Aging in short-ranged attractive colloids: a numerical study

We study the aging dynamics in a model for dense simple liquids, in which particles interact through a hard-core repulsion complemented by a short-ranged attractive potential, of the kind found in colloidal suspensions. In this system, at large packing fractions, kinetically arrested disordered states can be created both on cooling (attractive glass) and on heating (repulsive glass). The possibility of having two distinct glasses, at the same packing fraction, with two different dynamics offers the unique possibility of comparing-within the same model-the differences in aging dynamics. We find that, while the aging dynamics of the repulsive glass is similar to the one observed in atomic and molecular systems, the aging dynamics of the attractive glass shows novel unexpected features.     

Gel to glass transition in simulation of a valence-limited colloidal system

We numerically study a simple model for thermoreversible colloidal gelation in which particles can form reversible bonds with a predefined maximum number of neighbors. We focus on three and four maximally coordinated particles, since in these two cases the low valency makes it possible to probe, in equilibrium, slow dynamics down to very low temperatures T. By studying a large region of T and packing fraction phi we are able to estimate both the location of the liquid-gas phase separation spinodal and the locus of dynamic arrest, where the system is trapped in a disordered nonergodic state. We find that there are two distinct arrest lines for the system: a glass line at high packing fraction, and a gel line at low phi and T. The former is rather vertical (phi controlled), while the latter is rather horizontal (T controlled) in the phi-T plane. Dynamics on approaching the glass line along isotherms exhibit a power-law dependence on phi, while dynamics along isochores follow an activated (Arrhenius) dependence. The gel has clearly distinct properties from those of both a repulsive and an attractive glass. A gel to glass crossover occurs in a fairly narrow range in phi along low-T isotherms, seen most strikingly in the behavior of the nonergodicity factor. Interestingly, we detect the presence of anomalous dynamics, such as subdiffusive behavior for the mean squared displacement and logarithmic decay for the density correlation functions in the region where the gel dynamics interferes with the glass dynamics.     

Attraction-driven disorder in a hard-core colloidal monolayer

Monte Carlo simulation techniques were employed to explore the effect of short-range attraction on the orientational ordering in a two-dimensional assembly of monodisperse spherical particles. We find that if the range of square-well attraction is approximately 15% of the particle diameter, the dense attractive fluid shows the same ordering behavior as the same density fluid composed of purely repulsive hard spheres. Fluids with an attraction range larger than 15% show an enhanced tendency to crystallization, while disorder occurs for fluids with an attractive range shorter than 15% of the particle diameter. A possible link with the existence of "repulsive" and "attractive" states in dense colloidal systems is discussed.     

Theory of nanoparticle diffusion in unentangled and entangled polymer melts

We propose a statistical dynamical theory for the violation of the hydrodynamic Stokes-Einstein (SE) diffusion law for a spherical nanoparticle in entangled and unentangled polymer melts based on a combination of mode coupling, Brownian motion, and polymer physics ideas. The non-hydrodynamic friction coefficient is related to microscopic equilibrium structure and the length-scale-dependent polymer melt collective density fluctuation relaxation time. When local packing correlations are neglected, analytic scaling laws (with numerical prefactors) in various regimes are derived for the non-hydrodynamic diffusivity as a function of particle size, polymer radius-of-gyration, tube diameter, degree of entanglement, melt density, and temperature. Entanglement effects are the origin of large SE violations (orders of magnitude mobility enhancement) which smoothly increase as the ratio of particle radius to tube diameter decreases. Various crossover conditions for the recovery of the SE law are derived, which are qualitatively distinct for unentangled and entangled melts. The dynamical influence of packing correlations due to both repulsive and interfacial attractive forces is investigated. A central finding is that melt packing fraction, temperature, and interfacial attraction strength all influence the SE violation in qualitatively different directions depending on whether the polymers are entangled or not. Entangled systems exhibit seemingly anomalous trends as a function of these variables as a consequence of the non-diffusive nature of collective density fluctuation relaxation and the different response of polymer-particle structural correlations to adsorption on the mesoscopic entanglement length scale. The theory is in surprisingly good agreement with recent melt experiments, and new parametric studies are suggested.     

