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

Potential energy landscape and inherent dynamics of a hard-sphere fluid

Hard-sphere models exhibit many of the same kinds of supercooled-liquid behavior as more realistic models of liquids, but the highly nonanalytic character of their potentials makes it a challenge to think of that behavior in potential energy landscape terms. We show here that it is possible to calculate an important topological property of hard-sphere landscapes, the geodesic pathways through those landscapes, and to do so without artificially coarse-graining or softening the potential. We show, moreover, that the rapid growth of the lengths of those pathways with increasing packing fraction quantitatively predicts the precipitous decline in diffusion constants in a glass-forming hard-sphere mixture model. The geodesic paths themselves can be considered as defining the intrinsic dynamics of hard spheres, so it is also revealing to find that they (and therefore the features of the underlying potential energy landscape) correctly predict the occurrence of dynamic heterogeneity and nonzero values of the non-Gaussian parameter. The success of these landscape predictions for the dynamics of such a singular model emphasizes that there is more to potential energy landscapes than is revealed by looking at the minima and saddle points.

Binary diamondoid building blocks for molecular gels

Adamantane is a type of diamondoid molecules that has a cage or globular shape with a diameter of 6.34 ± 0.04 Å.8 Anisotropic interactions between these truly nanoscopic particles can be induced through the derivatization of the diamondoid cage. Here we explore the gelation of paired systems of adamantane where attractions are introduced through van der Waals forces and hydrogen bonding. Gels are produced through the mixing of 1-adamantanecarboxylic acid (A1C) and 1-adamantylamine (A1N). Upon mixing dimethyl sulfoxide solutions of these molecules at vanishing concentrations, these diamondoid molecules rapidly precipitate. A space-filling gel of the resulting aggregates is observed at approximately 3% by weight. These resulting gels have elastic moduli of 10(2)-10(4) Pa in the 3-7 wt % concentration range. At a 1:1 mol ratio of 1-adamantanecarboxylic acid (A1C) and 1-adamantylamine (A1N), the gel's elastic modulus and yield stress increase as volume fractions ϕ(x) and ϕ(y) with x ≈ 4.2 and y ≈ 3.5. The dependencies of moduli and yield stress on the volume fraction display characteristics of colloidal gels. Transmission electron microscope (TEM) images indicate that the gels are formed from a network of interwoven and branched fibers which are composed of ∼30 nm crystallites that have undergone oriented aggregation to form fibers.

Dynamics and thermodynamics of polymer glasses

The fate of matter when decreasing the temperature at constant pressure is that of passing from gas to liquid and, subsequently, from liquid to crystal. However, a class of materials can exist in an amorphous phase below the melting temperature. On cooling such materials, a glass is formed; that is, a material with the rigidity of a solid but exhibiting no long-range order. The study of the thermodynamics and dynamics of glass-forming systems is the subject of continuous research. Within the wide variety of glass formers, an important sub-class is represented by glass forming polymers. The presence of chain connectivity and, in some cases, conformational disorder are unfavourable factors from the point of view of crystallization. Furthermore, many of them, such as amorphous thermoplastics, thermosets and rubbers, are widely employed in many applications. In this review, the peculiarities of the thermodynamics and dynamics of glass-forming polymers are discussed, with particular emphasis on those topics currently the subject of debate. In particular, the following aspects will be reviewed in the present work: (i) the connection between the pronounced slowing down of glassy dynamics on cooling towards the glass transition temperature (Tg) and the thermodynamics; and, (ii) the fate of the dynamics and thermodynamics below Tg. Both aspects are reviewed in light of the possible presence of a singularity at a finite temperature with diverging relaxation time and zero configurational entropy. In this context, the specificity of glass-forming polymers is emphasized.

