Non-equilibrium view of the amorphous solidification of liquids with competing interactions.

The interplay between short-range attractions and long-range repulsions (SALR) characterizes the so-called liquids with competing interactions, which are known to exhibit a variety of equilibrium and non-equilibrium phases. The theoretical description of the phenomenology associated with glassy or gel states in these systems has to take into account both the presence of thermodynamic instabilities (such as those defining the spinodal line and the so called λ line) and the limited capability to describe genuine non-equilibrium processes from first principles. Here, we report the first application of the non-equilibrium self-consistent generalized Langevin equation theory to the description of the dynamical arrest processes that occur in SALR systems after being instantaneously quenched into a state point in the regions of thermodynamic instability. The physical scenario predicted by this theory reveals an amazing interplay between the thermodynamically driven instabilities, favoring equilibrium macro- and micro-phase separation, and the kinetic arrest mechanisms, favoring non-equilibrium amorphous solidification of the liquid into an unexpected variety of glass and gel states.

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.

"Inner clocks" of glass-forming liquids.

Providing a physically sound explanation of aging phenomena in non-equilibrium amorphous materials is a challenging problem in modern statistical thermodynamics. The slow evolution of physical properties after quenches of control parameters is empirically well interpreted via the concept of material time (or internal clock) based on the Tool-Narayanaswamy-Moynihan model. Yet, the fundamental reasons of its striking success remain unclear. We propose a microscopic rationale behind the material time on the basis of the linear laws of irreversible thermodynamics and its extension that treats the corresponding kinetic coefficients as state functions of a slowly evolving material state. Our interpretation is based on the recognition that the same mathematical structure governs both the Tool model and the recently developed non-equilibrium extension of the self-consistent generalized Langevin equation theory, guided by the universal principles of Onsager's theory of irreversible processes. This identification opens the way for a generalization of the material-time concept to aging systems where several relaxation modes with very different equilibration processes must be considered, and partially frozen glasses manifest the appearance of partial ergodicity breaking and, hence, materials with multiple very distinct inner clocks.

Non-equilibrium relaxation and aging in the dynamics of a dipolar fluid quenched towards the glass transition.

The recently developed non-equilibrium self-consistent generalized Langevin equation theory of the dynamics of liquids of non-spherically interacting particles [2016J. Phys. Chem. B1207975] is applied to the description of the irreversible relaxation of a thermally and mechanically quenched dipolar fluid. Specifically, we consider a dipolar hard-sphere liquid quenched (attw= 0) from full equilibrium conditions towards different ergodic-non-ergodic transitions. Qualitatively different scenarios are predicted by the theory for the time evolution of the system after the quench (tw> 0), that depend on both the kind of transition approached and the specific features of the protocol of preparation. Each of these scenarios is characterized by the kinetics displayed by a set of structural correlations, and also by the development of two characteristic times describing the relaxation of the translational and rotational dynamics, allowing us to highlight the crossover from equilibration to aging in the system and leading to the prediction of different underlying mechanisms and relaxation laws for the dynamics at each of the glass transitions explored.

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.

Effect of attractions on the hard-sphere dynamic universality class.

The fundamental understanding of the dynamic and transport properties of liquids is crucial for the better processing of most materials. The usefulness of this understanding increases when it involves general scaling rules, such as the concept of the hard-sphere dynamic universality class, which provides a unifying scaling of the dynamics of soft-sphere repulsive systems. A relevant question is how far this concept extends to systems that also involve attractive interactions. To answer this question, in this work we performed systematic molecular and Brownian dynamics simulations with the Lennard-Jones system in a wide range of temperatures and densities and verify the extent to which its static and dynamic properties map onto those of the hard-sphere system. We determine that in most of the fluid regime, the Lennard-Jones liquid exhibits the same dynamic equivalence with the hard-sphere system as most purely repulsive fluids, thus establishing the degree of its inclusion in the hard-sphere dynamic universality class.

Spherical harmonic projections of the static structure factor of the dipolar hard sphere model: Theory vs simulations.

