Collisions, caging, thermodynamics, and jamming in the barrier hopping theory of glassy hard sphere fluids

Probing cage dynamics in concentrated hard-sphere suspensions and glasses with high frequency rheometry

The cage concept, a central microscopic mechanism for glassy dynamics, has been utilized in concentrated colloidal suspensions to describe a number of phenomena. Here, we probe the evolution of cage formation and shear elasticity with increasing volume fraction in hard sphere suspensions, with emphasis on the short-time dynamics. To this end, we utilize linear viscoelastic (LVE) measurements, by means of conventional rotational rheometers and a home-made HF piezo-rheometer, to probe the dynamic response over a broad range of volume fractions up to the very dense glassy regime in proximity to random close packing. We focus on the LVE spectra and times shorter than those corresponding to the dynamic shear modulus G' plateau, where the system approaches transient localization and cage confinement. At these short times (higher frequencies), a dynamic cage has not yet fully developed and particles are not (strictly) transiently localized. This corresponds to an effective solid-to-liquid transition in the LVE spectrum (dynamic moduli) marked by a high frequency (HF) crossover. On the other hand, as the volume fraction increases caging becomes tighter, particles become more localized, and the onset of the localization time scale becomes shorter. This onset of transient localization to shorter times shifts the HF crossover to higher values. Therefore, the study of the dependence of the HF crossover properties (frequency and moduli) on volume fractions provides direct insights concerning the onset of particle in-cage motion and allows direct comparison with current theoretical models. We compare the experimental data with predictions of a microscopic statistical mechanical theory where qualitative and quantitative agreements are found. Findings include the discovery of microscopic mechanisms for the crossover between the two exponential dependences of the onset of the localization time scale and the elastic shear modulus at high volume fractions as a consequence of emergent many body structural correlations and their consequences on dynamic constraints. Moreover, an analytic derivation of the relationship between the high frequency localized short-time scale and the elastic shear modulus is provided which offers new physical insights and explains why these two variables are experimentally observed to exhibit nearly-identical behaviors.

Spider-silk inspired ultrafast alkali-induced molecular aggregation for 3D printing arbitrary tubular hydrogels

Fabricating tubular hydrogel models with arbitrary structural complexity and controllable diameters using an ultrafast, facile yet universal method is desirable for vascular prototypes yet still a great challenge. Herein, inspired by the denaturing ability of spider silks, a novel strategy to induce complexation via applying highly concentrated alkali into a polyvinyl alcohol/ionic liquid (PVA/IL) solution, i.e., alkali-induced molecular aggregation (AMA), is proposed to achieve such purpose. This strategy enables the rapid and facile fabrication of tubular hydrogel architectures with tunable diameters, controllable thicknesses, and excellent mechanical performance with a tensile strength of up to 1.1 MPa and stretchability exceeding 600%. Importantly, this novel strategy combined with 3D printing facilitates the rapid fabrication of a variety of precise tubular hydrogel models with connected cavity structures which are difficult to achieve using current methods. This ultrafast solidification strategy could also be extended to various alkalis, cations and anions to build different hydrogels, showcasing its versatility and universality. Hence, this strategy can be pioneering to rapidly fabricate complex three-dimensional and hollow enclosed hydrogel models for simulating endovascular interventional therapy.

Superionic UO_{2} crystal: How to model its relaxation and diffusion via a microscopic theory of glass-forming liquids

UO_{2} is a crucial nuclear material but its behaviors are elusive due to the impact of superionic diffusion. Herein, we introduce a simple but effective theoretical model to describe the intrinsic superionicity of UO_{2} at the quantitative level. Our idea stems from a close similarity between superionic crystals and supercooled liquids. Namely, we view UO_{2} as a randomly pinned hard-sphere fluid in the framework of the elastically collective nonlinear Langevin equation theory. This treatment allows us to fully evaluate the contribution of local, collective, pinning, and screening effects to the molecular dynamics of UO_{2} without complex computational processes. Finite-temperature factors are considered via volumetric expansion during isobaric heating. On that basis, we satisfactorily explain recent large-scale atomistic simulations on UO_{2} under various thermodynamic conditions. Our calculations also reveal that UO_{2} is equivalent to an intermediate glass former. Its structural relaxation, self-diffusion, and shear deformation are strongly correlated near the onset of superionicity. These intimate correlations are reminiscent of the famed Dyre shoving model in the soft-matter community. Our results promise to facilitate the development of diverse energy applications of UO_{2}.

