Dynamics Of Glass-forming Liquids Research Articles

Determination of self and cross contributions to the dipole–dipole correlations function from analysis of dielectric measurements

The nonexponential nature of the structural relaxation is one of the most characteristic features of the molecular dynamics in glass-forming liquids. Various experimental techniques can be employed to probe this process; however, broadband dielectric spectroscopy (BDS) is the most frequently used. Based on MD simulations, we provide strong evidence of bi-modal nature of the dielectric loss peak of primary relaxation. Further, we point out that the primary dielectric relaxation process measured at constant displacement D is dominated by the self-correlation term in the dipole–dipole correlation function. In practice, it means that the dielectric spectra should be presented in the dielectric modulus representations to disclose the spectral features of the self mode.

Elasticity, Facilitation, and Dynamic Heterogeneity in Glass-Forming Liquids.

We study the role of elasticity-induced facilitation on the dynamics of glass-forming liquids by a coarse-grained two-dimensional model in which local relaxation events, taking place by thermal activation, can trigger new relaxations by long-range elastically mediated interactions. By simulations and an analytical theory, we show that the model reproduces the main salient facts associated with dynamic heterogeneity and offers a mechanism to explain the emergence of dynamical correlations at the glass transition. We also discuss how it can be generalized and combined with current theories.

Theory of the Effects of Specific Attractions and Chain Connectivity on the Activated Dynamics and Selective Transport of Penetrants in Polymer Melts

We generalize and apply a microscopic force level statistical mechanical theory of activated spherical penetrant dynamics in glass-forming liquids to study the influence of semiflexible polymer connectivity and penetrant–polymer attractive interactions on the penetrant hopping rate. The detailed manner that attractions of highly variable strength and spatial range modify the penetrant size and polymer melt density (from the rubbery state to slightly beyond the kinetic glass transition) dependences of penetrant activation barriers is established. Of special interest are possible nonadditive consequences of physical bonding and steric caging, the degree of coupling of penetrant hopping and the Kuhn segment scale alpha relaxation process, the relative importance of local caging and long-range matrix collective elasticity as a function of penetrant size, and implications for optimizing transport selectivity. With increasing attraction strength, the repulsive caging-restriction effect on penetrant mobility is predicted to grow, in contrast to the effect of the equilibrium penetrant–matrix solvation shell size, which decreases. The former dynamical effect results in a significant enhancement of the importance of the local cage barrier, while the latter effect results in a decrease of the importance of the nonlocal collective elastic barrier. These two competing effects have a very strong influence on selective penetrant transport for different sized penetrants: selectivity varies nonmonotonically with attraction strength in the deeply supercooled state but decreases monotonically in the rubbery state and at fixed attraction strength, exhibits a nonmonotonic variation with the matrix packing fraction. By comparing results based on modeling the matrix as semiflexible polymer chains with analogous calculations using the same dynamical theory but for a disconnected hard sphere matrix, the effect of chain connectivity is revealed and found to have quantitative, but not qualitative, consequences on penetrant-activated dynamics.

Effect of structure on molecular dynamics in glass-forming liquids. The case of aromaticity

An ultimate aim of researchers is to predict the properties of matter based on the molecular structure. However, despite many efforts, this goal is still far from being achieved. Herein, using an example of two compounds differing from each other only in the type of six-carbon ring, i.e., benzene vs. cyclohexane, we show how aromaticity affects the relaxation dynamics behavior of supercooled liquid and glass. By performing the experiments at ambient and elevated pressure, we recognized which dynamic and thermodynamic quantities are sensitive to such a difference in structure and which are not.

A Dynamically Correlated Network Model for the Collective Dynamics in Glass-Forming Molecular Liquids and Polymers.

The non-Arrhenius behavior of segmental dynamics in glass-forming liquids is one of the most profound mysteries in soft matter physics. In this article, we propose a dynamically correlated network (DCN) model to understand the growing behavior of dynamically correlated regions during cooling, which leads to the viscous slowdown of supercooled liquids. The fundamental concept of the model is that the cooperative region of collective motions has a network structure that consists of string-like parts, and networks of various sizes interpenetrate each other. Each segment undergoes dynamical coupling with its neighboring segments via a finite binding energy. Monte Carlo simulations showed that the fractal dimension of the DCNs generated at different temperatures increased and their size distribution became broader with decreasing temperature. The segmental relaxation time was evaluated based on a power law with four different exponents for the activation energy of rearrangement with respect to the DCN size. The results of the present DCN model are consistent with the experimental results for various materials of molecular and polymeric liquids.

