Dynamics of uniaxial hard ellipsoids

Boltzmann's H-function for molecules with orientational degrees of freedom: Emergence of unique features

Boltzmann's H-function H(t), often regarded as an analog of time-dependent entropy, holds a venerable place in the history of science. However, accurate numerical evaluation of H(t) for particles other than atoms is rare. To remove this lacuna, we generalize Boltzmann's H-function to a gas of molecules with orientational degrees of freedom and evaluate H(t) from the time-dependent joint probability distribution function f(p, L, t) for linear (p) and angular (L) momenta, evolving from an initial nonequilibrium state, by molecular dynamics simulations. We consider both prolate- and oblate-shaped particles, interacting via the well-known Gay-Berne potential and obtain the relaxation of the generalized molecular H(t) from initial (t = 0) nonequilibrium states. In the long-time limit, the H function saturates to its exact equilibrium value, which is the sum of translational and rotational contributions to the respective entropies. Both the translational and rotational components of H(t) decay nearly exponentially with time; the rotational component is more sensitive to the molecular shape that enters through the aspect ratio. A remarkable rapid decrease in the rotational relaxation time is observed as the spherical limit is approached, in a way tantalizingly reminiscent of Hu-Zwanzig hydrodynamic prediction with the slip boundary condition. In addition, we obtain H(t) analytically by solving the appropriate translational and rotational Fokker-Planck equation and obtain a modest agreement with simulations. We observe a remarkable signature of translation-rotation coupling as a function of molecular shape, captured through a physically meaningful differential term that quantifies the magnitude of translation-rotation coupling.

Glassy dynamics in a liquid of anisotropic molecules: Bifurcation of relaxation spectrum

In experimental and theoretical studies of glass transition phenomena, one often finds a sharp crossover in dynamical properties at a temperature Tcr. A bifurcation of a relaxation spectrum is also observed at a temperature TB≈Tcr; both lie significantly above the glass transition temperature. In order to better understand these phenomena, we introduce a new model of glass-forming liquids, a binary mixture of prolate and oblate ellipsoids. This model system exhibits sharp thermodynamic and dynamic anomalies, such as the specific heat jump during heating and a sharp variation in the thermal expansion coefficient around a temperature identified as the glass transition temperature, Tg. The same temperature is obtained from the fit of the calculated relaxation times to the Vogel-Fulcher-Tammann (VFT) form. As the temperature is lowered, the calculated single peak rotational relaxation spectrum splits into two peaks at TB above the estimated Tg. Similar bifurcation is also observed in the distribution of short-to-intermediate time translational diffusion. Interrogation of the two peaks reveals a lower extent of dynamic heterogeneity in the population of the faster mode. We observe an unexpected appearance of a sharp peak in the product of rotational relaxation time τ2 and diffusion constant D at a temperature Tcr, close to TB, but above the glass transition temperature. Additionally, we coarse-grain the system into cubic boxes, each containing, on average, ∼62 particles, to study the average dynamical properties. Clear evidence of large-scale sudden changes in the diffusion coefficient and rotational correlation time signals first-order transitions between low and high-mobility domains.

Observation of liquid glass in molecular dynamics simulations

Molecular anisotropy plays an important role in the glass transition of a liquid. Recently, a novel bulk glass state has been discovered by optical microscopy experiments on suspensions of ellipsoidal colloids. "Liquid glass" is a disordered analog of a nematic liquid crystal, in which rotation motion is hindered but particles diffuse freely. Global nematic order is suppressed as clusters of aligned particles intertwine. We perform Brownian dynamics simulations to test the structure and dynamics of a dense system of soft ellipsoidal particles. As seen in the experiments and in accordance with predictions from the mode coupling theory, on the time scale of our simulations, rotation motion is frozen but translation motion persists in liquid glass. Analyses of the dynamic structure functions for translation and rotation corroborates the presence of two separate glass transitions for rotation and translation, respectively. Even though the equilibrium state should be nematic, aligned structures remain small and orientational order rapidly decays with increasing size. Long-wavelength fluctuations are remnants of the isotropic-nematic transition.