Medium-Range Structural Order as the Driver of Activated Dynamics and Complexity Reduction in Glass-Forming Liquids

We analyze in depth the Elastically Collective Nonlinear Langevin Equation theory of activated dynamics in metastable liquids to establish that the predicted inter-relationships between the alpha relaxation time, local cage and collective elastic barriers, dynamic localization length, and shear modulus are causally related within the theory to the medium range order (MRO) static correlation length. The latter grows exponentially with density for metastable hard sphere fluids and as a nonuniversal inverse power law with temperature for supercooled liquids under isobaric conditions. The physical origin of predicted connections between the alpha time and other metrics of cage order and the thermodynamic inverse dimensionless compressibility is fully established. It is discovered that although kinetic constraints from the real space first coordination shell are important for the alpha time, they are of secondary importance compared to the consequences of the more universal MRO correlations in both the modestly and deeply metastable regimes. This understanding sheds new light on the theoretical basis for, and prior successes of, the predictive mapping of chemically complex thermal liquids to effective hard sphere fluids based on matching their dimensionless compressibilities, a scheme we call "complexity reduction". In essence, the latter is equivalent to the physical requirement that the thermal liquid MRO correlation equals that of its effective hard sphere analog. The mapping alone is shown to provide a remarkable level of quantitative predictive power for the glass transition temperature Tg of 21 molecular and polymer liquids. Predictions for the chemically specific absolute magnitude and growth with cooling of the MRO correlation length are obtained and lie in the window of 2-6 nm at Tg. Dynamic heterogeneity, elastic facilitation, and beyond pair structure issues are briefly discussed. Future opportunities to theoretically analyze the equilibrated deep glass regime are outlined.

Theoretical analysis of the structure, thermodynamics, and shear elasticity of deeply metastable hard sphere fluids

The structure, thermodynamics, and slow activated dynamics of the equilibrated metastable regime of glass-forming fluids remain a poorly understood problem of high theoretical and experimental interest. We apply a highly accurate microscopic equilibrium liquid state integral equation theory, in conjunction with naïve mode coupling theory of particle localization, to study in a unified manner the structural correlations, thermodynamic properties, and dynamic elastic shear modulus in deeply metastable hard sphere fluids. Distinctive behaviors are predicted including divergent inverse critical power laws for the contact value of the pair correlation function, pressure, and inverse dimensionless compressibility, and a splitting of the second peak and large suppression of interstitial configurations of the pair correlation function. The dynamic elastic modulus is predicted to exhibit two distinct exponential growth regimes with packing fraction that have strongly different slopes. These thermodynamic, structural, and elastic modulus results are consistent with simulations and experiments. Perhaps most unexpectedly, connections between the amplitude of long wavelength density fluctuations, dimensionless compressibility, local structure, and the dynamic elastic shear modulus have been theoretically elucidated. These connections are more broadly relevant to understanding the slow activated relaxation and mechanical response of colloidal suspensions in the ultradense metastable region and deeply supercooled thermal liquids in equilibrium.

Effect of the nature of the solid substrate on spatially heterogeneous activated dynamics in glass forming supported films

We extend the force-level elastically collective nonlinear Langevin equation theory to treat the spatial gradients of the alpha relaxation time and glass transition temperature, and the corresponding film-averaged quantities, to the geometrically asymmetric case of finite thickness supported films with variable fluid-substrate coupling. The latter typically nonuniversally slows down motion near the solid-liquid interface as modeled via modification of the surface dynamic free energy caging constraints that are spatially transferred into the film and which compete with the accelerated relaxation gradient induced by the vapor interface. Quantitative applications to the foundational hard sphere fluid and a polymer melt are presented. The strength of the effective fluid-substrate coupling has very large consequences for the dynamical gradients and film-averaged quantities in a film thickness and thermodynamic state dependent manner. The interference of the dynamical gradients of opposite nature emanating from the vapor and solid interfaces is determined, including the conditions for the disappearance of a bulk-like region in the film center. The relative importance of surface-induced modification of local caging vs the generic truncation of the long range collective elastic component of the activation barrier is studied. The conditions for the accuracy and failure of a simple superposition approximation for dynamical gradients in thin films are also determined. The emergence of near substrate dead layers, large gradient effects on film-averaged response functions, and a weak non-monotonic evolution of dynamic gradients in thick and cold films are briefly discussed. The connection of our theoretical results to simulations and experiments is briefly discussed, as is the extension to treat more complex glass-forming systems under nanoconfinement.

