Cooperative activated dynamics in dense mixtures of hard and sticky spheres

Correlated matrix-fluctuation-mediated activated transport of dilute penetrants in glass-forming liquids and suspensions

We formulate a microscopic, force-level statistical mechanical theory for the activated diffusion of dilute penetrants in dense liquids, colloidal suspensions, and glasses. The approach explicitly and self-consistently accounts for coupling between penetrant hopping and matrix dynamic displacements that actively facilitate the hopping event. The key new ideas involve two mechanistically (at a stochastic trajectory level) coupled dynamic free energy functions for the matrix and spherical penetrant particles. A single dynamic coupling parameter quantifies how much the matrix displaces relative to the penetrant when the latter reaches its transition state which is determined via the enforcement of a temporal causality or coincidence condition. The theory is implemented for dilute penetrants smaller than the matrix particles, with or without penetrant-matrix attractive forces. Model calculations reveal a rich dependence of the penetrant diffusion constant and degree of dynamic coupling on size ratio, volume fraction, and attraction strength. In the absence of attractions, a near exponential decrease of penetrant diffusivity with size ratio over an intermediate range is predicted, in contrast to the much steeper, non-exponential variation if one assumes local matrix dynamical fluctuations are not correlated with penetrant motion. For sticky penetrants, the relative and absolute influence of caging versus physical bond formation is studied. The conditions for a dynamic crossover from the case where a time scale separation between penetrant and matrix activated hopping exists to a "slaved" or "constraint release" fully coupled regime are determined. The particle mixture model is mapped to treat experimental thermal systems and applied to make predictions for the diffusivity of water, toluene, methanol, and oxygen in polyvinylacetate liquids and glasses. The theory agrees well with experiment with values of the penetrant-matrix size ratio close to their chemically intuitive values.

Big Effect of Small Nanoparticles: A Shift in Paradigm for Polymer Nanocomposites

Polymer nanocomposites (PNCs) are important materials that are widely used in many current technologies and potentially have broader applications in the future due to their excellent property tunability, light weight, and low cost. However, expanding the limits in property enhancement remains a fundamental scientific challenge. Here, we demonstrate that well-dispersed, small (diameter ∼1.8 nm) nanoparticles with attractive interactions lead to unexpectedly large and qualitatively different changes in PNC structural dynamics in comparison to conventional nanocomposites based on particles of diameters ∼10-50 nm. At the same time, the zero-shear viscosity at high temperatures remains comparable to that of the neat polymer, thereby retaining good processability and resolving a major challenge in PNC applications. Our results suggest that the nanoparticle mobility and relatively short lifetimes of nanoparticle-polymer associations open qualitatively different horizons in the tunability of macroscopic properties in nanocomposites with a high potential for the development of advanced functional materials.

Coupling of gelation and glass transition in a biphasic colloidal mixture-from gel-to-defective gel-to-glass

The state transition from gel to glass is studied in a biphasic mixture of polystyrene core/poly(N-isopropylacrylamide) shell (CS) microgels and sulfonated polystyrene (PSS) particles. At 35 °C, the interaction between CS microgels is due to short-range van der Waals attraction, while that between PSS particles is from long-range electrostatic repulsion. During the variation of the relative ratio of the two species at a fixed apparent total volume fraction, the mixture exhibits a gel-to-defective gel-to-glass transition. When small amounts of PSS are introduced into the CS gel network, some of them are kinetically trapped, causing a change in its fractal structure, and act as defects to weaken the macroscopic gel strength. An increase of the PSS content in the mixture promotes the switch from the gel to the defective gel, e.g., the typical two-step yielding gel merges into one-step yielding. This phenomenon is an indication that inter-cluster bond breakage coincides with intra-cluster bond fracture. As the relative volume fraction of PSS exceeds a critical threshold, the gel network can no longer be formed; hence, the mixture exhibits characteristics of glass. A state diagram of the biphasic mixture is constructed, and the landscapes of the different transitions will be described in future studies.

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.

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.

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.

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.

Roles of bond orientational ordering in glass transition and crystallization

It is widely believed that crystallization in three dimensions is primarily controlled by positional ordering, and not by bond orientational ordering. In other words, bond orientational ordering is usually considered to be merely a consequence of positional ordering and thus has often been ignored. This one-order-parameter (density) description may be reasonable when we consider an equilibrium liquid-solid transition, but may not be enough to describe a metastable state and the kinetics of the transition. Here we propose that bond orientational ordering can play a key role in (i) crystallization, (ii) the ordering to quasi-crystal and (iii) vitrification, which occurs under rather weak frustration against crystallization. In a metastable supercooled state before crystallization, a system generally tends to have bond orientational order at least locally as a result of a constraint of dense packing. For a system interacting with hard-core repulsions, the constraint is intrinsically of geometrical origin and thus the basic physics is the same as nematic ordering of rod-like particles upon densification. Furthermore, positional ordering is easily destroyed even by weak frustration such as polydispersity and anisotropic interactions which favour a symmetry not consistent with that of the equilibrium crystal. Thus we may say that vitrification can be achieved by disturbing and prohibiting long-range positional ordering. Even in such a situation, bond orientational ordering still survives, accompanying its critical-like fluctuations, which are the origin of dynamic heterogeneity for this case. This scenario naturally explains both the absence of positional order and the development of bond orientational order upon cooling in a supercooled state. Although our argument is speculative in nature, we emphasize that this physical picture can coherently explain crystallization, vitrification, quasi-crystallization and their relationship in a natural manner. For a strongly frustrated system, even bond orientational order can be destroyed. Even in such a case there may still appear a structural signature of dense packing, which is linked to slow dynamics.

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.

Colloidal glasses and gels: The interplay of bonding and caging

We report simulations of glassy arrest in hard-core particles with short-range interparticle attraction. Previous experiments, theory, and simulations suggest that in this kind of system, two qualitatively distinct kinds of glasses exist, dominated respectively by repulsion and attraction. It is thought that in the former, particles are trapped "topologically," by nearest-neighbor cages, whereas in the latter, nonergodicity is due to interparticle "bonds." Subsequent experiments and simulations have suggested that bond breaking destabilizes attractive glasses, but the long-term fate of these arrested states remains unknown. By running simulations to times a few orders of magnitude longer than those reached by previous experiments or simulations, we show that arrest in an attractive glass is, in the long run, also topological. Nevertheless, it is still possible to distinguish between "nonbonded" and "bonded" repulsive glassy states. We study the melting of bonded repulsive glasses into a hitherto unknown "dense gel" state, which is distinct from dense, ergodic fluids. We propose a "modified state diagram" for concentrated attractive particles, and discuss the relevance of our results in the light of recent rheological measurements in colloid-polymer mixtures.

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.