Colloid-polymer Mixtures Research Articles

Confocal imaging of confined quiescent and flowing colloid-polymer mixtures.

The behavior of confined colloidal suspensions with attractive interparticle interactions is critical to the rational design of materials for directed assembly(1-3), drug delivery(4), improved hydrocarbon recovery(5-7), and flowable electrodes for energy storage(8). Suspensions containing fluorescent colloids and non-adsorbing polymers are appealing model systems, as the ratio of the polymer radius of gyration to the particle radius and concentration of polymer control the range and strength of the interparticle attraction, respectively. By tuning the polymer properties and the volume fraction of the colloids, colloid fluids, fluids of clusters, gels, crystals, and glasses can be obtained(9). Confocal microscopy, a variant of fluorescence microscopy, allows an optically transparent and fluorescent sample to be imaged with high spatial and temporal resolution in three dimensions. In this technique, a small pinhole or slit blocks the emitted fluorescent light from regions of the sample that are outside the focal volume of the microscope optical system. As a result, only a thin section of the sample in the focal plane is imaged. This technique is particularly well suited to probe the structure and dynamics in dense colloidal suspensions at the single-particle scale: the particles are large enough to be resolved using visible light and diffuse slowly enough to be captured at typical scan speeds of commercial confocal systems(10). Improvements in scan speeds and analysis algorithms have also enabled quantitative confocal imaging of flowing suspensions(11-16,37). In this paper, we demonstrate confocal microscopy experiments to probe the confined phase behavior and flow properties of colloid-polymer mixtures. We first prepare colloid-polymer mixtures that are density- and refractive-index matched. Next, we report a standard protocol for imaging quiescent dense colloid-polymer mixtures under varying confinement in thin wedge-shaped cells. Finally, we demonstrate a protocol for imaging colloid-polymer mixtures during microchannel flow.

Confocal Imaging of Confined Quiescent and Flowing Colloid-polymer Mixtures

Confocal Imaging of Confined Quiescent and Flowing Colloid-polymer Mixtures

Phase behavior of active swimmers in depletants: molecular dynamics and integral equation theory.

We study the structure and phase behavior of a binary mixture where one of the components is self-propelling in nature. The interparticle interactions in the system are taken from the Asakura-Oosawa model for colloid-polymer mixtures for which the phase diagram is known. In the current model version, the colloid particles are made active using the Vicsek model for self-propelling particles. The resultant active system is studied by molecular dynamics methods and integral equation theory. Both methods produce results consistent with each other and demonstrate that the Vicsek model-based activity facilitates phase separation, thus, broadening the coexistence region.

Quantifying the effects of neglecting many-body interactions in coarse-grained models of complex fluids.

We describe a general simulation scheme for assessing the thermodynamic consequences of neglecting many-body effects in coarse-grained models of complex fluids. The method exploits the fact that the asymptote of a simple-to-measure structural function provides direct estimates of virial coefficients. Comparing the virial coefficients of an atomistically detailed system with those of a coarse-grained version described by pair potentials, permits the role of many-body effects to be quantified. The approach is applied to two models: (i) a size-asymmetrical colloid-polymer mixture, and (ii) a solution of star polymers. In the latter case, coarse-graining to an effective fluid described by pair potentials is found to neglect important aspects of the true behavior.

Flow-induced demixing of polymer-colloid mixtures in microfluidic channels

We employ extensive computer simulations to study the flow behavior of spherical, nanoscale colloids in a viscoelastic solvent under Poiseuille flow. The systems are confined in a slit-like microfluidic channel, and viscoelasticity is introduced explicitly through the inclusion of polymer chains on the same length scale as the dispersed solute particles. We systematically study the effects of flow strength and polymer concentration, and identify a regime in which the colloids migrate to the centerline of the microchannel, expelling the polymer chains to the sides. This behavior was recently identified in experiments, but a detailed understanding of the underlying physics was lacking. To this end, we provide a detailed analysis of this phenomenon and discuss ways to maximize its effectiveness. The focusing mechanism can be exploited to separate and capture particles at the sub-micrometer scale using simple microfluidic devices, which is a crucial task for many biomedical applications, such as cell counting and genomic mapping.

Computer simulation of heterogeneous nucleation of colloidal crystals at planar walls

A mini-review of the classical theory of heterogeneous nucleation at planar walls is given, and tests by Monte Carlo simulations for simple models of colloidal suspensions exhibiting a fluid-solid transition are described. This theory (due to Turnbull) assumes sphere-cap-shaped “sessile” droplets at the substrate, and the nucleation barrier that appears in the classical theory of homogeneous nucleation then is reduced by a factor depending on the Young contact angle. Various approximations inherent in this theory are examined: curvature corrections to the interfacial free energy of small droplets; neglect of anisotropy of the surface tension between crystal and fluid; neglect of corrections due to the line tension of the three-phase contact line; continuum rather than atomistic description. Also the problem of precise identification of the particles belonging (or not) to the “droplet” is discussed, and an alternative concept of extracting droplet properties from an analysis of finite size effects on phase coexistence in finite simulation boxes is explored. While the focus of our treatment is on the Asakura-Oosawa model of colloid polymer mixtures, also simple Ising/lattice gas models are considered to test some of these questions.

