Glass Transition Of Hard Spheres Research Articles

Complex optical transport, dynamics, and rheology of intermediately attractive emulsions

Introducing short-range attractions in Brownian systems of monodisperse colloidal spheres can substantially impact their structures and consequently their optical transport and rheological properties. Here, for size-fractionated colloidal emulsions, we show that imposing an intermediate strength of attraction, well above but not much larger than thermal energy (approx 5.6k_{textrm{B}}T), through micellar depletion leads to a striking notch in the measured inverse mean free path of optical transport, 1/ell ^*, as a function of droplet volume fraction, phi. This notch, which appears between the hard-sphere glass transition, phi _{textrm{g}}, and maximal random jamming, phi _{textrm{MRJ}}, implies the existence of a greater population of compact dense clusters of droplets, as compared to tenuous networks of droplets in strongly attractive emulsion gels. We extend a prior decorated core-shell network model for strongly attractive colloidal systems to include dense non-percolating clusters that do not contribute to shear rigidity. By constraining this extended model using the measured 1/ell ^*(phi ), we improve and expand the microrheological interpretation of diffusing wave spectroscopy (DWS) experiments made on attractive colloidal systems. Our measurements and modeling demonstrate richness and complexity in optical transport and shear rheological properties of dense, disordered colloidal systems having short-range intermediate attractions between moderately attractive glasses and strongly attractive gels.

Understanding charged vesicle suspensions as Wigner glasses: dynamical aspects

Suspensions of charged vesicles in water with added salt are widespread in nature and industrial production. Here we investigate, via Brownian dynamics simulations, a model that grasps the key features of these systems, with bidisperse colloidal beads interacting via a hard-core and an electrostatic double layer potential. Our goal is to focus on a set of interaction parameters that is not generic but measured in recent experiments, and relevant for a class of consumer products, such as liquid fabric softeners. On increasing the volume fraction in a range relevant to real formulation, we show that the dynamics become progressively slower and heterogeneous, displaying the typical signatures of an approaching glass transition. On lowering the salt concentration, which corresponds to increasing the strength and range of the electrostatic repulsion, the emergence of glassy dynamics becomes significantly steeper, and, remarkably, occurs at volume fractions well below the hard-sphere glass transition. The volume fraction dependence of the structural relaxation time at different salt concentration is well described through a functional law inspired by a recently proposed model (Krausser et al 2015 Proc. Natl Acad. Sci. USA 112 13762). According to our results, the investigated system may be thought of as a Wigner glass, i.e. a low-density glassy state stabilized by long-range repulsive interactions. Overall, our study suggests that glassy dynamics plays an important role in controlling the stability of these suspensions.

Non-equilibrium theory of arrested spinodal decomposition.

The non-equilibrium self-consistent generalized Langevin equation theory of irreversible relaxation [P. E. Ramŕez-González and M. Medina-Noyola, Phys. Rev. E 82, 061503 (2010); 82, 061504 (2010)] is applied to the description of the non-equilibrium processes involved in the spinodal decomposition of suddenly and deeply quenched simple liquids. For model liquids with hard-sphere plus attractive (Yukawa or square well) pair potential, the theory predicts that the spinodal curve, besides being the threshold of the thermodynamic stability of homogeneous states, is also the borderline between the regions of ergodic and non-ergodic homogeneous states. It also predicts that the high-density liquid-glass transition line, whose high-temperature limit corresponds to the well-known hard-sphere glass transition, at lower temperature intersects the spinodal curve and continues inside the spinodal region as a glass-glass transition line. Within the region bounded from below by this low-temperature glass-glass transition and from above by the spinodal dynamic arrest line, we can recognize two distinct domains with qualitatively different temperature dependence of various physical properties. We interpret these two domains as corresponding to full gas-liquid phase separation conditions and to the formation of physical gels by arrested spinodal decomposition. The resulting theoretical scenario is consistent with the corresponding experimental observations in a specific colloidal model system.

The structural origin of the hard-sphere glass transition in granular packing.