Rheology and gelation kinetics in laponite dispersions containing poly(ethylene oxide)

We report results on the rheology of a model polymer/clay system, laponite clay particles with added poly(ethylene oxide) (PEO), focusing on the kinetics of gel formation and on molecular weight effects. We examined solutions at both pH = 7, where interparticle attractions are present and a networked gel is formed; and at pH = 10, where repulsive forces dominate and laponite forms a colloidal glass. We found that PEO of low to moderate molecular weight significantly slows down gelation and decreases the complex viscosity and elastic modulus of the dispersion by several orders of magnitude for both pH = 7 and 10. In the former case, adsorbed PEO likely forms a steric barrier to the formation of an attractive gel. In the latter case, we propose that free PEO chains in solution induce a depletion attraction between particles, preventing or slowing the formation of a colloidal glass. At higher molecular weights, PEO chains are long enough to bridge between particles and form an associative network, enhancing the viscosity and elastic modulus for both pH = 7 and 10. Finally, we have shown the critical molecular weight for transitioning between these two types of behavior scales with the interparticle distance. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 233–240, 2005     

Micrometer scale adhesion on nanometer-scale patchy surfaces: adhesion rates, adhesion thresholds, and curvature-based selectivity

Using a model system based on electrostatics, we probe interactions between spherical particles (negative silica) and planar surfaces that present randomly placed discrete attractive regions, 10 nm in size, in a repulsive background (silica flats carrying cationic surface constructs). Experiments measure the adhesion rates of particles onto the patchy collecting surfaces from flowing dispersions, as a function of the surface loading of the attractive patches, for different particle sizes (0.5 and 1 mum diameter spheres) and different ionic strengths. Surfaces densely populated with patches, such that they present net electrostatic attractions to approaching particles, capture particles at the transport-limited (maximum) rate. Surfaces sparsely loaded with attractive patches (which present a repulsive mean field to approaching particles) are usually still adhesive, but the particle adhesion rate depends on particle size, ionic strength, and patch loading. Most significant is an adhesion threshold, a critical density of patches needed to capture particles. This threshold, which occurs at average patch spacings of 30 nm and larger and which can be tuned through ionic strength, comprises the ability of the patchy surfaces to selectively distinguish particles of different sizes or objects of different local curvature or roughness. The observation of such an adhesion threshold implicates spatial fluctuations in patch arrangement. In addition to experiments, this paper develops arguments for lengthscales that govern adhesion rate behavior, comparing particle geometry and fluctuation lengthscales, and then demonstrating qualitative consistency with the localized colloidal potentials involved.     

Complex phase behavior of the system of particles with smooth potential with repulsive shoulder and attractive well

We report a detailed simulation study of the phase behavior of core-softened system with attractive well. Different repulsive shoulder widths and attractive well depths are considered which allows to monitor the influence of repulsive and attractive forces on the phase diagram of the system. Thermodynamic anomalies in the systems are also studied. It is shown that the diffusion anomaly is stabilized by small attraction.     

Molecular flexibility effects upon liquid dynamics

Simulation results for the diffusive behavior of polymer chain/penetrant systems are analyzed. The attractive range and flexibility of simple chain molecules were varied in order to gauge the effect on dynamics. In all cases, the dimensionless diffusion coefficient, D*, is found to be a smooth, single-valued function of the packing fraction, eta. The functions D*(eta) are found to be power laws with exponents that are sensitive to both chain stiffness and particle type. For a specific system type, the D*'s for both penetrant and chain-center-of-mass extrapolate to zero at the same packing fraction, eta0. This limiting packing fraction is interpreted to be the location of the glass transition, and (eta0-eta), the distance to the glass transition.     

Direct imaging of repulsive and attractive colloidal glasses

Coherent anti-Stokes Raman scattering microscopy is performed on glassy systems of poly(methylmethacrylate) colloidal particles in density- and refractive-index-matched solvents. Samples are prepared with varying amounts of linear polystyrene, which induces a depletion driven attraction between the nearly hard-sphere particles. Images collected over several hours confirm the existence of a reentrant glass transition. The images also reveal that the dynamics of repulsive and attractive glasses are qualitatively different. Colloidal particles in repulsive glasses exhibit cage rattling and escape, while those in attractive glasses are nearly static while caged but exhibit large displacements upon (infrequent) cage escape.     