Screening and collective effects in randomly pinned fluids: a new theoretical framework

We propose a theoretical framework for the dynamics of bulk isotropic hard-sphere systems in the presence of randomly pinned particles and apply this theory to supercooled water to validate it. Structural relaxation is mainly governed by local and non-local activated process. As the pinned fraction grows, a local caging constraint becomes stronger and the long range collective aspect of relaxation is screened by immobile obstacles. Different responses of the local and cooperative motions results in subtle predictions for how the alpha relaxation time varies with pinning and density. Our theoretical analysis for the relaxation time of water with pinned molecules quantitatively well describe previous simulations. In addition, the thermal dependence of relaxation for unpinned bulk water is also consistent with prior computational and experimental data.

Activation free energy gradient controls interfacial mobility gradient in thin polymer films

We examine the mobility gradient in the interfacial region of substrate-supported polymer films using molecular dynamics simulations and interpret these gradients within the string model of glass-formation. No large gradients in the extent of collective motion exist in these simulated films, and an analysis of the mobility gradient on a layer-by-layer basis indicates that the string model provides a quantitative description of the relaxation time gradient. Consequently, the string model indicates that the interfacial mobility gradient derives mainly from a gradient in the high-temperature activation enthalpy ΔH₀ and entropy ΔS₀ as a function of depth z, an effect that exists even in the high-temperature Arrhenius relaxation regime far above the glass transition temperature. To gain insight into the interfacial mobility gradient, we examined various material properties suggested previously to influence ΔH₀ in condensed materials, including density, potential and cohesive energy density, and a local measure of stiffness or u²(z)^-3/2, where u²(z) is the average mean squared particle displacement at a caging time (on the order of a ps). We find that changes in local stiffness best correlate with changes in ΔH₀(z) and that ΔS₀(z) also contributes significantly to the interfacial mobility gradient, so it must not be neglected.

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.

Microscopic ergodicity breaking governs the emergence and evolution of elasticity in glass-forming nanoclay suspensions

We report a study combining x-ray photon correlation spectroscopy (XPCS) with in situ rheology to investigate the microscopic dynamics and mechanical properties of aqueous suspensions of the synthetic hectorite clay Laponite, which is composed of charged, nanometer-scale, disk-shaped particles. The suspensions, with particle concentrations ranging from 3.25 to 3.75 wt %, evolve over time from a fluid to a soft glass that displays aging behavior. The XPCS measurements characterize the localization of the particles during the formation and aging of the soft-glass state. The fraction of localized particles, f_{0}, increases rapidly during the early formation stage and grows more slowly during subsequent aging, while the characteristic localization length r_{loc} steadily decreases. Despite the strongly varying rates of aging at different concentrations, both f_{0} and r_{loc} scale with the elastic shear modulus G^{'} in a manner independent of concentration. During the later aging stage, the scaling between r_{loc} and G^{'} agrees quantitatively with a prediction of naive mode coupling theory. Breakdown of agreement with the theory during the early formation stage indicates the prevalence of dynamic heterogeneity, suggesting the soft solid forms through precursors of dynamically localized clusters.

