Glassy dynamics and mechanical response in dense fluids of soft repulsive spheres. I. Activated relaxation, kinetic vitrification, and fragility

Transition in the Glassy Dynamics of Melts of Acid-Hydrolyzed Phytoglycogen Nanoparticles

The deformability, responsiveness, and tunability of soft nanoparticles (NPs) offer unique opportunities to learn about their complex properties and the interactions between particles. In the present study, we provide new insights into the physical properties of phytoglycogen (PG) NPs, which are soft, compact particles with a dendritic architecture that are produced in the kernels of sweet corn. In particular, we study PG NPs modified using acid hydrolysis, which not only reduces their diameter but also alters their stiffness, internal structure, and the interactions between particles in aqueous dispersions. We used steady shear rheology to determine the dependence of the relative zero-shear viscosity η_r of aqueous dispersions of acid-hydrolyzed PG NPs on the effective volume fraction ϕ_eff, which indicated a reduction in stiffness of the particles relative to that of native PG NPs. We quantified this difference by analyzing the nature of the colloidal glasses formed at high ϕ_eff. We measured a smaller value of the fragility index m for acid-hydrolyzed PG NP glasses than that for native PG NP glasses, indicating that acid-hydrolyzed PG NPs form stronger glasses and are therefore softer than native PG NPs. Unlike the native PG NPs, we observed a distinctive change in the character of the glass transition of the acid-hydrolyzed PG NPs as ϕ_eff was increased above ϕ_eff∼1: a crossover in the dependence of η_r on ϕ_eff from Vogel-Fulcher-Tammann behavior to a more gradual, Arrhenius-like behavior. By expressing the steady shear and oscillatory rheology data in terms of generalized Péclet numbers, we obtained collapse of the data onto master curves. We interpret this result in terms of the acid-hydrolyzed PG NPs predominantly interpenetrating neighboring particles at large ϕ_eff, for which fluctuations of the outer chains enhance the mobility of the particles and make α-relaxation times τ_α experimentally accessible.

Dynamics of Confined Microgel Liquids: Weakened Spatial Confinement Effect by Microgel Particle Compliance

Spatial confinement has a great impact on the structures and dynamics of interfacial molecular and polymer liquid films. Most prior research has focused on confined liquids of fixed material compliance and often treated them in approximation to the "hard-sphere" interaction model. In this study, we microscopically investigate the structural dynamics of highly deformable poly(N-isopropylacrylamide) (PNIPAM) microgels confined between two solid surfaces in comparison to that of nearly nondeformable microgels of the same chemistry. We observe that the mobility and structural relaxation of highly deformable PNIPAM microgels at an apparent volume fraction, ϕ = 0.49-0.70, show little change with the reduction of gap spacing, in stark contrast to confinement-induced dynamic retardation of "hard-sphere"-like stiff PNIPAM microgels. The critical gap spacing, defined as the onset of confinement effect to deviate from the bulk behavior, is found to be approximately 17-22 particle layers for highly deformable microgels of ϕ = 0.56-0.70, much smaller than that of approximately 40 particle layers or larger for stiff microgels or model "hard-sphere" colloidal liquids of similar ϕ. Additionally, we observe no evident confinement-enhanced structural reorganization of deformable microgels near the confining surfaces when gap spacing approaches the critical gap spacing. Microgel deformation upon strong confinement is attributed to the disrupted confinement-induced ordering of confined microgels. Hence, it is clearly indicated that spatial confinement exhibits a much weaker effect on highly compliant microgel particles than stiff ones, resulting in a significantly less reduction in microgel interfacial dynamics. It therefore gives insights into the molecular design of polymeric thin films of variable compliance to control friction and lubrication.

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.

"Dense diffusion" in colloidal glasses: short-ranged long-time self-diffusion as a mechanistic model for relaxation dynamics