Theory of activated dynamics and glass transition of hard colloids in two dimensions

The microscopic nonlinear Langevin equation theory is applied to study the localization and activated hopping of two-dimensional hard disks in the deeply supercooled and glass states. Quantitative comparisons of dynamic characteristic length scales, barrier, and their dependence on the reduced packing fraction are presented between hard-disk and hard-sphere suspensions. The dynamic barrier of hard disks emerges at higher absolute and reduced packing fractions and correspondingly, the crossover size of the dynamic cage which correlates to the Lindemann length for melting is smaller. The localization lengths of both hard disks and spheres decrease exponentially with packing fraction. Larger localization length of hard disks than that of hard spheres is found at the same reduced packing fraction. The relaxation time of hard disks rises dramatically above the reduced packing fraction of 0.88, which leads to lower reduced packing fraction at the kinetic glass transition than that of hard spheres. The present work provides a foundation for the subsequent study of the glass transition of binary or polydisperse mixtures of hard disks, normally adopted in experiments and simulations to avoid crystallization, and further, the rheology and mechanical response of the two-dimensional glassy colloidal systems.

Theory of Entanglements and Tube Confinement in Rod-Sphere Nanocomposites

We formulate a microscopic theory for the polymer transverse confinement length and associated dynamic potential for a mixture of infinitely thin rods and hard spheres based solely on topological entanglements and excluded volume constraints. For fixed spheres, the needle effective tube diameter decreases with particle loading, and is largely controlled by a single dimensionless parameter involving all three key length-scales in the problem. A crossover from polymer entanglement to nanoparticle-controlled tube localization with increased loading is predicted. A preliminary extension to chain melts exhibits reasonable agreement with a recent simulation, and experimentally testable predictions are made. This work establishes a first-principles theoretical foundation to investigate a variety of dynamical problems in entangled polymer nanocomposites.

Theory of kinetic arrest, elasticity, and yielding in dense binary mixtures of rods and spheres

We extend the quiescent and stressed versions of naïve mode coupling theory to treat the dynamical arrest, shear modulus, and absolute yielding of particle mixtures where one or more species is a nonrotating nonspherical object. The theory is applied in detail to dense isotropic "chemically matched" mixtures of variable aspect ratio rods and spheres that interact via repulsive and short range attractive site-site pair potentials. A remarkably rich ideal kinetic arrest behavior is predicted with up to eight "dynamical phases" emerging: an ergodic fluid, partially localized states where the spheres remain fluid but the rods can be a gel, repulsive glass or attractive glass, doubly localized glasses and gels, a porous rod gel plus sphere glass, and a narrow window where a type of rod glass and gel localization coexist. Dynamical complexity increases with rod length and the introduction of attractive forces between all species which both enhance gel network formation. Multiple dynamic reentrant features and triple points are predicted, and each dynamic phase has unique particle localization characteristics and mechanical properties. Orders of magnitude variation of the linear shear modulus and absolute yield stress are found as rod length, mixture composition and the detailed nature of interparticle attractions are varied. The interplay of total (high) mixture packing fraction and composition at fixed temperature is also briefly studied. The present work provides a foundation to study more complex rod-sphere mixtures of both biological and synthetic interest that include physical features such as interaction site size asymmetry, rod-sphere specific attractions, and/or Coulomb repulsion.

On the dynamics of liquids in their viscous regime approaching the glass transition

Recently, Mallamace et al. (Eur. Phys. J. E 34, 94 (2011)) proposed a crossover temperature, T(×), and claimed that the dynamics of many supercooled liquids follow an Arrhenius-type temperature dependence between T(×) and the glass transition temperature T(g). The opposite, namely super-Arrhenius behavior in this viscous regime, has been demonstrated repeatedly for molecular glass-former, for polymers, and for the majority of the exhaustively studied inorganic glasses of technological interest. Therefore, we subject the molecular systems of the Mallamace et al. study to a "residuals" analysis and include not only viscosity data but also the more precise data available from dielectric relaxation experiments over the same temperature range. Although many viscosity data sets are inconclusive due to their noise level, we find that Arrhenius behavior is not a general feature of viscosity in the T(g) to T(×) range. Moreover, the residuals of dielectric relaxation times with respect to an Arrhenius law clearly reveal systematic curvature consistent with super-Arrhenius behavior being an endemic feature of transport properties in this viscous regime. We also observe a common pattern of how dielectric relaxation times decouple slightly from viscosity.