Uncovering the mechanism of dynamics in metallic glass-forming liquids based on local symmetry entropy

Molecular dynamics simulations were performed to investigate the relationship of structure-dynamics in metallic glass-forming liquids. Fundamentally, it is found the degree of local symmetry plays an important role in the dynamics of glass-forming liquids. The local symmetry entropy is proposed and used for quantifying the degree of local symmetry. Local symmetry entropy is related to the rearrangements of a cage and translational diffusion. Particularly, the diffusion coefficient of metallic glass-forming liquids can be described by a local symmetry entropy scaling. Further exploration shows local symmetry entropy has a well linear correlation with two-pair entropy, suggesting that the decrease of symmetry entropy can contribute to the decrease of thermodynamic entropy in undercooled liquids in the cooling process.

A theory of localized excitations in supercooled liquids.

A new connection between the structure and dynamics in glass-forming liquids is presented. We show how the origin of spatially localized excitations, as defined by the dynamical facilitation (DF) theory, can be understood from a structure-based framework. This framework is constructed by associating excitation events in the DF theory to hopping events between energy minima in the potential energy landscape (PEL). By reducing the PEL to an equal energy well picture and applying a harmonic approximation, we develop a field theory to describe elastic fluctuations about inherent states, which are energy minimizing configurations of the PEL. We model an excitation as a shear transformation zone (STZ) inducing a localized pure shear deformation onto an inherent state. We connect STZs to T1 transition events that break the elastic bonds holding the local structure of an inherent state. A formula for the excitation energy barrier, denoted as Jσ, is obtained as a function of inherent-state elastic moduli and the radial distribution function. The energy barrier from the current theory is compared to the one predicted by the DF theory where good agreement is found in various two-dimensional continuous poly-disperse atomistic models of glass formers. These results strengthen the role of structure and elasticity in driving glassy dynamics through the creation and relaxation of localized excitations.

MD simulations of charged binary mixtures reveal a generic relation between high- and low-temperature behavior.

Experimental studies of the glassy slowdown in molecular liquids indicate that the high-temperature activation energy E∞ of glass-forming liquids is directly related to their glass transition temperature Tg. To further investigate such a possible relation between high- and low-temperature dynamics in glass-forming liquids, we analyze the glassy dynamics of binary mixtures using molecular dynamics simulations. We consider a binary mixture of charged Lennard-Jones particles and vary the partial charges of the particles and, thus, the high-temperature activation energy and the glass transition temperature of the system. Based on previous results, we introduce a phenomenological model describing relaxation times over the whole temperature regime from high temperatures to temperatures well inside the supercooled regime. By investigating the dynamics of both particle species on molecular and diffusive length scales along isochoric and isobaric pathways, we find a quadratic charge dependence of both E∞ and Tg, resulting in an approximately constant ratio of both quantities independent of the underlying observable, the thermodynamic ensemble, and the particle species, and this result is robust against the actual definition of Tg. This generic relation between the activation energy and the glass transition temperature indicates that high-temperature dynamics and the glassy slowdown are related phenomena, and the knowledge of E∞ may allow us to approximately predict Tg.

Activated penetrant dynamics in glass forming liquids: size effects, decoupling, slaving, collective elasticity and correlation with matrix compressibility.