Effect of particle polydispersity on the structure and dynamics of complex formation between small particles and large polymer

The effect of particle polydispersity on the structure and dynamics of small silica particle–large polymer chain mixtures at low polymer concentration has been investigated. Two types of silica particles were used as model systems, having similar mean size, specific surface area and surface properties but differing substantially in size polydispersity. Mixtures of PEO with the polydisperse silica particles showed strong shear-thickening upon shaking, while mixtures of the same composition with the monodisperse silica did not. Fluorescence correlation spectroscopy revealed that larger flocs were formed in the polydisperse particle–PEO systems. Particle polydispersity was identified as the major factor accounting for these differences and a plausible mechanism was proposed based on the spatial distribution of the silica particles within the complexes. This work suggests that the rheological behavior of colloid–polymer mixtures can be dramatically modified by a simple change in particle polydispersity, rather than more involved surface modifications or the use of additives.

Computer simulations of structure, dynamics, and phase behavior of colloidal fluids in confined geometry and under shear

Using computer simulations, colloidal systems in different external fields are investigated. Colloid-polymer mixtures, described in terms of the Asakura-Oosawa (AO) model, are considered under strong confinement. Both in cylindrical and spherical confinement, the demixing transition of the three-dimensional AO model is rounded and, using Monte Carlo simulations, we analyze in detail the consequences of this rounding (occurrence of multi-domain states in cylindrical geometry, non-equivalence of conjugate ensembles due to different finite-size corrections in spherical geometry etc.). For the case of the AO model confined between two parallel walls, spinodal decomposition is studied using a combination of molecular dynamics simulation and the multiparticle collision dynamics method. This allows us to investigate the influence of hydrodynamic interactions on the domain growth during spinodal decomposition. For a binary glass-forming Yukawa mixture, non-linear active micro-rheology is considered, i.e. a single particle is pulled through a deeply supercooled liquid. The diffusion dynamics of the pulled particle is analyzed in terms of the van Hove correlation function. Finally, the Yukawa mixture in the glass state, confined between walls, is studied under the imposition of a uniform shear stress. Below and around the yield stress, persistent creep in the form of shear-banded structures is observed.

Phase behavior of charge stablized colloid dispersion with added water soluble polymers

Demixing and colloidal crystallization in the mixture of charge stabilized colloidal poly(methyl methacrylate) particles and soluble poly(ethylene oxide) were investigated by means of synchrotron small-angle X-ray scattering (SAXS) technique. Phase diagram of the mixture was obtained based on visual inspection and SAXS results. The phase behavior is determined as a function of the concentration of the polymer as well as the volume fraction of the colloidal particles. The system shows a one phase region when the concentration of the polymer is low, whereas a two-phase region is present when the concentration of the polymer is larger than a critical concentration at certain volume fraction of the colloids. Interestingly, a face centered cubic colloidal crystalline structure was formed under certain conditions, which has been rarely observed in experiments of colloid-polymer mixtures with competing interactions.

Phase transitions and phase equilibria in spherical confinement

Phase transitions in finite systems are rounded and shifted and affected by boundary effects due to the surface of the system. This interplay of finite size and surface effects for fluids confined inside of a sphere of radius $R$ is studied by a phenomenological theory and Monte Carlo simulations of a model for colloid-polymer mixtures. For this system the phase separation in a colloid-rich phase and a polymer-rich phase has been previously studied extensively in the bulk. It is shown that spherical confinement can strongly enhance the miscibility of the mixture. Depending on the wall potentials at the confining surface, the wetting properties of the wall can be controlled, and this interplay between preferential adsorption of one species to the confining surface and bulk unmixing leads to very special shapes of the loops observed for the chemical potential of the colloids as a function of their packing fraction. We also discuss the extent to which concepts used for phase transitions in macroscopic systems, such as critical exponents of the order parameter distinguishing the phases, or the Kelvin equation describing the shift of the chemical potential at phase coexistence with the radius $R$, are applicable.

