Heterogeneity In Supercooled Liquids Research Articles

Automated characterization of spatial and dynamical heterogeneity in supercooled liquids via implementation of machine learning

A computational approach by an implementation of the principle component analysis (PCA) with K-means and Gaussian mixture (GM) clustering methods from machine learning algorithms to identify structural and dynamical heterogeneities of supercooled liquids is developed. In this method, a collection of the average weighted coordination numbers () of particles calculated from particles’ positions are used as an order parameter to build a low-dimensional representation of feature (structural) space for K-means clustering to sort the particles in the system into few meso-states using PCA. Nano-domains or aggregated clusters are also formed in configurational (real) space from a direct mapping using associated meso-states’ particle identities with some misclassified interfacial particles. These classification uncertainties can be improved by a co-learning strategy which utilizes the probabilistic GM clustering and the information transfer between the structural space and configurational space iteratively until convergence. A final classification of meso-states in structural space and domains in configurational space are stable over long times and measured to have dynamical heterogeneities. Armed with such a classification protocol, various studies over the thermodynamic and dynamical properties of these domains indicate that the observed heterogeneity is the result of liquid–liquid phase separation after quenching to a supercooled state.

Activation induced fluidization of a confined viscous liquid

Confinement of supercooled liquids into nano-pores induces a strong modification of the dynamics. In this work we raise the issue as how this confinement effect is modified when the liquid is out of equilibrium. To answer that question, we use molecular dynamics simulations to investigate the effect of confinement on a supercooled liquid activated by the periodic folding of a molecular motor. The excitation (i.e. elementary diffusion processes) density calculation shows that the motor’s opening angle controls the activation of the medium. We then use that result to study the effect of different activations on the confined supercooled liquid. When our liquid is not activated, the confinement generates a strong slowing down of the dynamics, and the excitation density decreases sharply around the pore wall. In contrast when the liquid is activated the motor generates excitations inside the medium localized mostly in the pore center. The combination of these two effects leads to a localization of the excitation density when the motor is on. Results show that the activation is able to wash out the confinement-induced slowing down while the main characteristics of supercooled liquids are maintained or increased. We observe actually an increase of the tail of the Van Hove correlation function upon activation inside the pores leading to the increase of the Non Gaussian parameter, two signatures of dynamic heterogeneity in supercooled liquids.

Large deviations of glassy effective potentials

The theory of glassy fluctuations can be formulated in terms of disordered effective potentials. While the properties of the average potentials are well understood, the study of the fluctuations has been so far quite limited. Close to the MCT transition, fluctuations induced by the dynamical heterogeneities in supercooled liquids can be described by a cubic field theory in presence of a random field term. In this paper, we set up the general problem of the large deviations going beyond the assumption of the vicinity to T MCT and analyze it in the paradigmatic case of spherical (p-spin) glass models. This tool can be applied to study the probability of the observation of dynamic trajectories with memory of the initial condition in regimes where, typically, the correlation C(t, 0) decays to zero at long times, at finite T and at T = 0.

Flow heterogeneities in supercooled liquids and glasses under shear.

Using extensive nonequilibrium molecular dynamics simulations, we investigate a glass-forming binary Lennard-Jones mixture under shear. Both supercooled liquids and glasses are considered. Our focus is on the characterization of inhomogeneous flow patterns such as shear bands that appear as a transient response to the external shear. For the supercooled liquids, we analyze the crossover from Newtonian to non-Newtonian behavior with increasing shear rate γ[over ̇]. Above a critical shear rate γ[over ̇]_{c} where a non-Newtonian response sets in, the transient dynamics are associated with the occurrence of short-lived vertical shear bands, i.e., bands of high mobility that form perpendicular to the flow direction. In the glass states, long-lived horizontal shear bands, i.e., bands of high mobility parallel to the flow direction, are observed in addition to vertical ones. The systems with shear bands are characterized in terms of mobility maps, stress-strain relations, mean-squared displacements, and (local) potential energies. The initial formation of a horizontal shear band provides an efficient stress release, corresponds to a local minimum of the potential energy, and is followed by a slow broadening of the band towards the homogeneously flowing fluid in the steady state. Whether a horizontal or a vertical shear band forms cannot be predicted from the initial undeformed sample. Furthermore, we show that with increasing system size, the probability for the occurrence of horizontal shear bands increases.