Glass transition is accompanied by a rapid growth of the structural relaxation time and a concomitant decrease of configurational entropy. It remains unclear whether the transition has a thermodynamic origin, and whether the dynamic arrest is associated with the growth of a certain static order. Using granular packing as a model hard-sphere glass, we show the glass transition as a thermodynamic phase transition with a ‘hidden' polytetrahedral order. This polytetrahedral order is spatially correlated with the slow dynamics. It is geometrically frustrated and has a peculiar fractal dimension. Additionally, as the packing fraction increases, its growth follows an entropy-driven nucleation process, similar to that of the random first-order transition theory. Our study essentially identifies a long-sought-after structural glass order in hard-sphere glasses.

On polydispersity and the hard sphere glass transition.

We investigate the dynamics of polydisperse hard spheres at high packing fractions ϕ. We use extensive numerical simulations based on an experimentally-realistic particle size distribution (PSD) and compare to commonly-used PSDs such as Gaussian or top hat distribution. We find that the mode of kinetic arrest depends on the PSD's shape and not only on its variance. For the experimentally-realistic PSD we find ageing dynamics even though the density correlators decay fully to zero for ϕ ≥ 0.59. We observe substantial decoupling of the dynamics of the smallest and largest particles. While the smallest particles remain diffusive in all our simulations, a power-law describes the largest-particle diffusion, suggesting an ideal arrest at ϕc ∼ 0.588. The latter is however averted just before ϕc, due to the presence of the mobile smallest particles. In addition, we identify that a partial aging mechanism is at work, whose effects are most pronounced for the largest particles. By comparing our results with recent experimental observations of ergodic behavior up to ϕ ∼ 0.6 in a hard-sphere system, we argue that this is an effect of polydispersity, which smears out the glass transition.

Anomalous dynamics at the hard-sphere glass transition.

We use X-ray photon correlation spectroscopy to study the dynamics of hard sphere suspensions and report the emergence of ergodicity restoring anomalous intermittent relaxation modes in the highest concentration suspension that is estimated to be above the glass transition concentration. We associate these phenomena with non-thermal stress induced relaxations and support our interpretation by a direct comparison of the results with predictions of the mode coupling theory.

Systematic expansion in the order parameter for replica theory of the dynamical glass transition

It has been shown recently that predictions from mode-coupling theory for the glass transition of hard-spheres become increasingly bad when dimensionality increases, whereas replica theory predicts a correct scaling. Nevertheless if one focuses on the regime around the dynamical transition in three dimensions, mode-coupling results are far more convincing than replica theory predictions. It seems thus necessary to reconcile the two theoretic approaches in order to obtain a theory that interpolates between low-dimensional, mode-coupling results, and "mean-field" results from replica theory. Even though quantitative results for the dynamical transition issued from replica theory are not accurate in low dimensions, two different approximation schemes--small cage expansion and replicated hyper-netted-chain (RHNC)--provide the correct qualitative picture for the transition, namely, a discontinuous jump of a static order parameter from zero to a finite value. The purpose of this work is to develop a systematic expansion around the RHNC result in powers of the static order parameter, and to calculate the first correction in this expansion. Interestingly, this correction involves the static three-body correlations of the liquid. More importantly, we separately demonstrate that higher order terms in the expansion are quantitatively relevant at the transition, and that the usual mode-coupling kernel, involving two-body direct correlation functions of the liquid, cannot be recovered from static computations.

Glass transition of hard spheres in high dimensions

We have investigated analytically and numerically the liquid-glass transition of hard spheres for dimensions d-->infinity in the framework of mode-coupling theory. The numerical results for the critical collective and self-nonergodicity parameters fc(k;d) and fc(s)(k;d) exhibit non-Gaussian k dependence even up to d=800.fc(s)(k;d) and fc(k;d) differ for k approximately d1/2, but become identical on a scale k approximately d, which is proven analytically. The critical packing fraction phic(d) approximately d(2)2(-d) is above the corresponding Kauzmann packing fraction phiK(d) derived by a small cage expansion. Its quadratic pre-exponential factor is different from the linear one found earlier. The numerical values for the exponent parameter and therefore the critical exponents a and b depend on d, even for the largest values of d.

Thermodynamic signature of the dynamic glass transition in hard spheres

We use extensive event-driven molecular dynamics simulations to study the thermodynamic,structural and dynamic properties of hard-sphere glasses. We determine the equation ofstate of the metastable fluid branch for hard spheres with a size polydispersity of10%. Our results show a clear jump in the slope of the isothermal compressibility. Theobservation of a thermodynamic signature at the transition from a metastable fluid to aglassy state is analogous to the abrupt change in the specific heat or thermal expansioncoefficient as observed for molecular liquids at the glass transition. The dynamic glasstransition becomes more pronounced and shifts to higher densities for longer equilibrationtimes.

