Hard-sphere Colloidal Suspensions Research Articles

Effect of polydispersity on the crystallization kinetics of suspensions of colloidal hard spheres when approaching the glass transition

We present a comprehensive study of the solidification scenario in suspensions of colloidal hard spheres for three polydispersities between 4.8% and 5.8%, over a range of volume fractions from near freezing to near the glass transition. From these results, we identify four stages in the crystallization process: (i) an induction stage where large numbers of precursor structures are observed, (ii) a conversion stage as precursors are converted to close packed structures, (iii) a nucleation stage, and (iv) a ripening stage. It is found that the behavior is qualitatively different for volume fractions below or above the melting volume fraction. The main effect of increasing polydispersity is to increase the duration of the induction stage, due to the requirement for local fractionation of particles of larger or smaller than average size. Near the glass transition, the nucleation process is entirely frustrated, and the sample is locked into a compressed crystal precursor structure. Interestingly, neither polydispersity nor volume fraction significantly influences the precursor stage, suggesting that the crystal precursors are present in all solidifying samples. We speculate that these precursors are related to the dynamical heterogeneities observed in a number of dynamical studies.

Shear Zones and Wall Slip in the Capillary Flow of Concentrated Colloidal Suspensions

We image the flow of a nearly random close packed, hard-sphere colloidal suspension (a "paste") in a square capillary using confocal microscopy. The flow consists of a "plug" in the center while shear occurs localized adjacent to the channel walls, reminiscent of yield-stress fluid behavior. However, the observed scaling of the velocity profiles with the flow rate strongly contrasts yield-stress fluid predictions. Instead, the velocity profiles can be captured by a theory of stress fluctuations originally developed for chute flow of dry granular media. We verified this both for smooth and rough walls.

Morphological instability in freezing colloidal suspensions

We present a linear stability analysis of a planar ice interface during unidirectional solidification of a hard-sphere colloidal suspension. We find that the interface can become unstable due to constitutional supercooling, yielding a new mechanism for pattern formation in colloidal systems. The interfacial stability is shown to depend strongly on the size and concentration of the particles. Increasing the particle radius tends to stabilize the interface, while increasing the concentration has a destabilizing effect. Additional effects that may influence the stability and morphology of such a system are described.

Small changes in particle-size distribution dramatically delay and enhance nucleation in hard sphere colloidal suspensions

We present hard-sphere crystallization kinetics for three samples with small differences in polydispersity. We show that an increase in polydispersity of 1% is sufficient to cause dramatic changes in the crystallization kinetics: crystallization is delayed by almost one decade in time and quantitative and qualitative changes in the crystallization scenario are observed. Surprisingly the nucleation rate density is enhanced by almost a factor of 10. We interpret these results in terms of polydispersity limited growth, where local fractionation processes lead to a delayed but faster nucleation.

Void structure and cage fluctuations in simulations of concentrated suspensions.

We analyse the mesoscopic structure and structural fluctuations in simulated high-concentration hard sphere colloidal suspensions by means of calculations based on the void space. We show that remoteness, a quantity measuring the scale of spaces, is useful in studying crystallization, since ordering of the particles involves a change in the way empty space is distributed. Calculation of remoteness also allows breakdown of the system into mesoscopic neighbour sets. In the case of crystallizing systems, statistics of mean remoteness and local volume fraction in these neighbour sets are consistent with nuclei forming at locally higher concentration, nucleation involves increased heterogeneity of the system, as previously demonstrated in experiments with model colloidal particles. Meanwhile in dense amorphous systems, local volume fractions in neighbour sets reveal significant details of mesoscale structural fluctuations, indicating that abrupt dilations and compressions of local regions may be important physical components of cage fluctuations in the colloidal glass.

Dilatancy, jamming, and the physics of granulation

Granulation is a process whereby a dense colloidal suspension is converted into pastygranules (surrounded by air) by application of shear. Central to the stability of the granulesis the capillary force arising from the interfacial tension between solvent and air. This forceappears capable of maintaining a granule in a jammed solid state, under conditions wherethe same amount of solvent and colloid could also exist as a flowable droplet. We arguethat in the early stages of granulation the physics of dilatancy, which requires that apowder expand on shearing, is converted by capillary forces into the physics ofarrest. Using a schematic model of colloidal arrest under stress, we speculateupon various jamming and granulation scenarios. Some preliminary experimentalresults on aspects of granulation in hard-sphere colloidal suspensions are alsopresented.