Structure and assembly of dense solutions and melts of single tethered nanoparticles

The microscopic polymer reference interaction site model theory is generalized and applied to study intermolecular pair correlation functions and collective structure factors of dense solutions and melts of spherical nanoparticles carrying a single tethered chain. The complex interplay of entropy (translational, conformational, and packing) and enthalpy (particle-particle attraction) leads to different structural arrangements with distinctive small and wide angle scattering signatures. Strong concentration fluctuations, indicative of aggregate formation and/or a tendency for microphase separation, occur as the total packing fraction and/or particle-particle attraction strength increase. In analogy with block copolymers, the microphase spinodal curve is estimated by extrapolation of the inverse of the amplitude of the small angle scattering peak. For nanoparticles that are twice the diameter of monomers, the microphase separation boundary spinodal occurs at higher particle-particle attraction strength (or lower temperature) as compared to the macrophase demixing curve for nanoparticles with no tethers when the packing fraction is below 0.45, while the opposite trend is observed above 0.45. Increasing nanoparticle diameter results in a reduction in the microphase spinodal temperature and a qualitative change in its packing fraction dependence.     

Structures and Surface States of Polymer Brushes in Good Solvents: Effects of Surface Interactions

The influence of the surface interaction on the mesoscopic structure of grafted polymers in good solvents has been examined. At high surface coverage, tethered polymers are in the brush state and the parabolic segment density profile is confirmed by self-consistent field theory (SCFT) calculations. It is found that this is a universal behavior for a whole range of surface interactions from complete repulsion to strong attraction. More interestingly, finite surface repulsion may lead to the maximum in the proximal layer of its segment density profile, which is significantly different from both the depletion layer of pure repulsion and the adsorbing layer of attraction. In addition to the brush state on both repulsive and attractive surfaces, three additional surface states were identified by analyzing the scaling behavior of the layer thickness of polymer brushes: the mushroom state on repulsive substrates, the dilute and the semidilute surface states on attractive substrates.     

Arrested phase separation in a short-ranged attractive colloidal system: a numerical study

We numerically investigate the competition between phase separation and dynamical arrest in a colloidal system interacting via a short-ranged attractive potential. Equilibrium fluid configurations are quenched at two different temperatures below the critical temperature and followed during their time evolution. At the lowest studied T, the phase-separation process is interrupted by the formation of an attractive glass in the dense phase. At the higher T, no arrest is observed and the phase-separation process proceeds endlessly in the simulated time window. The final structure of the glass retains memory of the interrupted phase-separation process in the form of a frozen spinodal decomposition peak, whose location and amplitude is controlled by the average packing fraction. We also discuss the time evolution of the nonergodicity parameter, providing evidence of a progressively decreasing localization length on increasing the packing fraction. Finally, we confirm that the reported results are independent of the microscopic dynamics.     

Cluster kinetics of pressure-induced glass formation

A prior correlation model for glass formation based on cluster-size distribution kinetics is here extended to account for pressure effects as well as temperature effects. The model describes how rapidly cooling or compressing a liquid or colloid leads to structural arrest and a consequent sharp rise in viscosity or dielectric relaxation time. In addition to activation energies, we include activation volumes in the rate coefficients for monomer-cluster addition and dissociation and cluster aggregation and breakage. The approach leads to scaled pressure correlations and plots for viscosity that reveal strong and fragile glass behavior, and agree with experimental data. A simple relationship among viscosity, attractive interparticle energy, and particle volume fraction displays how hard spheres with attractive forces can vitrify at small particle densities.     

