behaviours as well as crystal structures with nanoscale and micron-scale lattice spacings. This provides model systems in which to study fundamental problems in condensed matter physics, such as the dynamics of crystal nucleation and melting, and the nature of the glass transition, at experimentally accessible lengthscales and timescales. Tunable control of these interactions provides reversible control. This will enable quantitative studies of phase transition kinetics as well as the creation of advanced materials with switchability of function and properties.

Gravitational stability of suspensions of attractive colloidal particles

Colloidal suspensions are susceptible to gravitationally induced phase separation. This can be mitigated by the formation of a particle network caused by depletion attraction. The effectiveness of this network in supporting the buoyant weight of the suspension can be characterized by its compressional modulus. We measure the compressional modulus for emulsion networks induced by depletion attraction and present a model that quantitatively predicts their gravitational stability. We also determine the relationship between the strength of the depletion attraction and the magnitude of the compressional modulus.

A new generalization of the Carnahan-Starling equation of state to additive mixtures of hard spheres

We introduce an expansion of the equation of state for additive hard-sphere mixtures in powers of the total packing fraction with coefficients which depend on a set of weighted densities used in scaled particle theory and fundamental measure theory. We demand that the mixture equation of state recovers the quasiexact Carnahan-Starling [J. Chem. Phys. 51, 635 (1969)] result in the case of a one-component fluid and show from thermodynamic considerations and consistency with an exact scaled particle relation that the first and second orders of the expansion lead unambiguously to the Boublik-Mansoori-Carnahan-Starling-Leland [J. Chem. Phys. 53, 471 (1970); J. Chem. Phys. 54, 1523 (1971)] equation and the extended Carnahan-Starling equation introduced by Santos et al. [Mol. Phys. 96, 1 (1999)]. In the third order of the expansion, our approach allows us to define a new equation of state for hard-sphere mixtures which we find to be more accurate than the former equations when compared to available computer simulation data for binary and ternary mixtures. Using the new mixture equation of state, we calculate expressions for the surface tension and excess adsorption of the one-component fluid at a planar hard wall and compare its predictions to available simulation data.

Crystallization of colloidal hard spheres under gravity

Using grand canonical Monte Carlo simulations, we study the crystallization of colloidal hard spheres under gravity. More specifically, we investigate the nature of the freezing transition as a function of gravity and chemical potential of the hard spheres. We find a discontinuous freezing transition where several fluid layers close to the bottom of the sample freeze simultaneously, i.e., at the same chemical potential. We also find that the number of layers that freezes at the same chemical potential decreases for higher gravitational field strength. Upon increasing the chemical potential further, the crystalline film thickness increases continuously.

Nonequilibrium sedimentation of colloids on the particle scale

We investigate sedimentation of model hard-sphere-like colloidal dispersions confined in horizontal capillaries using laser scanning confocal microscopy, dynamical density functional theory, and Brownian dynamics computer simulations. For homogenized initial states we obtain quantitative agreement of the results from the respective approaches for the time evolution of the one-body density distribution and the osmotic pressure on the walls. We demonstrate that single-particle information can be obtained experimentally in systems that were initialized further out of equilibrium such that complex lateral patterns form.

Sedimentation of charged colloids: the primitive model and the effective one-component approach

Sedimentation-diffusion equilibrium density profiles of suspensions of charge-stabilized colloids are calculated theoretically and by Monte Carlo (MC) simulations, both for a one-component model of colloidal particles interacting through pairwise screened-Coulomb repulsions and for a three-component model of colloids, cations, and anions with unscreened-Coulomb interactions. We focus on a state point for which experimental measurements are available [C. P. Royall, J. Phys.: Condens Matter 17, 2315 (2005)]. Despite the apparently different picture that emerges from the one- and three-component models (repelling colloids pushing each other to high altitude in the former, versus a self-generated electric field that pushes the colloids up in the latter), we find similar colloidal density profiles for both models from theory as well as simulation, thereby suggesting that these pictures represent different viewpoints of the same phenomenon. The sedimentation profiles obtained from an effective one-component model by MC simulations and theory, together with MC simulations of the multicomponent primitive model are consistent among themselves, but differ quantitatively from the results of a theoretical multicomponent description at the Poisson-Boltzmann level. We find that for small and moderate colloid charge the Poisson-Boltzmann theory gives profiles in excellent agreement with the effective one-component theory if a smaller effective charge is used. We attribute this discrepancy to the poor treatment of correlations in the Poisson-Boltzmann theory.