Barrier hopping, viscous flow, and kinetic gelation in particle-polymer suspensions

The naive mode coupling-polymer reference interaction site model (MCT-PRISM) theory of gelation and elasticity of suspensions of hard sphere colloids or nanoparticles mixed with nonadsorbing polymers has been extended to treat the emergence of barriers, activated transport, and viscous flow. The barrier makes the dominant contribution to the single particle relaxation time and shear viscosity, and is a rich function of the depletion attraction strength via the polymer concentration, polymer-particle size asymmetry ratio, and particle volume fraction. The dependences of the barrier on these three system parameters can be accurately collapsed onto a single scaling variable, and the resultant master curve is well described by a power law. Nearly universal master curves are also constructed for the hopping or alpha relaxation time for system conditions not too close to the ideal MCT transition. Based on the calculated barrier hopping time, a theory for kinetic gel boundaries is proposed. The form and dependence on system parameters of the kinetic gel lines are qualitatively the same as obtained from prior ideal MCT-PRISM studies. The possible relevance of our results to the phenomenon of gravity-driven gel collapse is studied. The general approach can be extended to treat nonlinear viscoelasticity and rheology of polymer-colloid suspensions and gels.

Structure of hard-sphere colloid observed in real space by spin-echo small-angle neutron scattering

Spin-echo small-angle neutron scattering (SESANS) opens a wide range of potential applications. One of them is the study of colloids. Using SESANS we measured the structure of hard-sphere colloidal suspensions at two concentrations. We show that SESANS measures real-space correlations due to the particle shape as well as interactions between them. The dilute suspension showed no correlations exceeding the particle diameter. For a concentrated colloid the effect of the excluded volume is observed as a minimum in correlation function. Experimental correlation functions are compared with theoretical ones for noninteracting spheres and a hard-sphere liquid. The scattering density, volume fraction and the radius of particles are also determined from SESANS correlation function.

Toward a Theoretical Understanding of the Colloidal Glass Transition

The liquid-glass transition for colloidal suspensions of hard spheres is discussed from a new theoretical point of view. The important role of the hydrodynamic interactions between colloids near the glass transition is pointed out. Two kinds of computer simulations are also performed to verify such an important role. Thus, those interactions are shown to be indispensable to explain the experimental data near the colloidal glass transition.

Activated Hopping, Barrier Fluctuations, and Heterogeneity in Glassy Suspensions and Liquids

Our entropic barrier hopping theory of glassy hard sphere colloidal suspensions is extended to include heterogeneity within a simple trap model framework. The origin of local domains, their size, and the corresponding static barrier fluctuations are attributed to mesoscopic density fluctuations of an amplitude controlled by the bulk compressibility. Based on typical values of the density fluctuation correlation length in dense liquids, the domain size on which correlated hopping occurs is estimated to be 3−4 particle or molecular diameters. Consequences of barrier fluctuations include an increased average relaxation time, faster diffusion, stretched exponential relaxation, diffusion-viscosity decoupling, and a fractional Stokes−Einstein relation. The common origin of the fluctuation effects is the heterogeneity-induced component of the barrier. For colloidal suspensions in the typically studied volume fraction regime the barrier fluctuations have modest consequences, but significantly larger effects are predicted in the putative glassy regime. A statistical dynamical analysis of domain lifetime suggests that for suspensions the relaxation time of mesoscopic collective density fluctuations is at least as long as the single particle hopping time. A general, model-independent analysis of the single molecule incoherent dynamic structure factor for suspensions and thermal liquids has also been performed in the long time and intermediate wavevector regime. The coupling of single particle density and longitudinal stress fluctuations results in a wavevector-dependent apparent diffusion constant and a dynamic correlation length scale which is strongly temperature dependent and directly related to the translation-rotation decoupling factor. This dynamic length is estimated to be 10 times larger than a molecular diameter for tris-naphthyl benzene near the glass transition temperature but shrinks to a molecular size above the crossover temperature that signals the emergence of collective barriers.

Phonons in suspensions of hard sphere colloids: volume fraction dependence.

