Dynamics Of Supercooled Liquids Research Articles

Supercooled Liquid Dynamics Studied via Shear-Mechanical Spectroscopy

We report dynamical shear-modulus measurements for five glass-forming liquids (pentaphenyltrimethyltrisiloxane, diethyl phthalate, dibutyl phthalate, 1,2-propanediol, and m-touluidine). The shear-mechanical spectra are obtained by the piezoelectric shear-modulus gauge (PSG) method. This technique allows one to measure the shear modulus (10(5)-10(10) Pa) of the liquid within a frequency range from 1 mHz to 10 kHz. We analyze the frequency-dependent response functions to investigate whether time-temperature superposition (TTS) is obeyed. We also study the shear-modulus loss-peak position and its high-frequency part. It has been suggested that when TTS applies, the high-frequency side of the imaginary part of the dielectric response decreases like a power law of the frequency with an exponent -1/2. This conjecture is analyzed on the basis of the shear mechanical data. We find that TTS is obeyed for pentaphenyltrimethyltrisiloxane and in 1,2-propanediol while in the remaining liquids evidence of a mechanical beta process is found. Although the high-frequency power law behavior w(-alpha) of the shear loss may approach a limiting value of alpha = 0.5 when lowering the temperature, we find that the exponent lies systematically above this value (around 0.4). For the two liquids without beta relaxation (pentaphenyltrimethyltrisiloxane and 1,2-propanediol) we also test the shoving model prediction, according to which the relaxation time activation energy is proportional to the instantaneous shear modulus. We find that the data are well described by this model.

A Phenomenological Description of the PALS Response in Glass - Forming Systems

A phenomenological description of the ortho-positronium (o-Ps) response from positron annihilation spectroscopy (PALS) and the dynamics from viscosity studies on two typical glass-forming compounds within the framework of the two-order parameter (TOP) model is presented. The dynamical data are accounted for by the modified Vogel – Fulcher – Tamman - Hesse (M-VFTH) equation. Subsequently, the quasi-sigmoidal course of the o-Ps lifetime, τ3, with or without the high-temperature plateau region as a function of the temperature over a wide temperature range can be described by an effective free volume version of the TOP model. This simultaneous description suggests a close relationship between the PALS response and the dynamics of supercooled liquids and seems to support the liquid - like and solid - like domain physical picture of all the three physical states of the disordered phase of the condensed systems.

Facilitation, complexity growth, mode coupling, and activated dynamics in supercooled liquids

In low-temperature-supercooled liquids, below the ideal mode-coupling theory transition temperature, hopping and continuous diffusion are seen to coexist. Here, we present a theory that shows explicitly the interplay between the two processes and shows that activated hopping facilitates continuous diffusion in the otherwise frozen liquid. Several universal features arise from nonlinear interactions between the continuous diffusive dynamics described here by the mode coupling theory (MCT)] and the activated hopping (described here by the random first-order transition theory). We apply the theory to a specific system, Salol, to show that the theory correctly predicts the temperature dependence of the nonexponential stretching parameter, beta, and the primary alpha relaxation timescale, tau. The study explains why, even below the mean field ergodic to nonergodic transition, the dynamics is well described by MCT. The nonlinear coupling between the two dynamical processes modifies the relaxation behavior of the structural relaxation from what would be predicted by a theory with a complete static Gaussian barrier distribution in a manner that may be described as a facilitation effect. Furthermore, the theory correctly predicts the observed variation of the stretching exponent beta with the fragility parameter, D. These two predictions also allow the complexity growth to be predicted, in good agreement with the results of Capaccioli et al. [Capaccioli S, Ruocco G, Zamponi F (2008) J Phys Chem B 112:10652-10658].

From particles to spins: Eulerian formulation of supercooled liquids and glasses.