Percolation, phase separation, and gelation in fluids and mixtures of spheres and rods

The relationship between kinetic arrest, connectivity percolation, structure and phase separation in protein, nanoparticle, and colloidal suspensions is a rich and complex problem. Using a combination of integral equation theory, connectivity percolation methods, nai?ve mode coupling theory, and the activated dynamics nonlinear Langevin equation approach, we study this problem for isotropic one-component fluids of spheres and variable aspect ratio rigid rods, and also percolation in rod-sphere mixtures. The key control parameters are interparticle attraction strength and its (short) spatial range, total packing fraction, and mixture composition. For spherical particles, formation of a homogeneous one-phase kinetically stable and percolated physical gel is predicted to be possible, but depends on non-universal factors. On the other hand, the dynamic crossover to activated dynamics and physical bond formation, which signals discrete cluster formation below the percolation threshold, almost always occurs in the one phase region. Rods more easily gel in the homogeneous isotropic regime, but whether a percolation or kinetic arrest boundary is reached first upon increasing interparticle attraction depends sensitively on packing fraction, rod aspect ratio and attraction range. Overall, the connectivity percolation threshold is much more sensitive to attraction range than either the kinetic arrest or phase separation boundaries. Our results appear to be qualitatively consistent with recent experiments on polymer-colloid depletion systems and brush mediated attractive nanoparticle suspensions.     

Rheological aspects of colloidal gels in thermoresponsive microgel suspensions: formation,structure, and linear and nonlinear viscoelasticity

This review focuses on the rheological aspects of colloidal gels that are a three-dimensional sparse network made of aggregated attractive particles formed in the aqueous suspensions of microgels composed of thermoresponsive polymers. Heating changes the dominant interparticle interactions from repulsive to attractive because of the hydrophilic-to-hydrophobic transition. Under appropriate conditions, the hydrophobic microgel suspensions form colloidal gels behave as a yield fluid. The elastic and yielding features of the colloidal gels are considerably different from those of the repulsive glass which is formed by the dense packing of the hydrophilic microgels at low temperatures. The thermoresponsive microgel suspensions undergoing colloidal gelation have attracted much attention from not only the academic interests but also the potentials as a functional suspension because they show interesting and marked changes in viscoelasticity when subjected to temperature variation. We discuss the criteria and dynamics of colloidal gelation, the structure, and linear and nonlinear viscoelasticity of the colloid gels with an emphasis on the results of the experimental studies.     

Effect of the number and placement of polymer tethers on the structure of concentrated solutions and melts of hybrid nanoparticles

We have generalized and applied the microscopic polymer reference interaction site model theory to study intermolecular pair correlation functions and collective structure factors of concentrated solutions and melts of spherical nanoparticles carrying one, two, or four tethered polymer chains. A complex interplay of entropy (translational, conformational, and packing) and enthalpy (particle-particle attraction) leads to different structural arrangements with distinctive small- and wide-angle scattering signatures. Strong concentration fluctuations indicative of aggregate formation and/or a tendency for microphase separation occur as the total packing fraction and/or particle-particle attraction strength increase. In analogy with block copolymers, the microphase spinodal curve is estimated by extrapolation of the inverse of the amplitude of the small-angle scattering peak. As the number of tethered chains on nanoparticles increases, the microphase separation boundary spinodal occurs at higher particle-particle attraction strength or lower temperature. For nanoparticles with two tethers, increasing the angle between the attached chains shifts the microphase spinodal to lower temperatures. For nanoparticles with four tethers, the structural correlations are insensitive to various symmetric placements. The tendency for microphase transition is enhanced upon asymmetrically placing all four tethers on one side of the particle due to the high anisotropy of steric hindrance.     

Protein interactions studied by SAXS: effect of ionic strength and protein concentration for BSA in aqueous solutions

We have studied a series of samples of bovine serum albumin (BSA) solutions with protein concentration, c, ranging from 2 to 500 mg/mL and ionic strength, I, from 0 to 2 M by small-angle X-ray scattering (SAXS). The scattering intensity distribution was compared to simulations using an oblate ellipsoid form factor with radii of 17 x 42 x 42 A, combined with either a screened Coulomb, repulsive structure factor, SSC(q), or an attractive square-well structure factor, SSW(q). At pH = 7, BSA is negatively charged. At low ionic strength, I < 0.3 M, the total interaction exhibits a decrease of the repulsive interaction when compared to the salt-free solution, as the net surface charge is screened, and the data can be fitted by assuming an ellipsoid form factor and screened Coulomb interaction. At moderate ionic strength (0.3-0.5 M), the interaction is rather weak, and a hard-sphere structure factor has been used to simulate the data with a higher volume fraction. Upon further increase of the ionic strength (I >or= 1.0 M), the overall interaction potential was dominated by an additional attractive potential, and the data could be successfully fitted by an ellipsoid form factor and a square-well potential model. The fit parameters, well depth and well width, indicate that the attractive potential caused by a high salt concentration is weak and long-ranged. Although the long-range, attractive potential dominated the protein interaction, no gelation or precipitation was observed in any of the samples. This is explained by the increase of a short-range, repulsive interaction between protein molecules by forming a hydration layer with increasing salt concentration. The competition between long-range, attractive and short-range, repulsive interactions accounted for the stability of concentrated BSA solution at high ionic strength.     