We investigate the static correlations of a dipolar fluid in terms of the irreducible coefficients of the spherical harmonic expansion of the static structure factor. To this end, we develop a theoretical framework based on a soft-core version of Wertheim's solution of the mean spherical approximation (MSA), which renders the analytical determination of such coefficients possible. The accuracy of this approximation is tested by a comparison against the results obtained with the assistance of extensive molecular dynamics simulations at different regimes of concentration and temperature. Crucial aspects for the comparison of the results provided by the two methods are carefully discussed, concerning the different reference frames used in theory and simulations to describe rotations and orientations, and leading to important differences in the behavior of correlation functions with the same combination of spherical harmonic indices. We find a remarkable agreement between the two approaches in the fluid regime, thus providing a first stringent comparison of the irreducible coefficients of the spherical harmonic expansion of the dipolar fluid's static structure factor, provided by the MSA theory and molecular dynamics simulations.

Arrested dynamics of the dipolar hard sphere model.

We report the combined results of molecular dynamics simulations and theoretical calculations concerning various dynamical arrest transitions in a model system representing a dipolar fluid, namely, N (soft core) rigid spheres interacting through a truncated dipole-dipole potential. By exploring different regimes of concentration and temperature, we find three distinct scenarios for the slowing down of the dynamics of the translational and orientational degrees of freedom: at low (η = 0.2) and intermediate (η = 0.4) volume fractions, both dynamics are strongly coupled and become simultaneously arrested upon cooling. At high concentrations (η≥ 0.6), the translational dynamics shows the features of an ordinary glass transition, either by compressing or cooling down the system, but with the orientations remaining ergodic, thus indicating the existence of partially arrested states. In this density regime, but at lower temperatures, the relaxation of the orientational dynamics also freezes. The physical scenario provided by the simulations is discussed and compared against results obtained with the self-consistent generalized Langevin equation theory, and both provide a consistent description of the dynamical arrest transitions in the system. Our results are summarized in an arrested states diagram which qualitatively organizes the simulation data and provides a generic picture of the glass transitions of a dipolar fluid.

Interference between the glass, gel, and gas-liquid transitions.

Recent experiments and computer simulations have revealed intriguing phenomenological fingerprints of the interference between the ordinary equilibrium gas-liquid phase transition and the non-equilibrium glass and gel transitions. We thus now know, for example, that the liquid-gas spinodal line and the glass transition loci intersect at a finite temperature and density, that when the gel and the glass transitions meet, mechanisms for multistep relaxation emerge, and that the formation of gels exhibits puzzling latency effects. In this work we demonstrate that the kinetic perspective of the non-equilibrium self-consistent generalized Langevin equation (NE-SCGLE) theory of irreversible processes in liquids provides a unifying first-principles microscopic theoretical framework to describe these and other phenomena associated with spinodal decomposition, gelation, glass transition, and their combinations. The resulting scenario is in reality the competition between two kinetically limiting behaviors, associated with the two distinct dynamic arrest transitions in which the liquid-glass line is predicted to bifurcate at low densities, below its intersection with the spinodal line.

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.

Different routes into the glass state for soft thermo-sensitive colloids.

We report an experimental and theoretical investigation of glass formation in soft thermo-sensitive colloids following two different routes: a gradual increase of the particle number density at constant temperature and an increase of the radius in a fixed volume at constant particle number density. Confocal microscopy experiments and the non-equilibrium self-consistent generalized Langevin equation (NE-SCGLE) theory consistently show that the two routes lead to a dynamically comparable state at sufficiently long aging times. However, experiments reveal the presence of moderate but persistent structural differences. Successive cycles of radius decrease and increase lead instead to a reproducible glass state, indicating a suitable route to obtain rejuvenation without using shear fields.

Communication: Probing the existence of partially arrested states in ionic liquids.

The recent predictions of the self-consistent generalized Langevin equation theory, describing the existence of unusual partially arrested states in the context of ionic liquids, were probed using all-atom molecular dynamics simulations of a room-temperature ionic liquid. We have found a slower diffusion of the smaller anions compared with the large cations for a wide range of temperatures. The arrest mechanism consists on the formation of a strongly repulsive glass by the anions, stabilized by the long range electrostatic potential. The diffusion of the less repulsive cations occurs through the holes left by the small particles. All of our observations in the simulated system coincide with the theoretical picture.