The dynamics of supercooled liquid and glassy systems are usually studied within the Lagrangian representation, in which the positions and velocities of distinguishable interacting particles are followed. Within this representation, however, it is difficult to define measures of spatial heterogeneities in the dynamics, as particles move in and out of any one given region within long enough times. It is also nontransparent how to make connections between the structural glass and the spin glass problems within the Lagrangian formulation. We propose an Eulerian formulation of supercooled liquids and glasses that allows for a simple connection between particle and spin systems, and that permits the study of dynamical heterogeneities within a fixed frame of reference similar to the one used for spin glasses. We apply this framework to the study of the dynamics of colloidal particle suspensions for packing fractions corresponding to the supercooled and glassy regimes, which are probed via confocal microscopy.

The Prigogine–Defay ratio and the microscopic theory of supercooled liquids

Prigogine-Defay ratios and, more recently, their frequency extension have been proposed to be a measure of the number of nonmacroscopic processes involved in the relaxation dynamics of supercooled liquids. We show that the microscopic theory of the Navier-Stokes equations of those liquids provides a consistent thermodynamic framework in which all possible dynamical Prigogine-Defay ratios can be expressed in terms of the same relaxation functions and that these ratios provide less information than the microscopic theory itself. The latter shows that more than one relaxation process is certainly always involved in this relaxation dynamics, whatever is the molecular dynamics, or experimental, technique used to determine the latter.

Nonaffine Deformation of Inherent Structure as a Static Signature of Cooperativity in Supercooled Liquids

We unveil the existence of nonaffinely rearranging regions in the inherent structures (IS) of supercooled liquids by numerical simulations of model glass formers subject to static shear deformations combined with local energy minimizations. In the liquid state IS, we find a broad distribution of large rearrangements which are correlated only over small distances. At low temperatures, the onset of the cooperative dynamics corresponds to much smaller displacements correlated over larger distances. This finding indicates the presence of nonaffinely rearranging domains of relevant size in the IS deformation, which can be seen as the static counterpart of the cooperatively rearranging regions in the dynamics. This idea provides new insight into possible structural signatures of slow cooperative dynamics of supercooled liquids and supports the connections with elastic heterogeneities found in amorphous solids.

From elementary steps to structural relaxation: A continuous-time random-walk analysis of a supercooled liquid

We show that the dynamics of supercooled liquids, analyzed from computer simulations of the binary mixture Lennard-Jones system, can be described in terms of a continuous-time random walk (CTRW). The required discretization comes from mapping the dynamics on transitions between metabasins. This yields a quantitative link between the elementary step and the full structural relaxation. The analysis involves a verification of the CTRW conditions as well as a quantitative test of the predictions. The wave-vector dependence of the relaxation time and the degree of nonexponentiality can be expressed in terms of the first moments of the waiting time distribution.

Properties of ideal Gaussian glass-forming systems

We introduce the ideal Gaussian glass-forming system as a model to describe the thermodynamics and dynamics of supercooled liquids on a local scale in terms of the properties of the potential energy landscape (PEL). The first ingredient is the Gaussian distribution of inherent structures, the second a specific relation between energy and mobility. This model is compatible with general considerations as well as with several computer simulations on atomic computer glass formers. Important observables such as diffusion constants, structural relaxation times, and kinetic as well as thermodynamic fragilities can be calculated analytically. In this way it becomes possible to identify a relevant PEL parameter determining the kinetic fragility. Several experimental observations can be reproduced. The remaining discrepancies in the experiment can be qualitatively traced back to the difference between small and large systems.