Brownian dynamics simulations of associating diblock copolymers

A novel coarse-grained computational model for associating polymers is proposed that is based on a Gaussian "blob" representation of the polymer chains. The model allows a large number of model polymers to be simulated at moderate computational cost over a wide packing fraction range using the Brownian dynamics, BD, technique. The attraction of the hydrophobic part of the polymer to those on other molecules can lead to strong aggregation of the polymer molecules in real systems, and this is included in the model by an attractive potential felt by the Gaussian blobs to a common "nodal" point that represents the center of the micelle. Attention here is confined to model AB diblock copolymers in which the hydrophilic block, A, has a much higher mass than the hydrophobic moiety, B, which leads to relatively small aggregation numbers, Nagg, of approximately 8. The aggregation number at low packing fractions is found to increase with packing fraction, as observed in experiments, with a functional form that closely follows a simple theory derived here that is based on entropy-derived mean-field terms for the free-energy change associated with the incorporation of the polymer molecule into the micelle. The computational model exhibits an extremely low critical micelle concentration (cmc), and micelles with Nagg approximately 5 are observed at the lowest packing fractions, phi, simulated ( approximately 10-4), which is consistent with experiment. The long-time self-diffusion coefficient of the polymers (and hence micelles) decreases logarithmically with packing fraction, and the viscosity increased with concentration according to the Huggins equation. The spherical blob coarse graining results in the simulable time scales being longer than the Rouse time of the chain, and hence for the nonassociating polymers the intrinsic viscosity is an input parameter in the model. The introduction of association leads to the partial inclusion of the intrinsic viscosity in the simulation and has an effect on the computed Huggins coefficient, kH, which is found to be approximately 6 in those cases.     

Re-entrant kinetic arrest and elasticity of concentrated suspensions of spherical and nonspherical repulsive and attractive colloids

We have designed and studied a new experimental colloidal system to probe how the weak shape anisotropy of uniaxial particles and variable repulsive (Coulombic) and attractive (van der Waals) forces influence slow dynamics, shear elasticity, and kinetic vitrification in dense suspensions. The introduction of shape anisotropy dramatically delays kinetic vitrification and reduces the shear elastic modulus of colloidal diatomics relative to their chemically identical spherical analogs. Tuning the interparticle interaction from repulsive, to nearly hard, to attractive by increasing suspension ionic strength reveals a nonmonotonic re-entrant dynamical phase behavior (glass-fluid-gel) and a rich variation of the shear modulus. The experimental results are quantitatively confronted with recent predictions of ideal mode coupling and activated barrier hopping theories of kinetic arrest and elasticity, and good agreement is generally found with a couple of exceptions. The systems created may have interesting materials science applications such as flowable ultrahigh volume fraction suspensions, or responsive fluids that can be reversibly switched between a flowing liquid and a solid nonequilibrium state based on in situ modification of suspension ionic strength.     

Phase behavior in highly concentrated assemblies of microgels with soft repulsive interaction potentials

Microgel particles with a soft repulsive interaction potential are investigated with particle tracking methods to study the phase behavior of soft-sphere systems. The use of poly(N-isopropylacrylamide) particles allows the effective volume fraction of a sample to be tuned via thermal modulation without altering the particle number density. This allows for investigation of the phase behavior of an assembly as a function of its initial packing density. In particular, we have elucidated the influence of soft colloid "overpacking" on the freezing effective volume fraction (phieff,f). These studies thereby illustrate the interplay between energetics/packing forces occurring at the colloidal and polymer chain length scales.