Stratification and Size Segregation of Ternary and Polydisperse Colloidal Suspensions during Drying.

We investigate the drying process of three-component and polydisperse colloidal suspensions using Brownian dynamics simulations. We have previously reported (Phys. Rev. Lett. 2016, 116, 118301) on the drying of binary mixtures. For binary mixtures, we found that a gradient of colloidal osmotic pressure develops during drying and that this leads to the final film being stratified with a layer of smaller particles on top of a layer of larger particles. Here, we find that stratification by size is very general and also occurs in ternary and polydisperse mixtures. We name the segregation effect colloidal diffusiophoresis. In particular, we show that by changing the composition of a ternary mixture, different stratification morphologies can be achieved and hence the film properties can be tuned. In polydisperse spheres, colloidal diffusiophoresis leads to enrichment in the large particles at the bottom part of the film, whereas the top part is enriched with smaller particles. This segregation means that in the final film, the particle size distribution depends on height. Thus, the properties of the film will then depend on height. We propose a model that predicts a power-law dependence of the phoretic velocity on particle size. Results from the model and simulation show a good agreement.

Erratum: Dynamic Stratification in Drying Films of Colloidal Mixtures [Phys. Rev. Lett. 116, 118301 (2016)].

This corrects the article DOI: 10.1103/PhysRevLett.116.118301.

Publisher's Note: Dynamic Stratification in Drying Films of Colloidal Mixtures [Phys. Rev. Lett. 116, 118301 (2016)].

This corrects the article DOI: 10.1103/PhysRevLett.116.118301.

Dynamic Stratification in Drying Films of Colloidal Mixtures.

In simulations and experiments, we study the drying of films containing mixtures of large and small colloidal particles in water. During drying, the mixture stratifies into a layer of the larger particles at the bottom with a layer of the smaller particles on top. We developed a model to show that a gradient in osmotic pressure, which develops dynamically during drying, is responsible for the segregation mechanism behind stratification.

Superadiabatic forces in Brownian many-body dynamics.

Theoretical approaches to nonequilibrium many-body dynamics generally rest upon an adiabatic assumption, whereby the true dynamics is represented as a sequence of equilibrium states. Going beyond this simple approximation is a notoriously difficult problem. For the case of classical Brownian many-body dynamics, we present a simulation method that allows us to isolate and precisely evaluate superadiabatic correlations and the resulting forces. Application of the method to a system of one-dimensional hard particles reveals the importance for the dynamics, as well as the complexity, of these nontrivial out-of-equilibrium contributions. Our findings help clarify the status of dynamical density functional theory and provide a rational basis for the development of improved theories.

Monte Carlo computer simulations and electron microscopy of colloidal cluster formation via emulsion droplet evaporation.

We consider a theoretical model for a binary mixture of colloidal particles and spherical emulsion droplets. The hard sphere colloids interact via additional short-ranged attraction and long-ranged repulsion. The droplet-colloid interaction is an attractive well at the droplet surface, which induces the Pickering effect. The droplet-droplet interaction is a hard-core interaction. The droplets shrink in time, which models the evaporation of the dispersed (oil) phase, and we use Monte Carlo simulations for the dynamics. In the experiments, polystyrene particles were assembled using toluene droplets as templates. The arrangement of the particles on the surface of the droplets was analyzed with cryogenic field emission scanning electron microscopy. Before evaporation of the oil, the particle distribution on the droplet surface was found to be disordered in experiments, and the simulations reproduce this effect. After complete evaporation, ordered colloidal clusters are formed that are stable against thermal fluctuations. Both in the simulations and with field emission scanning electron microscopy, we find stable packings that range from doublets, triplets, and tetrahedra to complex polyhedra of colloids. The simulated cluster structures and size distribution agree well with the experimental results. We also simulate hierarchical assembly in a mixture of tetrahedral clusters and droplets, and find supercluster structures with morphologies that are more complex than those of clusters of single particles.

The van Hove distribution function for brownian hard spheres: dynamical test particle theory and computer simulations for bulk dynamics.

We describe a test particle approach based on dynamical density functional theory (DDFT) for studying the correlated time evolution of the particles that constitute a fluid. Our theory provides a means of calculating the van Hove distribution function by treating its self and distinct parts as the two components of a binary fluid mixture, with the "self " component having only one particle, the "distinct" component consisting of all the other particles, and using DDFT to calculate the time evolution of the density profiles for the two components. We apply this approach to a bulk fluid of Brownian hard spheres and compare to results for the van Hove function and the intermediate scattering function from Brownian dynamics computer simulations. We find good agreement at low and intermediate densities using the very simple Ramakrishnan-Yussouff [Phys. Rev. B 19, 2775 (1979)] approximation for the excess free energy functional. Since the DDFT is based on the equilibrium Helmholtz free energy functional, we can probe a free energy landscape that underlies the dynamics. Within the mean-field approximation we find that as the particle density increases, this landscape develops a minimum, while an exact treatment of a model confined situation shows that for an ergodic fluid this landscape should be monotonic. We discuss possible implications for slow, glassy, and arrested dynamics at high densities.

