Motions in binary mixtures of hard colloidal spheres: melting of the glass

Decoupling of rotation and translation at the colloidal glass transition

In dense particle systems, the coupling of rotation and translation motion becomes intricate. Here, we report the results of confocal fluorescence microscopy where simultaneous recording of translational and rotational particle trajectories from a bidisperse colloidal dispersion is achieved by spiking the samples with rotational probe particles. The latter consist of colloidal particles containing two fluorescently labeled cores suited for tracking the particle's orientation. A comparison of the experimental data with event driven Brownian simulations gives insights into the system's structure and dynamics close to the glass transition and sheds new light onto the translation-rotation coupling. The data show that with increasing volume fractions, translational dynamics slows down drastically, whereas rotational dynamics changes very little. We find convincing agreement between simulation and experiments, even though the simulations neglect far-field hydrodynamic interactions. An additional analysis of the glass transition following mode coupling theory works well for the structural dynamics but indicates a decoupling of the diffusion of the smaller particle species. Shear stress correlations do not decorrelate in the simulated glass states and are not affected by rotational motion.

Cooperative activated hopping dynamics in binary glass-forming liquids: effects of the size ratio, composition, and interparticle interactions

Slow dynamics in supercooled and glassy liquids is an important research topic in soft matter physics. Compared to the traditionally focused one-component systems, glassy dynamics in mixture systems adds in a rich set of new complexities, which are fundamentally interesting and also relevant for many technological applications. In this paper, we apply the recently developed self-consistent cooperative hopping theory (SCCHT) to systematically investigate the effects of the size ratio, composition and interparticle interactions on the cooperative activated hopping dynamics of matrix (in larger size) and penetrant (in smaller size) particles in varied binary sphere mixture model systems, with a specific focus on ultrahigh mixture packing fractions that mimic the deeply supercooled glass transition conditions for molecular/polymeric mixture materials. Analysis shows that in these high activation barrier cases, the long-range elastic distortion associated with a matrix particle hopping over its cage confinement always generates an elastic barrier of a nonnegligible magnitude, although the ratio between the elastic barrier and local barrier contribution is sensitively dependent on all three mixture-specific system factors considered in this work. SCCHT predicts two general scenarios of penetrant-matrix cooperative activated hopping dynamics: matrix/penetrant co-hopping (regime 1) or the penetrant mean barrier hopping time shorter than that of the matrix (regime 2). Increasing the penetrant-to-matrix size ratio or the penetrant-matrix cross-attraction strength is found to universally enlarge the composition window of regime 1. Diverse dynamical properties characterising different aspects of the cooperative activated hopping process, including the penetrant and matrix transient localization lengths, penetrant and matrix hopping jump distances, different types of local and elastic activated barriers, and matrix long-time diffusivity, relaxation time and dynamic fragility are quantitatively studied against a wide range of variations over the three system factors. Of particular interest is the universal "anti-plasticization" phenomenon achievable for sufficiently strong cross-attractive interactions. The prospects this work opens for the exploration of a wide variety of polymer-based mixture materials are briefly discussed at the end.

Approaching the hard sphere limit in colloids suitable for confocal microscopy - the end of a decade lasting quest

PMMA-PHSA particles serve as the hard sphere model system since the 1980s. We investigate the fluid structure of fluorescent ones in three different solvents by laser scanning confocal microscopy: a decalin-tetrachloroethylene (TCE)-mixture and a decalin-cyclohexylbromide (CHB)-mixture with and without tetrabutylammoniumbromide (TBAB). The experimental 3D radial distribution functions are modeled by analytical theory and computer simulations taking polydispersity and the experimental position uncertainty into account. The quantitative comparison between experiment and simulation/theory establishes hard sphere like behavior for particles in decalin-TCE for a wide range of particle packing fractions. To the best of our knowledge, we present the first experimental dataset of a fluid structure that agrees convincingly with Percus-Yevick over a wide concentration range. Furthermore, charged sphere behavior is confirmed both for the decalin-CHB and the decalin-CHB-TBAB solvents, and it is demonstrated that a finite particle concentration reduces screening in the decalin-CHB-TBAB system compared to the bulk solvent.

Unveiling the structural relaxation of microgel suspensions at hydrophilic and hydrophobic interfaces

HYPOTHESIS

Poly(N-isopropylacrylamide) (PNIPAM) microgel particles show considerable hydrophilicity below the lower critical solution temperature (LCST) while they become hydrophobic above LCST. We hypothesize that interfacial wettability could tune particle-surface interaction and subsequent structural relaxation of microgel suspensions at interfaces during the volume phase transition.