Experimental probing of dynamic self-organized columnar assemblies in colloidal liquid crystals

Self-organized supramolecular assemblies are widespread in nature and technology in the form of liquid crystals, colloids, and gels. The reversible nature of non-covalent bonding leads to dynamic functions such as stimuli-responsive switching and self-healing, which are unachievable from an isolated molecule. However, multiple intermolecular interactions generate diverse conformational and configurational molecular motions over various time scales in their self-assembled states, and their specific dynamics remains unclear. In the present study, we have experimentally unveiled the static structures and dynamical behaviors in columnar colloidal liquid crystals by a coherent X-ray scattering technique using refined model samples. We have found that controlling the size distribution of the colloidal nanoplates dramatically changed their static and dynamic properties. Furthermore, the resulting dynamical behaviors obtained by X-ray photon correlation spectroscopy have been successfully decomposed into multiple distinct modes, allowing us to explore the dynamical origin in the colloidal liquid-crystalline state. The present approaches using a columnar liquid crystal may contribute to a better understanding of the dynamic nature of molecular assemblies and dense colloidal systems and bring valuable insights into rational design of functional properties of self-assembled materials such as stimuli-responsive liquid crystals, self-healing gels, and colloidal crystals. For these materials, the motion of constituent particles and molecules in the self-assembled state is a key factor for structural formation and dynamically responsive performance.

Enhancement in the diffusivity of Brownian spheroids in the presence of spheres

In the present paper, we have extended the simulation technique Brownian cluster dynamics (BCD) to analyze the dynamics of the binary mixture of hard ellipsoids and spheres. The shape dependent diffusional properties have been incorporated into BCD using Perrin's factor and compared with analytical results of a one-component ellipsoidal system. We have investigated pathways to enhance the diffusivity of spheroids in the binary mixture by manipulating the phase behavior of the system through varying the fraction of spheres in the binary mixture. We show that at low volume fraction the spherical particles have a higher diffusion coefficient than the ellipsoids due to the higher friction coefficient. However, at a higher volume fraction, we show that the diffusion coefficient of the ellipsoids increases irrespective of the aspect ratio due to the anisotropic shape.

Reorientational dynamics in highly asymmetric binary low-molecular mixtures-A quantitative comparison of dielectric and NMR spectroscopy results

Previously, we scrutinized the dielectric spectra of a binary glass former made by a low-molecular high-T_g component 2-(m-tertbutylphenyl)-2'-tertbutyl-9,9'-spirobi[9H]fluorene (m-TPTS; T_g = 350 K) and low-T_g tripropyl phosphate (TPP; T_g = 134 K) [Körber et al., Phys. Chem. Chem. Phys. 23, 7200 (2021)]. Here, we analyze nuclear magnetic resonance (NMR) spectra and stimulated echo decays of deuterated m-TPTS-d₄ (²H) and TPP (³¹P) and attempt to understand the dielectric spectra in terms of component specific dynamics. The high-T_g component (α₁) shows relaxation similar to that of neat systems, yet with some broadening upon mixing. This correlates with high-frequency broadening of the dielectric spectra. The low-T_g component (α₂) exhibits highly stretched relaxations and strong dynamic heterogeneities indicated by "two-phase" spectra, reflecting varying fractions of fast and slow liquid-like reorienting molecules. Missing for the high-T_g component, such two-phase spectra are identified down to w_TPP = 0.04, indicating that isotropic reorientation prevails in the rigid high-T_g matrix stretching from close to T_g ^TPP to T_g1 w_TPP. This correlates with low-frequency broadening of the dielectric spectra. Two T_g values are defined: T_g1 (w_TPP) displays a plasticizer effect, whereas T_g2 (w_TPP) passes through a maximum, signaling extreme separation of the component dynamics at low w_TPP. We suggest understanding the latter counter-intuitive feature by referring to a crossover from "single glass" to "double glass" scenario revealed by recent MD simulations. Analyses reveal that a second population of TPP molecules exists, which is associated with the dynamics of the high-T_g component. However, the fractions are lower than suggested by the dielectric spectra. We discuss this discrepancy considering the role of collective dynamics probed by dielectric but not by NMR spectroscopy.

Observation of liquid glass in suspensions of ellipsoidal colloids

Despite the omnipresence of colloidal suspensions, little is known about the influence of colloid shape on phase transformations, especially in nonequilibrium. To date, real-space imaging results at high concentrations have been limited to systems composed of spherical colloids. In most natural and technical systems, however, particles are nonspherical, and their structural dynamics are determined by translational and rotational degrees of freedom. Using confocal microscopy of fluorescently labeled core-shell particles, we reveal that suspensions of ellipsoidal colloids form an unexpected state of matter, a liquid glass in which rotations are frozen while translations remain fluid. Image analysis unveils hitherto unknown nematic precursors as characteristic structural elements of this state. The mutual obstruction of these ramified clusters prevents liquid crystalline order. Our results give insight into the interplay between local structures and phase transformations. This helps to guide applications such as self-assembly of colloidal superstructures and also gives evidence of the importance of shape on the glass transition in general.

