Publications (13)28.62 Total impact
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ABSTRACT: The \emph{nonequilibrium} selfconsistent generalized Langevin equation (NESCGLE) theory of irreversible processes in liquids is shown to provide a coherent and conceptually simple picture of the crossover from ergodic equilibration to nonequilibrium aging in structural glassforming liquids. According to this picture, the glass transition is in essence a discontinuous, ``modecoupling''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 hardsphere glassforming 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 selfconsistent generalized Langevin equation theory of irreversible relaxation [RamírezGonzález and MedinaNoyola, Phys. Rev. E 82, 061503 (2010); RamírezGonzález and MedinaNoyola, Phys. Rev. E 82, 061504 (2010)] is applied to the description of the irreversible process of equilibration and aging of a glassforming softsphere 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 selfintermediate 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 αrelaxation 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 hardsphere dynamicarrest 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)}.  [Show abstract] [Hide abstract]
ABSTRACT: We review the recentlyproposed nonequilibrium selfconsistent generalized Langevin equation (NESCGLE) theory of irreversible processes in liquids, and describe the scenario that emerges from its application to the equilibration (or absence of equilibration!) of quenched glassforming liquids. This theory extends to nonequilibrium conditions the SCGLE theory of dynamic arrest, which (just like the wellknown mode coupling theory) determines the boundary of the ergodic domain of the system. In this first systematic application of the nonequilibrium theory we consider a model softsphere glassforming 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 tevolution of the measured static structure factor S(k;t) and of the dynamic properties such as the selfintermediate scattering function FS(k, τt).  [Show abstract] [Hide abstract]
ABSTRACT: We employ the principle of dynamic equivalence between softsphere and hardsphere 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 glassforming softsphere liquids in terms of simple scaling rules. The main prediction is the existence of a dynamic universality class associated with the hardsphere fluid, constituted by the softsphere 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 glassforming fluids with repulsive shortrange 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 hardsphere 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 welldefined nonequilibrium static structure factor S(0)(k;ϕ). The evolution of the αrelaxation time τ(α)(k) and longtime selfdiffusion 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: A nonequilibrium extension of Onsager's canonical theory of thermal fluctuations is employed to derive a selfconsistent 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 timeevolution 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 coarsegrained equations involve a local mobility function b(r,t) which, in its turn, is written in terms of the memory function of the twotime correlation function [Formula in text]. For given effective interactions between colloidal particles and applied external fields, the resulting selfconsistent 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: The nonequilibrium selfconsistent generalized Langevin equation theory of colloid dynamics is used to describe the nonstationary aging processes occurring in a suddenly quenched model colloidal liquid with hardsphere plus shortranged 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: 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 selfconsistent set of equations involving now the spatially and temporally nonlocal timedependent correlation functions, which in a uniform system in equilibrium reduces to the selfconsistent 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 nonequilibrium theory.  [Show abstract] [Hide abstract]
ABSTRACT: The concept of dynamic equivalence among monodisperse softsphere fluids is employed in the framework of the selfconsistent generalized Langevin equation (SCGLE) theory of colloid dynamics to calculate the ideal glass transition phase diagram of model softsphere 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 softmicrogel 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 softsphere 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 selfconsistent generalized Langevin equation (SCGLE) theory of colloid dynamics is employed to describe the ergodicnonergodic transition in model monodisperse colloidal dispersions whose particles interact through hardsphere plus shortranged attractive forces. The ergodicnonergodic phase diagram in the temperatureconcentration state space is determined for the hardsphere 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 nonergodicity and determines the nonergodic 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 ergodicattractive glass transition does not preempt the gasliquid phase transition, but always intersects the corresponding spinodal curve on its highconcentration side. We also calculate the ergodicnonergodic phase diagram for the sticky hardsphere 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 selfconsistent generalized Langevin equation (SCGLE) theory of colloid dynamics [Phys. Rev. E 62, 3382 (2000); 72, 031107 (2005)] is the introduction of exact shorttime moment conditions in its formulation. The need to previously calculate these exact shorttime properties constitutes a practical barrier for its application. In this Brief Report, we report that a simplified version of this theory, in which this shorttime information is eliminated, leads to the same results in the intermediate and longtime 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. 
Article: Dynamic arrest within the selfconsistent generalized Langevin equation of colloid dynamics
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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 selfconsistent generalized Langevin equation (SCGLE) theory, was devised to describe the tracer and collective diffusion properties of colloidal dispersions in the short and intermediatetime regimes. Its selfconsistent character, however, introduces a nonlinear dynamic feedback, leading to the prediction of dynamic arrest in these systems, similar to that exhibited by the wellestablished mode coupling theory of the ideal glass transition. The full numerical solution of this selfconsistent theory provides in principle a route to the location of the fluidglass transition in the space of macroscopic parameters of the system, given the interparticle forces (i.e., a nonequilibrium analog of the statisticalthermodynamic prediction of an equilibrium phase diagram). In this paper we focus on the derivation from the same selfconsistent theory of the more straightforward route to the location of the fluidglass 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 hardsphere and with screened Coulomb interactions.  [Show abstract] [Hide abstract]
ABSTRACT: This letter presents a remarkably simple approach to the firstprinciples determination of the ergodic/nonergodic transition in monodisperse colloidal suspensions. It consists of an equation for the longtime asymptotic value ° of the mean squared displacement of the colloidal particles, whose finite real solutions signal the nonergodic state, and determines the nonergodic parameter f(k). We illustrate its concrete application to three simple model colloidal systems, namely, hardspheres, hardspheres plus repulsive (screened Coulomb) Yukawa interaction, and hardsphere plus attractive Yukawa tail. The results indicate that this is quite a competitive theory, similar in spirit to, but conceptually independent from, the wellknown mode coupling theory.
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162  Citations  
28.62  Total Impact Points  
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20072013

Universidad Autónoma de San Luis Potosí
 Instituto de Física
San Luis, San Luis Potosí, Mexico