Mechanical properties of thin confined polymer films close to the glass transition in the linear regime of deformation: theory and simulations

Over the past twenty years experiments performed on thin polymer films deposited on substrates have shown that the glass transition temperature T(g) can either decrease or increase depending on the strength of the interactions. Over the same period, experiments have also demonstrated that the dynamics in liquids close to the glass transition temperature is strongly heterogeneous, on the scale of a few nanometers. A model for the dynamics of non-polar polymers, based on percolation of slow subunits, has been proposed and developed over the past ten years. It proposes a unified mechanism regarding these two features. By extending this model, we have developed a 3D model, solved by numerical simulations, in order to describe and calculate the mechanical properties of polymers close to the glass transition in the linear regime of deformation, with a spatial resolution corresponding to the subunit size. We focus on the case of polymers confined between two substrates with non-negligible interactions between the polymer and the substrates, a situation which may be compared to filled elastomers. We calculate the evolution of the elastic modulus as a function of temperature, for different film thicknesses and polymer-substrate interactions. In particular, this allows to calculate the corresponding increase of glass transition temperature, up to 20 K in the considered situations. Moreover, between the bulk T(g) and T(g) + 50 K the modulus of the confined layers is found to decrease very slowly in some cases, with moduli more than ten times larger than that of the pure matrix at temperatures up to T(g) + 50 K. This is consistent with what is observed in reinforced elastomers. This slow decrease of the modulus is accompanied by huge fluctuations of the stress at the scale of a few tens of nanometers that may even be negative as compared to the solicitation, in a way that may be analogous to mechanical heterogeneities observed recently in molecular dynamics simulations. As a consequence, confinement may result not only in an increase of the glass transition temperature, but in a huge broadening of 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.

Space-time correlated two-particle hopping in glassy fluids: structural relaxation, irreversibility, decoupling, and facilitation

The microscopic nonlinear Langevin equation (NLE) theory of correlated two-particle dynamics in dense fluids of spherical particles is extended to construct a predictive model of multiple correlated hopping and recaging events of a pair of tagged particles as a function of their initial separation. Modest coarse graining over the liquid structural disorder allows contact to be made with various definitions of irreversible particle motion within the context of a multistate Markov model. The correlated space-time hopping process that underlies structural relaxation can also be analyzed in the context of kinetically constrained models. The dependence of microscopically defined mean persistence and exchange times, their distributions, and relaxation-diffusion decoupling on hard-sphere fluid volume fraction is derived from a model in which irreversible jumps serve as the nucleating persistence event. For a subset of questions, the predictions of the two-particle theory are compared with results from the earlier single-particle NLE approach.

Free-energy landscape for cage breaking of three hard disks

We investigate cage breaking in dense hard-disk systems using a model of three Brownian disks confined within a circular corral. This system has a six-dimensional configuration space, but can be equivalently thought to explore a symmetric one-dimensional free-energy landscape containing two energy minima separated by an energy barrier. The exact free-energy landscape can be calculated as a function of system size by a direct enumeration of states. Results of simulations show the average time between cage breaking events follows an Arrhenius scaling when the energy barrier is large. We also discuss some of the consequences of using a one-dimensional representation to understand dynamics through a multidimensional space, such as diffusion acquiring spatial dependence and discontinuities in spatial derivatives of free energy.

Direct evidence of heterogeneous mechanical relaxation in supercooled liquids

Dynamic heterogeneity is now considered to be an intrinsic kinetic feature of a supercooled liquid. Here, we access the nonlocal complex modulus of a glass-forming liquid using molecular dynamics simulations. We find that the shear-stress relaxation exhibits a marked wave number dependence in a supercooled state. This dependence provides direct evidence that slow mechanical relaxation takes place heterogeneously in space. Its characteristic length ξ increases with decreasing temperature and becomes mesoscopic. The response involves particle rearrangements over ξ and takes a time comparable to the structural relaxation time τ(α). Our finding suggests that the heterogeneous structural relaxation is of fundamental importance in anomalous viscous transport and viscoelasticity in supercooled liquids.

