Physical aging and structural recovery in a colloidal glass subjected to volume-fraction jump conditions

Nonlinear susceptibilities and higher-order responses related to physical aging: Wiener-Volterra approach and extended Tool-Narayanaswamy-Moynihan models

Large-amplitude thermal excursions imposed on deeply supercooled liquids modulate the nonlinear time evolution of their structural rearrangements. The consequent aftereffects are treated within a Wiener-Volterra expansion in laboratory time that allows one to calculate the associated physical-aging and thermal response functions. These responses and the corresponding higher-harmonic susceptibilities are illustrated using calculations based on the Tool-Narayanaswamy-Moynihan (TNM) model. The conversion from laboratory to material time is thoroughly discussed. Similarities and differences to field-induced higher-harmonic susceptibilities are illustrated using Lissajous and Cole-Cole plots and discussed in terms of aging nonlinearity parameters. For the Lissajous plots, banana-type shapes emerge, while the Cole-Cole plots display cardioidic and other visually appealing patterns. For application beyond the regime in which conventional single-parameter aging concepts work, the Wiener-Volterra material-time-series is introduced as the central tool. Calculations and analyses within this general framework in conjunction with suitable choices of higher-order memory kernels and employing correspondingly extended TNM models yield at least qualitative agreement with recent large-perturbation physical aging experiments. Implications for differential scanning calorimetry and related methods are discussed. The introduced concepts and analyses provide a solid foundation for a generalized description of nonlinear thermal out-of-equilibrium dynamics of glass forming materials, differing from the nonlinear responses known from rheology and dielectric spectroscopy.

Real-space model for activated processes in rejuvenation and memory behavior of glassy systems

We offer an alternative real-space description, based purely on activated processes, for the understanding of relaxation dynamics in hierarchical landscapes. To this end, we use the cluster model, a coarse-grained lattice model of a jammed system, to analyze rejuvenation and memory effects during aging after a hard quench. In this model, neighboring particles on a lattice aggregate through local interactions into clusters that fragment with a probability based on their size. Despite the simplicity of the cluster model, it has been shown to reproduce salient observables of the aging dynamics in colloidal systems, such as those accounting for particle mobility and displacements. Here, we probe the model for more complex quench protocols and show that it exhibits rejuvenation and memory effects similar to those attributed to the complex hierarchical structure of a glassy energy landscape.

Controlling the volume fraction of glass-forming colloidal suspensions using thermosensitive host "mesogels"

The key parameter controlling the glass transition of colloidal suspensions is φ, the fraction of the sample volume occupied by the particles. Unfortunately, changing φ by varying an external parameter, e.g., temperature T as in molecular glass formers, is not possible, unless one uses thermosensitive colloidal particles, such as the popular poly(N-isopropylacrylamide) (PNiPAM) microgels. These, however, have several drawbacks, including high deformability, osmotic deswelling, and interpenetration, which complicate their use as a model system to study the colloidal glass transition. Here, we propose a new system consisting of a colloidal suspension of non-deformable spherical silica nanoparticles, in which PNiPAM hydrogel spheres of ∼100-200μm size are suspended. These non-colloidal "mesogels" allow for controlling the sample volume effectively available to the silica nanoparticles and hence their φ, thanks to the T-induced change in mesogels' volume. Using optical microscopy, we first show that the mesogels retain their ability to change size with T when suspended in Ludox suspensions, similarly as in water. We then show that their size is independent of the sample thermal history such that a well-defined, reversible relationship between T and φ may be established. Finally, we use space-resolved dynamic light scattering to demonstrate that, upon varying T, our system exhibits a broad range of dynamical behaviors across the glass transition and beyond, comparable with those exhibited by a series of distinct silica nanoparticle suspensions of various φ.

Temperature dependence of aging dynamics in highly non-equilibrium model polymer glasses

A central feature of the non-equilibrium glassy “state” is its tendency to age toward equilibrium, obeying signatures identified by Kovacs over 50 years ago. The origin of these signatures, their fate far from equilibrium and at high temperatures, and the underlying nature of the glassy “state” far from equilibrium remain unsettled. Here, we simulate physical aging of polymeric glasses, driven much farther from equilibrium and at much higher temperatures than possible in experimental melt-quenched glasses. While these glasses exhibit Kovacs’ signatures of glassy aging at sufficiently low temperatures, these signatures disappear above the onset TA of non-Arrhenius equilibrium dynamics, suggesting that TA demarcates an upper bound to genuinely glassy states. Aging times in glasses after temperature up-jumps are found to obey an Arrhenius law interpolating between equilibrium dynamics at TA and at the start of the temperature up-jump, providing a zero-parameter rule predicting their aging behavior and identifying another unrecognized centrality of TA to aging behavior. This differs qualitatively from behavior of our glasses produced by temperature down-jumps, which exhibit a fractional power law decoupling relation with equilibrium dynamics. While the Tool–Narayanaswamy–Moynihan model can predict the qualitative single-temperature behavior of these systems, we find that it fails to predict the disappearance of Kovacs signatures above TA and the temperature dependence of aging after large temperature up-jumps. These findings highlight a need for new theoretical insights into the aging behavior of glasses at ultra-high fictive temperatures and far from equilibrium.