EXPERIMENTS

The evanescent-wave scattering images of microgels at hydrophilic and hydrophobic interfaces are analyzed by a density-fluctuation autocorrelation function (δACF) over a wide range of particle volume fraction ϕ. The structural relaxation is characterized by the decay behavior of δACF. The scattering images in bulk are also processed as a comparison.

FINDINGS

A two-step relaxation decay is observed at both hydrophilic and hydrophobic interfaces. Relative to fast decay, the rate of structural relaxation in slow decay is reduced by a factor of ∼ 500 and ∼ 50 at hydrophilic and hydrophobic interfaces, respectively. The relaxation times obey divergent power-law dependences on intermediate regime of observing length scales at the two interfaces. Besides, the distribution of fluctuation for relaxation time at different local regions reveals that the structural relaxation is much more homogenous at hydrophilic interfaces than that at hydrophobic interfaces, especially at high ϕ.

Structure ordering and glass transition in size-asymmetric ternary mixtures of hard spheres: Variation from fragile to strong glasses

We investigate the structure and activated dynamics of a binary mixture of colloidal particles dispersed in a solvent of much smaller-sized particles. The solvent degrees of freedom are traced out from the grand partition function of the colloid-solvent mixture which reduces the system from ternary to effective binary mixture of colloidal particles. In the effective binary mixture colloidal particles interact via effective potential that consists of bare potential plus the solvent-induced interaction. Expressions for the effective potentials and pair correlation functions are derived. We used the result of pair correlation functions to determine the number of particles in a cooperatively reorganizing cluster (CRC) in which localized particles form "long-lived" nonchemical bonds with the central particle. For an event of relaxation to take place these bonds have to reorganize irreversibly, the energy involved in the processes is the effective activation energy of relaxation. Results are reported for hard sphere colloidal particles dispersed in a solvent of hard sphere particles. Our results show that the concentration of solvent can be used as a control parameter to fine-tune the microscopic structural ordering and the size of CRC that governs the glassy dynamics. We show that a small variation in the concentration of solvent creates a bigger change in the kinetic fragility which highlights a wide variation in behavior, ranging from fragile to strong glasses. We conclude that the CRC which is determined from the static pair correlation function and the fluctuations embedded in the system is probably the sole player in the physics of glass transition.

Many-Body Correlations Are Non-negligible in Both Fragile and Strong Glassformers

It is widely believed that the emergence of slow glassy dynamics is encoded in a material's microstructure. First-principles theory [mode-coupling theory (MCT)] is able to predict the dramatic slowdown of the dynamics from only static two-point correlations as input, yet it cannot capture all of the observed dynamical behavior. Here we go beyond two-point spatial correlation functions by extending MCT systematically to include higher-order static and dynamic correlations. We demonstrate that only adding the static triplet direct correlations already qualitatively changes the predicted glass-transition diagram of binary hard spheres and silica. Moreover, we find a nontrivial competition between static triplet correlations that work to stabilize the glass state and dynamic higher-order correlations that destabilize it for both materials. We conclude that the conventionally neglected static triplet direct correlations as well as higher-order dynamic correlations are, in fact, non-negligible in both fragile and strong glassformers.

Connecting Packing Efficiency of Binary Hard Sphere Systems to Their Intermediate Range Structure

Using computed x-ray tomography we determine the three dimensional (3D) structure of binary hard sphere mixtures as a function of composition and size ratio of the particles q. Using a recently introduced four-point correlation function we reveal that this 3D structure has on intermediate and large length scales a surprisingly regular order, the symmetry of which depends on q. The related structural correlation length has a minimum at the composition at which the packing fraction is highest. At this composition also the number of different local particle arrangements has a maximum, indicating that efficient packing of particles is associated with a structure that is locally maximally disordered.

Monodisperse patchy particle glass former

Glass formers are characterized by their ability to avoid crystallization. As monodisperse systems tend to rapidly crystallize, the most common glass formers in simulations are systems composed of mixtures of particles with different sizes. Here, we make use of the ability of patchy particles to change their local structure to propose them as monodisperse glass formers. We explore monodisperse systems with two patch geometries: a 12-patch geometry that enhances the formation of icosahedral clusters and an 8-patch geometry that does not appear to strongly favor any particular local structure. We show that both geometries avoid crystallization and present glassy features at low temperatures. However, the 8-patch geometry better preserves the structure of a simple liquid at a wide range of temperatures and packing fractions, making it a good candidate for a monodisperse glass former.