Despite decades of exploration of the colloidal glass transition, mechanistic explanation of glassy relaxation processes has remained murky. State-of-the-art theoretical models of the colloidal glass transition such as random first order transition theory, active barrier hopping theory, and non-equilibrium self-consistent generalized Langevin theory assert that relaxation reported at volume fractions above the ideal mode coupling theory prediction φg,MCT requires some sort of activated process, and that cooperative motion plays a central role. However, discrepancies between predicted and measured values of φg and ambiguity in the role of cooperative dynamics persist. Underlying both issues is the challenge of conducting deep concentration quenches without flow and the difficulty in accessing particle-scale dynamics. These two challenges have led to widespread use of fitting methods to identify divergence, but most a priori assume divergent behavior; and without access to detailed particle dynamics, it is challenging to produce evidence of collective dynamics. We address these limitations by conducting dynamic simulations accompanied by experiments to quench a colloidal liquid into the putative glass by triggering an increase in particle size, and thus volume fraction, at constant particle number density. Quenches are performed from the liquid to final volume fractions 0.56 ≤ φ ≤ 0.63. The glass is allowed to age for long times, and relaxation dynamics are monitored throughout the simulation. Overall, correlated motion acts to release dynamics from the glassy plateau - but only over length scales much smaller than a particle size - allowing self-diffusion to re-emerge; self-diffusion then relaxes the glass into an intransient diffusive state, which persists for φ < 0.60. We observe similar relaxation dynamics up to φ = 0.63 before achieving the intransient state. We find that this long-time self-diffusion is short-ranged: analysis of mean-square displacement reveals a glassy cage size a fraction of a particle size that shrinks with quench depth, i.e. increasing volume fraction. Thus the equivalence between cage size and particle size found in the liquid breaks down in the glass, which we confirm by examining the self-intermediate scattering function over a range of wave numbers. The colloidal glass transition can hence be viewed mechanistically as a shift in the long-time self-diffusion from long-ranged to short-ranged exploration of configurations. This shift takes place without diverging dynamics: there is a smooth transition as particle mobility decreases dramatically with concomitant emergence of a dense local configuration space that permits sampling of many configurations via local particle motion.

Monte Carlo simulation and integral equation study of Hertzian spheres in the low-temperature regime

We investigate the behavior of Hertzian spheres in the fluid phase and in proximity of the freezing threshold by using Monte Carlo (MC) simulations and integral equation theories, based on the Ornstein-Zernike (OZ) approach. The study is motivated by the importance of the Hertzian model in representing a large class of systems interacting via soft interactions, such as star polymers or microgels. Radial distribution functions, structure factors, and excess entropy clearly show the reentrant behavior typical of the Hertzian fluid, well caught by both MC simulations and OZ theory. Then, we make use of some phenomenological one-phase criteria for testing their reliability in detecting the freezing threshold. All criteria provide evidence of the fluid-solid transition with different degrees of accuracy. This suggests the possibility to adopt these empirical rules to provide a quick and reasonable estimate of the freezing transition in model potentials of wide interest for soft matter systems.

Physical aging and compressed exponential behaviors in a model soft colloidal system

Diffusing wave spectroscopy (DWS)-based micro-rheology has been used in different optical geometries (backscattering and transmission) as well as different sample thicknesses in order to probe system dynamics at different length scales [D. J. Pine, D. A. Weitz, J. X. Zhu, E. Herbolzheimer. J. Phys., 1990, 51(18), 2101-2127]. Previous study from this lab [Q. Li, X. Peng, G. B. McKenna. Soft Matter, 2017, 13(7), 1396-1404] indicates the DWS-based micro-rheology observes the system non-equilibrium behaviors differently from macro-rheology. The object of the present work was to further explore the non-equilibrium dynamics and to address the range of utility of DWS as a micro-rheological method. A thermo-sensitive core-shell colloidal system was investigated both during aging and subsequent to aging into a metastable equilibrium state using temperature-jump induced volume fraction-jump experiments. We find that in the non-equilibrium state, significant differences in the measured dynamics are observed for the different geometries and length scales. Compressed exponential relaxations for the autocorrelation function g2(t) were observed for large length scales. However, upon converting the g2(t) data to the mean square displacement (MSD), such differences with length scale diminished and the long-time MSD behavior was consistent with diffusive behavior. These observations in the non-equilibrium behaviors for different length scales leads to questioning of some interpretations in the current field of light scattering-based micro-rheology and provides a possibility to interrogate the aging mechanisms in colloidal glasses from a broader perspective than normally considered in measurements of g2(t) using DWS-based micro-rheology.

Linear and nonlinear rheology and structural relaxation in dense glassy and jammed soft repulsive pNIPAM microgel suspensions

We present an integrated experimental and quantitative theoretical study of the mechanics of self-crosslinked, slightly charged, repulsive pNIPAM microgel suspensions over a very wide range of concentrations (c) that span the fluid, glassy and putative "soft jammed" regimes. In the glassy regime we measure a linear elastic dynamic shear modulus over 3 decades which follows an apparent power law concentration dependence G' ∼ c5.64, a variation that appears distinct from prior studies of crosslinked ionic microgel suspensions. At very high concentrations there is a sharp crossover to a nearly linear growth of the modulus. To theoretically understand these observations, we formulate an approach to address all three regimes within a single conceptual Brownian dynamics framework. A minimalist single particle description is constructed that allows microgel size to vary with concentration due to steric de-swelling effects. Using a Hertzian repulsion interparticle potential and a suite of statistical mechanical theories, quantitative predictions under quiescent conditions of microgel collective structure, dynamic localization length, elastic modulus, and the structural relaxation time are made. Based on a constant inter-particle repulsion strength parameter which is determined by requiring the theory to reproduce the linear elastic shear modulus over the entire concentration regime, we demonstrate good agreement between theory and experiment. Testable predictions are then made. We also measured nonlinear rheological properties with a focus on the yield stress and strain. A theoretical analysis with no adjustable parameters predicts how the quiescent structural relaxation time changes under deformation, and how the yield stress and strain change as a function of concentration. Reasonable agreement with our observations is obtained. To the best of our knowledge, this is the first attempt to quantitatively understand structure, quiescent relaxation and shear elasticity, and nonlinear yielding of dense microgel suspensions using microscopic force based theoretical methods that include activated hopping processes. We expect our approach will be useful for other soft polymeric particle suspensions in the core-shell family.

