Alternative view of dynamic arrest in colloid-polymer mixtures

Cooperative activated hopping dynamics in binary glass-forming liquids: effects of the size ratio, composition, and interparticle interactions

Slow dynamics in supercooled and glassy liquids is an important research topic in soft matter physics. Compared to the traditionally focused one-component systems, glassy dynamics in mixture systems adds in a rich set of new complexities, which are fundamentally interesting and also relevant for many technological applications. In this paper, we apply the recently developed self-consistent cooperative hopping theory (SCCHT) to systematically investigate the effects of the size ratio, composition and interparticle interactions on the cooperative activated hopping dynamics of matrix (in larger size) and penetrant (in smaller size) particles in varied binary sphere mixture model systems, with a specific focus on ultrahigh mixture packing fractions that mimic the deeply supercooled glass transition conditions for molecular/polymeric mixture materials. Analysis shows that in these high activation barrier cases, the long-range elastic distortion associated with a matrix particle hopping over its cage confinement always generates an elastic barrier of a nonnegligible magnitude, although the ratio between the elastic barrier and local barrier contribution is sensitively dependent on all three mixture-specific system factors considered in this work. SCCHT predicts two general scenarios of penetrant-matrix cooperative activated hopping dynamics: matrix/penetrant co-hopping (regime 1) or the penetrant mean barrier hopping time shorter than that of the matrix (regime 2). Increasing the penetrant-to-matrix size ratio or the penetrant-matrix cross-attraction strength is found to universally enlarge the composition window of regime 1. Diverse dynamical properties characterising different aspects of the cooperative activated hopping process, including the penetrant and matrix transient localization lengths, penetrant and matrix hopping jump distances, different types of local and elastic activated barriers, and matrix long-time diffusivity, relaxation time and dynamic fragility are quantitatively studied against a wide range of variations over the three system factors. Of particular interest is the universal "anti-plasticization" phenomenon achievable for sufficiently strong cross-attractive interactions. The prospects this work opens for the exploration of a wide variety of polymer-based mixture materials are briefly discussed at the end.

Phase separation and dynamical arrest of protein solutions dominated by short-range attractions

The interplay of liquid-liquid phase separation (LLPS) and dynamical arrest can lead to the formation of gels and glasses, which is relevant for such diverse fields as condensed matter physics, materials science, food engineering, and the pharmaceutical industry. In this context, protein solutions exhibit remarkable equilibrium and non-equilibrium behaviors. In the regime where attractive and repulsive forces compete, it has been demonstrated, for example, that the location of the dynamical arrest line seems to be independent of ionic strength, so that the arrest lines at different ionic screening lengths overlap, in contrast to the LLPS coexistence curves, which strongly depend on the salt concentration. In this work, we show that the same phenomenology can also be observed when the electrostatic repulsions are largely screened, and the range and strength of the attractions are varied. In particular, using lysozyme in brine as a model system, the metastable gas-liquid binodal and the dynamical arrest line as well as the second virial coefficient have been determined for various solution conditions by cloud-point measurements, optical microscopy, centrifugation experiments, and light scattering. With the aim of understanding this new experimental phenomenology, we apply the non-equilibrium self-consistent generalized Langevin equation theory to a simple model system with only excluded volume plus short-range attractions, to study the dependence of the predicted arrest lines on the range of the attractive interaction. The theoretical predictions find a good qualitative agreement with experiments when the range of the attraction is not too small compared with the size of the protein.

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.

Waiting-time dependent non-equilibrium phase diagram of simple glass- and gel-forming liquids

Under numerous circumstances, many soft and hard materials are present in a puzzling wealth of non-equilibrium amorphous states, whose properties are not stationary and depend on preparation. They are often summarized in unconventional "phase diagrams" that exhibit new "phases" and/or "transitions" in which time, however, is an essential variable. This work proposes a solution to the problem of theoretically defining and predicting these non-equilibrium phases and their time-evolving phase diagrams, given the underlying molecular interactions. We demonstrate that these non-equilibrium phases and the corresponding non-stationary (i.e., aging) phase diagrams can indeed be defined and predicted using the kinetic perspective of a novel non-equilibrium statistical mechanical theory of irreversible processes. This is illustrated with the theoretical description of the transient process of dynamic arrest into non-equilibrium amorphous solid phases of an instantaneously quenched simple model fluid involving repulsive hard-sphere plus attractive square well pair interactions.