Super-Arrhenius diffusion in a binary colloidal mixture at low volume fraction: an effect of depletion interaction due to an asymmetric barrier

We report results from the molecular dynamics simulations of a binary colloidal mixture subjected to an external potential barrier along one of the spatial directions at low volume fraction, ϕ = 0.2. The variations in the asymmetry of the external potential barrier do not change the dynamics of the smaller particles, showing Arrhenius diffusion. However, the dynamics of the larger particles shows a crossover from sub-Arrhenius to super-Arrhenius diffusion with the asymmetry in the external potential at the low temperatures and low volume fraction. Super-Arrhenius diffusion is generally observed in the high density systems where the transient cages are present due to dense packing, e.g., supercooled liquids, jammed systems, diffusion through porous membranes, dynamics within the cellular environment, etc. This model can be applied to study the molecular transport across cell membranes, nano-, and micro-channels which are characterized by spatially asymmetric potentials.

"Dense diffusion" in colloidal glasses: short-ranged long-time self-diffusion as a mechanistic model for relaxation dynamics

Despite decades of exploration of the colloidal glass transition, mechanistic explanation of glassy relaxation processes has remained murky. State-of-the-art theoretical models of the colloidal glass transition such as random first order transition theory, active barrier hopping theory, and non-equilibrium self-consistent generalized Langevin theory assert that relaxation reported at volume fractions above the ideal mode coupling theory prediction φg,MCT requires some sort of activated process, and that cooperative motion plays a central role. However, discrepancies between predicted and measured values of φg and ambiguity in the role of cooperative dynamics persist. Underlying both issues is the challenge of conducting deep concentration quenches without flow and the difficulty in accessing particle-scale dynamics. These two challenges have led to widespread use of fitting methods to identify divergence, but most a priori assume divergent behavior; and without access to detailed particle dynamics, it is challenging to produce evidence of collective dynamics. We address these limitations by conducting dynamic simulations accompanied by experiments to quench a colloidal liquid into the putative glass by triggering an increase in particle size, and thus volume fraction, at constant particle number density. Quenches are performed from the liquid to final volume fractions 0.56 ≤ φ ≤ 0.63. The glass is allowed to age for long times, and relaxation dynamics are monitored throughout the simulation. Overall, correlated motion acts to release dynamics from the glassy plateau - but only over length scales much smaller than a particle size - allowing self-diffusion to re-emerge; self-diffusion then relaxes the glass into an intransient diffusive state, which persists for φ < 0.60. We observe similar relaxation dynamics up to φ = 0.63 before achieving the intransient state. We find that this long-time self-diffusion is short-ranged: analysis of mean-square displacement reveals a glassy cage size a fraction of a particle size that shrinks with quench depth, i.e. increasing volume fraction. Thus the equivalence between cage size and particle size found in the liquid breaks down in the glass, which we confirm by examining the self-intermediate scattering function over a range of wave numbers. The colloidal glass transition can hence be viewed mechanistically as a shift in the long-time self-diffusion from long-ranged to short-ranged exploration of configurations. This shift takes place without diverging dynamics: there is a smooth transition as particle mobility decreases dramatically with concomitant emergence of a dense local configuration space that permits sampling of many configurations via local particle motion.

Effective one-component model of binary mixture: molecular arrest induced by the spatially correlated stochastic dynamics

Spatially correlated noise (SCN), i.e. the thermal noise that affects neighbouring particles in a similar manner, is ubiquitous in soft matter systems. In this work, we apply the over-damped SCN-driven Langevin equations as an effective, one-component model of the dynamics in dense binary mixtures. We derive the thermodynamically consistent fluctuation-dissipation relation for SCN to show that it predicts the molecular arrest resembling the glass transition, i.e. the critical slow-down of dynamics in the disordered phases. We show that the mechanism of singular dissipation is embedded in the dissipation matrix, accompanying SCN. We are also able to identify the characteristic length of collective dissipation, which diverges at critical packing. This novel physical quantity conveniently describes the difference between the ergodic and non-ergodic dynamics. The model is fully analytically solvable, one-dimensional and admits arbitrary interactions between the particles. It qualitatively reproduces several different modes of arrested disorder encountered in binary mixtures, including e.g. the re-entrant arrest. The model can be effectively compared to the mode coupling theory.

Persistent Anti-Correlations in Brownian Dynamics Simulations of Dense Colloidal Suspensions Revealed by Noise Suppression

Transport properties of a hard-sphere colloidal fluid are investigated by Brownian dynamics simulations. We implement a novel algorithm for the time-dependent velocity-autocorrelation function (VACF) essentially eliminating the noise of the bare random motion. The measured VACF reveals persistent anti-correlations manifested by a negative algebraic power-law tail t^{-5/2} at all densities. At small packing fractions the simulations fully agree with the analytic low-density prediction, yet the amplitude of the tail becomes dramatically suppressed as the packing fraction is increased. The mode-coupling theory of the glass transition provides a qualitative explanation for the strong variation in terms of the static compressibility as well as the slowing down of the structural relaxation.

