Binary Colloidal Mixtures Research Articles

Rheology of high density glass of binary colloidal mixtures in unentangled polymer melts

We explore the rheology of high density glasses formed by binary colloidal mixtures in unentangled polyethylene glycol melts with a molecular weight of 400. A particle size ratio δ = dl/ds = 4.8 is chosen to ensure that mixing results in a reduction in composite rheology without phase separation for a fixed high total volume fraction, ϕc. We explore frequency dependent linear viscoelastic behaviors, yielding and shear-thickening behaviors, and study properties as a function of the volume fraction ratio of the large particles, R. We characterize the cross-over volume fractions which denote the onset of transient particle localization, ϕx, and the maximum packing fractions, ϕm, and find that both are non-monotonic functions of R, with ϕm/ϕx being a constant as R is varied from 0 to 1. Hard sphere scaling fails to capture the effects of particle size when R = 0 and R = 1, demonstrating that, even for these low molecular weight oligomers, polymer absorption and alterations of polymer configurations modify pair potentials away from being solely volume exclusion in nature. Changes in linear rheology, yielding behavior and shear-thickening are discussed in terms of a pseudo one-component model that depends on the dimensionless volume fraction ϕ* = (ϕm − ϕx)/(ϕm − ϕc).

Arrested demixing opens route to bigels

Understanding and, ultimately, controlling the properties of amorphous materials is one of the key goals of material science. Among the different amorphous structures, a very important role is played by colloidal gels. It has been only recently understood that colloidal gels are the result of the interplay between phase separation and arrest. When short-ranged attractive colloids are quenched into the phase-separating region, density fluctuations are arrested and this results in ramified amorphous space-spanning structures that are capable of sustaining mechanical stress. We present a mechanism of aggregation through arrested demixing in binary colloidal mixtures, which leads to the formation of a yet unexplored class of materials--bigels. This material is obtained by tuning interspecies interactions. Using a computer model, we investigate the phase behavior and the structural properties of these bigels. We show the topological similarities and the geometrical differences between these binary, interpenetrating, arrested structures and their well-known monodisperse counterparts, colloidal gels. Our findings are supported by confocal microscopy experiments performed on mixtures of DNA-coated colloids. The mechanism of bigel formation is a generalization of arrested phase separation and is therefore universal.

The nature of the laning transition in two dimensions

If a binary colloidal mixture is oppositely driven by an external field, a transition towards a laned state occurs at sufficiently large drives, where particles driven alike form elongated structures (‘lanes’) characterized by a large correlation length ξ along the drive. Here we perform extensive Brownian dynamics computer simulations on a two-dimensional equimolar binary Yukawa system driven by a constant force that acts oppositely on the two species. We systematically address finite-size effects on lane formation by exploring large systems up to 262 144 particles under various boundary conditions. It is found that the correlation length ξ along the field depends exponentially on the driving force (or Peclet number). Conversely, in a finite system, ξ reaches a fraction of the system size at a driving force which is logarithmic in the system size, implying massive finite-size corrections. For a fixed finite drive, ξ does not diverge in the thermodynamic limit. Therefore, though laning has a signature as a sharp transition in a finite system, it is a smooth crossover in the thermodynamic limit.

Using self-driven microswimmers for particle separation

Microscopic self-propelled swimmers capable of autonomous navigation through complex environments provide appealing opportunities for localization, pick-up and delivery of micro-and nanoscopic objects. Inspired by motile cells and bacteria, man-made microswimmers have been fabricated, and their motion in patterned surroundings has been experimentally studied. We propose to use self-driven artificial microswimmers for separation of binary mixtures of colloids. We revealed different regimes of separation including one with a velocity inversion. Our finding could be of use for various biological and medical applications.

Doubled heterogeneous crystal nucleation in sediments of hard sphere binary-mass mixtures

Crystallization during the sedimentation process of a binary colloidal hard spheres mixture is explored by Brownian dynamics computer simulations. The two species are different in buoyant mass but have the same interaction diameter. Starting from a completely mixed system in a finite container, gravity is suddenly turned on, and the crystallization process in the sample is monitored. If the Peclet numbers of the two species are both not too large, crystalline layers are formed at the bottom of the cell. The composition of lighter particles in the sedimented crystal is non-monotonic in the altitude: it is first increasing, then decreasing, and then increasing again. If one Peclet number is large and the other is small, we observe the occurrence of a doubled heterogeneous crystal nucleation process. First, crystalline layers are formed at the bottom container wall which are separated from an amorphous sediment. At the amorphous-fluid interface, a secondary crystal nucleation of layers is identified. This doubled heterogeneous nucleation can be verified in real-space experiments on colloidal mixtures.