Non-equilibrium theory of arrested spinodal decomposition.

The non-equilibrium self-consistent generalized Langevin equation theory of irreversible relaxation [P. E. Ramrez-González and M. Medina-Noyola, Phys. Rev. E 82, 061503 (2010); 82, 061504 (2010)] is applied to the description of the non-equilibrium processes involved in the spinodal decomposition of suddenly and deeply quenched simple liquids. For model liquids with hard-sphere plus attractive (Yukawa or square well) pair potential, the theory predicts that the spinodal curve, besides being the threshold of the thermodynamic stability of homogeneous states, is also the borderline between the regions of ergodic and non-ergodic homogeneous states. It also predicts that the high-density liquid-glass transition line, whose high-temperature limit corresponds to the well-known hard-sphere glass transition, at lower temperature intersects the spinodal curve and continues inside the spinodal region as a glass-glass transition line. Within the region bounded from below by this low-temperature glass-glass transition and from above by the spinodal dynamic arrest line, we can recognize two distinct domains with qualitatively different temperature dependence of various physical properties. We interpret these two domains as corresponding to full gas-liquid phase separation conditions and to the formation of physical gels by arrested spinodal decomposition. The resulting theoretical scenario is consistent with the corresponding experimental observations in a specific colloidal model system.

Localization and dynamical arrest of colloidal fluids in a disordered matrix of polydisperse obstacles.

The mobility of a colloidal particle in a crowded and confined environment may be severely reduced by its interactions with other mobile colloidal particles and the fixed obstacles through which it diffuses. The latter may be modelled as an array of obstacles with random fixed positions. In this contribution, we report on the effects of the size-polydispersity of such fixed obstacles on the immobilization and dynamical arrest of the diffusing colloidal particles. This complex system is modelled as a monodisperse Brownian hard-sphere fluid diffusing through a polydisperse matrix of fixed hard spheres with a given size distribution. In the Lorentz gas limit (absence of interactions between the mobile particles), we first develop a simple excluded-volume theory to describe the localization transition of the tracer mobile particles. To take into account the interactions among the mobile particles, we adapt the multi-component self-consistent generalized Langevin equation (SCGLE) theory of colloid dynamics, which also allows us to calculate the dynamical arrest transition line, and in general, all the dynamical properties of the mobile particles (mean-squared displacement, self-diffusion coefficient, etc.). The scenarios described by both approaches in the Lorentz gas limit are qualitatively consistent, but the SCGLE formalism describes the dependence of the dynamics of the adsorbed fluid on the polydispersity of the porous matrix at arbitrary concentrations of the mobile spheres and arbitrary volume fractions of the obstacles. Two mechanisms for dynamical arrest (glass transition and localization) are analyzed and we also discuss the crossover between them using the SCGLEs.

Non-equilibrium dynamics of glass-forming liquid mixtures.

The non-equilibrium self-consistent generalized Langevin equation theory of irreversible processes in glass-forming liquids [P. Ramírez-González and M. Medina-Noyola, Phys. Rev. E 82, 061503 (2010)] is extended here to multi-component systems. The resulting theory describes the statistical properties of the instantaneous local particle concentration profiles nα(r, t) of species α in terms of the coupled time-evolution equations for the mean value n̄α(r, t) and for the covariance σ(αß)(r, r'; t) ≡ δn(α)(r, t)δn(ß)(r', t) of the fluctuations δn(α)(r, t) = n(α)(r, t) - n̄α(r, t). As in the monocomponent case, these two coarse-grained equations involve a local mobility function bα(r, t) for each species, written in terms of the memory function of the two-time correlation function C(αß)(r, r'; t, t') ≡ δn(α)(r, t)δn(ß)(r', t'). If the system is constrained to remain spatially uniform and subjected to a non-equilibrium preparation protocol described by a given temperature and composition change program T(t) and n̄α(r, t), these equations predict the irreversible structural relaxation of the partial static structure factors Sαß(k; t) and of the (collective and self) intermediate scattering functions Fαß(k, τ; t) and F(αß)(S)(k, τ; t). We illustrate the applicability of the resulting theory with two examples involving simple model mixtures subjected to an instantaneous temperature quench: an electroneutral binary mixture of equally sized and oppositely charged hard-spheres, and a binary mixture of soft-spheres of moderate size-asymmetry.