Theory of relaxation dynamics in glass-forming hydrogen-bonded liquids

We address the relaxation dynamics in hydrogen-bonded supercooled liquids near (but above) the glass transition, measured via broadband dielectric spectroscopy (BDS). We propose a theory based on decomposing the relaxation of the macroscopic dipole moment into contributions from hydrogen-bonded clusters of s molecules, with s(min) < or = s < or = s(max) . The existence of s(max) is translated into a sum rule on the concentrations of clusters of size s . We construct the statistical mechanics of the supercooled liquid subject to this sum rule as a constraint, to estimate the temperature-dependent density of clusters of size s . With a theoretical estimate of the relaxation time of each cluster, we provide predictions for the real and imaginary parts of the frequency-dependent dielectric response. The predicted spectra and their temperature dependence are in accord with measurements, explaining a host of phenomenological fits like the Vogel-Fulcher fit and the stretched exponential fit. Using glycerol as a particular example, we demonstrate quantitative correspondence between theory and experiments. The theory also demonstrates that the alpha peak and the "excess wing" stem from the same physics in this material. The theory also shows that in other hydrogen-bonded glass formers the excess wing can develop into a beta peak, depending on the molecular material parameters (predominantly the surface energy of the clusters). We thus argue that alpha and beta peaks can stem from the same physics. We address the BDS in constrained geometries (pores) and explain why recent experiments on glycerol did not show a deviation from bulk spectra. Finally, we discuss the dc part of the BDS spectrum and argue why it scales with the frequency of the alpha peak, providing an explanation for the remarkable data collapse observed in experiments.

Role of hydrogen bonds in the supercooled dynamics of glass-forming liquids at high pressures

The effect of pressure on the dynamics of supercooled liquids shows a variety of remarkable similarities for different glass-forming systems. However, an important group of liquids, characterized by hydrogen-bond interactions, show some deviations from these general behaviors. To investigate this, we use broadband dielectric spectroscopy to study the temperature dependent dynamics of a supercooled hydrogen bonded oligomeric glycol and its non-hydrogen-bonded analog over a wide range of pressures. With the chosen model system, we are able to directly link the presence of hydrogen bonding to deviations from the general pattern of the pressure response of supercooled dynamics.

Crystal growth kinetics exhibit a fragility-dependent decoupling from viscosity

In this paper we establish the temperature dependence of the kinetic coefficient associated with crystal growth into the supercooled liquid for a wide range of organic and inorganic materials. We show that the kinetic coefficient for crystal growth scales with the shear viscosity eta as eta(-xi) and that the exponent depends systematically on the fragility of the liquid. The greater the fragility (i.e., deviation away from an Arrhenius temperature dependence for eta), the larger the difference 1-xi. We argue that this breakdown in scaling between the crystal growth kinetics and the viscosity is a manifestation of heterogeneous dynamics in supercooled liquids. In addition, we show that the absolute growth rate at intermediate viscosities is correlated with the entropy difference between the liquid and the crystal.

Vibrational and configurational parts of the specific heat at glass formation

The specific heat ${C}_{p}$ of a liquid is partly vibrational, arising from change in phonons and anharmonic forces with temperature $T$, and partly configurational, arising from change in the structure with $T$. The first determines a liquid's elastic resistance to stress or rigidity and the second its fluid behavior. Both are thought to decrease on liquid's vitrification, and their ad hoc estimates are currently used for understanding a supercooled liquid's dynamics. We report measurements of the vibrational part, ${C}_{p,\mathrm{vib}}$, and determine the configurational part. It is found that there is almost no decrease in ${C}_{p,\mathrm{vib}}$ on structural freezing of the polymer melts, and the decrease in ${C}_{p}$ is configurational. An interpretation of the finding is that the curvature of the fixed configurational energy minimum in which a polymer glass structure is trapped and the associated anharmonicity have quantitatively the same effect on ${C}_{p}$ as the corresponding two sources when its melt explores a multiplicity of high energy minima and its volume changes.