Aging of a hard-sphere glass: effect of the microscopic dynamics

We present simulations of the aging of a quasi-hard-sphere glass, with Newtonian andBrownian microscopic dynamics. The system is equilibrated at the desired density (abovethe glass transition in hard spheres) with short-range attractions, which are removed att = 0. The structural part of the decay of the density correlation function can be timerescaled to collapse onto a master function independent of the waiting time,tw, and the timescale follows a power law withtw, withexponent z ∼ 0.89; the non-ergodicity parameter is larger than that of the glass transitionpoint (the localization length is smaller) and oscillates in harmony withSq. Theaging with both microscopic dynamics is identical, except for a scale factor from the age in Newtonianto the age in Brownian dynamics. This factor is approximately the same as that which scales theα-decay of the correlation function in fluids close to the glass transition.

Equivalence of Glass Transition and Colloidal Glass Transition in the Hard-Sphere Limit

We show that the slowing of the dynamics in simulations of several model glass-forming liquids is equivalent to the hard-sphere glass transition in the low-pressure limit. In this limit, we find universal behavior of the relaxation time by collapsing molecular-dynamics data for all systems studied onto a single curve as a function of T/p, the ratio of the temperature to the pressure. At higher pressures, there are deviations from this universal behavior that depend on the interparticle potential, implying that additional physical processes must enter into the dynamics of glass formation.

Rheology and structural arrest of casein suspensions

The rheology of milk powder suspensions is investigated up to very high concentrations, where structural arrest occurs. The main component of the milk powder investigated is casein, so that the suspensions can be regarded as casein suspensions. Four concentration regimes are identified. For effective casein volume fractions less than 0.54 the concentration dependence of the zero-shear viscosity is similar to that of hard-sphere suspensions. However, due to the elastic deformation of the caseins, the viscosity does not diverge at the hard sphere glass transition. In the volume-fraction range of 0.55–0.61 the viscosity exhibits a surprisingly weak dependence on concentration. The shape of the curve of the shear viscosity versus concentration deviates from hard sphere behavior in an unusual way, due to the observation of a region of almost constant viscosity. This concentration regime is followed by a regime where the viscosity steeply increases, eventually diverging at an effective volume fraction of 0.69. Frequency dependent rheology and diffusing wave spectroscopy measurements indicate that the suspensions are jammed for volume fractions above 0.69. Finally we found the concentration dependence of the relative zero-shear viscosity of casein suspensions to be very similar with the one of the micro-gels at volume fractions below 0.50 and above 0.55, which are know to shrink above a certain volume fraction, due to osmotic stress.

The ideal glass transition of hard spheres

We use the replica method to study the ideal glass transition of a liquid of identical hard spheres. We obtain estimates of the configurational entropy in the liquid phase, of the Kauzmann packing fraction phi(K), in the range of 0.58-0.62, and of the random close packing density phi(c), in the range of 0.64-0.67, depending on the approximation we use for the equation of state of the liquid. We also compute the pair-correlation function in the glassy states (i.e., dense amorphous packings) and we find that the mean coordination number at phi(c) is equal to 6. All these results compare well with numerical simulations and with other existing theories.

Rheology and microstructure in concentrated noncolloidal suspensions

The rheological behavior of a monodisperse suspension of non-Brownian particles undergoing simple shear flow in the presence of a weak interparticle force is studied using accelerated Stokesian dynamics. The availability of a faster numerical algorithm permits the investigation of larger systems (typically of 512 particles), and accurate results for the suspension viscosity, first and second normal stress differences, and the particle pressure are determined as a function of the volume fraction. The system microstructure, expressed through the pair-distribution function, is also studied and it is demonstrated how the resulting anisotropy in the pair-distribution function is correlated with the suspension non-Newtonian behavior. The ratio of the normal to excess shear stress is found to be an increasing function of the volume fraction, suggesting different volume fraction scalings for different elements of the stress tensor. The relative strength and range of the interparticle force is varied and its effect on the shear and normal stresses is analyzed. Volume fractions above the equilibrium freezing volume fraction (φ≈0.494) are also studied and it is found that the system exhibits a strong tendency to order under flow for volume fractions below the hard-sphere glass transition; limited results for φ=0.60, however, show that the system is again disordered under shear.

