Ideal vitrification, barrier hopping, and jamming in fluids of modestly anisotropic hard objects

Penetrant shape effects on activated dynamics and selectivity in polymer melts and networks based on self-consistent cooperative hopping theory

We generalize and apply the microscopic self-consistent cooperative hopping theory for activated penetrant dynamics in polymer melts and crosslinked networks to address the role of highly variable non-spherical molecular shape. The focus is on vastly different shaped penetrants that have identical space filling volume in order to isolate how non-spherical shape explicitly modifies dynamics over a wide range of temperature down to the kinetic glass transition temperature. The theory relates intramolecular and intermolecular structure and kinetic constraints, and reveals how different solvation packing of polymer monomers around variable shaped penetrants impact penetrant hopping. A highly shape-dependent penetrant activated relaxation, including alpha time decoupling and trajectory level cooperativity of the hopping process, is predicted in the deeply supercooled regime for relatively larger penetrants which is sensitive to whether the polymer matrix is a melt or heavily crosslinked network. In contrast, for smaller size penetrants or at high/medium temperatures the effect of isochoric penetrant shape is relatively weak. We propose an aspect ratio variable that organizes how penetrant shape influences the activated relaxation times, leading to a (near) collapse or master curve. The relative absolute values of the penetrant relaxation time (inverse hopping rate) in polymer melts versus in crosslinked networks are found to be opposite when compared at a common absolute temperature versus when they are compared at a fixed value of distance from the glass transition based on the variable Tg/T with Tg the glass transition temperature. Quantitative comparison with recent diffusion experiments on chemically complex molecular penetrants of variable shape but fixed volume in crosslinked networks reveals good agreement, and testable new predictions are made. Extension of the theoretical approach to more complex systems of high experimental interest are discussed, including applications to realize selective transport in membrane separation applications.

Activated penetrant dynamics in glass forming liquids: size effects, decoupling, slaving, collective elasticity and correlation with matrix compressibility

We employ the microscopic self-consistent cooperative hopping theory of penetrant activated dynamics in glass forming viscous liquids and colloidal suspensions to address new questions over a wide range of high matrix packing fractions and penetrant-to-matrix particle size ratios. The focus is on the mean activated relaxation time of smaller tracers in a hard sphere fluid of larger particle matrices. This quantity also determines the penetrant diffusion constant and connects directly with the structural relaxation time probed in an incoherent dynamic structure factor measurement. The timescale of the non-activated fast dissipative process is also studied and is predicted to follow power laws with the contact value of the penetrant-matrix pair correlation function and the penetrant-matrix size ratio. For long time penetrant relaxation, in the relatively lower packing fraction metastable regime the local cage barriers are dominant and matrix collective elasticity effects unimportant. As packing fraction and/or penetrant size grows, much higher barriers emerge and the collective elasticity associated with the correlated matrix dynamic displacement that facilitates penetrant hopping becomes important. This results in a non-monotonic variation with packing fraction of the degree of decoupling between the matrix and penetrant alpha relaxation times. The conditions required for penetrant hopping to become slaved to the matrix alpha process are determined, which depend mainly on the penetrant to matrix particle size ratio. By analyzing the absolute and relative importance of the cage and elastic barriers we establish a mechanistic understanding of the origin of the predicted exponential growth of the penetrant hopping time with size ratio predicted at very high packing fractions. A dynamics-thermodynamics power law connection between the penetrant activation barrier and the matrix dimensionless compressibility is established as a prediction of theory, with different scaling exponents depending on whether matrix collective elasticity effects are important. Quantitative comparisons with simulations of the penetrant relaxation time, diffusion constant, and transient localization length of tracers in dense colloidal suspensions and cold viscous liquids reveal good agreements. Multiple new predictions are made that are testable via future experiments and simulations. Extension of the theoretical approach to more complex systems of high experimental interest (nonspherical molecules, semiflexible polymers, crosslinked networks) interacting via variable hard or soft repulsions and/or short range attractions is possible, including under external deformation.