Refractive index matched, nearly hard polymer colloids

Refractive index matched particles serve as essential model systems for colloid scientists, providing nearly hard spheres to explore structure and dynamics. The poly(methyl methacrylate) latexes typically used are often refractive index matched by dispersing them in binary solvent mixtures, but this can lead to undesirable changes, such as particle charging or swelling. To avoid these shortcomings, we have synthesized refractive index matched colloids using polymerization-induced self-assembly (PISA) rather than as polymer latexes. The crucial difference is that these diblock copolymer nanoparticles consist of a single core-forming polymer in a single non-ionizable solvent. The diblock copolymer chosen was poly(stearyl methacrylate)-poly(2,2,2-trifluoroethyl methacrylate) (PSMA-PTFEMA), which self-assembles to form PTFEMA core spheres in n-alkanes. By monitoring scattered light intensity, n-tetradecane was found to be the optimal solvent for matching the refractive index of such nanoparticles. As expected for PISA syntheses, the diameter of the colloids can be controlled by varying the PTFEMA degree of polymerization. Concentrated dispersions were prepared, and the diffusion of the PSMA-PTFEMA nanoparticles as a function of volume fraction was measured. These diblock copolymer nanoparticles are a promising new system of transparent spheres for future colloidal studies.

Glassy dynamics in asymmetric binary mixtures of hard spheres

We perform a systematic and detailed study of the glass transition in highly asymmetric binary mixtures of colloidal hard spheres, combining differential dynamic microscopy experiments, event-driven molecular dynamics simulations, and theoretical calculations, exploring the whole state diagram and determining the self-dynamics and collective dynamics of both species. Two distinct glassy states involving different dynamical arrest transitions are consistently described, namely, a double glass with the simultaneous arrest of the self-dynamics and collective dynamics of both species, and a single glass of large particles in which the self-dynamics of the small species remains ergodic. In the single-glass scenario, spatial modulations in the collective dynamics of both species occur due to the structure of the large spheres, a feature not observed in the double-glass domain. The theoretical results, obtained within the self-consistent generalized Langevin equation formalism, are in agreement with both simulations and experimental data, thus providing a stringent validation of this theoretical framework in the description of dynamical arrest in highly asymmetric mixtures. Our findings are summarized in a state diagram that classifies the various amorphous states of highly asymmetric mixtures by their dynamical arrest mechanisms.

Different scenarios of dynamic coupling in glassy colloidal mixtures

The composition of mixtures determines the mechanism of glass formation and dynamic coupling of different species.

Crossover from equilibration to aging: Nonequilibrium theory versus simulations

Understanding glasses and the glass transition requires comprehending the nature of the crossover from the ergodic (or equilibrium) regime, in which the stationary properties of the system have no history dependence, to the mysterious glass transition region, where the measured properties are nonstationary and depend on the protocol of preparation. In this work we use nonequilibrium molecular dynamics simulations to test the main features of the crossover predicted by the molecular version of the recently developed multicomponent nonequilibrium self-consistent generalized Langevin equation theory. According to this theory, the glass transition involves the abrupt passage from the ordinary pattern of full equilibration to the aging scenario characteristic of glass-forming liquids. The same theory explains that this abrupt transition will always be observed as a blurred crossover due to the unavoidable finiteness of the time window of any experimental observation. We find that within their finite waiting-time window, the simulations confirm the general trends predicted by the theory.

Self-diffusion in two-dimensional binary colloidal hard-sphere fluids

We present a systematic experimental study of the dynamic behavior of monodisperse and bidisperse two-dimensional colloidal hard-sphere fluids. We consider the diffusive behavior of the two types of particles for systems with a variety of compositions and total area fractions. In particular, we measure the short- and long-time diffusion coefficients for both species independently. We find that the short-time self-diffusion coefficients show an approximately linear dependence on the area fraction and that the long-time self-diffusion coefficients are well described by an expression dependent upon only the area fraction and contact value of the radial distribution function. Finally, we consider the effect of composition change and find some variation in the long-time self-diffusion coefficients, which we ascribe to the complex packing effects exhibited by binary systems.

Qualitatively different collective and single-particle dynamics in a supercooled liquid

The equations of fluctuating nonlinear hydrodynamics for a two component mixture are obtained with a proper choice of slow variables which correspond to the conservation laws in the system. Using these nonlinear equations we construct the basic equations of the mode coupling theory (MCT) and consequent ergodic-nonergodic (ENE) transition in a binary mixture. The model is also analyzed in the one component limit of the mixture to study the dynamics of a tagged particle in the sea of identical particles. According to the existing MCT, dynamics of the single-particle correlation is slaved to that of the collective density fluctuations and, hence, both correlations freeze simultaneously at the ENE transition. We show here from a nonperturbative approach that at the ENE transition, characterized by the freezing of the long time limit of the dynamic correlation of collective density fluctuations to a nonzero value, the tagged-particle correlation still decays to zero. Our result implies that the point at which simulation or experimental data of the self-diffusion constant extrapolate to zero would not correspond to the ENE transition of simple MCT.