Gravity-induced liquid crystal phase transitions of colloidal platelets

The influence of gravity on a suspension of sterically stabilized colloidal gibbsite platelets is studied. An initially isotropic-nematic biphasic sample of such a suspension develops a columnar phase on the bottom on prolonged standing. This phenomenon is described using a simple osmotic compression model. We performed Monte Carlo simulations of cut spheres with aspect ratio L/D=1/15 and took data from the literature to supply the equations of state required for the model. We find that the model describes the observed three-phase equilibrium quite well.

Density functional theory for hard-sphere mixtures: the White Bear version mark II

In the spirit of the White Bear version of fundamental measure theory we derive a new density functional for hard-sphere mixtures which is based on a recent mixture extension of the Carnahan-Starling equation of state. In addition to the capability to predict inhomogeneous density distributions very accurately, like the original White Bear version, the new functional improves upon consistency with an exact scaled-particle theory relation in the case of the pure fluid. We examine consistency in detail within the context of morphological thermodynamics. Interestingly, for the pure fluid the degree of consistency of the new version is not only higher than for the original White Bear version but also higher than for Rosenfeld's original fundamental measure theory.

The density profile of hard sphere liquid system under gravity

The density profile of hard sphere liquid under gravity is calculated by using density functional theory and Monte Carlo simulation method. The two methods give consistent results for a wide range of parameters. Meanwhile, the validity range of the density functional theory is also established. The results are quite different from the barometric height distribution rho(z)=rho(0) exp(-zL(G)) in almost all cases studied, which indicates that the interaction between particles plays an important role in the density distribution under external fields. Moreover, the crystallizing phenomenon is also predicted at the bottom part of the system under strong gravitation.

Layering in sedimentation of suspensions of charged colloids: simulation and theory

We study the equilibrium sediment of a multicomponent system of charged colloids using primitive model Monte Carlo simulations, which include counterions explicitly. We find separation of the different colloidal components into almost pure layers, where colloids with large charge-to-mass ratio sediment higher in the sample. This effect appears due to a competition between ionic entropy, gravitational energy, and electrostatic energy. Our simulations provide a direct confirmation of recent theoretical predictions on the sedimentation of multicomponent mixtures of charged colloids in regimes with relatively low total densities and low colloidal charges. To explore the limitations of the theory we perform simulations at higher total densities for monodisperse and multicomponent systems and at stronger electrostatic couplings by increasing the colloidal charge for monodisperse suspensions. We find good agreement between theory and simulation when the colloidal charge is increased in the monodisperse case. However, we find deviations between simulations and theory upon increasing the total densities in the monodisperse and multicomponent systems. The density profiles obtained from simulations are more homogeneous than those predicted by theory. The spontaneous formation of layered structures predicted by the theory and found by simulation can serve as a useful tool to separate different components from a mixture of charged colloids.

Long-ranged electrostatic repulsion and crystallization of emulsion droplets in an ultralow dielectric medium supercritical carbon dioxide

Electrostatic repulsion stabilizes micrometer-sized water droplets with spacings greater than 10 microm in an ultralow dielectric medium, CO2 (epsilon = 1.5), at elevated pressures. The morphology of the water/CO2 emulsion is characterized by optical microscopy and laser diffraction as a function of height. The counterions, stabilized with a nonionic, highly branched, stubby hydrocarbon surfactant, form an extremely thick double layer with a Debye screening length of 8.9 microm. As a result of the balance between electrostatic repulsion and the downward force due to gravity, the droplets formed a hexagonal crystalline lattice at the bottom of the high-pressure cell with spacings of over 10 microm. The osmotic pressure, calculated by solving the Poisson-Boltzmann equation in the framework of the Wigner-Seitz cell model, is in good agreement with that determined from the sedimentation profile measured by laser diffraction. Thus, the long-ranged stabilization of the emulsion may be attributed to electrostatic stabilization. The ability to form new types of colloids in CO2 with electrostatic stabilization is beneficial because steric stabilization is often unsatisfactory because of poor solvation of the stabilizers.