Structure of phase-separated athermal colloid-polymer systems in the protein limit

Structural features of phase-separated athermal colloid-polymer mixtures in the so-called "protein limit," where polymer chain dimensions exceed those of the colloid, are investigated using grand canonical Monte Carlo simulations on a fine lattice. Previous work [N. A. Mahynski et al., Phys. Rev. E 85, 051402 (2012)] has shown that this model accurately captures the phase behavior of experimental systems, and that colloids with sufficiently small diameters, σ(c), relative to that of the monomeric segments, σ(s), phase separate more readily than their large-diameter counterparts. In the present study, we directly connect colloid and polymer structure with their phase behavior by investigating these solutions along their binodal curves; we also explore the role of colloid surface curvature in destabilizing such solutions. Our findings suggest that simple consideration of an additional depletion radius, on the order of the σ(s), leads to a quantitatively accurate prediction of the division between stable and unstable ranges of d=σ(s)/σ(c). We compare these results to continuum models with different bonding potentials between monomer segments in order to elucidate the significance of the lattice model's bond fluctuations and inherently coarse colloid surface. In a number of cases, the continuum models deviate both qualitatively and quantitatively from the lattice results, but the binodals of the continuum models are presently not known, making a strong conclusion about these differences impossible.

Hydrodynamic mechanisms of spinodal decomposition in confined colloid-polymer mixtures: A multiparticle collision dynamics study

A multiscale model for a colloid-polymer mixture is developed. The colloids are described as point particles interacting with each other and with the polymers with strongly repulsive potentials, while polymers interact with each other with a softer potential. The fluid in the suspension is taken into account by the multiparticle collision dynamics method (MPC). Considering a slit geometry where the suspension is confined between parallel repulsive walls, different possibilities for the hydrodynamic boundary conditions (b.c.) at the walls (slip versus stick) are treated. Quenching experiments are considered, where the system volume is suddenly reduced (keeping the density of the solvent fluid constant, while the colloid and polymer particle numbers are kept constant) and thus an initially homogeneous system is quenched deeply into the miscibility gap, where it is unstable. For various relative concentrations of colloids and polymers, the time evolution of the growing colloid-rich and polymer-rich domains are studied by molecular dynamics simulation, taking hydrodynamic effects mediated by the solvent into account via MPC. It is found that the domain size [script-l](d)(t) grows with time t as [script-l](d)(t) [proportionality] t(1/3) for stick and (at late stages) as [script-l](d)(t) [proportionality] t(2/3) for slip b.c., while break-up of percolating structures can cause a transient "arrest" of growth. While these findings apply for films that are 5-10 colloid diameters wide, for ultrathin films (1.5 colloid diameters wide) a regime with [script-l](d)(t) [proportionality] t(1/2) is also identified for rather shallow quenches.

Slip of gels in colloid–polymer mixtures under shear

Download options Please wait... Supplementary files Supplementary information PDF (1575K) Article information DOI https://doi.org/10.1039/C3SM27626K Article type Paper Submitted 14 Nov 2012 Accepted 15 Jan 2013 First published 07 Feb 2013 Download Citation Soft Matter, 2013,9, 3237-3245 BibTex EndNote MEDLINE ProCite ReferenceManager RefWorks RIS Permissions Request permissions Slip of gels in colloid–polymer mixtures under shear P. Ballesta, N. Koumakis, R. Besseling, W. C. K. Poon and G. Petekidis, Soft Matter, 2013, 9, 3237 DOI: 10.1039/C3SM27626K To request permission to reproduce material from this article, please go to the Copyright Clearance Center request page. If you are an author contributing to an RSC publication, you do not need to request permission provided correct acknowledgement is given. If you are the author of this article, you do not need to request permission to reproduce figures and diagrams provided correct acknowledgement is given. If you want to reproduce the whole article in a third-party publication (excluding your thesis/dissertation for which permission is not required) please go to the Copyright Clearance Center request page. Read more about how to correctly acknowledge RSC content. Social activity Tweet Share Search articles by author Pierre Ballesta Nick Koumakis Rut Besseling Wilson C. K. Poon George Petekidis

Phase separation dynamics in colloid–polymer mixtures: the effect of interaction range

Colloid–polymer mixtures may undergo either fluid–fluid phase separation or gelation. This depends on the depth of the quench (polymer concentration) and the polymer–colloid size ratio. We present a real-space study of dynamics in phase separating colloid–polymer mixtures with medium- to long-range attractions (polymer–colloid size ratio qR = 0.45–0.89), with the aim of understanding the mechanism of gelation as the range of attraction is changed. In contrast to previous studies of short-range attractive systems, where gelation occurs shortly after crossing the equilibrium phase boundary, we find a substantial region of fluid–fluid phase separation. Upon quenching deeper, the system undergoes a continuous crossover to gel formation. We identify two regimes, ‘classical’ phase separation, where single particle relaxation is much faster than the dynamics of phase separation, and ‘viscoelastic’ phase separation, where demixing is slowed down appreciably due to slow dynamics in the colloid-rich phase. Particles at the surface of the strands of the network exhibit significantly greater mobility than those buried inside the gel strand which presents a method for coarsening.