Mysteries of the glass transition

As someone who has long been interested in the glass transition and glassy-state kinetics, I would like to comment on some of the issues raised by James Langer in his Reference Frame column.I affirm Langer’s statement about healthy contentiousness. Whether or not the glass transition has thermodynamic roots definitely makes for exciting science. The reason some of us think thermodynamics is important is that we find it difficult to dismiss as co-incidences the similarities in the values of the kinetic temperature T 0 and the thermodynamic Kauzmann temperature T K. One common objection to the Kauzmann analysis, that an amorphous solid should not have zero entropy, can be assuaged by noting that the entropy at T K does not have to be zero, just very small.Langer briefly mentions the success of the simplistic Adam–Gibbs (AG) model in describing the dynamics of supercooled liquids. Its nonlinear extension into the glass-transition region and glassy state (NLAG) is also surprisingly successful. 1 1. G. W. Scherer,J. Amer. Ceram. Soc. 67, 504 (1984); I. M. Hodge, Macromolecules 20, 2897 (1987). https://doi.org/10.1021/ma00177a044 That extension is based on concepts introduced by several researchers over several decades: Simon Rekhson in 1994, George Scherer in 1984, Cornelius Moynihan in 1976, O. S. Narayanaswamy in 1971, and others. The successes of the NLAG model go far beyond expectations, and raise issues of their own. The resolution of these issues might provide important clues to a theoretical understanding of the glass transition. ▸As noted by Langer, the experimentally observed effective activation energy E(T) increases rapidly with decreasing temperature down to the glass-transition temperature T g, but it then decreases through the T g range until it reaches a constant value E(T g), so that glassy-state relaxation exhibits Arrhenius behavior. The singularity at T 0 noted by Langer only occurs in the equilibrium supercooled liquid state and not in the experimentally observed nonequilibrium glassy state. The change from non-Arrhenius to Arrhenius behavior at T g is well described by the NLAG model and its precursor, the Tool-Narayanaswamy-Moynihan model. ▸NLAG predicts a simple relation between the ratio T K/T g and an empirical constant that parameterizes the nonlinearity of the glass transition and glassy-state kinetics. This intriguing prediction needs to be independently confirmed or unambiguously refuted.▸The NLAG model, together with the plausible assumption that smaller localized activation energies Δµ enable the kinetic T g to get closer to the thermodynamic T K, generates many of the correlations captured by Angell’s fragility. In fact, the ratio T K/T g is an excellent metric that allows fragility to be applied to the glassy state.▸Estimated values of Δµ for canonical glasses are often comparable with rotational energy barriers in polymers, and ionic, covalent, and hydrogen bond strengths. In these cases the NLAG model is almost quantitatively accurate.▸Incorporation of a distribution in Δµ yields a respectable account 2,3 2. G. Sartor, E. Mayer, G. P. Johari, Biophys. J. 66, 249 (1994). https://doi.org/10.1016/S0006-3495(94)80774-X 3. I. M. Hodge, Biophys. J. 91, 993 (2006). https://doi.org/10.1529/biophysj.106.080796 of thermal manifestations of motions in hydrated proteins and B-DNA. 2,4 2. G. Sartor, E. Mayer, G. P. Johari, Biophys. J. 66, 249 (1994). https://doi.org/10.1016/S0006-3495(94)80774-X 4. J. L. Green, J. Fan, C. A. Angell, J. Phys. Chem. 98, 13780 (1994). https://doi.org/10.1021/j100102a052 The mean value for Δµ is comparable with hydrogen bond strengths, albeit with a large uncertainty, and the large standard deviation—30% of the average—is consistent with the insightful but qualitative analysis of Jennifer Green and coworkers. 4 4. J. L. Green, J. Fan, C. A. Angell, J. Phys. Chem. 98, 13780 (1994). https://doi.org/10.1021/j100102a052 The fact that NLAG gives a decent account of annealing in hydrated proteins and B-DNA strongly supports Austen Angell’s suggestion that the glass transition and protein dynamics have much in common. 5 5. C. A. Angell, Science 267, 1924 (1995). https://doi.org/10.1126/science.267.5206.1924 I share Langer’s belief that short-range interactions are probably the key. Since the current models accommodate a wide range of interactions, such as covalent, hydrogen, and ionic bonding, the glass-transition phenomenon is evidently insensitive to the details of those interactions. This generality is missing from too many theoretical attempts at explaining the problem. Perhaps the averaging of details is why the simplistic NLAG model is so successful.REFERENCESSection:ChooseTop of pageREFERENCES <<CITING ARTICLES1. G. W. Scherer,J. Amer. Ceram. Soc. 67, 504 (1984); Google Scholar I. M. Hodge, Macromolecules 20, 2897 (1987). https://doi.org/10.1021/ma00177a044 , Google ScholarCrossref, ISI, CAS2. G. Sartor, E. Mayer, G. P. Johari, Biophys. J. 66, 249 (1994). https://doi.org/10.1016/S0006-3495(94)80774-X , Google ScholarCrossref, CAS3. I. M. Hodge, Biophys. J. 91, 993 (2006). https://doi.org/10.1529/biophysj.106.080796 , Google ScholarCrossref, CAS4. J. L. Green, J. Fan, C. A. Angell, J. Phys. Chem. 98, 13780 (1994). https://doi.org/10.1021/j100102a052 , Google ScholarCrossref, CAS5. C. A. Angell, Science 267, 1924 (1995). https://doi.org/10.1126/science.267.5206.1924 , Google ScholarCrossref, ISI, CAS© 2008 American Institute of Physics.