Direct imaging of structural disordering and heterogeneous dynamics of fullerene molecular liquid

Structural rearrangements govern the various properties of disordered systems and visualization of these dynamical processes can provide critical information on structural deformation and phase transformation of the systems. However, direct imaging of individual atoms or molecules in a disordered state is quite challenging. Here, we prepare a model molecular system of C70 molecules on graphene and directly visualize the structural and dynamical evolution using aberration-corrected transmission electron microscopy. E-beam irradiation stimulates dynamics of fullerene molecules, which results in the first-order like structural transformation from the molecular crystal to molecular liquid. The real-time tracking of individual molecules using an automatic molecular identification process elucidates the relaxation behavior of a stretched exponential functional form. Moreover, the directly observed heterogeneous dynamics bear similarity to the dynamical heterogeneity in supercooled liquids near the glass transition. Fullerenes on graphene can serve as a new model system, which allows investigation of molecular dynamics in disordered phases.

Correlation of local order with particle mobility in supercooled liquids is highly system dependent.

We investigate the connection between local structure and dynamical heterogeneity in supercooled liquids. Through the study of four different models, we show that the correlation between a particle's mobility and the degree of local order in nearby regions is highly system dependent. Our results suggest that the correlation between local structure and dynamics is weak or absent in systems that conform well to the mean-field picture of glassy dynamics and strong in those that deviate from this paradigm. Finally, we investigate the role of order-agnostic point-to-set correlations and reveal that they provide similar information content to local structure measures, at least in the system where local order is most pronounced.

Universal Features of Dynamic Heterogeneity in Supercooled Liquids

A few years ago it was shown that some systems that have very similar local structure, as quantified by the pair correlation function, exhibit vastly different slowing down upon supercooling. Recently, a more subtle structural quantity, the so-called "point-to-set" length, was found to reliably correlate with the average dynamics. Here we use computer simulations to examine the behavior of fluctuations around the average dynamics, i.e., dynamic heterogeneity. We study five model glass-forming liquids: three model liquids used in previous works and two additional model liquids with finite range interactions. Some of these systems have very similar local structure but vastly different dynamics. We show that for all these systems the spatial extent and the anisotropy of dynamic heterogeneity have the same correlation with the average dynamics. This result complements a recent experimental finding of a universal correlation between the number of correlated particles and the apparent activation enthalpy.

Single molecule rotational probing of supercooled liquids

Much of the interesting behavior that has been observed in supercooled liquids appears to be related to dynamic heterogeneity, the presence of distinct dynamic environments - with no apparent underlying structural basis - in these systems. To most directly interrogate these environments, proposed to span regions just a few nanometers across, molecular length scale probes are required. Single molecule fluorescent microscopy was introduced to the field a decade ago and has provided strong evidence of dynamic heterogeneity in supercooled systems. However, only more recently has the full set of challenges associated with interpreting results of these experiments been described. With a fuller understanding of these challenges in hand, single molecule measurements can be employed to provide a more precise picture of dynamic heterogeneity in supercooled liquids and other complex systems. In this tutorial review, experimental and data analysis details are presented for the most commonly employed single molecule approach to studying supercooled liquids, the measurement of rotational dynamics of single molecule probes. Guidance is provided in experimental set-up and probe selection, with a focus on choices that affect data interpretation and probe sensitivity to dynamic heterogeneity.

Heterogeneity in Single-Molecule Observables in the Study of Supercooled Liquids

Bulk approaches to studying heterogeneous systems obscure important details, as they report average behavior rather than the distribution of behaviors in such environments. Small-molecule and polymeric supercooled liquids, which display heterogeneity in their dynamics without an underlying structural heterogeneity that sets those dynamics, are important constituents of this category of condensed matter systems. A variety of approaches have been devised to unravel ensemble averaging in supercooled liquids. This review focuses on the ultimate subensemble approach, single-molecule measurements, as they have been applied to the study of supercooled liquids. We detail how three key experimental observables (single-molecule probe rotation, translation, and fluorescence lifetime) have been employed to provide detail on dynamic heterogeneity in supercooled liquids. Special attention is given to the potential for, but also the challenges in, discriminating spatial and temporal heterogeneity and detailing the length scales and timescales of heterogeneity in these systems.

Communication: Crystallite nucleation in supercooled glycerol near the glass transition

Heterogeneity and solid-like structures found near the glass transition provide a key to a better understanding of supercooled liquids and of the glass transition. However, the formation of solid-like structures and its effect on spatial heterogeneity in supercooled liquids is neither well documented nor well understood. In this work, we reveal the crystalline nature of the solid-like structures in supercooled glycerol by means of neutron scattering. The results indicate that inhomogeneous nucleation happens at temperatures near T(g). Nevertheless, the thermal history of the sample is essential for crystallization. This implies such structures in supercooled liquids strongly depend on thermal history. Our work suggests that different thermal histories may lead to different structures and therefore to different length and time scales of heterogeneity near the glass transition.

