Binary Colloidal Mixtures Research Articles

Short-time self-diffusion in binary colloidal suspensions

The Brownian dynamics of a colloidal particle is consistently modified by the presence in the solvent of other particles of comparable size, whose effects on the particle diffusion coefficient cannot be attributed to a change of the effective solvent viscosity. So far, despite their impact on subjects ranging from microrheology to phoretic transport in crowded environments, a detailed experimental survey of these effects is still lacking. By exploiting the peculiar properties of fluorinated colloidal particle, we have performed an extensive dynamic light scattering (DLS) investigation of short-time self-diffusion in binary colloidal mixtures, focusing on systems where one of the two species (the “tracer” particles) is very diluted compared to the other one (the “host” particles). From the dependence on the host concentration of the DLS correlation function, we have obtained the first-order correction hs1s to the tracer single-particle diffusion coefficient, varying the tracer-to-host size ratio q in the range 0.2 ≤ q ≤ 2. Our results support the functional relation of hs1s on q proposed to account for the theoretical and numerical results for hard-sphere mixtures. However, hs1s seems to have a weaker dependence on the size ratio than theoretically predicted, possibly because of an imperfect matching of the suspensions we used for an ideal hard-sphere mixture. This may be due to the presence of a stabilizing surfactant layer on the particle surface that, although very thin, has significant effects on hydrodynamic lubrication forces.

Active Stratification of Colloidal Mixtures for Asymmetric Multilayers.

Stratified films offer high performance and multifunctionality, yet achieving fully stratified films remains a challenge. The layer-by-layer method, involving the sequential deposition of each layer, has been commonly utilized for stratified film fabrication. However, this approach is time-consuming, labor-intensive, and prone to leaving defects within the film. Alternatively, the self-stratification process exploiting a drying binary colloidal mixture is intensively developed recently, but it relies on strict operating conditions, typically yielding a heterogeneous interlayer. In this study, an active interfacial stratification process for creating completely stratified nanoparticle (NP) films is introduced. The technique leverages NPs with varying interfacial activity at the air-water interface. With the help of depletion pressure, the lateral compression of NP mixtures at the interface induces individual desorption of less interfacial active NPs into the subphase, while more interfacial active NPs remain at the interface. This simple compression leads to nearly perfect stratified NP films with controllability, universality, and scalability. Combined with a solvent annealing process, the active stratification process enables the fabrication of stratified films comprising a polymeric layer atop a NP layer. This work provides insightful implications for designing drug encapsulation and controlled release, as well as manufacturing transparent and flexible electrodes.

Speed-up of the collective dynamics induced by non-observable components in binary suspensions of highly charged colloids

By light scattering, we study the collective dynamics of binary mixtures of charged colloids at low ionic strength. The size asymmetry between colloids gives us access to the intermediate scattering function corresponding to the big colloids. We find that the global dynamic correlations relax faster as the number of small undetectable components increases, and Brownian Dynamics numerical simulations confirm this finding. From simulations, we identify that the gradual softening of interparticle correlations, as the number of small colloids increases, is at the origin of the weakening of the measured dynamic correlations. Furthermore, we put forward a semi-empirical scheme to estimate the hydrodynamic interactions, allowing us to improve the comparison between the dynamic light scattering data and numerical simulation results.

Lane formation in gravitationally driven colloid mixtures consisting of up to three different particle sizes.