Softness mapping of the concentration dependence of the dynamics in model soft colloidal systems

The dynamics of a series of soft colloids comprised of polystyrene cores with poly(N-isopropylacrylamide) (PNIPAM) coronas was investigated by diffusing wave spectroscopy (DWS). The modulus of the coronas was varied by changing the cross-link density and we were able to interpret the results within a hard-soft mapping framework. The soft, swellable particle properties were modeled using an extended Flory-Rehner theory and a Hertzian pair potential. Following volume fraction jumps, softness effects on the concentration dependence of dynamics were determined, with a 'soft colloids make strong glass-forming liquid'-type of behavior observed close to the nominal glass transition volume fraction, φ_g. Such behavior from the current systems cannot be fully explained by the osmotic deswelling model alone. However, inspired by the soft-hard mapping from Schmiedeberg et al, [Europhys. Lett. 2011, 96(3), 36010] we estimated effective hard-sphere diameters and achieved a successful mapping of the α-relaxation times to a master curve below φ_g. Above φ_g, the curves no longer collapse but show strong deviations from a Vogel-Fulcher type of divergence onto soft jamming plateaux. Our results provide evidence that osmotic deswelling itself cannot fully explain the observed dynamics. Softness also plays an important role in the dynamics of soft, concentrated colloids.

On a fundamental description of the Kovacs' kinetic signatures in glass-forming systems

The time-evolution equation for the time-dependent static structure factor of the non-equilibrium self-consistent generalized Langevin equation (NE-SCGLE) theory was used to investigate the kinetics of glass-forming systems under isochoric conditions. The kinetics are studied within the framework of the fictive temperature (T_F) of the glassy structure. We solve for the kinetics of T_F(t) and the time-dependent structure factor and find that they are different but closely related by a function that depends only on temperature. Furthermore, we are able to solve for the evolution of T_F(t) in a set of temperature-jump histories referred to as the Kovacs' signatures. We demonstrate that the NE-SCGLE theory reproduces all the Kovacs' signatures, namely, intrinsic isotherm, asymmetry of approach, and memory effect. In addition, we extend the theory into largely unexplored, deep glassy state, regions that are below the notionally "ideal" glass temperature.

Signatures of Overaging in an Aqueous Dispersion of Carbopol

In this work, we study the effect of the deformation field on the physical aging behavior of an aqueous Carbopol dispersion. It is composed of soft swollen particles of gel that get deformed and acquire a polygonal shape, with flat interfaces rendering the dispersion a soft solid-like consistency as filled volume fraction approaches unity. It has been proposed that owing to release of stored elastic energy in the deformed particles, Carbopol dispersion undergoes microstructural evolution that is reminiscent of physical aging in soft glassy materials. We observe that application of moderate magnitude of oscillatory strain to Carbopol dispersion slows down its relaxation dynamics, thereby showing characteristics of overaging. On the other hand, the sufficiently high magnitude of strain makes the relaxation dynamics faster, causing rejuvenation. We also solve the soft glassy rheology model, which, when subjected to the same flow field, corroborates with experimental observations on the Carbopol dispersion. This behavior, therefore, suggests that in a system of jammed soft particles of Carbopol, the particles occupying shallow energy wells upon application of moderate strain field adjust themselves in such a manner that they predominantly occupy the deeper energy wells leading to observe the overaging dynamics.

"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.

Maximum entropy approach to reliability

The aging process is a common phenomenon in engineering, biological, and physical systems. The hazard rate function, which characterizes the aging process, is a fundamental quantity in the disciplines of reliability, failure, and risk analysis. However, it is difficult to determine the entire hazard function accurately with limited observation data when the degradation mechanism is not fully understood. Inspired by the seminal work pioneered by Jaynes [Phys. Rev. 106, 620 (1956)PHRVAO0031-899X10.1103/PhysRev.106.620], this study develops an approach based on the principle of maximum entropy. In particular, the time-dependent hazard rate function can be established using limited observation data in a rational manner. It is shown that the developed approach is capable of constructing and interpreting many typical hazard rate curves observed in practice, such as the bathtub curve, the upside down bathtub, and so on. The developed approach is applied to model a classical single function system and a numerical example is used to demonstrate the method. In addition its extension to a more general multifunction system is presented. Depending on the interaction between different functions of the system, two cases, namely reducible and irreducible, are discussed in detail. A multifunction electrical system is used for demonstration.