We employ the microscopic self-consistent cooperative hopping theory of penetrant activated dynamics in glass forming viscous liquids and colloidal suspensions to address new questions over a wide range of high matrix packing fractions and penetrant-to-matrix particle size ratios. The focus is on the mean activated relaxation time of smaller tracers in a hard sphere fluid of larger particle matrices. This quantity also determines the penetrant diffusion constant and connects directly with the structural relaxation time probed in an incoherent dynamic structure factor measurement. The timescale of the non-activated fast dissipative process is also studied and is predicted to follow power laws with the contact value of the penetrant-matrix pair correlation function and the penetrant-matrix size ratio. For long time penetrant relaxation, in the relatively lower packing fraction metastable regime the local cage barriers are dominant and matrix collective elasticity effects unimportant. As packing fraction and/or penetrant size grows, much higher barriers emerge and the collective elasticity associated with the correlated matrix dynamic displacement that facilitates penetrant hopping becomes important. This results in a non-monotonic variation with packing fraction of the degree of decoupling between the matrix and penetrant alpha relaxation times. The conditions required for penetrant hopping to become slaved to the matrix alpha process are determined, which depend mainly on the penetrant to matrix particle size ratio. By analyzing the absolute and relative importance of the cage and elastic barriers we establish a mechanistic understanding of the origin of the predicted exponential growth of the penetrant hopping time with size ratio predicted at very high packing fractions. A dynamics-thermodynamics power law connection between the penetrant activation barrier and the matrix dimensionless compressibility is established as a prediction of theory, with different scaling exponents depending on whether matrix collective elasticity effects are important. Quantitative comparisons with simulations of the penetrant relaxation time, diffusion constant, and transient localization length of tracers in dense colloidal suspensions and cold viscous liquids reveal good agreements. Multiple new predictions are made that are testable via future experiments and simulations. Extension of the theoretical approach to more complex systems of high experimental interest (nonspherical molecules, semiflexible polymers, crosslinked networks) interacting via variable hard or soft repulsions and/or short range attractions is possible, including under external deformation.

Construction of a quantitative relation between structural relaxation and dynamic heterogeneity by vibrational dynamics in glass-forming liquids and polymers.

The structural relaxation slows down drastically upon approaching the glass transition, accompanied by the significant growth of dynamic heterogeneity. The fundamental question of elusiveness and interest is whether there exists an underlying quantitative relationship between structural relaxation and dynamic heterogeneity. Here, we reveal that b̃ which is related to the reduced mean square displacements to overcome the energy barriers of activated jumps, instead of the kinetic fragility m, is the genuine key parameter connecting dynamic heterogeneity with structural relaxation for varying types of glass formers. Furthermore, based on the dependence of dynamic heterogeneity on the Debye-Waller factor we obtained a direct quantitative relation between dynamic heterogeneity and structural relaxation is built for different glass-forming liquids. More importantly, a scaling collapse of structural relaxation and dynamic heterogeneity is achieved by the important parameter b̃. These results are of fundamental and critical importance for developing a unified theory of glassy dynamics.

Forecasting the experimental glass transition from short time relaxation data

While molecular simulations have contributed to the modern understanding of the glass transition, they are constrained in prediction of experimental glass temperatures Tg because they are limited to times far shorter than those associated with experimental glass formation. Here, we bridge this gap via a model-based forecasting approach. We assess models of the temperature dependence of dynamics in glass forming liquids based upon the rate at which their prediction of Tg and fragility converge upon incorporating increasingly long timescale data. We find that the Cooperative Model of Schmidtke et al. typically provides the best predictions, ultimately enabling good Tg predictions from all-atom simulations of a range of polymers. Together with a protocol for efficient simulation of dynamics in glass-forming liquids, this strategy enables high-throughput computational screening of the glass transition. The success of the Cooperative Model in predicting low temperature behavior adds support to the two-barrier scenario underlying this model.

Role of Attractive Interactions in Structure Ordering and Dynamics of Glass-Forming Liquids

A key question in glass physics is what the origin of slow glassy dynamics is. The liquid structure is a natural candidate; however, an apparently severe counterexample has been known. Two model glass-forming liquids, with the standard Lennard-Jones interaction potential and its Weeks-Chandler-Andersen variation without the attractive tail, exhibit very similar structures at the two-body level but drastically different dynamical behaviors in the supercooled states. Here we look at the liquid structure through a (many-body) structural order parameter Θ characterizing the packing capability of local particle arrangements. We show that the structures of these two systems seen by Θ are actually very different at a many-body level, but, quite surprisingly, the macroscopic structure (Θ)-dynamics (τ_{α}) relationships commonly follow a Vogel-Fulcher-Tammann-like function. Furthermore, the mutual information analysis reveals strong local structure-dynamics correlations. Therefore, we conclude that attractive interactions affect the liquid structure in a nonperturbative manner, but a general structural origin of slow dynamics holds for these systems.