Brownian dynamics simulations are utilized to study segregation phenomena far from thermodynamic equilibrium. In the present study, we expand upon the analysis of binary colloid mixtures and introduce a third particle species to further our understanding of colloidal systems. Gravitationally driven, spherical colloids immersed in an implicit solvent are confined in two-dimensional linear microchannels. The interaction between the colloids is modeled by the Weeks-Chandler-Andersen potential, and the confinement of the colloids is realized by hard walls based on the solution of the Smoluchowski equationin half space. In binary and ternary colloidal systems, a difference in the driving force is achieved by differing colloid sizes but fixed mass density. We observe for both the binary and ternary systems that a driving force difference induces a nonequilibrium phase transition to lanes. For ternary systems, we study the tendency of lane formation to depend on the diameter of the medium-sized colloids. Here we find a sweet spot for lane formation in ternary systems. Furthermore, we study the interaction of two differently sized colloids at the channel walls. Recently we observed that driven large colloids push smaller colloids to the walls. This results in small particle lanes at the walls at early simulation times. In this work we additionally find that thin lanes are unstable and dissolve over very long time frames. Furthermore, we observe a connection between lane formation and the nonuniform distribution of particles along the channel length. This nonuniform distribution occurs either alongside lane formation or in shared lanes (i.e., lanes consisting of two colloid types).

Effects of charge and size on the coadsorption of counterionic colloids in Gibbs monolayers

This study uses a coarse-grained Monte Carlo algorithm to model and simulate the coadsorption of a binary mixture of counterionic colloids in Gibbs monolayers. These monolayers form at a idealized air-water interface, with one non-soluble species confined at the interface and the second one partially soluble in the aqueous phase. The investigation focuses on the effect of colloidal size and charge on the thermodynamics and microstructure of the monolayer. We find that the composition of the monolayer evolves non-trivially with surface coverage, depending on the balance of steric and electrostatic forces. When the electrostatic interactions are weak, the soluble species is expelled from the monolayer upon compression, yielding a phase behaviour particularly sensitive to the relative size of the soluble and non-soluble colloids. By contrast, strong electrostatic interactions favour the stabilization of the soluble particles in the monolayer and the formation of quasi-equimolar fluids, with only a weak dependence on particle size. The combination of these phenomena results in the formation of a number of two-dimensional mesoscopic arrangements in the monolayer, ranging from diluted gas-phase behaviour to domains of aggregates and percolates, and to incipient crystalline structures.

Self-organization of active colloids mediated by chemical interactions.

Self-propelled colloidal particles exhibit rich non-equilibrium phenomena and have promising applications in fields such as drug delivery and self-assembled active materials. Previous experimental and theoretical studies have shown that chemically active colloids that consume or produce a chemical can self-organize into clusters with diverse characteristics depending on the effective phoretic interactions. In this paper, we investigate self-organization in systems with multiple chemical species that undergo a network of reactions and multiple colloidal species that participate in different reactions. Active colloids propelled by complex chemical reactions with potentially nonlinear kinetics can be realized using enzymatic reactions that occur on the surface of enzyme-coated particles. To demonstrate how the self-organizing behavior depends on the chemical reactions active colloids catalyze and their chemical environment, we consider first a single type of colloid undergoing a simple catalytic reaction, and compare this often-studied case with self-organization in binary mixtures of colloids with sequential reactions, and binary mixtures with nonlinear autocatalytic reactions. Our results show that in general active colloids at low particle densities can form localized clusters in the presence of bulk chemical reactions and phoretic attractions. The characteristics of the clusters, however, depend on the reaction kinetics in the bulk and on the particles and phoretic coefficients. With one or two chemical species that only undergo surface reactions, the space for possible self-organizations are limited. By considering the additional system parameters that enter the chemical reaction network involving reactions on the colloids and in the fluid, the design space of colloidal self-organization can be enlarged, leading to a variety of non-equilibrium structures.

Stability of binary colloidal mixtures of Au noble metal and ZnS semiconductor nanoparticles