Strength of the repulsive part of the interatomic potential determines fragility in metallic liquids

The dynamical behaviour of liquids is frequently characterized by the fragility, which can be defined from the temperature dependence of the shear viscosity, η (ref. ). For a strong liquid, the activation energy for η changes little with cooling towards the glass transition temperature, T_g. The change is much greater in fragile liquids, with the activation energy becoming very large near T_g. While fragility is widely recognized as an important concept-believed, for example, to play an important role in glass formation-the microscopic origin of fragility is poorly understood. Here, we present new experimental evidence showing that fragility reflects the strength of the repulsive part of the interatomic potential, which can be determined from the steepness of the pair distribution function near the hard-sphere cutoff. On the basis of an analysis of scattering data from ten different metallic alloy liquids, we show that stronger liquids have steeper repulsive potentials.

Segment-scale, force-level theory of mesoscopic dynamic localization and entropic elasticity in entangled chain polymer liquids

We develop a segment-scale, force-based theory for the breakdown of the unentangled Rouse model and subsequent emergence of isotropic mesoscopic localization and entropic elasticity in chain polymer liquids in the absence of ergodicity-restoring anisotropic reptation or activated hopping motion. The theory is formulated in terms of a conformational N-dynamic-order-parameter generalized Langevin equation approach. It is implemented using a universal field-theoretic Gaussian thread model of polymer structure and closed at the level of the chain dynamic second moment matrix. The physical idea is that the isotropic Rouse model fails due to the dynamical emergence, with increasing chain length, of time-persistent intermolecular contacts determined by the combined influence of local uncrossability, long range polymer connectivity, and a self-consistent treatment of chain motion and the dynamic forces that hinder it. For long chain melts, the mesoscopic localization length (identified as the tube diameter) and emergent entropic elasticity predictions are in near quantitative agreement with experiment. Moreover, the onset chain length scales with the semi-dilute crossover concentration with a realistic numerical prefactor. Distinctive novel predictions are made for various off-diagonal correlation functions that quantify the full spatial structure of the dynamically localized polymer conformation. As the local excluded volume constraint and/or intrachain bonding spring are softened to allow chain crossability, the tube diameter is predicted to swell until it reaches the radius-of-gyration at which point mesoscopic localization vanishes in a discontinuous manner. A dynamic phase diagram for such a delocalization transition is constructed, which is qualitatively consistent with simulations and the classical concept of a critical entanglement degree of polymerization.

Long-term aging behaviors in a model soft colloidal system

Colloidal and molecular systems share similar behaviors near to the glass transition volume fraction or temperature. Here, aging behaviors after volume fraction up-jump (induced by performing temperature down-jumps) conditions for a PS-PNIPAM/AA soft colloidal system were investigated using light scattering (diffusing wave spectroscopy, DWS). Both aging responses and equilibrium dynamics were investigated. For the aging responses, long-term experiments (100 000 s) were performed, and both equilibrium and non-equilibrium behaviors of the system were obtained. In the equilibrium state, as effective volume fraction increases (or temperature decreases), the colloidal dispersion displays a transition from the liquid to a glassy state. The equilibrium α-relaxation dynamics strongly depend on both the effective volume fraction and the initial mass concentration for the studied colloidal systems. Compared with prior results from our lab [X. Di, X. Peng and G. B. McKenna, J. Chem. Phys., 2014, 140, 054903], the effective volume fractions investigated spanned a wider range, to deeper into the glassy domain. The results show that the α-relaxation time τ_α of the samples aged into equilibrium deviate from the classical Vogel-Fulcher-Tammann (VFT)-type expectations and the super-Arrhenius signature disappears above the glass transition volume fraction. The non-equilibrium aging response shows that the time for the structural evolution into equilibrium and the α-relaxation time are decoupled. The DWS investigation of the aging behavior after different volume fraction jumps reveals a different non-equilibrium or aging behavior for the considered colloidal systems compared with either molecular glasses or the macroscopic rheology of a similar colloidal dispersions.