The propagation of sound waves in suspensions of hard sphere colloids is studied as a function of their volume fraction up to random close packing using Brillouin light scattering. The rich experimental phonon spectra of up to five phonon modes are successfully described by theoretical calculations based on the multiple scattering method. Two main types of phonon modes are revealed: Type A modes are acoustic excitations which set up deformations in both the solid (particles) and the liquid (solvent) phases; for type B modes the stress and strain are predominantly localized near the interface between the solid particles and the surrounding liquid (interface waves). While the former become harder (increase their effective sound velocity) as the particle volume fraction increases the latter become softer (the corresponding sound velocity decreases).

Interaction between a macrosphere and a flat wall mediated by a hard-sphere colloidal suspension.

The interaction between the macrosphere and the flat wall immersed in a binary fluid comprising small and large (size ratio around 1:10) hard spheres has been investigated. We find that the presence of the highly size-asymmetric particles qualitatively modifies the induced excluded-volume interaction between the macrosphere and the flat wall compared to that observed in a single-component suspending fluid comprised of only large or only small species. The role in the interaction between a macrosphere and a flat wall played by species of the fine component that usually is approximated by a continuum medium (primitive description of a bidisperse fluid) is emphasized. Particularly, we show that taking into account the smaller component of a bidisperse suspending fluid modifies significantly the macrosphere-wall depletion attraction that is predicted when only large particles are taken into account. The depletion attraction force created by the presence of small fluid particles enhances the adsorption of large particles and their structuring on the wall.

Jamming, two-fluid behavior, and "self-filtration" in concentrated particulate suspensions.

We study the flow of model hard-sphere colloidal suspensions at high volume fraction Phi driven through a constriction by a pressure gradient. Above a particle-size dependent limit Phi(0), direct microscopic observations demonstrate jamming and unjamming-conversion of fluid to solid and vice versa-during flow. We show that such a jamming flow produces a reduction in colloid concentration Phi(x) downstream of the constriction. We propose that this "self-filtration" effect is due to a combination of jamming of the particulate part of the system and continuing flow of the liquid part, i.e., the solvent, through the pores of the jammed solid. Thus we link jamming in colloidal and granular media with a "two-fluid-like" picture of the flow of concentrated suspensions. Results are also discussed in the light of the original experiments of Reynolds on dilation in granular materials.

Structural transitions of hard-sphere colloids studied by spin-echo small-angle neutron scattering

The structure of hard-sphere colloidal suspensions is measured at different concentrations using the recently developed spin-echo small-angle neutron scattering (SESANS) technique. It is shown that SESANS measures real-space correlations ranging from the size of a single particle for a dilute suspension to several particle diameters for a concentrated suspension, glass and crystalline state.

Universal effects of collective interactions on long-time self-diffusion coefficients in hard-sphere systems

We investigate how universal the collective behavior, due to the many-body interactions in polydisperse hard-sphere systems, is at higher volume fractions. We perform two types of computer simulations, a Brownian-dynamics simulation on colloidal suspensions of hard spheres, where the hydrodynamic interactions between particles are neglected, and a molecular-dynamic simulation on atomic systems of hard spheres. Thus, we show that the long-time self-diffusion coefficients D S L in both systems become singular as D S L ( φ)∼(1− φ/ φ c ) 2 because of the collective interactions due to the many-body collision processes, where φ is a particle volume fraction and φ c ≃0.586 for 6% polydispersity. Although D S L exhibits the same singular behavior as that obtained theoretically for the monodisperse suspension with the hydrodynamic interactions, no liquid–glass transition is found because even the polydisperse hard-sphere systems crystallize without the hydrodynamic interactions for all φ above the melting volume fraction, which is lower than φ c .

Entropic barriers, activated hopping, and the glass transition in colloidal suspensions

A microscopic kinetic description of single-particle transient localization and activated transport in glassy fluids is developed which combines elements of idealized mode-coupling theory, density functional theory, and activated rate theory. Thermal fluctuations are included via a random force which destroys the idealized glass transition and restores ergodicity through activated barrier hopping. The approach is predictive, containing no adjustable parameters or postulated underlying dynamic or thermodynamic divergences. Detailed application to hard-sphere colloidal suspensions reveals good agreement with experiment for the location of the kinetic glass transition volume fraction, the dynamic incoherent scattering relaxation time, apparent localization length, and length scale of maximum nongaussian behavior. Multiple connections are predicted between thermodynamics, short-time dynamics in the nearly localized state, and long-time relaxation by entropic barrier crossing. A critical comparison of the fluid volume fraction dependence of the hopping time with fit formulas which contain ideal divergences has been performed. Application of the derivative Stickel analysis suggests that the fit functions do not provide an accurate description over a wide range of volume fractions. Generalization to treat the kinetic vitrification of more complex colloidal and nanoparticle suspensions, and thermal glass-forming liquids, is possible.