Glassy dynamics and mechanical response in dense fluids of soft repulsive spheres. II. Shear modulus, relaxation-elasticity connections, and rheology

We apply the quiescent and mechanically driven versions of nonlinear Langevin equation theory to study how particle softness influences the shear modulus, the connection between shear elasticity and activated relaxation, and nonlinear rheology of the repulsive Hertzian contact model of dense soft sphere fluids. Below the soft jamming threshold, the shear modulus follows a power law dependence on volume fraction over a narrow interval with an apparent exponent that grows with particle stiffness. To a first approximation, the elastic modulus and transient localization length are controlled by a single coupling constant determined by local fluid structure. In contrast to the behavior of hard spheres, an approximately linear relation between the shear modulus and activation barrier is predicted. This connection has recently been observed for microgel suspensions and provides a microscopic realization of the elastic shoving model. Yielding, shear and stress thinning of the alpha relaxation time and viscosity, and flow curves are also studied. Yield strains are relatively weakly dependent on volume fraction and particle stiffness. Shear thinning commences at values of the effective Peclet number far less than unity, a signature of stress-assisted activated relaxation when barriers are high. Apparent power law reduction of the viscosity with shear rate is predicted with a thinning exponent less than unity. In the vicinity of the soft jamming threshold, a power law flow curve occurs over an intermediate reduced shear rate range with an apparent exponent that decreases as fluid volume fraction and/or repulsion strength increase.

Glassy relaxation and excess wing in mode-coupling theory: the dynamic susceptibility of propylene carbonate above and below T(c)

We explore the possibility of describing experimental susceptibility spectra of the glass former propylene carbonate with a two-component schematic model of mode-coupling theory (MCT) from above the melting point down to temperatures far below the critical temperature of MCT. By introducing a phenomenological time-dependent hopping rate, the spectra are reproduced in the full frequency and temperature range available. Literature data of dielectric susceptibilities and depolarized Brillouin light-scattering spectra are combined with our measurements of photon correlation spectroscopy to cover up to 18 decades in frequency of spectra for two different dynamical variables. A consistent description of all data sets is obtained by adjusting only a few physically motivated parameters. In particular the excess wing or slow β-relaxation commonly observed in the susceptibility spectra can consistently be modeled as originating from a coupling of the individual experimental probe correlator to the collective density fluctuations.

Testing "microscopic" theories of glass-forming liquids

We assess the validity of "microscopic" approaches of glass-forming liquids based on the sole knowledge of the static pair density correlations. To do so, we apply them to a benchmark provided by two liquid models that share very similar static pair density correlation functions while displaying distinct temperature evolutions of their relaxation times. We find that the approaches are unsuccessful in describing the difference in the dynamical behavior of the two models. Our study is not exhaustive, and we have not tested the effect of adding corrections by including, for instance, three-body density correlations. Yet, our results appear strong enough to challenge the claim that the slowdown of relaxation in glass-forming liquids, for which it is well established that the changes of the static structure factor with temperature are small, can be explained by "microscopic" approaches only requiring the static pair density correlations as nontrivial input.

Microscopic theory of the tube confinement potential for liquids of topologically entangled rigid macromolecules

We formulate and apply a microscopic self-consistent theory for the dynamic transverse confinement field in solutions of zero-excluded-volume rods based solely on topological entanglements. In agreement with the phenomenological tube model, an infinitely deep potential is predicted. However, strong anharmonicities are found to qualitatively soften localization, in quantitative agreement with experiments on heavily entangled biopolymer solutions. Predictions are also made for the effect of rod alignment on the transverse diffusion constant, tube diameter, and confinement force.