Molecular Modeling and Simulation of Polymer Nanocomposites with Nanorod Fillers

We present a coarse-grained (CG) molecular dynamics (MD) simulation study of polymer nanocomposites (PNCs) containing nanorods with homogeneous and patchy surface chemistry/functionalization, modeled with isotropic and directional nanorod-nanorod attraction, respectively. We show how the PNC morphology is impacted by the nanorod design (i.e., aspect ratio, homogeneous or patchy surface chemistry/functionalization) for nanorods with a diameter equal to the Kuhn length of the polymer in the matrix. For PNCs with 10 vol % nanorods that have an aspect ratio ≤5, we observe percolated morphology with directional nanorod-nanorod attraction and phase-separated (i.e., nanorod aggregation) morphology with isotropic nanorod-nanorod attraction. In contrast, for nanorods with higher aspect ratios, both types of attractions result in aggregated nanorods morphology due to the dominance of entropic driving forces that cause long nanorods to form orientationally ordered aggregates. For most PNCs with isotropic or directional nanorod-nanorod attractions, the average matrix polymer conformation is not perturbed by the inclusion of up to 20 vol % nanorods. The polymer chains in contact with nanorods (i.e., interfacial chains) are on average extended and statistically different from the conformations the matrix chains adopt in the pure melt state (with no nanorods); in contrast, the polymer chains far from nanorods (i.e., bulk chains) adopt the same conformations as the matrix chains adopt in the pure melt state. We also study the effect of other parameters, such as attraction strength, nanorod volume fraction, and matrix chain length, for PNCs with isotropic or directional nanorod-nanorod attractions. Collectively, our results provide valuable design rules to achieve specific PNC morphologies (i.e., dispersed, aggregated, percolated, and orientationally aligned nanorods) for various potential applications.

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.

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.

Rheology of dense suspensions of shape anisotropic particles designed to show pH-sensitive anisotropic pair potentials

Here we investigate the flow properties of suspensions of dicolloidal particles composed of interpenetrating spheres where one sphere is rich in polystyrene and the second is rich in poly 2-vinyl pyridine. The synthesis method is designed to create both anisotropic shape and anisotropic interaction potentials that should lead to head to tail clustering. These particles are referred to as copolymer dicolloids (CDCs). The viscoelastic properties of stable and gelled suspensions of CDC particles are compared with analogs composed of homopolymer dicolloids (HDCs), having the same shape but not displaying the anisotropic attractions. After coating the particles with a nonionic surfactant to minimize van der Waals attractions, the flow properties of glassy and gelled suspensions of CDCs and HDCs are studied as a function of volume fraction, ionic strength and pH. Suspensions of HDC particles display a high kinetic arrest volume fraction (φ(g) > 0.5) over a wide range of pH and ionic strength up to [I]=0.5 M, demonstrating that the particles experience repulsive or weakly attractive pair potentials. Suspensions of CDC particles behave in a similar manner at high or low pH when [I]=0.001 M, but gel at a volume fraction of φ(g) < 0.3 and display anomalously large elastic moduli at and above the gel transition point for intermediate pH or for pH=9 when [I]=0.5 M. The gelation processes for the CDC particles are reversible by adjusting the solution pH. Interaction potential anisotropy is evident in the processes, during which the CDC particles yield on increasing oscillatory strain.

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.

Percolation, phase separation, and gelation in fluids and mixtures of spheres and rods

The relationship between kinetic arrest, connectivity percolation, structure and phase separation in protein, nanoparticle, and colloidal suspensions is a rich and complex problem. Using a combination of integral equation theory, connectivity percolation methods, naïve mode coupling theory, and the activated dynamics nonlinear Langevin equation approach, we study this problem for isotropic one-component fluids of spheres and variable aspect ratio rigid rods, and also percolation in rod-sphere mixtures. The key control parameters are interparticle attraction strength and its (short) spatial range, total packing fraction, and mixture composition. For spherical particles, formation of a homogeneous one-phase kinetically stable and percolated physical gel is predicted to be possible, but depends on non-universal factors. On the other hand, the dynamic crossover to activated dynamics and physical bond formation, which signals discrete cluster formation below the percolation threshold, almost always occurs in the one phase region. Rods more easily gel in the homogeneous isotropic regime, but whether a percolation or kinetic arrest boundary is reached first upon increasing interparticle attraction depends sensitively on packing fraction, rod aspect ratio and attraction range. Overall, the connectivity percolation threshold is much more sensitive to attraction range than either the kinetic arrest or phase separation boundaries. Our results appear to be qualitatively consistent with recent experiments on polymer-colloid depletion systems and brush mediated attractive nanoparticle suspensions.

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.

Effect of particle size on the glass transition

The glass transition temperature of a broad class of molecules is shown to depend on molecular size. This dependency results from the size dependence of the pair potential. A generalized equation of state is used to estimate how the volume fraction at the glass transition depends on the size of the molecule, for rigid molecule glass-formers. The model shows that at a given pressure and temperature there is a size-induced glass transition: For molecules larger than a critical size, the volume fraction required to support the effective pressure due to particle attractions is above that which characterizes the glassy state. This observation establishes the boundary between nanoparticles, which exist in liquid form only as dispersions in low molecular weight solvents and large molecules which form liquids that have viscosities below those characterized by the glassy state.

