Heterogeneities in Supercooled Liquids: A Density-Functional Study

Kaur, Charanbir; Das, Shankar P.

doi:10.1103/physrevlett.86.2062

Cited by 53 publications

(64 citation statements)

References 21 publications

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“…Using a Gaussian superposition approximation [12,13,14], as well as unconstrained numerical minimization of a discretized version of the free-energy functional [8], we show that the width of the local density peaks at glassy minima exhibits large spatial variation similar to the spatial heterogeneity of the local Debye-Waller factor found in simulations [4,6]. We have also performed molecular dynamics (MD) simulations starting from a particle configuration corresponding to a glassy minimum.…”

Section: Pacs Numbersmentioning

confidence: 99%

“…We then minimize the RY functional with respect to the 2500 parameters, {R i }, {α i }, {η i }, and also with respect to the volume V at a reference liquid packing fraction φ l ≡ πρ 0 σ 3 /6, σ being the hard sphere diameter. We use the Hendersen-Grundke (HG) expression [15] for C(r), as has been done in previous calculations [12,13,14]. The minimization leads to structures similar to glassy states observed in simulations and experiments.…”

Section: Pacs Numbersmentioning

confidence: 99%

“…, with the centers of the Gaussians, {R i }, forming a fixed amorphous structure which was taken to be either a random close packing of hard spheres [12,13], or a particle configuration from MD simulations [14]. The free energy was then minimized with respect to the single variational parameter α.…”

Section: Pacs Numbersmentioning

confidence: 99%

“…(1), we have taken the zero of the free energy at its uniform liquid value. In earlier studies [12,13,14] of glassy minima of this free energy, the local density ρ(r) was approximated as a superposition of Gaussians,…”

Section: Pacs Numbersmentioning

confidence: 99%

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Signatures of Dynamical Heterogeneity in the Structure of Glassy Free-Energy Minima

2008

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From numerical minimization of a model free energy functional for a system of hard spheres, we show that the width of the local peaks of the time-averaged density field at a glassy free-energy minimum exhibits large spatial variation, similar to that of the "local Debye-Waller factor" in simulations of dynamical heterogeneity. Molecular dynamics simulations starting from a particle configuration generated from the density distribution at a glassy free-energy minimum show similar spatial heterogeneity in the degree of localization, implying a direct connection between dynamical heterogeneity and the structure of glassy free energy minima. PACS numbers:Observation of dynamical heterogeneity, both in experiments [1] and in simulations [2], has been a significant step in the attempt to understand the behaviour of glass forming liquids. The degree of spatial variation of the "propensity for motion" [3] of individual particles, defined as the mean-square displacement of a particle from its initial position, provides a direct measure of dynamical heterogeneity. The local Debye-Waller factor (short-time rms displacement from the average position) of individual particles in the initial configuration has been found [4] to be strongly correlated with the spatially heterogeneous propensity for motion over longer time scales. However, subsequent work [5] has shown that this correlation exists only for time scales shorter than the α-relaxation time. Spatial heterogeneity of the local Debye-Waller factor has also been observed [6] in simulations below the glass transition temperature.The physical origin of dynamical heterogeneity is not well-understood at present. In particular, it is not clear whether the occurrence of spatially heterogeneous dynamics can be explained within the "free-energy landscape" description [7,8,9] of glassy behavior in which the complex dynamics is attributed to the presence of a large number of "glassy" local minima of the free energy. Density functional theory (DFT) [10], in which the free energy is expressed as a functional of the timeaveraged local density, provides a convenient framework for exploring the free-energy landscape. In this description, a glassy free-energy minimum is a local minimum of the free energy functional with a strongly inhomogeneous but non-periodic density distribution. The local peaks of the density distribution represent the time-averaged positions of the particles, and the width of a local peak is analogous to the local Debye-Waller factor measured in simulations. In this description, the α-relaxation time corresponds to the time scale of transitions between different glassy minima [7,8]. Therefore, the density distribution at a typical glassy free-energy minimum should correspond to an average of the local density over a time scale shorter than the α-relaxation time. If this description is valid, then the spatial variation of the propensities for motion observed in simulations over time scales shorter than the α-relaxation time (which, as discussed above, is strongly co...

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Section: Pacs Numbersmentioning

confidence: 99%

Section: Pacs Numbersmentioning

confidence: 99%

Section: Pacs Numbersmentioning

confidence: 99%

Section: Pacs Numbersmentioning

confidence: 99%

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Signatures of Dynamical Heterogeneity in the Structure of Glassy Free-Energy Minima

2008

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“…The statics alone tell us about the equilibrium structure factor S k that we shall later need. It should be noted that beyond the replica approach, attempts have been made at connecting the minima of F to the supercooled state [31]. From a dynamical point of view, the particle density must be locally conserved, which constrains it to evolve according to a continuity equation…”

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Brownian dynamics: From glassy to trivial

et al. 2015

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We endow a system of interacting particles with two distinct, local, Markovian and reversible microscopic dynamics. Using common field-theoretic techniques used to investigate the presence of a glass transition, we find that while the first, standard, dynamical rules lead to glassy behavior, the other one leads to a simple exponential relaxation towards equilibrium. This finding questions the intrinsic link that exists between the underlying, thermodynamical, energy landscape, and the dynamical rules with which this landscape is explored by the system. Our peculiar choice of dynamical rules offers the possibility of a direct connection with replica theory, and our findings therefore call for a clarification of the interplay between replica theory and the underlying dynamics of the system.The microscopic phenomena driving the dynamical arrest in supercooled liquids and in glasses are still controversial. One line of thought, which originates in the work of Adam and Gibbs, pictures a glass-forming liquid as a system whose energy landscape complexity accounts for the slowing down of its dynamics. The original Adam-Gibbs [1] theory relates viscosity -the momentum transport coefficient-to configurational entropy. The more recent scenario due to Kirkpatrick, Thirumalai, and Wolynes [2] is based on the study of the metastable configurations of the system and on the concept of nucleating entropic droplets. This is the Random-First-Order Theory (RFOT) scenario. The idea is that metastability arises from the many valleys of the energy landscape the system can be trapped in. The RFOT scenario gives a large set of quantitative predictions including non-mean field particle models [4]. These aspects of the physics of glasses were reviewed by Debenedetti and Stillinger [5] and more recently by Biroli and Bouchaud [6].In another line of thought, no complex energy landscape needs to be invoked, and dynamically induced metastability alone is held responsible for the dynamics slowing down. This is a phenomenological approach in which at a coarse-grained scale local patches of activity are the only ingredients of the dynamics. This has led to the development of kinetically-constrained models (KCM) (see [7] for a review), which have the advantage of lending themselves with greater ease than molecular models to both numerical experiments and analytical treatment. The hallmark of the corresponding lattice models is the absence of any structure in the energy landscape (the equilibrium distribution is that of independent degrees of freedom). These somewhat simplistic descriptions are not directly built from the microscopics, and it is often argued that their glassy-like properties, like the existence of dynamical heterogeneities, are almost tautological, but recent works [8] have tried to bridge the gap from the microscopics to dynamic facilitation.A central concept in both approaches is that of metastability. A metastable state can be viewed as an eigenstate of the evolution operator with a nonzero but small relaxation rate. The existe...

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