Formation of nematic order in 3D systems of hard colloidal ellipsoids

Suspensions of hard ellipsoidal particles exhibit complex phase behavior as shown by theoretical predictions and simulations of phase diagrams. Here, we report quantitative confocal microscopy experiments of hard prolate colloidal ellipsoids with different aspect ratio a/b. We studied different volume fractions φ of ellipsoids in density and refractive index matched suspensions. Large 3D sample volumes were investigated and the positions as well as the orientations of all ellipsoids were extracted by image analysis routines. By evaluating the translational and orientational order in the system we determined the presence of isotropic and nematic phases. For ellipsoids with a/b = 2.0 we found that isotropic phases form at all φ, while ellipsoids with a/b = 7.0 formed nematic phases at high φ, as expected from theory and simulations. For a/b = 3.5 and a/b = 4.1, however, we observed the absence of long-range orientational order even at φ where nematic phases are expected. We show that local orientational order formed with the emergence of nematic precursors for a/b = 3.5 and short-ranged nematic domains for a/b = 4.1. Our results provide novel insight into the phase behavior and orientational order of ellipsoids with different aspect ratios.

Potential and limits of a colloid approach to protein solutions

Looking at globular proteins with the eyes of a colloid scientist has a long tradition, in fact a significant part of the early colloid literature was focused on protein solutions. However, it has also been recognized that proteins are much more complex than the typical hard sphere-like synthetic model colloids. Proteins are not perfect spheres, their interaction potentials are in general not isotropic, and using theories developed for such particles are thus clearly inadequate in many cases. In this perspective article, we now take a closer look at the field. In particular, we reflect on the fact that modern colloid science has been undergoing a tremendous development, where a multitude of novel systems have been developed in the lab and in silico. During the last decade we have seen a rapidly increasing number of reports on the synthesis of anisotropic, patchy and/or responsive synthetic colloids, that start to resemble their complex biological counterparts. This experimental development is also reflected in a corresponding theoretical and simulation effort. The experimental and theoretical toolbox of colloid science has thus rapidly expanded, and there is obviously an enormous potential for an application of these new concepts to protein solutions, which has already been realized and harvested in recent years. In this perspective article we make an attempt to critically discuss the exploitation of colloid science concepts to better understand protein solutions. We not only consider classical applications such as the attempt to understand and predict solution stability and phase behaviour, but also discuss new challenges related to the dynamics, flow behaviour and liquid-solid transitions found in concentrated or crowded protein solutions. It not only aims to provide an overview on the progress in experimental and theoretical (bio)colloid science, but also discusses current shortcomings in our ability to correctly reproduce and predict the structural and dynamic properties of protein solutions based on such a colloid approach.

Anisotropic dynamics and kinetic arrest of dense colloidal ellipsoids in the presence of an external field studied by differential dynamic microscopy

Anisotropic dynamics on the colloidal length scale is ubiquitous in nature. Of particular interest is the dynamics of systems approaching a kinetically arrested state. The failure of classical techniques for investigating the dynamics of highly turbid suspensions has contributed toward the limited experimental information available up until now. Exploiting the recent developments in the technique of differential dynamic microscopy (DDM), we report the first experimental study of the anisotropic collective dynamics of colloidal ellipsoids with a magnetic hematite core over a wide concentration range approaching kinetic arrest. In addition, we have investigated the effect of an external magnetic field on the resulting anisotropic collective diffusion. We combine DDM with small-angle x-ray scattering and rheological measurements to locate the glass transition and to relate the collective short- and long-time diffusion coefficients to the structural correlations and the evolution of the zero shear viscosity as the system approaches an arrested state.