Localization model description of the interfacial dynamics of crystalline Cu and Cu64Zr36 metallic glass films

Recent studies of structural relaxation in Cu-Zr metallic glass materials having a range of compositions and over a wide range of temperatures and in crystalline UO₂ under superionic conditions have indicated that the localization model (LM) can predict the structural relaxation time τ_α of these materials from the intermediate scattering function without any free parameters from the particle mean square displacement ⟨r²⟩ at a caging time on the order of ps, i.e., the "Debye-Waller factor" (DWF). In the present work, we test whether this remarkable relation between the "fast" picosecond dynamics and the rate of structural relaxation τ_α in these model amorphous and crystalline materials can be extended to the prediction of the local interfacial dynamics of model amorphous and crystalline films. Specifically, we simulate the free-standing amorphous Cu₆₄Zr₃₆ and crystalline Cu films and find that the LM provides an excellent parameter-free prediction for τ_α of the interfacial region. We also show that the Tammann temperature, defining the initial formation of a mobile interfacial layer, can be estimated precisely for both crystalline and glass-forming solid materials from the condition that the DWFs of the interfacial region and the material interior coincide.

Theory of microstructure-dependent glassy shear elasticity and dynamic localization in melt polymer nanocomposites

We present an integrated theoretical study of the structure, thermodynamic properties, dynamic localization, and glassy shear modulus of melt polymer nanocomposites (PNCs) that spans the three microstructural regimes of entropic depletion induced nanoparticle (NP) clustering, discrete adsorbed layer driven NP dispersion, and polymer-mediated bridging network. The evolution of equilibrium and dynamic properties with NP loading, total packing fraction, and strength of interfacial attraction is systematically studied based on a minimalist model. Structural predictions of polymer reference interaction site model integral equation theory are employed to establish the rich behavior of the interfacial cohesive force density, surface excess, and a measure of free volume as a function of PNC variables. The glassy dynamic shear modulus is predicted to be softened, reinforced, or hardly changed relative to the pure polymer melt depending on system parameters, as a result of the competing and qualitatively different influences of interfacial cohesion (physical bonding), free volume, and entropic depletion on dynamic localization and shear elasticity. The localization of polymer segments is the dominant factor in determining bulk PNC softening and reinforcement effects for moderate to strong interfacial attractions, respectively. While in the athermal entropy-dominated regime, the primary origin of mechanical reinforcement is the stress stored in the aggregated NP subsystem. The PNC shear modulus is often qualitatively correlated with the segment localization length but with notable exceptions. The present work provides the foundation for developing a theory of segmental relaxation, T_g changes, and collective NP dynamics in PNCs based on a self-consistent treatment of the cooperative activated motions of segments and NPs.

Thermodynamics-Structure-Dynamics Correlations and Nonuniversal Effects in the Elastically Collective Activated Hopping Theory of Glass-Forming Liquids

We employ the microscopic Elastically Collective Nonlinear Langevin Equation (ECNLE) theory of activated dynamics in combination with crystal-avoiding simulations to study four inter-related questions for metastable monodisperse hard sphere fluids. The first is how significantly improved integral equation theory structural input (Modified-Verlet (MV) closure) changes the dynamical predictions of ECNLE theory. The main consequence is a modest enhancement of the importance of the collective elastic barrier relative to its local cage contribution, which increases the alpha relaxation time and fragility relative to prior results based on the Percus-Yevick closure. Second, ECNLE-MV theory predictions for the alpha time and self-diffusion constant in the metastable regime are quantitatively compared to our new simulations. The small adjustment of a numerical prefactor that enters the collective elastic barrier leads to quantitative agreement over three decades. Third, using the more accurate MV structural input, ECNLE theory is shown to predict thermodynamics-structure-dynamics "correlations" based on various long and short wavelength scalar properties all related to static two-point collective density fluctuations. The logarithm of the alpha relaxation time scales as a power law with these scalar metrics with an exponent that is significantly lower in the less dense noncooperative activated regime compared to the very dense highly cooperative regime. However, the discovered correlation of activated relaxation with a thermodynamic property (dimensionless compressibility) is not causal in ECNLE theory, but rather reflects a strong connection between the local structural quantities that quantify kinetic constraints in the theory with the amplitude of long wavelength density fluctuations. Fourth, the consequences of chemically specific nonuniversalities associated with the onset condition and relative importance of collective elasticity are studied. The predicted thermodynamics-structure-dynamics correlations are found to be robust, albeit with nontrivial shifts of the onset condition.