Glassy dynamics in asymmetric binary mixtures of hard spheres

We perform a systematic and detailed study of the glass transition in highly asymmetric binary mixtures of colloidal hard spheres, combining differential dynamic microscopy experiments, event-driven molecular dynamics simulations, and theoretical calculations, exploring the whole state diagram and determining the self-dynamics and collective dynamics of both species. Two distinct glassy states involving different dynamical arrest transitions are consistently described, namely, a double glass with the simultaneous arrest of the self-dynamics and collective dynamics of both species, and a single glass of large particles in which the self-dynamics of the small species remains ergodic. In the single-glass scenario, spatial modulations in the collective dynamics of both species occur due to the structure of the large spheres, a feature not observed in the double-glass domain. The theoretical results, obtained within the self-consistent generalized Langevin equation formalism, are in agreement with both simulations and experimental data, thus providing a stringent validation of this theoretical framework in the description of dynamical arrest in highly asymmetric mixtures. Our findings are summarized in a state diagram that classifies the various amorphous states of highly asymmetric mixtures by their dynamical arrest mechanisms.

Transition from diffusive to subdiffusive motion in colloidal liquids

In this work we report experimental and theoretical results for the motion of single colloidal particles embedded in complex fluids with different interparticle interactions. The motion of particles is found to follow a similar behavior for the different systems. In particular, the transition from the short-time diffusive motion to the subdiffusive intermediate-time motion is found to occur when the square root of its mean squared displacement is in the order of 1 tenth of the neighbors' interparticle distance, thus following a quantitative criterion similar to Lindemann's criterion for melting.

Equilibration and aging of dense soft-sphere glass-forming liquids

The recently developed nonequilibrium extension of the self-consistent generalized Langevin equation theory of irreversible relaxation [Ramírez-González and Medina-Noyola, Phys. Rev. E 82, 061503 (2010); Ramírez-González and Medina-Noyola, Phys. Rev. E 82, 061504 (2010)] is applied to the description of the irreversible process of equilibration and aging of a glass-forming soft-sphere liquid that follows a sudden temperature quench, within the constraint that the local mean particle density remains uniform and constant. For these particular conditions, this theory describes the nonequilibrium evolution of the static structure factor S(k;t) and of the dynamic properties, such as the self-intermediate scattering function F(S)(k,τ;t), where τ is the correlation delay time and t is the evolution or waiting time after the quench. Specific predictions are presented for the deepest quench (to zero temperature). The predicted evolution of the α-relaxation time τ(α)(t) as a function of t allows us to define the equilibration time t(eq)(φ), as the time after which τ(α)(t) has attained its equilibrium value τ(α)(eq)(φ). It is predicted that both, t(eq)(φ) and τ(α)(eq)(φ), diverge as φ→φ((a)), where φ((a)) is the hard-sphere dynamic-arrest volume fraction φ((a))(≈0.582), thus suggesting that the measurement of equilibrium properties at and above φ((a)) is experimentally impossible. The theory also predicts that for fixed finite waiting times t, the plot of τ(α)(t;φ) as a function of φexhibits two regimes, corresponding to samples that have fully equilibrated within this waiting time (φ≤φ((c))(t)), and to samples for which equilibration is not yet complete (φ≥φ((c))(t)). The crossover volume fraction φ((c))(t) increases with t but saturates to the value φ((a)).

Crystallization time scales for polydisperse hard-sphere fluids

We study the evolution of crystallization in dense mono- and polydisperse hard sphere fluids, initially quenched to an amorphous configuration. We use as signatures of crystallization both the decay of the reduced pressure Z and the increase in the local and global orientational order parameters Q[over ¯](6). For a given realization of the crystallization process these parameters show sudden changes, both large and small, separated by long periods of quiescence. However, averaging over a large number of realizations, a well-defined scenario for their evolution appears. We find an initial fast relaxation to a disordered state, followed by a period of slow variation, associated to the presence of nucleation events, followed by a fast change, composed of the growth of a few crystals with different orientations, and a final and slow coarsening in a domain-growth process. No clear scaling for this whole process was found. We also find that the transition to an stable glassy fluid is quite sharp as the polydispersity is increased, showing a probable first-order phase transition behavior. A well-defined boundary between crystallizing and permanently amorphous fluids should exist, at least for a region in packing fractions. We looked for segregation at large values of polydispersity, but no effects of this type were found.