Freezing and glass transition of hard spheres in cavities

Dynamical and static properties of N=13-4000 hard spheres in spherical cavities with smooth and rough walls have been calculated by molecular-dynamics computer simulations. We use a dynamical criterion to distinguish between fluidlike and solidlike states. The associated crossover densities show a strong dependence both on the system size and on the surface roughness. For large N, these crossover densities tend to the bulk glass transition density for rough walls and to the bulk crystallization density for smooth walls. The crossover densities for finite N are found to be significantly smaller than the corresponding bulk densities. A detailed examination of the layer-resolved radial- and tangential mean-square displacements reveals qualitatively different dynamics for smooth and rough cavities.

The hard sphere glass transition

The thermodynamic properties of hard sphere fluids and their glasses, from molecular dynamics simulations, are described within a unified formalism, by expressing the number of configurations of a fluid as a sum, over all its glasses, of the number of configurations of each glass. For pure hard spheres and a mixture this provides an equation of state that interpolates between the ideal gas low density limit and an ideal glass high density limit, and includes a thermodynamic glass transition. On a finite timescale, a real glass transition pre-empts the ideal one. The real transition occurs when the root-mean-square displacement of the spheres, on the simulation timescale, becomes smaller than a sphere diameter.

The hard sphere glass transition

The thermodynamic properties of hard sphere fluids and their glasses, from molecular dynamics simulations, are described within a unified formalism, by expressing the number of configurations of a fluid as a sum, over all its glasses, of the number of configurations of each glass. For pure hard spheres and a mixture this provides an equation of state that interpolates between the ideal gas low density limit and an ideal glass high density limit, and includes a thermodynamic glass transition. On a finite timescale, a real glass transition pre-empts the ideal one. The real transition occurs when the root-mean-square displacement of the spheres, on the simulation timescale, becomes smaller than a sphere diameter.

Application of the scaled particle theory to the glass transition of hard spheres

In a previous article [1], an improved approach to the scaled particle theory of Reiss et al. was presented. As a result, we obtained a Pade-like expression of the compressibility factor of the fluid state. That expression contains two parameters p 1 and p 2, which we were able to calculate. In this paper we find other sets of values for p 1 and p 2. Two of these sets yield equations of state which agree with the simulation results of the glassy states obtained by Woodcock and Speedy. The calculations are based on two assumptions: firstly, that second order phase transitions may occur and secondly, that a hard sphere glass contains a fluid-like and a solid-like part. As an additional result, we found an upper and a lower limit for the fluid densities at which glass transitions may occur.

Quench rate independence of the hard sphere glass transition

About 200 glasses were made by compressing the hard sphere fluid. The location of the glass transition is not measurably changed when the rate at which the fluid is compressed through the transition is varied by a factor of 500. There is small variance in the properties of the glasses but no statistically significant effects of compression rate. The equation of state of each glass can be expressed as PV/NkT = Ci /(1 - z/zi ) where Ci = 2·67 ± 0·05 is the configurational heat capacity in units of Nk, and the limiting density of the glasses zi = 0·875 ± 0·003 (relative to the close packed crystal). The reproducibility of the glasses suggests that either the glass transition in hard spheres is not simply a kinetic phenomenon, or that the structural relaxation time in the fluid diverges near the glass transition density.

On the reproducibility of glasses

The reproducibility of glasses of 500 hard spheres is examined. Most amorphous packings are shown to tend to the limiting density z=0.870±0.008 (relative to the close packed crystal). When the fluid is compressed through the glass transition, in a molecular dynamics experiment, fast enough to avoid crystallites, the equation of state of the glasses, PV/NkT=2.67/(1−z/0.8754), and the statistical entropy, obtained by computing the configuration integral, are reproducible. The pressure of the reproducible glasses does not diverge as fast as that of the crystal, with the result that the excess entropy of the glass (relative to the crystal) diverges. It is argued that the glass transition in hard spheres is a consequence of the geometry of the configuration space, and not simply a kinetic phenomenon.