Theoretical and Experimental Study of Compression Effects on Structural Relaxation of Glass-Forming Liquids

We develop the elastically collective nonlinear Langevin equation theory of bulk relaxation of glass-forming liquids to investigate molecular mobility under compression conditions. The applied pressure restricts more molecular motion and therefore significantly slows down the molecular dynamics when increasing the pressure. We quantitatively determine the temperature and pressure dependence of the structural relaxation time. To validate our model, dielectric spectroscopy experiments for three rigid and nonpolymeric supramolecules are carried out at ambient and elevated pressures. The numerical results quantitatively agree with experimental data.

Integral equation theory of thermodynamics, pair structure, and growing static length scale in metastable hard sphere and Weeks-Chandler-Andersen fluids

We employ the Ornstein-Zernike integral equation theory with the Percus-Yevick (PY) and modified-Verlet (MV) closures to study the equilibrium structural and thermodynamic properties of metastable monodisperse hard sphere and continuous repulsion Weeks-Chandler-Andersen (WCA) fluids under density and temperature conditions where the system is strongly overcompressed or supercooled, respectively. The theoretical results are compared to crystal-avoiding simulations of these dense monodisperse model one-component fluids. The equation of state (EOS) and dimensionless compressibility are computed using both the virial and compressibility routes. For hard spheres, the MV-based virial route EOS and dimensionless compressibility are in very good agreement with simulation for all packing fractions, much better than the PY analogs. The corresponding MV-based predictions for the static structure factor are also very good. The amplitude of density fluctuations on the local cage scale and in the long wavelength limit, and three technically different measures of the density correlation length, are studied with both closures. All five properties grow in a roughly exponential manner with density in the metastable regime up to packing fractions of 58% with no sign of saturation. The MV-based results are in good agreement with our crystal-avoiding simulations. Interestingly, the density dependences of long and short wavelength quantities are closely related. The MV-based theory is also quite accurate for the thermodynamics and structure of supercooled monodisperse WCA fluids. Overall our findings are also relevant as critical input to microscopic theories that relate the equilibrium pair correlation function or static structure factor to dynamical constraints, barriers, and activated relaxation in glass-forming liquids.

Theory of the spatial transfer of interface-nucleated changes of dynamical constraints and its consequences in glass-forming films

We formulate a new theory for how caging constraints in glass-forming liquids at a surface or interface are modified and then spatially transferred, in a layer-by-layer bootstrapped manner, into the film interior in the context of the dynamic free energy concept of the Nonlinear Langevin Equation (NLE) theory approach. The dynamic free energy at any mean location (cage center) involves contributions from two adjacent layers where confining forces are not the same. At the most fundamental level of the theory, the caging component of the dynamic free energy varies essentially exponentially with distance from the interface, saturating deep enough into the film with a correlation length of modest size and weak sensitivity to the thermodynamic state. This imparts a roughly exponential spatial variation of all the key features of the dynamic free energy required to compute gradients of dynamical quantities including the localization length, jump distance, cage barrier, collective elastic barrier, and alpha relaxation time. The spatial gradients are entirely of dynamical, not structural or thermodynamic, origin. The theory is implemented for the hard sphere fluid and diverse interfaces which can be a vapor, a rough pinned particle solid, a vibrating (softened) pinned particle solid, or a smooth hard wall. Their basic description at the level of the spatially heterogeneous dynamic free energy is identical, with the crucial difference arising from the first layer where dynamical constraints can be weakened, softened, or hardly changed depending on the specific interface. Numerical calculations establish the spatial dependence and fluid volume fraction sensitivity of the key dynamical property gradients for five different model interfaces. A comparison of the theoretical predictions for the dynamic localization length and glassy modulus with simulations and experiments for systems with a vapor interface reveals good agreement. The present advance sets the stage for using the Elastically Collective NLE theory to make quantitative predictions for the alpha relaxation time gradient, decoupling phenomena, T_g gradient, and many film-averaged properties of both model and experimental (colloids, molecules, and polymers) systems with diverse interfaces and chemical makeup.

Structural arrest and dynamic localization in biocolloidal gels

Casein micelles interacting via an entropic intermediate-ranged depletion attraction exhibit a fluid-to-gel transition due to arrested spinodal decomposition. The bicontinuous networked structure of the gel freezes shortly after formation. We determine the timescales of structural arrest from the build-up of network rigidity after pre-shear rejuvenation, and find that the arrest time as well as the plateau elastic modulus of the gel diverge as a function of the volume fraction and interaction potential. Moreover, we show using scaling from naïve mode coupling theory that their mechanical properties are dictated by their microscopic dynamics rather than their heterogeneous large scale structure.