Microscopic theory of topologically entangled fluids of rigid macromolecules

We present a first-principles theory for the slow dynamics of a fluid of entangling rigid crosses of zero excluded volume based on a generalization of the dynamic mean-field approach of Szamel for infinitely thin nonrotating rods. The latter theory exactly includes topological constraints at the two-body collision level and self-consistently renormalizes an effective diffusion tensor to account for many-body effects. Remarkably, it predicts scaling laws consistent with the phenomenological reptation-tube predictions of Doi and Edwards for the long-time diffusion and the localization length in the heavily entangled limit. We generalize this approach to a different macromolecular architecture, infinitely thin three-dimensional crosses, and also extend the range of densities over which a dynamic localization length can be calculated for rods. Ideal gases of nonrotating crosses have recently received attention in computer simulations and are relevant as a simple model of both a strong-glass former and entangling star-branched polymers. Comparisons of our theory with these simulations reveal reasonable agreement for the magnitude and reduced density dependence of the localization length and also the self-diffusion constant if the consequences of local density fluctuations are taken into account.

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.

Yielding in dense suspensions: cage, bond, and rotational confinements

The effect of weak particle anisotropy on the onset of fluidity in dense suspensions of glasses of repulsive, weakly attractive and strongly attractive spherical and dumbbell shaped particles is explored. Yield stresses are found to scale with volume fraction showing a divergence at random close packing for all systems. However the onsets of yielding in suspensions of spherical and dumbbell shaped particles are shown to display qualitatively different behaviors. Suspensions of hard spheres exhibit a single yield stress (strain) while suspensions of spheres experiencing short range attractions in dense gels display two yielding events. Double yielding occurs when attractions between particles are only a few kT and the suspensions are sufficiently dense. For dumbbell suspensions, single yielding is observed for hard dumbbell glasses in a region where the glasses are expected to be plastic while double yielding is observed when the particles are expected to have localized centers of mass and localized orientations. Double yielding is also observed for dense dumbbell suspensions that experience attractions while only single yielding events are observed in strongly attractive gels for both dumbbells and spheres. These results are discussed in the light of recent theories and simulations of mechanisms of localization in suspensions of spherical and weakly anisotropic particles.

Theory of aging, rejuvenation, and the nonequilibrium steady state in deformed polymer glasses

The nonlinear Langevin equation theory of segmental relaxation, elasticity, and mechanical response of polymer glasses is extended to describe the coupled effects of physical aging, mechanical rejuvenation, and thermal history. The key structural variable is the amplitude of density fluctuations, and segmental dynamics proceeds via stress-modified activated barrier hopping on a dynamic free-energy profile. Mechanically generated disorder (rejuvenation) is quantified by a dissipative work argument and increases the amplitude of density fluctuations, thereby speeding up relaxation beyond that induced by the landscape tilting mechanism. The theory makes testable predictions for the time evolution and nonequilibrium steady state of the alpha relaxation time, density fluctuation amplitude, elastic modulus, and other properties. Model calculations reveal a rich dependence of these quantities on preaging time, applied stress, and temperature that reflects the highly nonlinear competition between physical aging and mechanical disordering. Thermal history is "erased" in the long-time limit, although the nonequilibrium steady state is not the literal "fully rejuvenated" freshly quenched glass. The present work provides the conceptual foundation for a quantitative treatment of the nonlinear mechanical response of polymer glasses under a variety of deformation protocols.

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.

Segmental dynamics in polymers: from cold melts to ageing and stressed glasses

Recent progress in developing statistical mechanical theories of supercooled polymer melts and glasses is reviewed. The focus is on those approaches that are either explicitly formulated for polymers, or are applications of more generic theories to interpret polymeric phenomena. These include two configurational entropy theories, a percolated free volume distribution model, and the activated barrier hopping nonlinear Langevin theory. Both chemically-specific and universal aspects are discussed. After a brief summary of classic phenomenological approaches, a discussion of the relevant length scales and key experimental phenomena in both the supercooled liquid and glassy solid state is presented including ageing and nonlinear mechanical response. The central concepts that underlie the theories in the molten state are then summarized and key predictions discussed, including the glass transition in oriented polymer liquids and deformed rubber networks. Physical ageing occurs in the nonequilibrium glass, and theories for its consequences on the alpha relaxation are discussed. Very recent progress in developing a segment scale theory for the dramatic effects of external stress on polymer glasses, including acceleration of relaxation, yielding, plastic flow and strain hardening, is summarized. The article concludes with a discussion of outstanding theoretical challenges.