Activated dynamics in dense fluids of attractive nonspherical particles. II. Elasticity, barriers, relaxation, fragility, and self-diffusion

In paper II of this series we apply the center-of-mass version of Nonlinear Langevin Equation theory to study how short-range attractive interactions influence the elastic shear modulus, transient localization length, activated dynamics, and kinetic arrest of a variety of nonspherical particle dense fluids (and the spherical analog) as a function of volume fraction and attraction strength. The activation barrier (roughly the natural logarithm of the dimensionless relaxation time) is predicted to be a rich function of particle shape, volume fraction, and attraction strength, and the dynamic fragility varies significantly with particle shape. At fixed volume fraction, the barrier grows in a parabolic manner with inverse temperature nondimensionalized by an onset value, analogous to what has been established for thermal glass-forming liquids. Kinetic arrest boundaries lie at significantly higher volume fractions and attraction strengths relative to their dynamic crossover analogs, but their particle shape dependence remains the same. A limited universality of barrier heights is found based on the concept of an effective mean-square confining force. The mean hopping time and self-diffusion constant in the attractive glass region of the nonequilibrium phase diagram is predicted to vary nonmonotonically with attraction strength or inverse temperature, qualitatively consistent with recent computer simulations and colloid experiments.

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.

Stress-strain behavior and geometrical properties of packings of elongated particles

We present a numerical analysis of the effect of particle elongation on the quasistatic behavior of sheared granular media by means of the contact dynamics method. The particle shapes are rounded-cap rectangles characterized by their elongation. The macroscopic and microstructural properties of several packings subjected to biaxial compression are analyzed as a function of particle elongation. We find that the shear strength is an increasing linear function of elongation. Performing an additive decomposition of the stress tensor based on a harmonic approximation of the angular dependence of branch vectors, contact normals, and forces, we show that the increasing mobilization of friction force and the associated anisotropy are key effects of particle elongation. These effects are correlated with partial nematic ordering of the particles which tend to be oriented perpendicular to the major principal stress direction and form side-to-side contacts. However, the force transmission is found to be mainly guided by cap-to-side contacts, which represent the largest fraction of contacts for the most elongated particles. Another interesting finding is that, in contrast to shear strength, the solid fraction first increases with particle elongation but declines as the particles become more elongated. It is also remarkable that the coordination number does not follow this trend so that the packings of more elongated particles are looser but more strongly connected.

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.

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.

Theory of physical aging in polymer glasses

A statistical segment scale theory for the physical aging of polymer glasses is proposed and applied. The approach is based on a nonlinear stochastic Langevin equation of motion and the concept of an effective free energy which quantifies temporary localization, collective barriers, and the activated segment hopping process. The key collective structural variable that plays the role of the dynamic order parameter for aging is the experimentally measurable nanometer and longer wavelength amplitude of density fluctuations, S0 . The degree of local cooperativity, and the bare activation energy of the high-temperature Arrhenius process, are determined in the molten state by utilizing experimental measurements of the glass temperature and dynamic crossover time, respectively. A first-order kinetic equation with a time varying rate is proposed for the temporal evolution of S0 which is self-consistently and nonlinearly coupled with the mean segmental relaxation time. The theory has been applied to study physical aging of the alpha relaxation time, shear relaxation modulus, amplitude of density fluctuations, cohesive energy, absolute yield stress, and fictive temperature of polymethylmethacrylate and other glasses over a range of temperatures. Temperature-dependent logarithmic and effective power-law aging is predicted at intermediate times. Time-aging time superposition is found for the mechanical relaxation function. A strongly asymmetric aging response is predicted for up and down temperature jump experiments. Comparison of the approach with the classic phenomenological model is presented.

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.

Theory of gelation, vitrification, and activated barrier hopping in mixtures of hard and sticky spheres

Naive mode coupling theory (NMCT) and the nonlinear stochastic Langevin equation theory of activated dynamics have been generalized to mixtures of spherical particles. Two types of ideal nonergodicity transitions are predicted corresponding to localization of both, or only one, species. The NMCT transition signals a dynamical crossover to activated barrier hopping dynamics. For binary mixtures of equal diameter hard and attractive spheres, a mixture composition sensitive "glass-melting" type of phenomenon is predicted at high total packing fractions and weak attractions. As the total packing fraction decreases, a transition to partial localization occurs corresponding to the coexistence of a tightly localized sticky species in a gel-like state with a fluid of hard spheres. Complex behavior of the localization lengths and shear moduli exist because of the competition between excluded volume caging forces and attraction-induced physical bond formation between sticky particles. Beyond the NMCT transition, a two-dimensional nonequilibrium free energy surface emerges, which quantifies cooperative activated motions. The barrier locations and heights are sensitive to the relative amplitude of the cooperative displacements of the different species.