On Measuring the Characteristic Length of the Cooperative Molecular Dynamics in the Glass-Forming Liquids

An analysis of the methods for measuring the characteristic length of the cooperative molecular dynamics in glass-forming liquids is submitted. The equations and methods for measuring the size of the cooperatively rearranging regions in post Adam-Gibbs theories are compered, and it is proved that they give one and the same number, but with different interpretation for the relaxed molecular units. The interpretation that the rearranging units defined by Wunderlich are smallest structural units, named beads, is supported by the predicted “universal” value for the cooperatively rearranging range at the glass-transition temperature, as well as from a precise modeling for the relaxations by the generalized entropy theory. It has been found that the characteristic length estimated by random first order transition theory, as well as by the “four-point” dynamic susceptibility method, measured as the number of the bead’s diameters coincide with the length of the cooperatively rearranging region in Adam-Gibbs theory extended at the molecular level.

Design rules for glass formation from model molecules designed by a neural-network-biased genetic algorithm.

The glass transition - an apparent amorphous solidification process - is a central feature of the physical properties of soft materials such as polymers and colloids. A key element of this phenomenon is the observation of a broad spectrum of deviations from an Arrhenius temperature of dynamics in glass-forming liquids, with the extent of deviation quantified by the "fragility" of glass formation. The underlying origin of "fragile" glass formation and its dependence on molecular structure remain major open questions in condensed matter physics and soft materials science. Here we employ molecular dynamics simulations, together with a neural-network-biased genetic algorithm, to design and study model rigid molecules spanning a broad range of fragilities of glass formation. Results indicate that fragility of glass formation can be controlled by tuning molecular asphericity, with extended molecules tending to exhibit low fragilities and compact molecules tending toward higher fragilities. The glass transition temperature itself, on the other hand, correlates well with high-temperature activation behavior and with density. These results point the way towards rational design of glass-forming liquids spanning a range of dynamical behavior, both via these physical insights and via future extensions of this evolutionary design strategy to real chemistries. Finally, we show that results compare well with predictions of the nonlinear Langevin theory of liquid dynamics, which is a precursor of the more recently developed elastically collective nonlinear Langevin equation theory of Mirigian and Schweizer, identifying this framework as a promising basis for molecular design of the glass transition.

Nonmonotonic dynamic correlations in quasi-two-dimensional confined glass-forming liquids.

It has been broadly accepted that the behavior of glass-forming liquids, where their relaxation dynamics exhibit a pronounced slowdown as they are cooled toward the glass transition temperature, is caused by the increase in one or more correlation lengths. However, the role of length scales in the dynamics of glass-forming liquids is not clearly established, and past simulation work that suggests a surprising nonmonotonic temperature evolution of spatial dynamical correlations near the mode-coupling crossover temperature has been both questioned and supported by subsequent work. Here, using molecular dynamics simulation, we also show a striking maximum in the dynamic length scale ξ_{c}^{dyn} at a given temperature, but the temperature of this maximum is found to shift as the size of the confined system increases. Furthermore, we find that such a maximum disappears for all geometry sizes considered when a rough wall is replaced with a smooth, hard wall, suggesting that the nature of the nonmonotonic temperature dependence of ξ_{c}^{dyn} does not reflect an intrinsic property of bulk liquids, but originates from wall effects. Our results provide new insights into the dynamics of glass-forming liquids, particularly for quasi-two-dimensional systems.

How Free Volume Does Influence the Dynamics of Glass Forming Liquids.

In this article we show that inverse free volume is a natural variable for analyzing relaxation data on glass-forming liquids, and that systems obey the general form, log(τ/τref) = (1/Vfree) × f(T), where f(T) is a function of temperature. We demonstrate for eight glass-forming liquids that when experimental relaxation times (log τ), captured over a broad pressure-volume-temperature (PVT) space, are plotted as a function of inverse free volume (1/Vfree), a fan-like set of straight line isotherms with T-dependent slopes ensues. The free volume is predicted independently of the dynamic results for each state point using PVT data and the Locally Correlated Lattice (LCL) equation of state. Taking f(T) ∝ 1/Tb, we show that, for each of the systems studied, only the single, system-dependent parameter, b, is required to collapse the fan of linear isotherms into a straight line. We conclude that log τ is a function of the combined variable, 1/(VfreeTb), and because it is linear, it allows us to write an explicit analytic expression for log τ that covers a broad PVT space.