Translational and rotational diffusion of rod shaped molecules by molecular dynamics simulations

The results of molecular dynamics simulations of the dynamical evolution of assemblies of linear rigid rods of variable aspect ratio, a, and number density, ρ, in the isotropic phase are reported. The rods consist of m equally spaced sites interacting with the Weeks-Chandler-Andersen repulsive pair potential, where 2 < m < 16. With increasing m, features specific to long rods, such as anisotropic self-diffusion, become apparent. There is also an increasing separation between the characteristic relaxation times of the torque, angular velocity, and reorientational time correlation functions with increasing density. The latter is exponential at high densities even for dimers. The isotropic translational diffusion coefficient, D_i, and rotational diffusion coefficient, D_r, are reported as a function of m and ρ or volume fraction, ξ. The mD_i data scale with ξ throughout much of the simulated range, while the rotational diffusion coefficients scale approximately as m³D_r against ρ at low densities but as ∼m⁶D_r at high ρ, consistent with theories of colloidal and noncolloidal rod-containing liquids. The crossover density between the two regimes is parameterized in analytic form. The probability distribution functions for displacements and angular jumps in a given time show evidence of non-Gaussian behavior with increasing density. The shear viscosity and D_i scale approximately as m and m^-1, respectively, in the semidilute regime, which is consistent with a Stokes-Einstein-like relationship. At high concentrations, a frustrated or glassy structure formed in which the rods were randomly oriented.

Detection and tracking of anisotropic core-shell colloids

Optical microscopy techniques with three dimensional (3D) resolution are powerful tools for the real-space imaging of the structure and dynamics of colloidal systems. While real-space imaging of spherical particles is well established, the observation of shape anisotropic particles has only recently met a lot of interest. Apart from translation, shape anisotropic particles also possess additional rotational degrees of freedom. In this manuscript, we introduce a novel technique to find the position and the orientation of anisotropic particles in 3D. It is based on an algorithm which is applicable to core-shell particles consisting of a spherical core and a shell with arbitrary shape. We demonstrate the performance of this algorithm using PMMA/PMMA (polymethyl methacrylate) core-shell ellipsoids. The algorithm is tested on artificial images and on experimental data. The correct identification of particle positions with subpixel accuracy and of their orientations with high angular precision in dilute and dense systems is shown. In addition, we developed an advanced particle tracking algorithm that takes both translational and rotational movements of the anisotropic particles into account. We show that our 3D detection and tracking technique is suitable for the accurate and reliable detection of large and dense colloidal systems containing several thousands of particles.

Density functional theory for dense nematic liquid crystals with steric interactions

The celebrated work of Onsager on hard particle systems, based on the truncated second order virial expansion, is valid at relatively low volume fractions for large aspect ratio particles. While it predicts the isotropic-nematic phase transition, it does not provide a realistic equation of state in that the pressure remains finite for arbitrarily high densities. In this work, we derive a mean field density functional form of the Helmholtz free energy for nematics with hard core repulsion. In addition to predicting the isotropic-nematic transition, the model provides a more realistic equation of state. The energy landscape is much richer, and the orientational probability distribution function in the nematic phase possesses a unique feature-it vanishes on a nonzero measure set in orientation space.

Implanted muon spin spectroscopy on 2-O-adamantane: a model system that mimics the liquid[Formula: see text]glasslike transitions

The transition taking place between two metastable phases in 2-O-adamantane, namely the [Formula: see text] cubic, rotator phase and the lower temperature P2₁/c, Z  =  4 substitutionally disordered crystal is studied by means of muon spin rotation and relaxation techniques. Measurements carried out under zero, weak transverse and longitudinal fields reveal a temperature dependence of the relaxation parameters strikingly similar to those exhibited by structural glass[Formula: see text]liquid transitions (Bermejo et al 2004 Phys. Rev. B 70 214202; Cabrillo et al 2003 Phys. Rev. B 67 184201). The observed behaviour manifests itself as a square root singularity in the relaxation rates pointing towards some critical temperature which for amorphous systems is located some tens of degrees above that shown as the characteristic transition temperature if studied by thermodynamic means. The implications of such findings in the context of current theoretical approaches concerning the canonical liquid-glass transition are discussed.

Introduction to the Colloidal Glass Transition

Colloids are suspensions of small solid particles in a liquid and exhibit glassy behavior when the particle concentration is high. In these samples, the particles are roughly analogous to individual molecules in a traditional glass. This model system has been used to study the glass transition since the 1980s. In this Viewpoint I summarize some of the intriguing behaviors of the glass transition in colloids and discuss open questions.

Self-Induced Glassiness and Pattern Formation in Spin Systems Subject to Long-Range Interactions

We study the glass formation in two- and three-dimensional Ising and Heisenberg spin systems subject to competing interactions and uniaxial anisotropy with a mean-field approach. In three dimensions, for sufficiently strong anisotropy the systems always modulate in a striped phase. Below a critical strength of the anisotropy, a glassy phase exists in a finite range of temperature, and it becomes more stable as the system becomes more isotropic. In two dimensions the criticality is always avoided and the glassy phase always exists.