Role of the Lifetime of Dynamical Heterogeneity in the Frequency-Dependent Stokes–Einstein Relation of Supercooled Liquids

We previously investigated the lifetime of dynamical heterogeneity in supercooled liquids in terms of a four-point, three-time density correlation function via molecular dynamics simulations [Phys. Rev. E 79 (2009) 060501(R); J. Chem. Phys. 133 (2010) 044511]. In this letter, we examine the physical role of the lifetime of dynamicsl heterogeneity in the violation of the Stokes–Einstein (SE) relation by calculating the frequency-dependent viscosity and self-diffusion constant. Our results demonstrate that the SE relation holds up to the time scale at which the non-Gaussian parameter is maximum. Large violations of the SE relation are characterized by time scales longer than the lifetime of the dynamical heterogeneity in highly supercooled liquids.

Communications: Comparison of activation barriers for the Johari–Goldstein and alpha relaxations and its implications

The range of activation barrier heights for the Johari-Goldstein (JG) relaxation in glasses is shown to overlap the range for the main (alpha) relaxation, but to be on the average somewhat lower. This suggests the JG relaxation, like the alpha, involve transitions between megabasins in the energy landscape, and that the original conjecture by Johari and this author that the JG relaxation is an intrabasin one cannot be correct. A further possibility is that there is a closer connection of the JG relaxation to the phenomenon of dynamic heterogeneity in supercooled liquids than so far assumed.

On dynamic heterogeneity in supercooled liquids

A simplified molecular theory for the dynamics of liquids near the glass transition temperature T(g) is developed and compared with experimental viscosity and diffusion behavior. Its basis is the spatial fluctuations of local density, a property that depends on isothermal compressibility and thus occurs naturally in all liquids at equilibrium. Instantaneous liquid structure is approximated by randomly distributed arrays of two domains having either higher or lower density than the average. The time dependence of fluctuations is represented by a sequence of such structures, each having a lifetime that varies with the macroscopic density. The dynamic environment of a molecule within a domain (slow or fast) depends on the density of its domain (high or low). Translational diffusion and orientational relaxation depend on different averages of the slow and fast domain contributions and lead, on approaching T(g), to a progressive departure from the Stoke-Einstein relationship. Predictions are made using macroscopic viscosity-density relationships within the individual domains. They depend only on the choice of domain size, which, according to this formulation, is insensitive to temperature. The data for three well-studied nonpolymeric liquids were found to be in reasonable accord with NMR assessments of domain size.

A method for measuring the nonlinear response in dielectric spectroscopy through third harmonics detection

We present a high sensitivity method allowing the measurement of the nonlinear dielectric susceptibility of an insulating material at finite frequency. It has been developed for the study of dynamic heterogeneities in supercooled liquids using dielectric spectroscopy at frequencies 0.05 Hz < or = f < or = 3x10(4) Hz. It relies on the measurement of the third harmonics component of the current flowing out of a capacitor. We first show that standard laboratory electronics (amplifiers and voltage sources) nonlinearities lead to limits on the third harmonics measurements that preclude reaching the level needed by our physical goal, a ratio of the third harmonics to the fundamental signal about 10(-7). We show that reaching such a sensitivity needs a method able to get rid of the nonlinear contributions both of the measuring device (lock-in amplifier) and of the excitation voltage source. A bridge using two sources fulfills only the first of these two requirements, but allows to measure the nonlinearities of the sources. Our final method is based on a bridge with two plane capacitors characterized by different dielectric layer thicknesses. It gets rid of the source and amplifier nonlinearities because in spite of a strong frequency dependence of the capacitor impedance, it is equilibrated at any frequency. We present the first measurements of the physical nonlinear response using our method. Two extensions of the method are suggested.

How does sensitivity to dynamical heterogeneity in supercooled colloidal liquids depend on tracer size?

Few experimental investigations have examined the dependence of probe length scale on the evolution of dynamical heterogeneity in supercooled liquids. In this study, we use fluorescent tracer probes, which are smaller than that of the constituent unlabeled particles in the matrix suspension, to investigate the tracer size sensitivity to the onset of dynamical heterogeneity in model hard-sphere colloidal suspensions close to the glass transition. The dynamics of poly(methyl methacrylate) (PMMA) tracer particles of radii a(S) = 137 nm embedded into constituent PMMA particles of a(L) = 212 and 637 nm with bulk volume fraction phi varied from 0.50 to 0.57 is examined using fluorescence correlation spectroscopy (FCS). Upon increasing phi for the largest tracer size ratio explored, f (= a(S)/a(L)) = 0.646, the onset of dynamic heterogeneity is observed from the broad distribution of characteristic decay times of the tracers, which is extracted from the measured FCS autocorrelation functions. The strong coupling between tracer size and its sensitivity to dynamical heterogeneity is reflected in the dynamic susceptibility, where dynamic correlation lengths are immeasurable for the smallest size ratio and show a marked increase to five tracer particle diameters for the largest size ratio.