Short-time diffusion in concentrated bidisperse hard-sphere suspensions

Diffusion in bidisperse Brownian hard-sphere suspensions is studied by Stokesian Dynamics (SD) computer simulations and a semi-analytical theoretical scheme for colloidal short-time dynamics, based on Beenakker and Mazur's method [Physica A 120, 388-410 (1983); 126, 349-370 (1984)]. Two species of hard spheres are suspended in an overdamped viscous solvent that mediates the salient hydrodynamic interactions among all particles. In a comprehensive parameter scan that covers various packing fractions and suspension compositions, we employ numerically accurate SD simulations to compute the initial diffusive relaxation of density modulations at the Brownian time scale, quantified by the partial hydrodynamic functions. A revised version of Beenakker and Mazur's δγ-scheme for monodisperse suspensions is found to exhibit surprisingly good accuracy, when simple rescaling laws are invoked in its application to mixtures. The so-modified δγ scheme predicts hydrodynamic functions in very good agreement with our SD simulation results, for all densities from the very dilute limit up to packing fractions as high as 40%.

Different mechanisms for dynamical arrest in largely asymmetric binary mixtures

Using confocal microscopy we investigate binary colloidal mixtures with large size asymmetry, in particular the formation of dynamically arrested states of the large spheres. The volume fraction of the system is kept constant, and as the concentration of small spheres is increased we observe a series of transitions of the large spheres to different arrested states: an attractive glass, a gel, and an asymmetric glass. These states are distinguished by the degree of dynamical arrest and the amount of structural and dynamical heterogeneity. The transitions between two different arrested states occur through melting and the formation of a fluid state. While a space-spanning network of bonded particles is found in both arrested and fluid states, only arrested states are characterized by the presence of a space-spanning network of dynamically arrested particles.

Relaxation dynamics in a binary hard-ellipse liquid

Structural relaxation in binary hard spherical particles has been shown recently to exhibit a wealth of remarkable features when size disparity or mixture composition is varied. In this paper, we test whether or not similar dynamical phenomena occur in glassy systems composed of binary hard ellipses. We demonstrate via event-driven molecular dynamics simulation that a binary hard-ellipse mixture with an aspect ratio of two and moderate size disparity displays characteristic glassy dynamics upon increasing density in both the translational and the rotational degrees of freedom. The rotational glass transition density is found to be close to the translational one for the binary mixtures investigated. More importantly, we assess the influence of size disparity and mixture composition on the relaxation dynamics. We find that an increase of size disparity leads, both translationally and rotationally, to a speed up of the long-time dynamics in the supercooled regime so that both the translational and the rotational glass transition shift to higher densities. By increasing the number concentration of the small particles, the time evolution of both translational and rotational relaxation dynamics at high densities displays two qualitatively different scenarios, i.e., both the initial and the final part of the structural relaxation slow down for small size disparity, while the short-time dynamics still slows down but the final decay speeds up in the binary mixture with large size disparity. These findings are reminiscent of those observed in binary hard spherical particles. Therefore, our results suggest a universal mechanism for the influence of size disparity and mixture composition on the structural relaxation in both isotropic and anisotropic particle systems.

Transient dynamics during stress overshoots in binary colloidal glasses

We investigate, using simultaneous rheology and confocal microscopy, the time-dependent stress response and transient single-particle dynamics following a step change in shear rate in binary colloidal glasses with large dynamical asymmetry and different mixing ratios. The transition from solid-like response to flow is characterised by a stress overshoot, whose magnitude is linked to transient superdiffusive dynamics as well as cage compression effects. These and the yield strain at which the overshoot occurs vary with the mixing ratio, and hence the prevailing caging mechanism. The yielding and stress storage are dominated by dynamics on different time and length scales, the short-time in-cage dynamics and the long-time structural relaxation respectively. These time scales and their relation to the characteristic time associated with the applied shear, namely the inverse shear rate, result in two different and distinct regimes of the shear rate dependencies of the yield strain and the magnitude of the stress overshoot.