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.

Dynamical facilitation governs glassy dynamics in suspensions of colloidal ellipsoids

One of the greatest challenges in contemporary condensed matter physics is to ascertain whether the formation of glasses from liquids is fundamentally thermodynamic or dynamic in origin. Although the thermodynamic paradigm has dominated theoretical research for decades, the purely kinetic perspective of the dynamical facilitation (DF) theory has attained prominence in recent times. In particular, recent experiments and simulations have highlighted the importance of facilitation using simple model systems composed of spherical particles. However, an overwhelming majority of liquids possess anisotropy in particle shape and interactions, and it is therefore imperative to examine facilitation in complex glass formers. Here, we apply the DF theory to systems with orientational degrees of freedom as well as anisotropic attractive interactions. By analyzing data from experiments on colloidal ellipsoids, we show that facilitation plays a pivotal role in translational as well as orientational relaxation. Furthermore, we demonstrate that the introduction of attractive interactions leads to spatial decoupling of translational and rotational facilitation, which subsequently results in the decoupling of dynamical heterogeneities. Most strikingly, the DF theory can predict the existence of reentrant glass transitions based on the statistics of localized dynamical events, called excitations, whose duration is substantially smaller than the structural relaxation time. Our findings pave the way for systematically testing the DF approach in complex glass formers and also establish the significance of facilitation in governing structural relaxation in supercooled liquids.

Non-Gaussian rotational diffusion in heterogeneous media

We employ a simple model for rotational diffusivity DR of dumbbells in porous media in order to study spatially heterogeneous and non-Gaussian dynamics at Fickian time scales. We obtain the distribution P(DR) of DR's of single dumbbells for both ergodic and nonergodic systems. When a pore percolating network disappears beyond the pore percolation transition and the rotational dynamics becomes nonergodic, each single dumbbell undergoes Gaussian rotational dynamics but with different DR, which depends solely on the local pore structure. We also construct a map of heterogeneous dynamic regions and illustrate that such seemingly Fickian but non-Gaussian dynamics could be understood as the linear combination of the Gaussian rotational displacement distribution functions of each dumbbell. With a percolating pore network, the rotational dynamics becomes ergodic, and P(DR) is a δ function at the average value of DR.

Orientational glass in mixtures of elliptic and circular particles: structural heterogeneities, rotational dynamics, and rheology

Using molecular dynamics simulation with an angle-dependent Lennard-Jones potential, we study orientational glass with quadrupolar symmetry in mixtures of elliptic particles and circular impurities in two dimensions. With a mild aspect ratio (= 1.23) and a mild size ratio (= 1.2), we realize a plastic crystal at relatively high temperature T. With further lowering T, we find a structural phase transition for very small impurity concentration c and pinned disordered orientations for not small c. The ellipses are anchored by the impurities in the planar alignment. With increasing c, the orientation domains composed of isosceles triangles gradually become smaller, resulting in orientational glass with crystal order. In our simulation, the impurity distribution becomes heterogeneous during quenching from liquid, which then produces rotational dynamic heterogeneities. We also examine rheology in orientational glass to predict a shape memory effect and a superelasticity effect, where a large fraction of the strain is due to collective orientation changes.

Two-dimensional system of hard ellipses: a molecular dynamics study

We have simulated the dynamics of a two-dimensional system of hard ellipses by event-oriented molecular dynamics in microcanonical NVE ensemble. Various quantities, namely longitudinal and transverse velocity auto-correlation functions, translational and rotational diffusion mean-squared displacements, pressure, intermediate self-scattering function, radial distribution function, and angular spatial correlation, have been obtained and their dependence on packing fraction is characterized. Despite absence of prominent positional ordering, the orientational degree of freedom behaves nontrivially and exhibits interesting features. Slowing down is observed in the angular part of the motion near isotropic-nematic phase transition. It is shown that above a certain packing fraction the rotational mean-squared displacement exhibits a three-stage temporal regime including a plateau. Comparison to 2D system of hard needles is made and it is shown that from positional viewpoint, the ellipse system is more ordered.