Effect of controlled corrugation on capillary condensation of colloid–polymer mixtures

We investigate with Monte Carlo computer simulations the capillary phase behaviour of model colloid–polymer mixtures confined between a flat wall and a corrugated wall. The corrugation is modelled via a sine wave as a function of one of the in-plane coordinates leading to a depletion attraction between colloids and the corrugated wall that is curvature dependent. We find that for an increased amplitude of corrugation the region of the phase diagram where capillary condensation occurs becomes larger. We derive a Kelvin equation for this system and compare its predictions to the simulation results. We find good agreement between the theory and simulation indicating that the primary reason for the stronger capillary condensation is an increased contact area between the fluid and the corrugated substrate. On the other hand, the colloid adsorption curves at colloid gas–liquid coexistence show that the increased area is not solely responsible for the stronger capillary condensation. Additionally, we analyse the dimensional crossover from a quasi-2D to a quasi-1D system and find that the transition is characterised by the appearance of a metastable phase.

Viscous fingering at ultralow interfacial tension

We experimentally study the viscous fingering instability in a fluid-fluid phase separated colloid-polymer mixture by means of laser scanning confocal microscopy and microfluidics. We focus on three aspects of the instability. (i) The interface between the two demixed phases has an ultralow surface tension, such that we can address the role of thermal interface fluctuations. (ii) We image the interface in three dimensions allowing us to study the interplay between interface curvature and flow. (iii) The displacing fluid wets all walls completely, in contrast to traditional viscous fingering experiments, in which the displaced fluid wets the walls. We also perform lattice Boltzmann simulations, which help to interpret the experimental observations.

Spinodal decomposition of a confined colloid-polymer system

We study the demixing via spinodal decomposition of a fluid-fluid phase separating colloid-polymer mixture confined between parallel plates, where one of the phases completely wets both walls. Using confocal scanning laser microscopy, we are able to obtain real space images, both parallel and perpendicular to the cell walls. We observe three distinct morphologies: the formation of a bicontinuous network, which coarsens into cylindrical tubes bridging the plates, and finally develops into a network structure in two dimensions. Through image analysis of the system as a whole, and the tracking of individual domains, we are able to perform a detailed study of the mechanisms of phase coarsening at each stage. We are able to directly test the condition for which bridges connecting both confining walls do not sever. Finally, we consider the role of hydrodynamics and of thermal interface fluctuations in our system.

Crystal-Arrested Phase Separation

We have studied the interplay between phase separation and crystallization in a colloid-polymer mixture along one kinetic pathway in samples which exhibit three-phase equilibrium coexistence. In analogy with atomic systems, the range of the effective attractive interaction between colloids is sufficiently long to allow for a stable liquid phase. By direct imaging in microgravity on the International Space Station, we observe a unique structure, a "crystal gel," that occurs when gas-liquid phase separation arrests due to crystallites within the liquid domain spanning the cell. From the initial onset of spinodal decomposition until arrest caused by this structure, the kinetics of phase separation remain largely unaffected by the formation of the third phase. This dynamic arrest appears to result from the stiffness of the crystalline strands exceeding the liquid-gas interfacial tension.

Confinement-induced screening of hydrodynamic interactions and spinodal decomposition: Multiscale simulations of colloid-polymer mixtures

Phase separation kinetics of a colloid-polymer mixture confined between two planar repulsive walls is studied by a multiscale simulation approach. Colloids and polymers are described by particles interacting with continuous potentials suitable for molecular-dynamics simulation, while hydrodynamic interactions mediated by solvent particles are accounted for by the multiparticle collision dynamics method. Varying the distance D between the walls and the character of the boundary conditions, the interplay of structure formation parallel and perpendicular to the walls is studied, and the effect of hydrodynamics on the growth of domain size ℓd(t) with time t is elucidated. Only for slip boundary conditions a growth law ℓd(t)∝t2/3 is observed, but break-up of the percolating polymer-rich phase may “arrest” this growth. For stick boundary conditions hydrodynamic interactions are to a large extent screened and the diffusive Lifshitz-Slyozov growth law ℓd(t)∝t1/3 results.

Depletion induced clustering in mixtures of colloidal spheres and fd-virus

We determined the phase boundary of an ideal rod–sphere mixture consisting of fd-virus, which is an established model system for mono-disperse colloidal rods, and density matched mono-disperse polystyrene beads employing diffuse wave spectroscopy. The low volume fraction of fd needed to induce a phase separation at relatively low ionic strength exemplifies the fact that slender rods are very effective depletion agents. Confocal microscopy showed that stable clusters are formed during phase separation. Relaxation after shear deformation of these clusters showed that the phase separation is gas–liquid-like and that the interfacial tension involved is very low as in colloid–polymer mixtures.