Dynamic equivalences in the hard-sphere dynamic universality class

We perform systematic simulation experiments on model systems with soft-sphere repulsive interactions to test the predicted dynamic equivalence between soft-sphere liquids with similar static structure. For this we compare the simulated dynamics (mean squared displacement, intermediate scattering function, α-relaxation time, etc.) of different soft-sphere systems, between them and with the hard-sphere liquid. We then show that the referred dynamic equivalence does not depend on the (Newtonian or Brownian) nature of the microscopic laws of motion of the constituent particles, and hence, applies independently to colloidal and to atomic simple liquids. Finally, we verify another more recently proposed dynamic equivalence, this time between the long-time dynamics of an atomic liquid and its corresponding Brownian fluid (i.e., the Brownian system with the same interaction potential).

The physics of the colloidal glass transition

As one increases the concentration of a colloidal suspension, the system exhibits a dramatic increase in viscosity. Beyond a certain concentration, the system is said to be a colloidal glass; structurally, the system resembles a liquid, yet motions within the suspension are slow enough that it can be considered essentially frozen. For several decades, colloids have served as a valuable model system for understanding the glass transition in molecular systems. The spatial and temporal scales involved allow these systems to be studied by a wide variety of experimental techniques. The focus of this review is the current state of understanding of the colloidal glass transition, with an emphasis on experimental observations. A brief introduction is given to important experimental techniques used to study the glass transition in colloids. We describe features of colloidal systems near and in glassy states, including increases in viscosity and relaxation times, dynamical heterogeneity and ageing, among others. We also compare and contrast the glass transition in colloids to that in molecular liquids. Other glassy systems are briefly discussed, as well as recently developed synthesis techniques that will keep these systems rich with interesting physics for years to come.

Depletion-induced structure and dynamics in bimodal colloidal suspensions

Combined small angle x-ray scattering and x-ray photon correlation spectroscopy studies of moderately concentrated bimodal hard-sphere colloidal suspensions in the fluid phase show that depletion-induced demixing introduces spatially heterogeneous dynamics with two distinct time scales. The adhesive nature, as well as the mobility, of the large particles is determined by the level of interaction within the monomodal domains. This interaction is driven by osmotic forces, which are governed by the relative concentration of the constituents.

Tests of mode-coupling theory in two dimensions

We analyze the glassy dynamics of binary mixtures of hard disks in two dimensions. Predictions of the mode-coupling theory (MCT) are tested with extensive Brownian dynamics simulations. Measuring the collective particle density correlation functions in the vicinity of the glass transition, we verify four predicted mixing effects. For instance, for large size disparities, adding a small amount of small particles at a fixed packing fraction leads to a speedup in the long-time dynamics, while for small size disparities it leads to a slowing-down. Qualitative features of the nonergodicity parameters and the β relaxation, which both depend in a nontrivial way on the mixing ratio, are found in the simulated correlators. Studying one system in detail, we are able to determine its ideal MCT glass transition point as φ(c)=0.7948 and test MCT predictions quantitatively.

Effect of mixing and spatial dimension on the glass transition

We study the influence of composition changes on the glass transition of binary hard disk and hard sphere mixtures in the framework of mode coupling theory. We derive a general expression for the slope of a glass transition line. Applied to the binary mixture in the low concentration limits, this method allows a fast prediction of some properties of the glass transition lines. The glass transition diagram we find for binary hard disks strongly resembles the random close packing diagram. Compared to three dimensions from previous studies, the extension of the glass regime due to mixing is much more pronounced in two dimensions where plasticization only sets in at larger size disparities. For small size disparities we find a stabilization of the glass phase quadratic in the deviation of the size ratio from unity.

Low-density ordered phase in brownian dipolar colloidal suspensions

We study the low volume fraction and electric field phase behavior of a Brownian colloidal suspension. On the application of a uniform ac field, we find a novel phase where chains of particles aggregate to form a well defined cellular network, consisting of particle-free "voids" surrounded by a percolating network of particle-rich walls. This cellular structure is stable to very long times, indicative of an equilibrium thermodynamic phase. The cell-cell spacing is not sensitive to the concentration of the sample but scales with sample thickness. Any self-consistent mechanism for the existence of this void phase must consist of long-ranged repulsions and shorter-ranged attractions.

Dynamics and structure of an aging binary colloidal glass

We study aging in a colloidal suspension consisting of micron-sized particles in a liquid. This system is made glassy by increasing the particle concentration. We observe samples composed of particles of two sizes, with a size ratio of 1:2.1 and a volume fraction ratio 1:6, using fast laser scanning confocal microscopy. This technique yields real-time, three-dimensional movies deep inside the colloidal glass. Specifically, we look at how the size, motion, and structural organization of the particles relate to the overall aging of the glass. Particles move in spatially heterogeneous cooperative groups. These mobile regions tend to be richer in small particles, and these small particles facilitate the motion of nearby particles of both sizes.