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.

Isochoric structural recovery in molecular glasses and its analog in colloidal glasses

Concentrated colloidal dispersions have been regarded as models for molecular glasses. One of the many ways to compare the behavior in these two different systems is by comparing the structural recovery or the physical aging behavior. However, recent investigations from our group to examine structural recovery in thermosensitive colloidal dispersions have shown contrasting results between the colloidal and the molecular glasses. The differences in the behaviors of the two systems have led us to pose this question: Is structural recovery behavior in colloidal glasses truly distinct from that of molecular glasses or is the conventional experimental condition (isobaric temperature-jumps) in determining the structural recovery in molecular glasses different from the experimental condition in the colloidal experiments (concentration- or volume fraction-jumps); i.e., are colloidal glasses inherently different from molecular glasses or not? To address the question, we resort to model calculations of structural recovery in a molecular glass under constant volume (isochoric) conditions following temperature only- and simultaneous volume- and temperature-jumps, which are closer to the volume fraction-jump conditions used in the thermosensitive-colloidal experiments. The current model predictions are then compared with the signatures of structural recovery under the conventional isobaric state in a molecular glass and with structural recovery behavior in colloidal glasses following volume fraction-jumps. We show that the results obtained from the experiments conducted by our group were contrasting to classical molecular glass behavior because the basis of our comparisons were incorrect (the histories were not analogous). The present calculations (with analogous histories) are qualitatively closer to the colloidal behavior. The signatures of "intrinsic isotherms" and "asymmetry of approach" in the current isochoric model predictions are quite different from those in the classical isobaric conditions while the "memory" signatures remain essentially the same. While there are qualitative similarities between the current isochoric model predictions and results from colloidal glasses, it appears from the calculations that the origins of these are different. The isochoric histories in the molecular glasses have compensating effects of pressure and departure from equilibrium which determines the structure dependence on mobility of the molecules. On the other hand, in the colloids it simply appears that the volume fraction-jump conditions simply do not exhibit such structure mobility dependence. The determining interplay of thermodynamic phase variables in colloidal and molecular systems might be very different or at least their correlations are yet to be ascertained. This topic requires further investigation to bring the similarities and differences between molecular and colloidal glass formers into fuller clarity.

Soft matter: rubber and networks

Rubber networks are important and form the basis for materials with properties ranging from rubber tires to super absorbents and contact lenses. The development of the entropy ideas of rubber deformation thermodynamics provides a powerful framework from which to understand and to use these materials. In addition, swelling of the rubber in the presence of small molecule liquids or solvents leads to materials that are very soft and 'gel' like in nature. The review covers the thermodynamics of polymer networks and gels from the perspective of the thermodynamics and mechanics of the strain energy density function. Important relationships are presented and experimental results show that the continuum ideas contained in the phenomenological thermodynamics are valid, but that the molecular bases for some of them remain to be fully elucidated. This is particularly so in the case of the entropic gels or swollen networks. The review is concluded with some perspectives on other networks, ranging from entropic polymer networks such as thermoplastic elastomers to physical gels in which cross-link points are formed by glassy or crystalline domains. A discussion is provided for other physical gels in which the network forms a spinodal-like decomposition, both in thermoplastic polymers that form a glassy network upon phase separation and for colloidal gels that seem to have a similar behavior.

Dynamical behavior of microgels of interpenetrated polymer networks

Microgel suspensions of an interpenetrated Polymer Network (IPN) of PNIPAM and PAAc in D2O have been investigated through dynamic light scattering as a function of temperature, pH and concentration across the Volume Phase Transition (VPT). The dynamics of the system is slowed down under H/D isotopic substitution due to different balance states between polymer/polymer and polymer/solvent interactions suggesting the crucial role played by H-bonding. The swelling behavior, reduced with respect to PNIPAM and water, has been described by the Flory-Rehner theory, tested for PNIPAM microgel and successfully expanded to higher order for IPN microgels. Moreover the concentration dependence of the relaxation time at neutral pH has highlighted two different routes to approach the glass transition: Arrhenius and super-Arrhenius (Vogel Fulcher Tammann) respectively below and above the VPT and a fragility plot has been derived. Fragility can be tuned by changing temperature: across the VPT particles undergo a transition from soft-strong to stiff-fragile.

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.

Introduction to the Colloidal Glass Transition

Colloids are suspensions of small solid particles in a liquid and exhibit glassy behavior when the particle concentration is high. In these samples, the particles are roughly analogous to individual molecules in a traditional glass. This model system has been used to study the glass transition since the 1980s. In this Viewpoint I summarize some of the intriguing behaviors of the glass transition in colloids and discuss open questions.