Controlling the stability of colloidal nanoparticles in multicomponent systems, i.e., mixtures of colloids, is of vital importance for product formulations and separation processes of nanoparticles. However, very few studies are currently found in literature regarding the generation of binary colloids by mixing of colloidal nanoparticles, particularly small nanoparticles (< 20 nm). In this study, we report on the development of a stable binary colloid made of nanoparticles of different sizes and compositions. As a model system for this study, we mixed aqueous dispersions of gold nanoparticles (Au NPs) and ZnS quantum dots (QDs). We investigated the stability of Au NPs with three different surface ligands after mixing them with ZnS QDs, both before and after functionalization of the Au NPs with bis(p-sulfonatophenyl) phenylphosphine (BSPP). We used UV–visible spectroscopy as the primary method to monitor stability of nanoparticles in the binary mixture over time. We found out that the released thioglycerol and acetate from the surface of ZnS QDs to the binary mixture induces agglomeration in Au NPs. The surface chemistry and the purification process of Au NPs after their synthesis and surface treatment were identified as key parameters to regulate the stability in the mixture. Thus, we successfully achieved a stable mixture of BSPP-functionalized Au NPs with ZnS QDs as a model of a stable binary mixture. We believe that this study is important to stimulate research directed towards real-world multicomponent formulations including their characterization and the understanding of surface interactions.

Drying of sessile droplets of binary colloidal aqueous mixtures of carbon nanotubes and platelets of Laponite®

Drying of sessile droplets of binary colloidal aqueous mixtures of carbon nanotubes (CNT) and platelets of Laponite® (Lap) has been studied. The concentration of CNT was fixed at CCNT= 0.01% wt., and the relative concentration of Lap and CNT, was varied within x = CLap/CCNT= 0–2. Formation of the three different zones related to formation of the almost transparent round "enlightenment" in the center, outer “gray” ring, and thin “coffer” ring at the external boundary was detected. Observed effects were explained accounting for the effects of Lap on the facilitation of dispersion of CNT in aqueous systems.

Structural Color Mixing in Microcapsules through Exclusive Crystallization of Binary and Ternary Colloids.

Colloidal crystals are designed as photonic microparticles for various applications. However, conventional microparticles generally have only one stopband from a single lattice constant, which restricts the range of colors and optical codes available. Here, photonic microcapsules are created that contain two or three distinct crystalline grains, resulting in dual or triple stopbands that offer a wider range of colors through structural color mixing. To produce distinct colloidal crystallites from binary or ternary colloidal mixtures, the interparticle interaction is manipulated using depletion forces in double-emulsion droplets. Aqueous dispersions of binary or ternary colloidal mixtures in the innermost droplet are gently concentrated in the presence of a depletant and salt by imposing hypertonic conditions. Different-sized particles crystallize into their own crystals rather than forming random glassy alloys to minimize free energy. The average size of the crystalline grains can be adjusted with osmotic pressure, and the relative ratio of distinct grains can be controlled with the mixing ratio of particles. The resulting microcapsules with small grains and high surface coverage are almost optically isotropic and exhibit highly-saturated mixed structural colors and multiple reflectance peaks. The mixed color and reflectance spectrum are controllable with the selection of particle sizes and mixing ratios.

BINARY HARD-SPHERE COLLOID-DROPLET MIXTURES WITH THE PYRITE-TYPE STRUCTURE

We investigate the assembly of a binary mixture of patchy colloids and droplets into crystal structures by use of the space-filling principle and Metropolis Monte Carlo simulations. Here, colloids with six patches in an octahedral symmetry attract droplets, whereas the colloid-colloid and droplet-droplet pairwise interactions are purely hard-core repulsions. Within parameter space regions that allow for stable binary crystals, we find the formation of different structure types, which are colloidal analogs of the NaCl phase and pyrite (FeS2) phase, as a function of the droplet-to-colloid sphere diameter ratio. This finding is consistent with theoretical predictions. Notably, while the NaCl structure type is a commonly known structure of hard-sphere colloids and nanoparticles, the formation of the FeS2 structure type from colloidal dispersion has not been explored. Our approach suggests a potential route to obtain colloidal crystals with more complex structures.

Stability of Binary Colloidal Mixtures of Au Noble Metal and ZnS Semiconductor Nanoparticles

Stability of Binary Colloidal Mixtures of Au Noble Metal and ZnS Semiconductor Nanoparticles

Multiphase Coexistence in Binary Hard Colloidal Mixtures: Predictions from a Simple Algebraic Theory.