Theory of dynamic arrest in colloidal mixtures

We present a first-principles theory of dynamic arrest in colloidal mixtures based on the multicomponent self-consistent generalized Langevin equation theory of colloid dynamics [M. A. Chávez-Rojo and M. Medina-Noyola, Phys. Rev. E 72, 031107 (2005); M. A. Chávez-Rojo and M. Medina-Noyola, Phys. Rev. E76, 039902 (2007)]. We illustrate its application with a description of dynamic arrest in two simple model colloidal mixtures: namely, hard-sphere and repulsive Yukawa binary mixtures. Our results include observation of the two patterns of dynamic arrest, one in which both species become simultaneously arrested and the other involving the sequential arrest of the two species. The latter case gives rise to mixed states in which one species is arrested while the other species remains mobile. We also derive the ("bifurcation" or fixed-point") equations for the nonergodic parameters of the system, which takes the surprisingly simple form of a system of coupled equations for the localization length of the particles of each species. The solution of this system of equations indicates unambiguously which species is arrested (finite localization length) and which species remains ergodic (infinite localization length). As a result, we are able to draw the entire ergodic-nonergodic phase diagram of the binary hard-sphere mixture.

Energy landscape, antiplasticization, and polydispersity induced crossover of heterogeneity in supercooled polydisperse liquids

Polydispersity is found to have a significant effect on the potential energy landscape; the average inherent structure energy decreases with polydispersity. Increasing polydispersity at a fixed volume fraction decreases the glass transition temperature and the fragility of glass formation analogous to the antiplasticization seen in some polymeric melts. An interesting temperature dependent crossover of heterogeneity with polydispersity is observed at low temperature due to the faster buildup of dynamic heterogeneity at lower polydispersity.

A new model system for diffusion NMR studies of concentrated monodisperse and bidisperse colloids

A method to prepare monodisperse and simultaneously NMR-visible and fluorescent colloidal particles is described, and a systematic approach to obtain spectrally resolved diffusion coefficient for every component in a monodisperse colloidal suspension is presented. We also prepared bidisperse colloidal suspensions, where each colloid component has a distinct NMR spectral signature, and obtained the diffusion coefficients of both colloid species simultaneously in concentrated colloidal suspensions, with volume fractions between 20 and 50%. The colloidal model system developed in this work enables the study of colloidal phase behavior in binary mixtures for different number and size ratios.

Relaxation scenarios in a mixture of large and small spheres: Dependence on the size disparity

We present a computational investigation on the slow dynamics of a mixture of large and small soft spheres. By varying the size disparity at a moderate fixed composition different relaxation scenarios are observed for the small particles. For small disparity density-density correlators exhibit moderate stretching. Only small quantitative differences are observed between dynamic features for large and small particles. On the contrary, large disparity induces a clear time scale separation between the large and small particles. Density-density correlators for the small particles become extremely stretched and display logarithmic relaxation by properly tuning the temperature or the wave vector. Self-correlators decay much faster than density-density correlators. For very large size disparity, a complete separation between self- and collective dynamics is observed for the small particles. Self-correlators decay to zero at temperatures where density-density correlations are frozen. The dynamic picture obtained by varying the size disparity resembles features associated with mode coupling transition lines of the types B and A at, respectively, small and very large size disparities. Both lines might merge, at some intermediate disparity, at a higher-order point, to which logarithmic relaxation would be associated. This picture resembles predictions of a recent mode coupling theory for fluids confined in matrices with interconnected voids [V. Krakoviack, Phys. Rev. Lett. 94, 065703 (2005)].

Sensitivity of arrest in mode-coupling glasses to low-q structure

We quantify, within mode coupling theory, how changes in the liquid structure affect that of the glass. Apart from the known sensitivity to the structure factor S(q) at wave vectors around the first sharp diffraction peak q0, we find a strong (and inverted) response to structure at wave vectors below this peak: an increase in S(q0/2) lowers the degree of arrest over a wide q-range. This strong sensitivity to "caged cage" packing effects, on length scales of order 2d, is much weaker in attractive glasses where short-range bonding dominates the steric caging effect.

Scattering for mixtures of hard spheres: comparison of total scattering intensities with model

The angular dependence of the intensity of x-rays scattered from binary and ternary hard sphere mixtures is investigated and compared to the predictions of two scattering models. Mixture ratio and total volume fraction dependent effects are investigated for size ratios equal to 0.51 and 0.22. Comparisons of model predictions with experimental results indicate the significant impact of the role of particle size distributions in interpreting the angular dependence of the scattering at wave vectors probing density fluctuations intermediate between the sizes of the particles in the mixture.