Intermolecular Forces and the Glass Transition

Random first-order transition theory is used to determine the role of attractive and repulsive interactions in the dynamics of supercooled liquids. Self-consistent phonon theory, an approximate mean field treatment consistent with random first-order transition theory, is used to treat individual glassy configurations, whereas the liquid phase is treated using common liquid-state approximations. Free energies are calculated using liquid-state perturbation theory. The transition temperature, T*A, the temperature where the onset of activated behavior is predicted by mean field theory; the lower crossover temperature, T*C, where barrierless motions actually occur through fractal or stringy motions (corresponding to the phenomenological mode coupling transition temperature); and T*K, the Kauzmann temperature (corresponding to an extrapolated entropy crisis), are calculated in addition to T*g, the glass transition temperature that corresponds to laboratory cooling rates. Relationships between these quantities agree well with existing experimental and simulation data on van der Waals liquids. Both the isobaric and isochoric behavior in the supercooled regime are studied, providing results for DeltaCV and DeltaCp that can be used to calculate the fragility as a function of density and pressure, respectively. The predicted variations in the alpha-relaxation time with temperature and density conform to the empirical density-temperature scaling relations found by Casalini and Roland. We thereby demonstrate the microscopic origin of their observations. Finally, the relationship first suggested by Sastry between the spinodal temperature and the Kauzmann temperatures, as a function of density, is examined. The present microscopic calculations support the existence of an intersection of these two temperatures at sufficiently low temperatures.

An equation for the description of volume and temperature dependences of the dynamics of supercooled liquids and polymer melts

A recently proposed expression to describe the temperature and volume dependences of the structural (or α-) relaxation time is discussed. This equation satisfies the scaling law for the relaxation times, τ ( T , V ) = I ( TV γ ) , where T is temperature, V the specific volume, and γ a material-dependent constant. The expression for the function I ( TV γ ) is shown to accurately fit experimental data for several glass-forming liquids and polymers over an extended range encompassing the dynamic crossover, providing a description of the dynamics with a minimal number of parameters. The results herein can be reconciled with previously found correlations of the isochoric fragility with both the isobaric fragility at atmospheric pressure and the scaling exponent γ.

Quantitative Link between Single-Particle Dynamics and Static Structure of Supercooled Liquids

ADVERTISEMENT RETURN TO ISSUEPREVAddition/CorrectionORIGINAL ARTICLEThis notice is a correctionQuantitative Link between Single-Particle Dynamics and Static Structure of Supercooled LiquidsJeetain Mittal, Jeffrey R. Errington, and Thomas M. TruskettCite this: J. Phys. Chem. B 2007, 111, 19, 5531Publication Date (Web):April 24, 2007Publication History Published online24 April 2007Published inissue 1 May 2007https://doi.org/10.1021/jp072284gCopyright © 2007 American Chemical SocietyRIGHTS & PERMISSIONSArticle Views227Altmetric-Citations2LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InReddit PDF (3 KB) Get e-Alerts Get e-Alerts