Effects of hydrodynamic interactions in binary colloidal mixtures driven oppositely byoscillatory external fields

The collective dynamics in a binary mixture of colloidal particles which are driven inopposite directions by an external oscillatory field is examined by computer simulations intwo spatial dimensions. Both Brownian dynamics (BD) computer simulations, which ignoresolvent-mediated hydrodynamic interactions between the colloidal particles, andmulti-particle collision dynamics (MPCD) simulations, which include hydrodynamicinteractions, are employed. We first review recent results obtained by BD. Depending onthe driving frequency and amplitude, lane formation parallel to the drive and bandformation perpendicular to the drive occur. Band formation is stable only in a finitewindow of oscillation frequencies and driving strengths and is taken over by lane formationif the driving force is increased or the oscillation frequency is decreased. MPCDsimulations, on the other hand, reveal that band formation is blurred by hydrodynamicinteractions. During the front collisions of oppositely driven particles there is a strongvortical movement of the solvent which tends to mix particles and broaden theinterface of the bands. This can either lead to a novel intermittent dynamicalbehaviour or to band rupture into local clusters. These effects, which are absentfor BD, are characterized by the strengths of the enstrophy and its spectrum.We finally discuss possible experimental realizations of the models employed.

Ultrasoft Colloid-Polymer Mixtures: Structure and Phase Diagram

Binary mixtures of ultrasoft colloids and linear polymer chains were investigated by small-angle neutron scattering and liquid state theory. We show that experimental data can be described by employing recently developed effective interactions between the colloid and the polymer chains, in which both components are modeled as point particles in a coarse-grained approach, in which the monomers have been traced out. Quantitative, parameter-free agreement between experiment and theory for the pair correlations, the phase behavior and the concentration dependence of the interaction length is achieved.

Probing glassy states in binary mixtures of soft interpenetrable colloids

We present experimental evidence confirming the recently established rich dynamic statediagram of asymmetric binary mixtures of soft colloidal spheres. These mixtures consist ofglassy suspensions of large star polymers to which different small stars are added at varyingconcentrations. Using rheology and dynamic light scattering measurements along with asimple phenomenological analysis, we show the existence of re-entrance and multiple glassystates, which exhibit distinct features. Cooperative diffusion, as a probe for star arminterpenetration, is proven to be sensitive to the formation of the liquid pockets whichsignal the melting of the large-star-glass upon addition of small stars. These resultsprovide ample opportunities for tailoring the properties of soft colloidal glasses.

Renormalized jellium mean-field approximation for binary mixtures of charged colloids

In this work the renormalized jellium model of colloidal suspensions, originally proposed by Trizac and Levin [Phys. Rev. E 69, 031403 (2004)], is extended to study mechanisms of charge renormalization in binary mixtures of charged colloids. We here apply our recent reformulation that introduces the requirement of self-consistency directly into the Poisson-Boltzmann equation, i.e., the background charge is explicitly replaced by the effective one, thus facilitating the whole charge renormalization scheme. We briefly discuss the reformulated model for monodisperse charged suspensions composed of either spheres or rods. In particular, we put emphasis on the effects of the surface charge variation, mixture composition, and particle size on the charge regulation of charge-stabilized colloidal suspensions.

Phase diagrams of binary mixtures of patchy colloids with distinct numbers and types of patches: The empty fluid regime

We investigate the effect of distinct bonding energies on the onset of criticality of low functionality fluid mixtures. We focus on mixtures of particles with two and three patches as this includes the mixture where "empty" fluids were originally reported. In addition to the number of patches, the species differ in the type of patches or bonding sites. For simplicity, we consider that the patches on each species are identical: one species has three patches of type A and the other has two patches of type B. We have found a rich phase behavior with closed miscibility gaps, liquid-liquid demixing, and negative azeotropes. Liquid-liquid demixing was found to pre-empt the "empty" fluid regime, of these mixtures, when the AB bonds are weaker than the AA or BB bonds. By contrast, mixtures in this class exhibit "empty" fluid behavior when the AB bonds are stronger than at least one of the other two. Mixtures with bonding energies ε(BB) = ε(AB) and ε(AA) < ε(BB), were found to exhibit an unusual negative azeotrope.