Direct measurement of relative and collective diffusion in a dilute binary colloidal suspension

Experimental characterization of the dynamics of multicomponent fluids is a problem of general importance to the field of complex fluids. We demonstrate a new experimental approach, termed two-color Fourier imaging correlation spectroscopy, which allows direct measurement of the partial dynamic structure factors, S(11)(k,tau), S(22)(k,tau), and S(12)(k,tau), where 1, 2 label the component species of a binary colloidal suspension. Linear combinations of the partial dynamic structure factors yield the characteristic time-correlation functions of the binary fluid. These are the correlation functions of concentration fluctuations S(CC)(k,tau), number density fluctuations S(NN)(k,tau), and cross-correlations between number density and concentration fluctuations S(NC)(k,tau). Test measurements are performed on a dilute symmetric mixture of fluorescently labeled 0.5 and 1.0 microm polystyrene spheres. From these data, we determine generalized collective and relative diffusion coefficients, and compare them to the predictions for an ideal mixture of noninteracting particles.

Crystallization kinetics of polydisperse colloidal hard spheres. II. Binary mixtures

In this paper we present measurements of the crystallization kinetics of binary mixtures of two different sized hard sphere particles. The growth of the Bragg reflections over time were analyzed to yield the crystallite scattering vector, the total amount of crystal, and the average linear crystal size. It was observed that a particle size distribution skewed to higher sized particles has a less detrimental effect on the crystal structure than a skew to smaller sized particles. In the latter case we observe that initial crystallite growth occurs at only a small number of sites, with further crystallization sites developing at later times. Based on these measurements we elaborate further on the previously proposed growth mechanism whereby crystallization occurs in conjunction with a local fractionation process in the fluid, which significantly affects the kinetic growth of crystallites in polydisperse systems.

Structure of colloidal crystals in sedimenting mixed dispersions of latex and silica particles

We report bcc-fcc transitions of colloidal crystals in mixed aqueous dispersions of polystyrene-based latex particles (diameter: D=55.8 nm) and silica particles (diameter: D=170 nm). In the single systems, the silica particles formed bcc crystals and the latex particles did not crystallize. In the binary mixtures of these particles, colloidal crystals with fcc structures were found by the analysis of Kikuchi-Kossel diffraction images. Especially, the samples at low latex fractions started out as bcc structures, and then changed to fcc structures. Due to gravitational sedimentation, the lattice constant increased as the height from the bottom of the dispersion became larger. Furthermore, the lattice constant became smaller at a given silica fraction as the latex fraction increased.

Influence of a depletion interaction on dynamical heterogeneity in a dense quasi-two-dimensional colloid liquid

We report the results of digital video microscopy studies of the large particle displacements in a quasi-two-dimensional binary mixture of large (L) and small (S) colloid particles with diameter ratio sigma(L)/sigma(S)=4.65, as a function of the large and small colloid particle densities. As in the case of the one-component quasi-two-dimensional colloid system, the binary mixtures exhibit structural and dynamical heterogeneity. The distribution of large particle displacements over the time scale examined provides evidence for (at least) two different mechanisms of motion, one associated with particles in locally ordered regions and the other associated with particles in locally disordered regions. When rhoL*=Npisigma(L) (2)/4A< or =0.35, the addition of small colloid particles leads to a monotonic decrease in the large particle diffusion coefficient with increasing small particle volume fraction. When rhoL* > or =0.35 the addition of small colloid particles to a dense system of large colloid particles at first leads to an increase in the large particle diffusion coefficient, which is then followed by the expected decrease of the large particle diffusion coefficient with increasing small colloid particle volume fraction. The mode coupling theory of the ideal glass transition in three-dimensional systems makes a qualitative prediction that agrees with the initial increase in the large particle diffusion coefficient with increasing small particle density. Nevertheless, because the structural and dynamical heterogeneities of the quasi-two-dimensional colloid liquid occur within the field of equilibrium states, and the fluctuations generate locally ordered domains rather than just disordered regions of higher and lower density, it is suggested that mode coupling theory does not account for all classes of relevant fluctuations in a quasi-two-dimensional liquid.

alpha-Relaxation processes in binary hard-sphere mixtures

Molecular-dynamics simulations are presented for two correlation functions formed with the partial density fluctuations of binary hard-sphere mixtures in order to explore the effects of mixing on the evolution of glassy dynamics upon compressing the liquid into high-density states. Partial-density-fluctuation correlation functions for the two species are reported. Results for the alpha-relaxation process are quantified by parameters for the strength, stretching, and time scale, where the latter varies over almost four orders of magnitude upon compression. The parameters exhibit an appreciable dependence on the wave vector, and this dependence is different for the correlation function referring to the smaller and that for the larger species. These features are shown to be in semiquantitative agreement with those calculated within the mode-coupling theory for ideal liquid-glass transitions.