Dynamic equivalences in the hard-sphere dynamic universality class.

We perform systematic simulation experiments on model systems with soft-sphere repulsive interactions to test the predicted dynamic equivalence between soft-sphere liquids with similar static structure. For this we compare the simulated dynamics (mean squared displacement, intermediate scattering function, α-relaxation time, etc.) of different soft-sphere systems, between them and with the hard-sphere liquid. We then show that the referred dynamic equivalence does not depend on the (Newtonian or Brownian) nature of the microscopic laws of motion of the constituent particles, and hence, applies independently to colloidal and to atomic simple liquids. Finally, we verify another more recently proposed dynamic equivalence, this time between the long-time dynamics of an atomic liquid and its corresponding Brownian fluid (i.e., the Brownian system with the same interaction potential).

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)).

The overdamped van Hove function of atomic liquids.

Using the generalized Langevin equation formalism and the process of contraction of the description we derive a general memory function equation for the thermal fluctuations of the local density of a simple atomic liquid. From the analysis of the long-time limit of this equation, a striking equivalence is suggested between the long-time dynamics of the atomic liquid and the dynamics of the corresponding Brownian liquid. This dynamic equivalence is confirmed here by comparing molecular and Brownian dynamics simulations of the self-intermediate scattering function and the long-time self-diffusion coefficient for the hard-sphere liquid.

Density-temperature-softness scaling of the dynamics of glass-forming soft-sphere liquids.

We employ the principle of dynamic equivalence between soft-sphere and hard-sphere fluids [Phys. Rev. E 68, 011405 (2003)] to describe the interplay of the effects of varying the density n, the temperature T, and the softness (characterized by a softness parameter ν(-1)) on the dynamics of glass-forming soft-sphere liquids in terms of simple scaling rules. The main prediction is the existence of a dynamic universality class associated with the hard-sphere fluid, constituted by the soft-sphere systems whose dynamic parameters depend on n, T, and ν only through the reduced density n*≡nσ(HS)(T*,ν). A number of scaling properties observed in recent experiments and simulations involving glass-forming fluids with repulsive short-range interactions are found to be a direct manifestation of this general dynamic equivalence principle.

Equilibration of concentrated hard-sphere fluids.

We report a systematic molecular dynamics study of the isochoric equilibration of hard-sphere fluids in their metastable regime close to the glass transition. The thermalization process starts with the system prepared in a nonequilibrium state with the desired final volume fraction ϕ for which we can obtain a well-defined nonequilibrium static structure factor S(0)(k;ϕ). The evolution of the α-relaxation time τ(α)(k) and long-time self-diffusion coefficient D(L) as a function of the evolution time t(w) is then monitored for an array of volume fractions. For a given waiting time the plot of τ(α)(k;ϕ,t(w)) as a function of ϕ exhibits two regimes corresponding to samples that have fully equilibrated within this waiting time [ϕ≤ϕ(c)(t(w))] and to samples for which equilibration is not yet complete [ϕ≥ϕ(c)(t(w))]. The crossover volume fraction ϕ(c)(t(w)) increases with t(w) but seems to saturate to a value ϕ(a)≡ϕ(c)(t(w)→∞)≈0.582. We also find that the waiting time t(w)(eq)(ϕ) required to equilibrate a system grows faster than the corresponding equilibrium relaxation time, t(w)(eq)(ϕ)≈0.27[τ(α)(eq)(k;ϕ)](1.43), and that both characteristic times increase strongly as ϕ approaches ϕ(a), thus suggesting that the measurement of equilibrium properties at and above ϕ(a) is experimentally impossible.