Two-step glass transition induced by attractive interactions in quasi-two-dimensional suspensions of ellipsoidal particles

We study experimentally the glass transition dynamics in quasi-two-dimensional suspensions of colloidal ellipsoids, aspect ratio α=2.1, with repulsive as well as attractive interactions. For the purely repulsive case, we find that the orientational and translational glass transitions occur at the same area fraction. Strikingly, for intermediate depletion attraction strengths, we find that the orientational glass transition precedes the translational one. By quantifying structure and dynamics, we show that quasi-long-range ordering is promoted at these attraction strengths, which subsequently results in a two-step glass transition. Most interestingly, within experimental certainty, we observe reentrant glass dynamics only in the translational degrees of freedom.

Glass transition in suspensions of charged rods: structural arrest and texture dynamics

We report on the observation of a glass transition in suspensions of very long and thin, highly charged colloidal rods (fd-virus particles). Structural particle arrest is found to occur at a low ionic strength due to caging of the charged rods in the potential setup by their neighbors through long-ranged electrostatic interactions. The relaxation time of density fluctuations as probed by dynamic light scattering is found to diverge within a small concentration range. The rod concentration where structural particle arrest occurs is well within the full chiral-nematic state, far beyond the two-phase isotropic-nematic coexistence region. The morphology of the suspensions thus consists of nematic domains with various orientations. We quantify the dynamics of the resulting texture with image-time correlation spectroscopy. Interestingly, the decay times of image correlation functions are found to diverge in a discontinuous fashion at the same concentration of charged rods where structural particle arrest is observed. At the glass-transition concentration, we thus find both structural arrest and freezing of the texture dynamics.

Structural relaxation in dense liquids composed of anisotropic particles

We perform extensive molecular dynamics simulations of dense liquids composed of bidisperse dimer- and ellipse-shaped particles in two dimensions that interact via purely repulsive contact forces. We measure the structural relaxation times obtained from the long-time α decay of the self part of the intermediate scattering function for the translational and rotational degrees of freedom (DOF) as a function of packing fraction φ, temperature T, and aspect ratio α. We are able to collapse the packing-fraction and temperature-dependent structural relaxation times for disks, and dimers and ellipses over a wide range of α, onto a universal scaling function F(±)(|φ-φ(0)|,T,α), which is similar to that employed in previous studies of dense liquids composed of purely repulsive spherical particles in three dimensions. F(±) for both the translational and rotational DOF are characterized by the α-dependent scaling exponents μ and δ and packing fraction φ(0)(α) that signals the crossover in the scaling form F(±) from hard-particle dynamics to super-Arrhenius behavior for each aspect ratio. We find that the fragility of structural relaxation at φ(0), m(φ(0)), decreases monotonically with increasing aspect ratio for both ellipses and dimers. For α>α(p), where α(p) is the location of the peak in the packing fraction φ(J) at jamming onset, the rotational DOF are strongly coupled to the translational DOF, and the dynamic scaling exponents and φ(0) are similar for the rotational and translational DOF. For 1<α<α(p), the translational DOF become frozen at higher temperatures than the rotational DOF, and φ(0) for the rotational degrees of freedom increases above φ(J). Moreover, the results for the slow dynamics of dense liquids composed of dimer- and ellipse-shaped particles are qualitatively the same, despite the fact that zero-temperature static packings of dimers are isostatic, while static packings of ellipses are hypostatic. Thus, zero-temperature contact counting arguments do not apply to structural relaxation of dense liquids of anisotropic particles near the glass transition.

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.

Frustration of the isotropic-columnar phase transition of colloidal hard platelets by a transient cubatic phase

Using simulations and theory, we show that the cubatic phase is metastable for three model hard platelets. The locally favored structures of perpendicular particle stacks in the fluid prevent the formation of the columnar phase through geometric frustration resulting in vitrification. Also, we find a direct link between structure and dynamic heterogeneities in the cooperative rotation of particle stacks, which is crucial for the devitrification process. Finally, we show that the lifetime of the glassy cubatic phase can be tuned by surprisingly small differences in particle shape.

Glass transitions in quasi-two-dimensional suspensions of colloidal ellipsoids

We observed a two-step glass transition in monolayers of colloidal ellipsoids by video microscopy. The glass transition in the rotational degree of freedom was at a lower density than that in the translational degree of freedom. Between the two transitions, ellipsoids formed an orientational glass. Approaching the respective glass transitions, the rotational and translational fastest-moving particles in the supercooled liquid moved cooperatively and formed clusters with power-law size distributions. The mean cluster sizes diverge in power law as they approach the glass transitions. The clusters of translational and rotational fastest-moving ellipsoids formed mainly within pseudonematic domains and around the domain boundaries, respectively.