A general theoretical framework is proposed to quantify the thermodynamic properties of multicomponent hard colloidal mixtures. This framework is used to predict the phase behavior of mixtures of rods with spheres and rods with plates taking into account (liquid) crystal phases of both components. We demonstrate a rich and complex range of phase behaviors featuring a large variety of different multiphase coexistence regions, including two five-phase coexistence regions for hard rod/sphere mixtures, and even a six-phase equilibrium for hard rod/plate dispersions. The various multiphase coexistences featured in a particular mixture are in line with a recently proposed generalized phase rule and can be tuned through subtle variations of the particle shape and size ratio. Our approach qualitatively accounts for certain multiphase equilibria observed in rod/plate mixtures of clay colloids and will be a useful guide in tuning the phase behavior of shape-disperse mixtures in general.

Structural correlations and phase separation in binary mixtures of charged and neutral colloids.

Structural correlations between colloids in a binary mixture of charged and neutral spheres are calculated using computer simulations of the primitive model with explicit microions. For aqueous suspensions in a solvent of large dielectric constant, the traditional Derjaguin-Landau-Vervey-Overbeek (DLVO) theory of linear screening, supplemented with hard core interactions, reproduces the structural correlations obtained in the full primitive model quantitatively. However, for lower dielectric contrast, the increasing Coulomb coupling between the counterions and charged colloids results in strong deviations. We find a fluid-fluid phase separation into two regions either rich in charged or rich in neutral colloids, which is not reproduced by DLVO theory. Our results are verifiable in scattering or real-space experiments on charged-neutral mixtures of colloids or nanoparticles.

Determining depletion interactions by contracting forces.

Depletion forces are fundamental for determining the phase behavior of a vast number of materials and colloidal dispersions and have been used for the manipulation of in- and out-of-equilibrium thermodynamic states. The entropic nature of depletion forces is well understood; however, most theoretical approaches, and also molecular simulations, work quantitatively at moderate size ratios in much diluted systems since large size asymmetries and high particle concentrations are difficult to deal with. The existing approaches for integrating out the degrees of freedom of the depletant species may fail under these extreme physical conditions. Thus, the main goal of this contribution is to introduce a general physical formulation for obtaining the depletion forces even in those cases where the concentration of all species is relevant. We show that the contraction of the bare forces uniquely determines depletion interactions. Our formulation is tested by studying depletion forces in binary and ternary colloidal mixtures. We report here results for dense systems with total packing fractions of 45% and 55%. Our results open up the possibility of finding an efficient route to determine effective interactions at a finite concentration, even under non-equilibrium thermodynamic conditions.

A Deep Learning Framework Discovers Compositional Order and Self-Assembly Pathways in Binary Colloidal Mixtures.

Binary colloidal superlattices (BSLs) have demonstrated enormous potential for the design of advanced multifunctional materials that can be synthesized via colloidal self-assembly. However, mechanistic understanding of the three-dimensional self-assembly of BSLs is largely limited due to a lack of tractable strategies for characterizing the many two-component structures that can appear during the self-assembly process. To address this gap, we present a framework for colloidal crystal structure characterization that uses branched graphlet decomposition with deep learning to systematically and quantitatively describe the self-assembly of BSLs at the single-particle level. Branched graphlet decomposition is used to evaluate local structure via high-dimensional neighborhood graphs that quantify both structural order (e.g., body-centered-cubic vs face-centered-cubic) and compositional order (e.g., substitutional defects) of each individual particle. Deep autoencoders are then used to efficiently translate these neighborhood graphs into low-dimensional manifolds from which relationships among neighborhood graphs can be more easily inferred. We demonstrate the framework on in silico systems of DNA-functionalized particles, in which two well-recognized design parameters, particle size ratio and interparticle potential well depth can be adjusted independently. The framework reveals that binary colloidal mixtures with small interparticle size disparities (i.e., A- and B-type particle radius ratios of rA/rB = 0.8 to rA/rB = 0.95) can promote the self-assembly of defect-free BSLs much more effectively than systems of identically sized particles, as nearly defect-free BCC-CsCl, FCC-CuAu, and IrV crystals are observed in the former case. The framework additionally reveals that size-disparate colloidal mixtures can undergo nonclassical nucleation pathways where BSLs evolve from dense amorphous precursors, instead of directly nucleating from dilute solution. These findings illustrate that the presented characterization framework can assist in enhancing mechanistic understanding of the self-assembly of binary colloidal mixtures, which in turn can pave the way for engineering the growth of defect-free BSLs.