Dynamics of glass-forming liquids. XX. Third harmonic experiments of non-linear dielectric effects versus a phenomenological model

We have re-measured the third harmonic non-linear dielectric response of supercooled glycerol using zero-bias sinusoidal electric fields, with the aim of comparing the resulting susceptibilities with a phenomenological model of non-linear dielectric responses. In the absence of known chemical effects in this liquid, the present model accounts for three sources of non-linear behavior: dielectric saturation, field induced entropy reduction, and energy absorption from the time dependent field. Using parameters obtained from static high field results, the present model reproduces the characteristic features observed in the third harmonic susceptibility spectra: a low frequency plateau originating from dielectric saturation and a peak positioned below the loss peak frequency whose amplitude increases with decreasing temperature. Semi-quantitative agreement is achieved between experiment and the present model, which does not involve spatial scales or dynamical correlations explicitly. By calculating the three contributions separately, the model reveals that the entropy effect is the main source of the “hump” feature of this third harmonic response.

Isochronal superposition and density scaling of the intermolecular dynamics in glass-forming liquids with varying hydrogen bonding propensity

We have tested the idea of thermodynamic scaling T−1ργ and isochronal superposition in glass-forming liquids with varying propensity to form hydrogen bonds.

Dynamics of glass-forming liquids. XIX. Rise and decay of field induced anisotropy in the non-linear regime.

For glycerol and three monohydroxy alcohols, we have measured the non-linear dielectric effects resulting from the application and removal of a high dc bias electric field. The field effects are detected by virtue of a small amplitude harmonic field, from which time resolved changes in the dielectric loss are derived. The changes in permittivity are dominated by modifications of the time constants (rather than amplitudes) which display two contributions: a heating-like decrease of relaxation times that originates from the time dependent field when the bias is switched on and off and a slowing down of the dynamics resulting from the field induced reduction of configurational entropy. As observed for the electro-optical Kerr effect, the rise of the entropy change is slower than its decay, a feature that we rationalize on the basis of the quadratic dependence of the entropy change on polarization. For glycerol, the observed steady state level of the field induced shift of the glass transition temperature (+84 mK) matches the expectation based on the entropy change and its impact on dynamics via the Adam-Gibbs relation (+88 mK). For the alcohols, these non-linear effects rise and decay on the time scales of the prominent dielectric Debye process, underscoring the relation of these features to polarization anisotropy, opposed to mechanical or enthalpy relaxation which are orders of magnitude faster in these systems. A model is discussed which captures the observed magnitudes as well as time dependences in a near quantitative fashion. It is demonstrated that the high bias field modifies the response of polarization to the ac field, including a temporary change in the low field susceptibility.

Dynamics of Glass Forming Liquids with Randomly Pinned Particles.

It is frequently assumed that in the limit of vanishing cooling rate, the glass transition phenomenon becomes a thermodynamic transition at a temperature TK. However, with any finite cooling rate, the system falls out of equilibrium at temperatures near Tg(>TK), implying that the very existence of the putative thermodynamic phase transition at TK can be questioned. Recent studies of systems with randomly pinned particles have hinted that the thermodynamic glass transition may be observed for liquids with randomly pinned particles. This expectation is based on the results of approximate calculations that suggest that the thermodynamic glass transition temperature increases with increasing concentration of pinned particles and it may be possible to equilibrate the system at temperatures near the increased transition temperature. We test the validity of this prediction through extensive molecular dynamics simulations of two model glass-forming liquids in the presence of random pinning. We find that extrapolated thermodynamic transition temperature TK does not show any sign of increasing with increasing pinning concentration. The main effect of pinning is found to be a rapid decrease in the kinetic fragility of the system with increasing pin concentration. Implications of these observations for current theories of the glass transition are discussed.