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.

Intrinsic nonlinearities in the mechanics of hard sphere suspensions

The onset of nonlinear responses in near hard sphere suspensions is characterized as a function of oscillatory frequency and strain amplitude. At low frequencies where the viscous behavior dominates, the onset of nonlinearities is driven by increases in rate of strain. At high deformation frequency, where suspension mechanics is dominated by an elastic response, the nonlinear responses occur when deformation exceeds a characteristic strain. This strain is associated with the transient confinement of particles by nearest neighbors and its volume fraction dependence is through cage parameters derived from the high frequency elastic modulus. The onset of nonlinear responses takes on a universal behavior when deformation frequency is normalized by the characteristic time governing the shift from viscous to elastic behavior indicating that this transition is associated with transient particle localization and is expected to be observed for all volume fractions where pair interactions are important.

Microscopic Theory for the Role of Attractive Forces in the Dynamics of Supercooled Liquids

We formulate a microscopic, no adjustable parameter, theory of activated relaxation in supercooled liquids directly in terms of the repulsive and attractive forces within the framework of pair correlations. Under isochoric conditions, attractive forces can nonperturbatively modify slow dynamics, but at high enough density their influence vanishes. Under isobaric conditions, attractive forces play a minor role. High temperature apparent Arrhenius behavior and density-temperature scaling are predicted. Our results are consistent with recent isochoric simulations and isobaric experiments on a deeply supercooled molecular liquid. The approach can be generalized to treat colloidal gelation and glass melting, and other soft matter slow dynamics problems.

Theory of activated penetrant diffusion in viscous fluids and colloidal suspensions

We heuristically formulate a microscopic, force level, self-consistent nonlinear Langevin equation theory for activated barrier hopping and non-hydrodynamic diffusion of a hard sphere penetrant in very dense hard sphere fluid matrices. Penetrant dynamics is controlled by a rich competition between force relaxation due to penetrant self-motion and collective matrix structural (alpha) relaxation. In the absence of penetrant-matrix attraction, three activated dynamical regimes are predicted as a function of penetrant-matrix size ratio which are physically distinguished by penetrant jump distance and the nature of matrix motion required to facilitate its hopping. The penetrant diffusion constant decreases the fastest with size ratio for relatively small penetrants where the matrix effectively acts as a vibrating amorphous solid. Increasing penetrant-matrix attraction strength reduces penetrant diffusivity due to physical bonding. For size ratios approaching unity, a distinct dynamical regime emerges associated with strong slaving of penetrant hopping to matrix structural relaxation. A crossover regime at intermediate penetrant-matrix size ratio connects the two limiting behaviors for hard penetrants, but essentially disappears if there are strong attractions with the matrix. Activated penetrant diffusivity decreases strongly with matrix volume fraction in a manner that intensifies as the size ratio increases. We propose and implement a quasi-universal approach for activated diffusion of a rigid atomic/molecular penetrant in a supercooled liquid based on a mapping between the hard sphere system and thermal liquids. Calculations for specific systems agree reasonably well with experiments over a wide range of temperature, covering more than 10 orders of magnitude of variation of the penetrant diffusion constant.

Writing in the granular gel medium

Gels made from soft microscale particles smoothly transition between the fluid and solid states, making them an ideal medium in which to create macroscopic structures with microscopic precision. While tracing out spatial paths with an injection tip, the granular gel fluidizes at the point of injection and then rapidly solidifies, trapping injected material in place. This physical approach to creating three-dimensional (3D) structures negates the effects of surface tension, gravity, and particle diffusion, allowing a limitless breadth of materials to be written. With this method, we used silicones, hydrogels, colloids, and living cells to create complex large aspect ratio 3D objects, thin closed shells, and hierarchically branched tubular networks. We crosslinked polymeric materials and removed them from the granular gel, whereas uncrosslinked particulate systems were left supported within the medium for long times. This approach can be immediately used in diverse areas, contributing to tissue engineering, flexible electronics, particle engineering, smart materials, and encapsulation technologies.