Theory of Structural Glasses and Supercooled Liquids

We review the random first-order transition theory of the glass transition, emphasizing the experimental tests of the theory. Many distinct phenomena are quantitatively predicted or explained by the theory, both above and below the glass transition temperature T(g). These include the following: the viscosity catastrophe and heat-capacity jump at T(g), and their connection; the nonexponentiality of relaxations and their correlation with the fragility; dynamic heterogeneity in supercooled liquids owing to the mosaic structure; deviations from the Vogel-Fulcher law, connected with strings or fractal cooperative rearrangements; deviations from the Stokes-Einstein relation close to T(g); aging and its correlation with fragility; and the excess density of states at cryogenic temperatures owing to two-level tunneling systems and the Boson peak.

Lifetime of dynamic heterogeneity in strong and fragile kinetically constrained spinmodels

Kinetically constrained spin models are schematic coarse-grained models for the glasstransition which represent an efficient theoretical tool to study detailed spatio-temporalaspects of dynamic heterogeneity in supercooled liquids. Here, we study how spatiallycorrelated dynamic domains evolve with time and compare our results to variousexperimental and numerical investigations. We find that strong and fragile models yielddifferent results. In particular, the lifetime of dynamic heterogeneity remainsconstant and roughly equal to the alpha relaxation time in strong models, while itincreases more rapidly in fragile models when the glass transition is approached.

Dynamical Heterogeneity and Jamming in Glass-Forming Liquids

The relationship between spatially heterogeneous dynamics (SHD) and jamming is studied in a glass-forming binary Lennard-Jones system via molecular dynamics simulations. It has been suggested [Phys. ReV. Lett. 2001, 86, 111] 1 that the probability distribution of interparticle forces P(F) develops a peak at the glass transition temperature Tg and that the large force inhomogeneities, responsible for structural arrest in granular materials, are related to dynamical heterogeneities in supercooled liquids that form glasses. It has been further suggested that “force chains” present in granular materials may exist in supercooled liquids and may provide an order parameter for the glass transition. Our goal is to investigate the extent to which the forces experienced by particles in a glass-forming liquid are related to SHD and compare these forces to those observed in granular materials and other glass-forming systems. Our results are summarized as follows. We calculate P(F) for positive (repulsive) instantaneous forces and find no peak in P(F) at any temperature in our system, even below Tg. We also find that particles that have been localized for a long time are less likely to experience high relative force and that mobile particles experience higher relative forces at shorter time scales, indicating a correlation between pairwise forces and particle mobility. We construct force chains based on the magnitude of pairwise positive instantaneous forces. We find that force chains constructed in this manner are composed of both localized and mobile particles; therefore there is no one-to-one correspondence between force chains as defined here and locally mobile or immobile regions of the liquid. We also find that force chains do not play the same role as force chains in granular materials but may indicate a difference in the evolution of the local environment of particles with different mobility. We also discuss a possible relationship between force chains found here and the development of stringlike motion found in this and other glass-forming liquids [Phys. ReV. Lett. 1998, 80, 2338; J. Chem. Phys. 2004, 120, 4415]. 2,3

Multifractal Analysis of the Dynamical Heterogeneity in a Two-Dimensional Supercooled Liquid

The dynamical heterogeneity in supercooled liquids measured by a molecular dynamics simulation has been quantified on the basis of the multifractal formalism. The singularity spectrum becomes broader as the glass transition is approached. This behavior is similar to that observed in the case of the Anderson-localization transition.

Static and dynamical heterogeneities in supercooled liquids

We present here some features of supercooled liquids from both the structural and dynamical consideration. We discuss the existence of heterogenous structures characterized by weak mass localization. The analysis is done using the standard methods of density functional theory. The dynamics governing the supercooled states that lead to non-exponential relaxation of the time–correlation functions, are also studied. The dynamical heterogeneities are studied in terms of departure of the single particle dynamics from simple Gaussian behavior over intermediate timescales. Other relevant properties like the velocity auto-correlation function and the mean square displacement associated with the tagged particle dynamics are also computed.