Correlation between Fragility and the Arrhenius Crossover Phenomenon in Metallic, Molecular, and Network Liquids

We report the observation of a distinct correlation between the kinetic fragility index m and the reduced Arrhenius crossover temperature θ_{A}=T_{A}/T_{g} in various glass-forming liquids, identifying three distinguishable groups. In particular, for 11 glass-forming metallic liquids, we universally observe a crossover in the mean diffusion coefficient from high-temperature Arrhenius to low-temperature super-Arrhenius behavior at approximately θ_{A}≈2 which is in the stable liquid phases. In contrast, for fragile molecular liquids, this crossover occurs at much lower θ_{A}≈1.4 and usually in their supercooled states. The θ_{A} values for strong network liquids spans a wide range higher than 2. Intriguingly, the high-temperature activation barrier E_{∞} is universally found to be ∼11k_{B}T_{g} and uncorrelated with the fragility or the reduced crossover temperature θ_{A} for metallic and molecular liquids. These observations provide a way to estimate the low-temperature glassy characteristics (T_{g} and m) from the high-temperature liquid quantities (E_{∞} and θ_{A}).

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.

Anisotropic pair correlations in binary and multicomponent hard-sphere mixtures in the vicinity of a hard wall: A combined density functional theory and simulation study

The fundamental measure approach to classical density functional theory has been shown to be a powerful tool to predict various thermodynamic properties of hard-sphere systems. We employ this approach to determine not only one-particle densities but also two-particle correlations in binary and six-component mixtures of hard spheres in the vicinity of a hard wall. The broken isotropy enables us to carefully test a large variety of theoretically predicted two-particle features by quantitatively comparing them to the results of Brownian dynamics simulations. Specifically, we determine and compare the one-particle density, the total correlation functions, their contact values, and the force distributions acting on a particle. For this purpose, we follow the compressibility route and theoretically calculate the direct correlation functions by taking functional derivatives. We usually observe an excellent agreement between theory and simulations, except for small deviations in cases where local crystal-like order sets in. Our results set the course for further investigations on the consistency of functionals as well as for structural analysis on, e.g., the primitive model. In addition, we demonstrate that due to the suppression of local crystallization, the predictions of six-component mixtures are better than those in bidisperse or monodisperse systems. Finally, we are confident that our results of the structural modulations induced by the wall lead to a deeper understanding of ordering in anisotropic systems in general, the onset of heterogeneous crystallization, caging effects, and glassy dynamics close to a wall, as well as structural properties in systems with confinement.

Relationship between particle elasticity, glass fragility, and structural relaxation in dense microgel suspensions

"Fragile" glassy materials, which include most polymeric materials and organic liquids, exhibit a steep and super-Arrhenius dependence of relaxation time with temperature upon the glass transition and have been extensively studied. Yet, a full understanding of strong glass formers that exhibit an Arrhenius dependence on temperature is still lacking. In this work, we have investigated the glassy dynamics of poly(N-isopropylacrylamide) (PNIPAM) microgel particles of varied elasticity in dense aqueous suspensions, giving rise to a full spectrum of strong to fragile glass-forming behaviors. We have observed the dependence of particle motions and structural relaxation on particle volume fraction can be weakened by decreasing particle elasticity, due to particle deformation and the resulting interparticle elastic interaction upon intimate particle contacts at high particle concentration. Both measured α-relaxation time scales and dynamic length scales for cooperative rearranging motions of microgels in suspensions show similarly dependence on particle volume fraction and elasticity, thereby quantifying the glass fragility of dense microgel suspension of varied particle elasticity.

Kinetic model for the mechanical response of suspensions of sponge-like particles

A dynamic two-scale model is developed that describes the stationary and transient mechanical behavior of concentrated suspensions made of highly porous particles. Particularly, we are interested in particles that not only deform elastically, but also can swell or shrink by taking up or expelling the viscous solvent from their interior, leading to rate-dependent deformability of the particles. The fine level of the model describes the evolution of particle centers and their current sizes, while the shapes are at present not taken into account. The versatility of the model permits inclusion of density- and temperature-dependent particle interactions, and hydrodynamic interactions, as well as to implement insight into the mechanism of swelling and shrinking. The coarse level of the model is given in terms of macroscopic hydrodynamics. The two levels are mutually coupled, since the flow changes the particle configuration, while in turn the configuration gives rise to stress contributions, that eventually determine the macroscopic mechanical properties of the suspension. Using a thermodynamic procedure for the model development, it is demonstrated that the driving forces for position change and for size change are derived from the same potential energy. The model is translated into a form that is suitable for particle-based Brownian dynamics simulations for performing rheological tests. Various possibilities for connection with experiments, e.g. rheological and structural, are discussed.

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

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