[Show abstract][Hide abstract] ABSTRACT: The \emph{non-equilibrium} self-consistent generalized Langevin equation
(NE-SCGLE) theory of irreversible processes in liquids is shown to provide a
coherent and conceptually simple picture of the crossover from ergodic
equilibration to non-equilibrium aging in structural glass-forming liquids.
According to this picture, the glass transition is in essence a discontinuous,
``mode-coupling''--like transition, characterized by the abrupt passage from
ergodic to dynamically arrested states and by the divergence of the
\emph{equilibrium} $\alpha$-relaxation time at the transition. The same
picture, however, also predicts that such discontinuous and singular scenario
will be blurred in real life by the unavoidable finiteness of the time window
of any experimental observation. The comparison of these predictions with
pertinent simulation experiments involving hard-sphere glass-forming liquids
reconciles the lack of observable diverging relaxation times in (real or
simulated) experiments, with the predicted critical condition at which the
\emph{equilibrium} $\alpha$-relaxation time is expected to diverge.
[Show abstract][Hide abstract] ABSTRACT: 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 ϕ exhibits 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)}.
Physical Review E 05/2013; 87(5-1):052306. DOI:10.1103/PhysRevE.87.052306 · 2.29 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We review the recently-proposed non-equilibrium self-consistent
generalized Langevin equation (NE-SCGLE) theory of irreversible
processes in liquids, and describe the scenario that emerges from its
application to the equilibration (or absence of equilibration!) of
quenched glass-forming liquids. This theory extends to non-equilibrium
conditions the SCGLE theory of dynamic arrest, which (just like the
well-known mode coupling theory) determines the boundary of the ergodic
domain of the system. In this first systematic application of the
non-equilibrium theory we consider a model soft-sphere glass-forming
liquid, initially at an ergodic equilibrium state, suddenly quenched to
a lower final temperature that lies either (a) also in the ergodic
domain, or (b) in the region of dynamically arrested states. In the
first case the liquid will equilibrate within a finite equilibration
time teq, while in the second the theory predicts that the liquid will
age forever, (i.e., teq = ∞). The dynamic arrest boundary is thus
predicted to determine the crossover from equilibration to aging, and to
be characterized by the divergence of the equilibration time. In either
case the theory predicts the irreversible t-evolution of the measured
static structure factor S(k;t) and of the dynamic properties such as the
self-intermediate scattering function FS(k, τt).
[Show abstract][Hide abstract] ABSTRACT: 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.
[Show abstract][Hide abstract] ABSTRACT: 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.
[Show abstract][Hide abstract] ABSTRACT: The non-equilibrium self-consistent generalized Langevin equation theory of
colloid dynamics is used to describe the non-stationary 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.
[Show abstract][Hide abstract] ABSTRACT: 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.
[Show abstract][Hide abstract] ABSTRACT: 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.
[Show abstract][Hide abstract] ABSTRACT: The concept of dynamic equivalence among mono-disperse soft-sphere fluids is employed in the framework of the self-consistent generalized Langevin equation (SCGLE) theory of colloid dynamics to calculate the ideal glass transition phase diagram of model soft-sphere colloidal dispersions in the softness-concentration state space. The slow dynamics predicted by this theory near the glass transition is compared with available experimental data for the decay of the intermediate scattering function of colloidal dispersions of soft-microgel particles. Increasing deviations from this simple scheme occur for increasingly softer potentials, and this is studied here using the Rogers-Young static structure factor of the soft-sphere systems as the input of the SCGLE theory, without assuming a priori the validity of the equivalence principle above.
[Show abstract][Hide abstract] ABSTRACT: The self-consistent generalized Langevin equation (SCGLE) theory of colloid dynamics is employed to describe the ergodic-non-ergodic transition in model mono-disperse colloidal dispersions whose particles interact through hard-sphere plus short-ranged attractive forces. The ergodic-non-ergodic phase diagram in the temperature-concentration state space is determined for the hard-sphere plus attractive Yukawa model within the mean spherical approximation for the static structure factor by solving a remarkably simple equation for the localization length of the colloidal particles. Finite real values of this property signals non-ergodicity and determines the non-ergodic parameters f(k) and f(s)(k). The resulting phase diagram for this system, which involves the existence of reentrant (repulsive and attractive) glass states, is compared with the corresponding prediction of mode coupling theory. Although both theories coincide in the general features of this phase diagram, there are also clear qualitative differences. One of the most relevant is the SCGLE prediction that the ergodic-attractive glass transition does not preempt the gas-liquid phase transition, but always intersects the corresponding spinodal curve on its high-concentration side. We also calculate the ergodic-non-ergodic phase diagram for the sticky hard-sphere model to illustrate the dependence of the predicted SCGLE dynamic phase diagram on the choice of one important constituent element of the SCGLE theory.
[Show abstract][Hide abstract] ABSTRACT: One of the main elements of the self-consistent generalized Langevin equation (SCGLE) theory of colloid dynamics [Phys. Rev. E 62, 3382 (2000); 72, 031107 (2005)] is the introduction of exact short-time moment conditions in its formulation. The need to previously calculate these exact short-time properties constitutes a practical barrier for its application. In this Brief Report, we report that a simplified version of this theory, in which this short-time information is eliminated, leads to the same results in the intermediate and long-time regimes. Deviations are only observed at short times, and are not qualitatively or quantitatively important. This is illustrated by comparing the two versions of the theory for representative model systems.
[Show abstract][Hide abstract] ABSTRACT: This paper presents a recently developed theory of colloid dynamics as an alternative approach to the description of phenomena of dynamic arrest in monodisperse colloidal systems. Such theory, referred to as the self-consistent generalized Langevin equation (SCGLE) theory, was devised to describe the tracer and collective diffusion properties of colloidal dispersions in the short- and intermediate-time regimes. Its self-consistent character, however, introduces a nonlinear dynamic feedback, leading to the prediction of dynamic arrest in these systems, similar to that exhibited by the well-established mode coupling theory of the ideal glass transition. The full numerical solution of this self-consistent theory provides in principle a route to the location of the fluid-glass transition in the space of macroscopic parameters of the system, given the interparticle forces (i.e., a nonequilibrium analog of the statistical-thermodynamic prediction of an equilibrium phase diagram). In this paper we focus on the derivation from the same self-consistent theory of the more straightforward route to the location of the fluid-glass transition boundary, consisting of the equation for the nonergodic parameters, whose nonzero values are the signature of the glass state. This allows us to decide if a system, at given macroscopic conditions, is in an ergodic or in a dynamically arrested state, given the microscopic interactions, which enter only through the static structure factor. We present a selection of results that illustrate the concrete application of our theory to model colloidal systems. This involves the comparison of the predictions of our theory with available experimental data for the nonergodic parameters of model dispersions with hard-sphere and with screened Coulomb interactions.
[Show abstract][Hide abstract] ABSTRACT: This letter presents a remarkably simple approach to the first-principles determination of the ergodic/non-ergodic transition in monodisperse colloidal suspensions. It consists of an equation for the long-time asymptotic value ° of the mean squared displacement of the colloidal particles, whose finite real solutions signal the non-ergodic state, and determines the non-ergodic parameter f(k). We illustrate its concrete application to three simple model colloidal systems, namely, hard-spheres, hard-spheres plus repulsive (screened Coulomb) Yukawa interaction, and hard-sphere plus attractive Yukawa tail. The results indicate that this is quite a competitive theory, similar in spirit to, but conceptually independent from, the well-known mode coupling theory.
Revista Mexicana de Fisica 01/2007; 53(005). · 0.34 Impact Factor