Crystal structures in binary hard-sphere colloid-droplet mixtures with patchy cross interactions.

A binary mixture of droplets and patchy colloids, where patches are arranged in tetrahedral symmetry, is studied with Metropolis Monte Carlo simulations. The colloidal patches attract droplets, while both the colloid-colloid and the droplet-droplet interactions are hard sphere like. We find stable crystal structures with atomic analogs ZnS, CaF_{2}, and fcc or hcp (face centered cubic or hexagonal close packed) of the droplets coexisting with a dispersed fluid of the colloids. The simulated crystal structures agree well with those predicted by close-packing calculations for an intermediate range of droplet-colloid size ratios. A discrepancy between the simulations and theoretical predictions occurs at low and high size ratios. The results of the simulations for mixtures with anisotropic colloid-droplet interactions reveal a richer phase diagram, with ZnS-gas and ZnS-fluid coexistence, as compared to the isotropic case. For the example of a square planar patch arrangement, we find a particular crystal structure, consisting of two interpenetrating fcc or hcp lattices with right bond angles. Such a structure has no known atomic analog. Our study of generic models of anisotropic colloid-droplet mixtures could provide a promising way towards the fabrication of novel and complex colloidal structures.

Gel formation in suspensions of oppositely charged colloids: mechanism and relation to the equilibrium phase diagram.

We study gel formation in a mixture of equally-sized oppositely charged colloids both experimentally and by means of computer simulations. Both the experiments and the simulations show that the mechanism by which a gel is formed from a dilute, homogeneous suspension is an interrupted gas-liquid phase separation. Furthermore, we use Brownian dynamics simulations to study the relation between gel formation and the equilibrium phase diagram. We find that, regardless of the interaction range, an interrupted liquid-gas phase separation is observed as the system is quenched into a state point where the gas-liquid separation is metastable. The structure of the gel formed in our experiments compares well with that of a simulated gel, indicating that gravity has only a minor influence on the local structure of this type of gel. This is supported by the experimental evidence that gels squeezed or stretched by gravity have similar structures, as well as by the fact that gels do not collapse as readily as in the case of colloid-polymer mixtures. Finally, we check whether or not crystallites are formed in the gel branches; we find crystalline domains for the longer ranged interactions and for moderate quenches to the metastable gas-liquid spinodal regime.

Crystallization and gelation in colloidal systems with short-ranged attractive interactions.

We systematically study the relationship between equilibrium and nonequilibrium phase diagrams of a system of short-ranged attractive colloids. Using Monte Carlo and Brownian dynamics simulations we find a window of enhanced crystallization that is limited at high interaction strength by a slowing down of the dynamics and at low interaction strength by the high nucleation barrier. We find that the crystallization is enhanced by the metastable gas-liquid binodal by means of a two-stage crystallization process. First, the formation of a dense liquid is observed and second the crystal nucleates within the dense fluid. In addition, we find at low colloid packing fractions a fluid of clusters, and at higher colloid packing fractions a percolating network due to an arrested gas-liquid phase separation that we identify with gelation. We find that this arrest is due to crystallization at low interaction energy and it is caused by a slowing down of the dynamics at high interaction strength. Likewise, we observe that the clusters which are formed at low colloid packing fractions are crystalline at low interaction energy, but glassy at high interaction energy. The clusters coalesce upon encounter.

Assembly of One-Patch Colloids into Clusters via Emulsion Droplet Evaporation.

We study the cluster structures of one-patch colloidal particles generated by droplet evaporation using Monte Carlo simulations. The addition of anisotropic patch-patch interaction between the colloids produces different cluster configurations. We find a well-defined category of sphere packing structures that minimize the second moment of mass distribution when the attractive surface coverage of the colloids χ is larger than 0 . 3 . For χ < 0 . 3 , the uniqueness of the packing structures is lost, and several different isomers are found. A further decrease of χ below 0 . 2 leads to formation of many isomeric structures with less dense packings. Our results could provide an explanation of the occurrence of uncommon cluster configurations in the literature observed experimentally through evaporation-driven assembly.

Phase behavior and structure of model colloid-polymer mixtures confined between two parallel planar walls.