Transport coefficients in glassy colloidal fluids

Our microscopic theory of entropic barrier formation and activated hopping for hard-sphere colloidal suspensions [K. S. Schweizer and E. J. Saltzman, J. Chem. Phys. 119, 1181 (2003), preceding paper] is combined with general statistical mechanical relations and a binary-collision-type model for the low-viscosity regime [E. G. D. Cohen, R. Verberg, and I. M. deSchepper, Physica A 251, 251 (1998)] to construct a theory for transport properties applicable for all particle concentrations. Quantitative, no adjustable parameter comparisons with experimental measurements of the self-diffusion constant and shear viscosity over a wide range of volume fractions show that the theory is quite accurate. The ability of model functions which contain dynamic singularities to describe our theoretical results is also established. Critical power laws and free-volume models can fit the theoretical calculations quite well over three to six orders of magnitude variation in the high-concentration regime, but all deviate qualitatively at sufficiently low and high volume fractions.

Phase behavior and concentration fluctuations in suspensions of hard spheres and nearly ideal polymers

The phase behavior and concentration fluctuations in suspensions of hard sphere colloids and nonadsorbing polymers under nearly ideal solvent conditions is studied experimentally. A remarkably different qualitative behavior compared to the athermal solvent case is observed for the dependence on polymer/particle size asymmetry of both the gelation and fluid–fluid phase separation boundaries. Near the theta state the effect of increasing the range of depletion attractions leads to a weak monotonic destabilization of the homogeneous phase at high particle volume fractions, with a reversal of the trend at lower volume fractions. In stark contrast to athermal solvent behavior, this nonmonotonic behavior results in multiple “curve crossings” of gel and phase separation boundaries as the polymer/particle size ratio is varied. Quantitative comparisons with no adjustable parameter PRISM integral equation theory for the fluid–fluid spinodals and osmotic compressibilities show good qualitative or semiquantitative agreement with all the experimental trends. The differences between good and ideal solvent conditions are largely attributed to changes in the polymer–polymer pair correlation functions due to the enhanced ability of coils to interpenetrate and cluster in theta solvents. Even for ideal solvent conditions the simplifying polymer model and statistical mechanical assumptions adopted by prior classic free volume and related approaches appear to miss fundamental aspects of the experimental behavior, especially for large size asymmetry ratios and/or moderate-to-high colloid volume fractions. The primary error can be identified with the approximation of a polymer chain by a phantom sphere with no conformational degrees of freedom.

Accurate Measurement of Small Polydispersities in Colloidal Suspensions

We demonstrate a simple method for the accurate characterization of the particle size distributions of colloidal particles with small polydispersities using a combination of dynamic light scattering and static light scattering. This method takes advantage of the variation in apparent radius observed using dynamic light scattering, as the scattering angle is increased through minima in the intensity form factor. Two-color dynamic light scattering is used to ensure there are no contributions from multiple scattering. We demonstrate that the poly(methyl methacrylate)-based particles used here have negatively skewed particle size distributions and in many cases can be characterized by a two parameter Weibull distribution. The importance of the accurate characterization of the particle size distribution for studies of crystallization in hard sphere colloidal suspensions is discussed.

Nonlinear equilibrium density fluctuations and spatial heterogeneities near the colloidal glass transition

Slow dynamics of equilibrium hard-sphere colloidal suspensions near the glass transition is discussed from a new viewpoint by numerically solving a cubic nonlinear stochastic diffusion equation for the density fluctuation recently proposed by one of the present authors (MT). The important role of the spatial heterogeneities near the glass transition is pointed out. Those heterogeneities, which originate from the long-range hydrodynamic interactions between colloids, are shown to be responsible for the slow relaxations of density fluctuations. Main results are also compared with those in nonequilibrium suspensions.