Kinetic arrest, dynamical transitions, and activated relaxation in dense fluids of attractive nonspherical colloids

The coupled translation-rotation activated dynamics in dense suspensions of attractive homogeneous and Janus uniaxial dicolloids are studied using microscopic statistical mechanical theory. Multiple kinetic arrest transitions and reentrant phenomena are predicted that are associated with fluid, gel, repulsive glass, attractive glass, plastic glass, and novel glass-gel states. The activated relaxation rate is a nonuniversal nonmonotonic function of attraction strength at high volume fractions due to the consequences of a change of the transient localization mechanism from caging to physical bonding.

Activated dynamics in dense fluids of attractive nonspherical particles. I. Kinetic crossover, dynamic free energies, and the physical nature of glasses and gels

We apply the center-of-mass versions of naïve mode coupling theory and nonlinear Langevin equation theory to study how short-range attractive interactions modify the onset of localization, activated single-particle dynamics, and the physical nature of the transiently arrested state of a variety of dense nonspherical particle fluids (and the spherical analog) as a function of volume fraction and attraction strength. The form of the dynamic crossover boundary depends on particle shape, but the reentrant glass-fluid-gel phenomenon and the repulsive glass-to-attractive glass crossover always occur. Diverse functional forms of the dynamic free energy are found for all shapes including glasslike, gel-like, a glass-gel form defined by the coexistence of two localization minima and two activation barriers, and a "mixed" attractive glass characterized by a single, very short localization length but an activation barrier located at a large displacement as in repulsive-force caged glasses. For the latter state, particle trajectories are expected to be of a two-step activated form and can be accessed at high attraction strength by increasing volume fraction, or by increasing attraction strength at fixed high enough volume fraction. A new classification scheme for slow dynamics of fluids of dense attractive particles is proposed based on specification of both the nature of the localized state and the particle displacements required to restore ergodicity via activated barrier hopping. The proposed physical picture appears to be in qualitative agreement with recent computer simulations and colloid experiments.

Glass formation and shear elasticity in dense suspensions of repulsive anisotropic particles

Kinetic vitrification, shear elasticity, and the approach to jamming are investigated for repulsive nonspherical colloids and contrasted with their spherical analog. Particle anisotropy dramatically increases the volume fraction for kinetic arrest. The shear modulus of all systems increases roughly exponentially with volume fraction, and a universal collapse is achieved based on either the dynamic crossover or random close packing volume fraction as the key nondimensionalizing quantity. Quantitative comparisons with recent microscopic theories are performed and good agreement demonstrated.

Glassy dynamics and kinetic vitrification of isotropic suspensions of hard rods

A nonlinear Langevin equation (NLE) theory for the translational center-of-mass dynamics of hard nonspherical objects has been applied to isotropic fluids of rigid rods. The ideal kinetic glass transition volume fraction is predicted to be a monotonically decreasing function beyond an aspect ratio of two. The functional form of the decrease is weaker than the inverse aspect ratio. Vitrification occurs at lower volume fractions for corrugated tangent bead rods compared to their smooth spherocylinder analogs. The ideal glass transition signals a crossover to activated dynamics, which is estimated to be observable before the nematic phase boundary is encountered if the aspect ratio is less than roughly 25. Calculations of the glassy elastic shear modulus and absolute yield stress reveal a roughly exponential growth with volume fraction. The dependence of entropic barriers and mean barrier hopping times on concentration for rods of variable aspect ratios can be collapsed quite well based on a difference volume fraction variable that quantifies the distance from the ideal glass boundary. Full numerical solution of the NLE theory via stochastic trajectory simulation was performed for tangent bead rods, and the results were compared to their hard sphere analogs. With increasing shape anisotropy the characteristic length scales of the nonequilibrium free energy increase and the magnitude of the localization well and entropic barrier curvatures decreases. These changes result in a significant aspect ratio dependence of dynamical properties and time correlation functions including weaker intermediate time subdiffusive transport, stronger two-step decay of the incoherent dynamic structure factor, longer mean alpha relaxation time, and stronger wavevector-dependent decoupling of relaxation times and the self-diffusion constant. The theoretical results are potentially testable via computer simulation, confocal microscopy, and dynamic light scattering.