On the study of collective dynamics in supercooled liquids through the statistics of the isoconfigurational ensemble

The use of the isoconfigurational ensemble to explore structure-dynamic correlations in supercooled liquids is examined. The statistical error of the dynamic propensity and its spatial distribution are determined. The authors present the spatial distribution of the particle non-Gaussian parameter as a measure of the intermittency with which particles exhibit their propensity for motion. The ensemble average of the direction of particle motion is introduced to establish the anisotropy of the dynamic propensity.

Effect of entropy on the dynamics of supercooled liquids: new results from high pressure data

We show that for arbitrary thermodynamic conditions, master curves of the entropy are obtained by expressing S(T, V) as a function of TV γ G , where T is temperature, V specific volume and γG the thermodynamic Grüneisen parameter. A similar scaling is known for structural relaxation times, τ = ℑ (TV γ); however, we find γG < γ. We show herein that this inequality reflects contributions to S(T, V) from processes, such as vibrations and secondary relaxations, that do not directly influence the supercooled dynamics. An approximate method is proposed to remove these contributions, S 0, yielding the relationship τ = ℑ1(S − S 0).

Non-ergodicity in a locally ordered fragile glass former

We measure the dynamic structure factor of m-toluidine through inelastic X-ray scattering in the mesoscopic Q range between 1 and 10nm−1, where the static structure factor exhibits a prepeak resulting from a molecular spatial organization in nanometer size clusters, due to the formation of hydrogen bonds. We present experimental evidence of the square-root cusp in the temperature behavior of the non-ergodicity factor of m-toluidine which supports the view that the mode-coupling theory succeeds in describing the dynamics of supercooled molecular liquids, even for liquids with a local order, notwithstanding the cage formation is controlled by a mechanism different from the packing constraints typical of simple liquids. Moreover, we report on the behavior of the non-ergodicity factor in the low-temperature and wavevector regimes, finding a confirmation of the phenomenologic law proposed by Scopigno et al. [T. Scopigno, G. Ruocco, F. Sette, G. Monaco, Science 302 (2003) 849] which correlates the vibrational dynamics of the glass to the fragility of the supercooled liquid.

Depolarized light scattering versus optical Kerr effect spectroscopy of supercooled liquids: Comparative analysis

Recently, heterodyne-detected optical Kerr effect (HD-OKE) spectroscopy was used to study dynamics of supercooled molecular liquids. The studies revealed an apparently new physical phenomenon that had not been reported before from the related depolarized light scattering (DLS), namely, an intermediate power law (nearly logarithmic decay) of the response functions [H. Cang et al., J. Chem. Phys. 118, 2800 (2003)]. Conceptually, HD-OKE and DLS data reflect optical anisotropy fluctuations mainly due to molecular reorientation dynamics in time and frequency domains, respectively. The above-mentioned effects are revealed in the mesoscopic range less, similar1 GHz ( greater, similar100 ps), where no direct comparison of the techniques was reported. In this Communication, we attempt such a comparison of exemplifying HD-OKE literature data of the glass-forming salol (phenyl salicylate), benzophenone, and liquid-crystal forming 4-cyano-4(')-pentylbiphenyl with DLS data of the same systems that we measured down to ca. 200 MHz by a combined tandem Fabry-Perot interferometer plus tandem-grating-monochromator technique. Generally, we find a satisfactory agreement, albeit in some cases with subtle differences at frequencies greater, similar10 GHz. We conclude that, in the mesoscopic dynamic range, HD-OKE and DLS studies provide consistent and comparable information, and therefore their conclusions must agree. We argue that the intermediate power law of HD-OKE is in essence a manifestation of the excess wing of the corresponding frequency-domain data, known long since from broadband dielectric spectroscopy and anticipated from DLS studies of supercooled liquids.