The kinetic fragility of liquids as manifestation of the elastic softening

We show that the fragility m , the steepness of the viscosity and relaxation time close to the vitrification, increases with the degree of elastic softening, i.e. the decrease of the elastic modulus with increasing temperature, in a universal way. This provides a novel connection between the thermodynamics, via the modulus, and the kinetics. The finding is evidenced by numerical simulations and comparison with the experimental data of glassformers with widely different fragilities (33 ≤ m ≤ 115), leading to a fragility-independent elastic master curve extending over eighteen decades in viscosity and relaxation time. The master curve is accounted for by a cavity model pointing out the roles of both the available free volume and the cage softness. A major implication of our findings is that ultraslow relaxations, hardly characterised experimentally, become predictable by linear elasticity. As an example, the viscosity of supercooled silica is derived over about fifteen decades with no adjustable parameters.

Mechanical properties of self-assembled Fmoc-diphenylalanine molecular gels

We explore the phase diagram and mechanical properties of molecular gels produced from mixing water with a dimethyl sulfoxide (DMSO) solution of the aromatic dipeptide derivative fluorenylmethoxycarbonyl-diphenylalanine (Fmoc-FF). Highly soluble in DMSO, Fmoc-FF assembles into fibrous networks that form gels upon addition of water. At high water concentrations, rigid gels can be formed at Fmoc-FF concentrations as low as 0.01 wt %. The conditions are established defining the Fmoc-FF and water concentrations at which gels are formed. Below the gel boundary, the solutions are clear and colorless and have long-term stability. Above the gel boundary, gels are formed with increasing rapidity with increasing water or Fmoc-FF concentrations. A systematic characterization of the effect of Fmoc-FF and water concentrations on the mechanical properties of the gels is presented, demonstrating that the elastic behavior of the gels follows a specific, robust scaling with Fmoc-FF volume fraction. Furthermore, we characterize the kinetics of gelation and demonstrate that these gels are reversible in the sense that they can be disrupted mechanically and rebuild strength over time.

Controlling the dynamics of a bidimensional gel above and below its percolation transition

The morphology and the microscopic internal dynamics of a bidimensional gel formed by spontaneous aggregation of gold nanoparticles confined at the water surface are investigated by a suite of techniques, including grazing-incidence x-ray photon correlation spectroscopy (GI-XPCS). The range of concentrations studied spans across the percolation transition for the formation of the gel. The dynamical features observed by GI-XPCS are interpreted in view of the results of microscopic imaging; an intrinsic link between the mechanical modulus and internal dynamics is demonstrated for all the concentrations. Our work presents an example of a transition from a stretched to a compressed correlation function actively controlled by quasistatically varying the relevant thermodynamic variable. Moreover, by applying a model proposed some time ago by Duri and Cipelletti [Europhys. Lett. 76, 972 (2006)] we are able to build a master curve for the shape parameter, whose scaling factor allows us to quantify a "long-time displacement length." This characteristic length is shown to converge, as the concentration is increased, to the "short-time localization length" determined by pseudo-Debye-Waller analysis of the initial contrast. Finally, the intrinsic dynamics of the system is then compared with that induced by means of a delicate mechanical perturbation applied to the interface.

Yield stress in amorphous solids: a mode-coupling-theory analysis

The yield stress is a defining feature of amorphous materials which is difficult to analyze theoretically, because it stems from the strongly nonlinear response of an arrested solid to an applied deformation. Mode-coupling theory predicts the flow curves of materials undergoing a glass transition and thus offers predictions for the yield stress of amorphous solids. We use this approach to analyze several classes of disordered solids, using simple models of hard-sphere glasses, soft glasses, and metallic glasses for which the mode-coupling predictions can be directly compared to the outcome of numerical measurements. The theory correctly describes the emergence of a yield stress of entropic nature in hard-sphere glasses, and its rapid growth as density approaches random close packing at qualitative level. By contrast, the emergence of solid behavior in soft and metallic glasses, which originates from direct particle interactions is not well described by the theory. We show that similar shortcomings arise in the description of the caging dynamics of the glass phase at rest. We discuss the range of applicability of mode-coupling theory to understand the yield stress and nonlinear rheology of amorphous materials.

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.

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.