Colloidal glass transition in unentangled polymer nanocomposite melts

The linear and non-linear rheology of a high volume fraction particle filled unentangled polymer melt is measured. The particles in the polymer melt behave like hard spheres as the particle volume fraction is raised. At high volume fractions, the suspension develops a plateau elastic modulus. Over the frequency range of the elastic modulus plateau, the viscous modulus develops a minimum and a maximum. The frequencies of the two local extrema initially have critical power law scaling, suggesting the approach of a singular glass transition. At higher volume fractions in excess of the glass transition, the viscous modulus continues to show a well defined minimum and a well defined maximum. The non-linear moduli show a single perturbative yield point beyond which the suspension softens. The yielding behavior of the nanocomposite is shown to be sensitive to the strain frequency and the proximity of the strain frequency to the maximum frequency for the linear viscous modulus from linear rheology which characterizes thermal relaxation of glassy particle clusters in the zero strain limit. The linear and non-linear measurements are compared against a recently developed mechanical theory for colloidal glasses.

Shear thinning in deeply supercooled melts

We compute, on a molecular basis, the viscosity of a deeply supercooled liquid at high shear rates. The viscosity is shown to decrease at growing shear rates, owing to an increase in the structural relaxation rate as caused by the shear. The onset of this non-Newtonian behavior is predicted to occur universally at a shear rate significantly lower than the typical structural relaxation rate, by approximately two orders of magnitude. This results from a large size—up to several hundred atoms—of the cooperative rearrangements responsible for mass transport in supercooled liquids and the smallness of individual molecular displacements during the cooperative rearrangements. We predict that the liquid will break down at shear rates such that the viscosity drops by approximately a factor of 30 below its Newtonian value. These phenomena are predicted to be independent of the liquid's fragility. In contrast, the degree of nonexponentiality and violation of the Stokes–Einstein law, which are more prominent in fragile substances, will be suppressed by shear. The present results are in agreement with existing measurements of shear thinning in silicate melts.

Theory of coupled translational-rotational glassy dynamics in dense fluids of uniaxial particles

The naïve mode coupling theory (NMCT) for ideal kinetic arrest and the nonlinear Langevin equation theory of activated single-particle barrier hopping dynamics are generalized to treat the coupled center-of-mass (CM) translational and rotational motions of uniaxial hard objects in the glassy fluid regime. The key dynamical variables are the time-dependent displacements of the particle center-of-mass and orientational angle. The NMCT predicts a kinetic arrest diagram with three dynamical states: ergodic fluid, plastic glass, and fully nonergodic double glass, the boundaries of which meet at a "triple point" corresponding to a most difficult to vitrify diatomic of aspect ratio approximately 1.43. The relative roles of rotation and translation in determining ideal kinetic arrest are explored by examining three limits of the theory corresponding to nonrotating, pure rotation, and rotationally ergodic models. The ideal kinetic arrest boundaries represent a crossover to activated dynamics described by two coupled stochastic nonlinear Langevin equations for translational and rotational motions. The fundamental quantity is a dynamic free-energy surface, which for small aspect ratios in the high-volume fraction regime exhibits two saddle points reflecting a two-step activated dynamics where relatively rapid rotational dynamics coexists with slower CM translational motions. For large-enough aspect ratios, the dynamic free-energy surface has one saddle point which corresponds to a system-specific coordinated translation-rotation motion. The entropic barriers as a function of the relative amount of rotation versus translation are determined.