Polymer Vesicles with a Colloidal Armor of Nanoparticles

The fabrication of polymer vesicles with a colloidal armor made from a variety of nanoparticles is demonstrated. In addition, it is shown that the armored supracolloidal structure can be postmodified through film-formation of soft polymer latex particles on the surface of the polymersome, hereby effectively wrapping the polymersome in a plastic bag, as well as through formation of a hydrogel by disintegrating an assembled polymer latex made from poly(ethyl acrylate-co-methacrylic acid) upon increasing the pH. Furthermore, ordering and packing patterns are briefly addressed with the aid of Monte Carlo simulations, including patterns observed when polymersomes are exposed to a binary mixture of colloids of different size.

Phase diagrams of binary mixtures of patchy colloids with distinct numbers of patches: the network fluid regime

We calculate the network fluid regime and phase diagrams of binary mixtures of patchy colloids, using Wertheim's first order perturbation theory and a generalization of Flory-Stockmayer's theory of polymerization. The colloids are modelled as hard spheres with the same diameter and surface patches of the same type, $A$. The only difference between species is the number of their patches -or functionality-, $f_A^{(1)}$ and $f_A^{(2)}$ (with $f_A^{(2)}>f_A^{(1)}$). We have found that the difference in functionality is the key factor controlling the behaviour of the mixture in the network (percolated) fluid regime. In particular, when $f_A^{(2)}\ge2f_A^{(1)}$ the entropy of bonding drives the phase separation of two network fluids which is absent in other mixtures. This changes drastically the critical properties of the system and drives a change in the topology of the phase diagram (from type I to type V) when $f_A^{(1)}>2$. The difference in functionality also determines the miscibility at high (osmotic) pressures. If $f_A^{(2)}-f_A^{(1)}=1$ the mixture is completely miscible at high pressures, while closed miscibility gaps at pressures above the highest critical pressure of the pure fluids are present if $f_A^{(2)}-f_A^{(1)}>1$. We argue that this phase behaviour is driven by a competition between the entropy of mixing and the entropy of bonding, as the latter dominates in the network fluid regime.

Hydrodynamic Rayleigh-Taylor-like instabilities in sedimenting colloidal mixtures

We study the sedimentation of an initially inhomogeneous distribution of binary colloidal mixtures confined to a slit using a coarse-grained hybrid molecular dynamics and stochastic rotation dynamics simulation technique. This technique allows us to take into account the Brownian motion and hydrodynamic interactions between colloidal particles in suspensions. The sedimentation of such systems results in the formation of Rayleigh-Taylor-like hydrodynamic instabilities, and here we examine both the process of the formation and the evolution of the instability, as well as the structural organization of the colloids, depending on the properties of the binary mixture. We find that the structural properties of the swirls that form as a consequence of the instability depend greatly on the relative magnitudes of the Peclet numbers, and much less on the composition of the mixture. We also calculate the spatial colloid velocity correlation functions which allow us to follow the time evolution of the instability and the time dependence of the characteristic correlation length. Finally, we calculate the growth rates of the unstable modes both directly from our simulation data, and also using a theoretical approach, finding good agreement.

Depletion interactions in binary mixtures of repulsive colloids

Acceptance ratio method, which has been used to calculate the depletion potential in binary hard-sphere mixtures, is extended to the computation of the depletion potential of non-rigid particle systems. The repulsive part of the Lennard-Jones pair potential is used as the direct pair potential between the non-rigid particles. The depletion potential between two big spheres immersed in a suspension of small spheres is determined with the acceptance ratio method through the application of Monte Carlo simulation. In order to check the validity of this method, our results are compared with those obtained by the Asakura-Oosawa approximation, and by Varial expansion approach, and by molecular dynamics simulation. The total effective potential and the depth of its potential well are computed for various softness parameters of the direct pair potential.

Impact of Polymer Graft Characteristics and Evaporation Rate on the Formation of 2-D Nanoparticle Assemblies

The effect of polymer functionalization on the two-dimensional (2-D) assembly of uniform as well as highly asymmetric binary colloidal mixtures with both neutral and incompatible polymer grafts is presented. In ordered assemblies of uniform particle brush systems, the observed size-segregation is analogous to that of hard sphere colloidal systems, suggesting that lateral capillary interactions are responsible for the crystal nucleation in the early stages of assembly formation. Structure formation in binary blends of asymmetric particle brush systems is found to be strongly influenced by three major energetic contributions, that is, the interfacial energies associated with the particle brush/air boundaries, the interfacial energies between the distinct brush components, as well as the elastic energy associated with the stretching of the polymer-brush to fill the interstitial regions within locally ordered particle arrays. Our results demonstrate the relevance of capillary interactions in soft particle brush systems but also highlight distinctive differences in the order formation as compared to hard sphere colloidal systems. In particular, the compliant response of grafted polymer chains is shown to promote phase separation in binary blends of incompatible and asymmetric colloidal systems.