Using Gibbs ensemble Monte Carlo simulations and density functional theory we investigate the fluid-fluid demixing transition in inhomogeneous colloid-polymer mixtures confined between two parallel plates with separation distances between one and ten colloid diameters covering the complete range from quasi-two-dimensional to bulklike behavior. We use the Asakura-Oosawa-Vrij model in which colloid-colloid and colloid-polymer interactions are hard-sphere like, while the pair potential between polymers vanishes. Two different types of confinement induced by a pair of parallel walls are considered--namely, either through two hard walls or through two semipermeable walls that repel colloids but allow polymers to freely penetrate. For hard (semipermeable) walls we find that the capillary binodal is shifted towards higher (lower) polymer fugacities and lower (higher) colloid fugacities as compared to the bulk binodal; this implies capillary condensation (evaporation) of the colloidal liquid phase in the slit. A macroscopic treatment is provided by a symmetric Kelvin equation for general binary mixtures based on the proximity in chemical potentials of statepoints at capillary coexistence and the reference bulk coexistence. Results for capillary binodals compare well with those obtained from the classic version of the Kelvin equation due to [Evans and Marini Bettolo Marconi, J. Chem. Phys. 86, 7138 (1987)] and are quantitatively accurate away from the fluid-fluid critical point, even at small wall separations. However, the significant shift of the critical polymer fugacity towards higher values upon increasing confinement, as found in simulations, is not reproduced. For hard walls the density profiles of polymers and colloids inside the slit display oscillations due to packing effects for all statepoints. For semipermeable walls either similar structuring or flat profiles are found, depending on the statepoint considered.

Effect of many-body interactions on the bulk and interfacial phase behavior of a model colloid-polymer mixture.

We study a model suspension of sterically stabilized colloidal particles and nonadsorbing ideal polymer coils, both in bulk and adsorbed against a planar hard wall. By integrating out the degrees of freedom of the polymer coils, we derive a formal expression for the effective one-component Hamiltonian of the colloids. We employ an efficient Monte Carlo simulation scheme for this mixture based on the exact effective colloid Hamiltonian; i.e., it incorporates all many-body interactions. The many-body character of the polymer-mediated effective interactions between the colloids yields bulk phase behavior and adsorption phenomena that differ substantially from those found for pairwise simple fluids. We determine the phase behavior for size ratios q=sigma(p)/sigma(c)=1, 0.6, and 0.1, where sigma(c) and sigma(p) denote the diameters of the colloids and polymer coils, respectively. For q=1 and 0.6, we find both a fluid-solid and a stable colloidal gas-liquid transition with an anomalously large bulk liquid regime caused by the many-body interactions. We compare the phase diagrams obtained from simulations with the results of the free-volume approach and with direct simulations of the true binary mixture. Although we did not simulate the polymer coils explicitly, we are able to obtain the three partial structure factors and radial distribution functions. We compare our results with those obtained from density functional theory and the Percus-Yevick approximation. We find good agreement between all results for the structure. We also study the mixture in contact with a single hard wall for q=1. Upon approach of the gas-liquid binodal, we find far from the triple point, three layering transitions in the partial wetting regime.

Phase behaviour of hard spheres confined between parallel hard plates: manipulation of colloidal crystal structures by confinement.

We study the phase behaviour of hard spheres confined between two parallel hard plates using extensive computer simulations. We determine the full equilibrium phase diagram for arbitrary densities and plate separations from one to five hard-sphere diameters using free energy calculations. We find a first-order fluid-solid transition, which corresponds to either capillary freezing or melting depending on the plate separation. The coexisting solid phase consists of crystalline layers with either triangular ([Formula: see text]) or square ([Formula: see text]) symmetry. Increasing the plate separation, we find a sequence of crystal structures from [Formula: see text], where n is the number of crystal layers, in agreement with experiments on colloids. At high densities, the transition between square to triangular phases is interrupted by intermediate structures, e.g., prism, buckled, and rhombic phases.

Minimal model for dynamic bonding in colloidal transient networks.

We investigate a model for colloidal network formation using Brownian dynamics computer simulations. Hysteretic springs establish transient bonds between particles with repulsive cores. If a bonded pair of particles is separated by a cutoff distance, the spring vanishes and reappears only if the two particles contact each other. We present results for the bond lifetime distribution and investigate the properties of the van Hove dynamical two-body correlation function. The model displays crossover from fluidlike dynamics, via transient network formation, to arrested quasistatic network behavior.

Assembly of open clusters of colloidal dumbbells via droplet evaporation.

We investigate the behavior of a mixture of asymmetric colloidal dumbbells and emulsion droplets by means of kinetic Monte Carlo simulations. The evaporation of the droplets and the competition between droplet-colloid attraction and colloid-colloid interactions lead to the formation of clusters built up of colloid aggregates with both closed and open structures. We find that stable packings and hence complex colloidal structures can be obtained by changing the relative size of the colloidal spheres and/or their interfacial tension with the droplets.