Mode-coupling theory for the glass transition: test of the convolution approximation for short-range interactions

We reexamine the convolution approximation commonly used in the mode-coupling theory (MCT) of nonergodic states of classical fluids. This approximation concerns the static correlation functions used as input in the MCT treatment of the dynamics. Besides the hard-sphere model, we consider interaction potentials that present a short-range tail, either attractive or repulsive, beyond the hard core. By using accurate static correlation functions obtained from the fundamental measures functional for hard spheres, we show that the role of three-body direct correlations can be more significant than what is inferred from previous simple ansatzs for pure hard spheres. This may in particular impact the location of the glass transition line and the nonergodicity parameter.

Correlation between dynamical heterogeneities, structure and potential-energy distribution in a 2D amorphous solid

We investigate the collective properties of particles in a 2D experimental system which consists of a bi-disperse mixture of colloidal particles confined at an air/water interface. We find a direct correlation between structure and dynamical heterogeneities in this system: particles belonging to locally ordered structures have lower potential energy and are slower than other particles. In a more general way we show that particles with high potential energy are dominating the dynamics especially in the α-relaxation regime.

General nonequilibrium theory of colloid dynamics

A nonequilibrium extension of Onsager's canonical theory of thermal fluctuations is employed to derive a self-consistent theory for the description of the statistical properties of the instantaneous local concentration profile n(r,t) of a colloidal liquid in terms of the coupled time-evolution equations of its mean value n(r,t) and of the covariance [Formula in text] of its fluctuations δn(r,t)=n(r,t)-n(r,t). These two coarse-grained equations involve a local mobility function b(r,t) which, in its turn, is written in terms of the memory function of the two-time correlation function [Formula in text]. For given effective interactions between colloidal particles and applied external fields, the resulting self-consistent theory is aimed at describing the evolution of a strongly correlated colloidal liquid from an initial state with arbitrary mean and covariance n(0)(r) and σ(0)(r,r') toward its equilibrium state characterized by the equilibrium local concentration profile n(eq)(r) and equilibrium covariance σ(eq)(r,r'). This theory also provides a general theoretical framework to describe irreversible processes associated with dynamic arrest transitions, such as aging, and the effects of spatial heterogeneities.

Aging of a homogeneously quenched colloidal glass-forming liquid

The nonequilibrium self-consistent generalized Langevin equation theory of colloid dynamics is used to describe the nonstationary aging processes occurring in a suddenly quenched model colloidal liquid with hard-sphere plus short-ranged attractive interactions, whose static structure factor and van Hove function evolve irreversibly from the initial conditions before the quench to a final dynamically arrested state. The comparison of our numerical results with available simulation data are highly encouraging.

Non-equilibrium relaxation and near-arrest dynamics in colloidal suspensions

In this work we propose a theory to describe the irreversible diffusive relaxation of the local concentration of a colloidal dispersion that proceeds toward its stable thermodynamic equilibrium state, but which may in the process be trapped in metastable or dynamically arrested states. The central assumption of this theory is that the irreversible relaxation of the macroscopically observed mean value [Formula: see text] of the local concentration of colloidal particles is described by a diffusion equation involving a local mobility b(*)(r,t) that depends not only on the mean value [Formula: see text] but also on the covariance [Formula: see text] of the fluctuations [Formula: see text]. This diffusion equation must hence be solved simultaneously with the relaxation equation for the covariance σ(r,r';t), and here we also derive the corresponding relaxation equation. The dependence of the local mobility b(*)(r,t) on the mean value and the covariance is determined by a self-consistent set of equations involving now the spatially and temporally non-local time-dependent correlation functions, which in a uniform system in equilibrium reduces to the self-consistent generalized Langevin equation (SCGLE) theory of colloid dynamics. The resulting general theory considers the possibility that these relaxation processes occur under the influence of external fields, such as gravitational forces acting in the process of sedimentation. In this paper, however, we describe a simpler application, in which the system remains spatially uniform during the irreversible relaxation process, and discuss the general features of the glass transition scenario predicted by this non-equilibrium theory.

Ionic and Wigner glasses, superionic conductors, and spinodal electrostatic gels: dynamically arrested phases of the primitive model

Based on the recently proposed self-consistent generalized Langevin equation theory of dynamic arrest, in this letter we show that the ergodic-nonergodic phase diagram of a classical mixture of charged hard spheres (the so-called "primitive model" of ionic solutions and molten salts) includes arrested phases corresponding to nonconducting ionic glasses, partially arrested states that represent solid electrolytes (or "superionic" conductors), low-density colloidal Wigner glasses, and low-density electrostatic gels associated with arrested spinodal decomposition.