Self-assembly in binary mixtures of dipolar colloids: Molecular dynamics simulations

Dipolar colloid particles tend to align end-to-end and self-assemble into micro- and nanostructures, including gels and cocrystals depending on external conditions. We use molecular dynamics computer simulation to explore the phase behavior including formation, structure, crystallization, and/or gelation of binary systems of colloid particles with permanent dipole moments. Particle-particle interactions are modeled with a discontinuous potential. The phase diagrams of an equimolar binary mixture of dipolar colloid particles with different diameter ratios and different dipole moment ratios are calculated in the temperature-volume fraction plane. Several types of phases are found in our simulations: ordered phases including face centered cubic (fcc), hexagonal-close packed (hcp), and body-centered tetragonal (bct) at high volume fractions, and fluid, string-fluid, and gel phases at low volume fractions. We also find several coexistence regions containing ordered phases including fcc(a)+fcc(b), fcc(a)+hcp(b), hcp(a)+hcp(b), bct(a)+bct(b), and bct(a)+bct(b)+large voids where a and b are the two species. Two novel aspects of our results are the appearance of a bicontinuous gel consisting of two interpenetrating networks--one formed by chains of particles with high dipole moment and the other formed by chains of particles with low dipole moment, and cocrystals of large and small dipolar colloid particles.

Tailoring the phonon band structure in binary colloidal mixtures

We analyze the phonon spectra of periodic structures formed by two-dimensional mixtures of dipolar colloidal particles. These mixtures display an enormous variety of complex ordered configurations [J. Fornleitner, Soft Matter 4, 480 (2008)], allowing for the systematic investigation of the ensuing phonon spectra and the control of phononic gaps. We show how the shape of the phonon bands and the number and width of the phonon gaps can be controlled by changing the susceptibility ratio, the composition, and the mass ratio between the two components.

Liquid crystalline phases and demixing in binary mixtures of shape-anisometric colloids

A theoretical model of shape-anisometric particles embedded in a cubic lattice is formulated for binary mixtures combining rod-like, plate-like and spherical particles. The model aims at providing a tool for the prediction and interpretation of complex phase behavior in a variety of liquid crystalline colloids, biological and macromolecular systems. Introducing just repulsive interactions among the particles, a rich variety of phase structures and multiphasic equilibria is obtained, including isotropic, nematic, lamellar and columnar phases, demixing into phases of the same or different symmetries and structural microsegregation of the different species of the mixture within the same phase.

Nonadditivity in the effective interactions of binary charged colloidal suspensions

Based on primitive model computer simulations with explicit microions, we calculate theeffective interactions in a binary mixture of charged colloids with species A and Bfor different size and charge ratios. An optimal pairwise interaction is obtainedby fitting the many-body effective forces. This interaction is close to a Yukawa(or Derjaguin–Landau–Verwey–Overbeek (DLVO)) pair potential but the ABcross-interaction is different from the geometric mean of the two direct AA and BBinteractions. As a function of charge asymmetry, the corresponding nonadditivityparameter is first positive, then significantly negative and is then positive again. Wefinally show that an inclusion of nonadditivity within an optimal effective Yukawamodel gives better predictions for the fluid pair structure than DLVO theory.

Crystal Structures of Two-Dimensional Binary Mixtures of Dipolar Colloids in Tilted External Magnetic Fields

We employ genetic algorithms, which allow for an efficient search for the global minimum of energy landscapes, to investigate the ordered equilibrium structures formed by a binary mixture of anisotropic dipolar particles confined on a plane, under the influence of an external magnetic field. The anisotropy is introduced by titling the external field with respect to the interface, and it is tuned by the degree of the tilt angle. For small tilt angles, the structures obtained for perpendicular fields are slightly perturbed but beyond system-dependent values of the tilt, novel structures emerge, characterized by the formation of complex arrangements of chains that lie parallel to the in-plane projection of the field.