Particle conservation in dynamical density functional theory.

We present the exact adiabatic theory for the dynamics of the inhomogeneous density distribution of a classical fluid. Erroneous particle number fluctuations of dynamical density functional theory are absent, both for canonical and grand canonical initial conditions. We obtain the canonical free energy functional, which yields the adiabatic interparticle forces of overdamped Brownian motion. Using an exact and one of the most advanced approximate hard core free energy functionals, we obtain excellent agreement with simulations. The theory applies to finite systems in and out of equilibrium.

Fast Assembly of Gold Nanoparticles in Large-Area 2D Nanogrids Using a One-Step, Near-Infrared Radiation-Assisted Evaporation Process.

When fabricating photonic crystals from suspensions in volatile liquids using the horizontal deposition method, the conventional approach is to evaporate slowly to increase the time for particles to settle in an ordered, periodic close-packed structure. Here, we show that the greatest ordering of 10 nm aqueous gold nanoparticles (AuNPs) in a template of larger spherical polymer particles (mean diameter of 338 nm) is achieved with very fast water evaporation rates obtained with near-infrared radiative heating. Fabrication of arrays over areas of a few cm(2) takes only 7 min. The assembly process requires that the evaporation rate is fast relative to the particles' Brownian diffusion. Then a two-dimensional colloidal crystal forms at the falling surface, which acts as a sieve through which the AuNPs pass, according to our Langevin dynamics computer simulations. With sufficiently fast evaporation rates, we create a hybrid structure consisting of a two-dimensional AuNP nanoarray (or "nanogrid") on top of a three-dimensional polymer opal. The process is simple, fast, and one-step. The interplay between the optical response of the plasmonic Au nanoarray and the microstructuring of the photonic opal results in unusual optical spectra with two extinction peaks, which are analyzed via finite-difference time-domain method simulations. Comparison between experimental and modeling results reveals a strong interplay of plasmonic modes and collective photonic effects, including the formation of a high-order stopband and slow-light-enhanced plasmonic absorption. The structures, and hence their optical signatures, are tuned by adjusting the evaporation rate via the infrared power density.

pH-Switchable Stratification of Colloidal Coatings: Surfaces "On Demand".

Stratified coatings are used to provide properties at a surface, such as hardness or refractive index, which are different from underlying layers. Although time-savings are offered by self-assembly approaches, there have been no methods yet reported to offer stratification on demand. Here, we demonstrate a strategy to create self-assembled stratified coatings, which can be switched to homogeneous structures when required. We use blends of large and small colloidal polymer particle dispersions in water that self-assemble during drying because of an osmotic pressure gradient that leads to a downward velocity of larger particles. Our confocal fluorescent microscopy images reveal a distinct surface layer created by the small particles. When the pH of the initial dispersion is raised, the hydrophilic shells of the small particles swell substantially, and the stratification is switched off. Brownian dynamics simulations explain the suppression of stratification when the small particles are swollen as a result of reduced particle mobility, a drop in the pressure gradient, and less time available before particle jamming. Our strategy paves the way for applications in antireflection films and protective coatings in which the required surface composition can be achieved on demand, simply by adjusting the pH prior to deposition.

Wall-fluid and liquid-gas interfaces of model colloid-polymer mixtures by simulation and theory.

We perform a study of the interfacial properties of a model suspension of hard sphere colloids with diameter sigma(c) and nonadsorbing ideal polymer coils with diameter sigma(p) . For the mixture in contact with a planar hard wall, we obtain from simulations the wall-fluid interfacial free energy, gamma(wf) , for size ratios q =sigma(p)/sigma(c) =0.6 and 1, using thermodynamic integration, and study the (excess) adsorption of colloids, Gamma(c) , and of polymers, Gamma(p) , at the hard wall. The interfacial tension of the free liquid-gas interface, gamma(lg) , is obtained following three different routes in simulations: (i) from studying the system size dependence of the interfacial width according to the predictions of capillary wave theory, (ii) from the probability distribution of the colloid density at coexistence in the grand canonical ensemble, and (iii) for state points where the colloidal liquid wets the wall completely, from Young's equation relating gamma(lg) to the difference of wall-liquid and wall-gas interfacial tensions, gamma(wl)-gamma(wg) . In addition, we calculate gamma(wf) ,Gamma(c) , and Gamma(p) using density functional theory and a scaled particle theory based on free volume theory. Good agreement is found between the simulation results and those from density functional theory, while the results from scaled particle theory quantitatively deviate but reproduce some essential features. Simulation results for gamma(lg) obtained from the three different routes are all in good agreement. Density functional theory predicts gamma(lg) with good accuracy for high polymer reservoir packing fractions, but yields deviations from the simulation results close to the critical point.