Power functional theory for many-body dynamics

The rich and diverse dynamics of particle-based systems ultimately originates from the coupling of their degrees of freedom via internal interactions. To arrive at a tractable approximation of such many-body problems, coarse-graining is often an essential step. Power functional theory provides a unique and microscopically sharp formulation of this concept. The approach is based on an exact one-body variational principle to describe the dynamics of both overdamped and inertial classical and quantum many-body systems. In equilibrium, density functional theory is recovered, and hence spatially inhomogeneous systems are described correctly. The dynamical theory operates on the level of time-dependent one-body correlation functions. Two- and higher-body correlation functions are accessible via the dynamical test particle limit and the nonequilibrium Ornstein-Zernike route. We describe the structure of this functional approach to many-body dynamics, including much background as well as applications to a broad range of dynamical situations, such as the van Hove function in liquids, flow in nonequilibrium steady states, motility-induced phase separation of active Brownian particles, lane formation in binary colloidal mixtures, and both steady and transient shear phenomena.

Structural correlations in highly asymmetric binary charged colloidal mixtures.

We explore structural correlations of strongly asymmetric mixtures of binary charged colloids within the primitive model of electrolytes considering large charge and size ratios of 10 and higher. Using computer simulations with explicit microions, we obtain the partial pair correlation functions between the like-charged colloidal macroions. Interestingly the big-small correlation peak amplitude is smaller than that of the big-big and small-small macroion correlation peaks, which is unfamiliar for additive repulsive interactions. Extracting optimal effective microion-averaged pair interactions between the macroions, we find that on top of non-additive Yukawa-like repulsions an additional shifted Gaussian attractive potential between the small macroions is needed to accurately reproduce their correct pair correlations. For small Coulomb couplings, the behavior is reproduced in a coarse-grained theory with microion-averaged effective interactions between the macroions. However, the accuracy of the theory deteriorates with increasing Coulomb coupling. We emphasize the relevance of entropic interactions exerted by the microions on the macroions. Our results are experimentally verifiable in binary mixtures of micron-sized colloids and like-charge nanoparticles.

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

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

Dynamics and phase behavior of two-dimensional size-asymmetric binary mixtures of core-softened colloids.

The self-assembly of binary colloidal mixtures provides a bottom-up approach to create novel functional materials. To elucidate the effect of composition, temperature, and pressure on the self-assembly behavior of size-asymmetric mixtures, we performed extensive dynamics simulations of a simple model of polymer-grafted colloids. We have used a core-softened interaction potential and extended it to represent attractive interactions between unlike colloids and repulsions between like colloids. Our study focused on size-asymmetric mixtures where the ratio between the sizes of the colloidal cores was fixed at σBσA=0.5. We have performed extensive simulations in the isothermal-isobaric and canonical (NVT) ensembles to elucidate the phase behavior and dynamics of mixtures with different stoichiometric ratios. Our simulation results uncovered a rich phase behavior, including the formation of hierarchical structures with many potential applications. For compositions where small colloids are the majority, sublattice melting occurs for a wide range of densities. Under these conditions, large colloids form a well-defined lattice, whereas small colloids can diffuse through the system. As the temperature is decreased, the small colloids localize, akin to a metal-insulator transition, with the small colloids playing a role similar to electrons. Our results are summarized in terms of phase diagrams.

Phase Behavior and Crystal Structure of Binary Mixtures of Droplets and Four-Patch Colloids

We report simulation studies on the phase behavior and crystal structures of anisotropic colloid–droplet binary mixtures. The droplets interact with the colloids at the patches of different geometr...