Spatially Heterogeneous Dynamics in the Density Scaling Regime: Time and Length Scales of Molecular Dynamics near the Glass Transition

Role of anisotropy in understanding the molecular grounds for density scaling in dynamics of glass-forming liquids

Molecular Dynamics (MD) simulations of glass-forming liquids play a pivotal role in uncovering the molecular nature of the liquid vitrification process. In particular, much focus was given to elucidating the interplay between the character of intermolecular potential and molecular dynamics behaviour. This has been tried to achieve by simulating the spherical particles interacting via isotropic potential. However, when simulation and experimental data are analysed in the same way by using the density scaling approaches, serious inconsistency is revealed between them. Similar scaling exponent values are determined by analysing the relaxation times and pVT data obtained from computer simulations. In contrast, these values differ significantly when the same analysis is carried out in the case of experimental data. As discussed thoroughly herein, the coherence between results of simulation and experiment can be achieved if anisotropy of intermolecular interactions is introduced to MD simulations. In practice, it has been realized in two different ways: (1) by using the anisotropic potential of the Gay-Berne type or (2) by replacing the spherical particles with quasi-real polyatomic anisotropic molecules interacting through isotropic Lenard-Jones potential. In particular, the last strategy has the potential to be used to explore the relationship between molecular architecture and molecular dynamics behaviour. Finally, we hope that the results presented in this review will also encourage others to explore how 'anisotropy' affects remaining aspects related to liquid-glass transition, like heterogeneity, glass transition temperature, glass forming ability, etc.

Entropy Scaling of Molecular Dynamics in a Prototypical Anisotropic Model near the Glass Transition

Dynamics and thermodynamics of molecular systems in the vicinity of the boundary between thermodynamically nonequilibrium glassy and metastable supercooled liquid states are still incompletely explored and their theoretical and simulation models are imperfect despite many previous efforts. Among them, the role of total system entropy, configurational entropy, and excess entropy in the temperature-pressure or temperature-density dependence of global molecular dynamics (MD) timescale relevant to the glass transition is an essential topic intensively studied for over half of a century. By exploiting a well-known simple ellipsoidal model recently successfully applied to simulate the supercooled liquid state and the glass transition, we gain a new insight into the different views on the relationship between entropy and relaxation dynamics of glass formers, showing the molecular grounds for the entropy scaling of global MD timescale. Our simulations in the anisotropic model of supercooled liquid, which involves only translational and rotational degrees of freedom, give evidence that the total system entropy is sufficient to scale global MD timescale. It complies with the scaling effect on relaxation dynamics exerted by the configurational entropy defined as the total entropy diminished by vibrational contributions, which was earlier discovered for measurement data collected near the glass transition. Moreover, we argue that such a scaling behavior is not possible to achieve by using the excess entropy that is in excess of the ideal gas entropy, which is contrary to the results earlier suggested within the framework of simple isotropic models of supercooled liquids. Thus, our findings also warn against an excessive reliance on isotropic models in theoretical interpretations of molecular phenomena, despite their simplicity and popularity, because they may reflect improperly various physicochemical properties of glass formers.

Density Scaling of Translational and Rotational Molecular Dynamics in a Simple Ellipsoidal Model near the Glass Transition

In this paper, we show that a simple anisotropic model of supercooled liquid properly reflects some density scaling properties observed for experimental data, contrary to many previous results obtained from isotropic models. We employ a well-known Gay–Berne model earlier parametrized to achieve a supercooling and glass transition at zero pressure to find the point of glass transition and explore volumetric and dynamic properties in the supercooled liquid state at elevated pressure. We focus on dynamic scaling properties of the anisotropic model of supercooled liquid to gain a better insight into the grounds for the density scaling idea that bears hallmarks of universality, as follows from plenty of experimental data collected near the glass transition for different dynamic quantities. As a result, the most appropriate values of the scaling exponent γ are established as invariants for a given anisotropy aspect ratio to successfully scale both the translational and rotational relaxation times considered as single variable functions of density^γ/temperature. These scaling exponent values are determined based on the density scaling criterion and differ from those obtained in other ways, such as the virial–potential energy correlation and the equation of state derived from the effective short-range intermolecular potential, which is qualitatively in accordance with the results yielded from experimental data analyses. Our findings strongly suggest that there is a deep need to employ anisotropic models in the study of glass transition and supercooled liquids instead of the isotropic ones very commonly exploited in molecular dynamics simulations of supercooled liquids over the last decades.

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.

Revealing the Link between Structural Relaxation and Dynamic Heterogeneity in Glass-Forming Liquids

Despite the use of glasses for thousands of years, the nature of the glass transition is still mysterious. On approaching the glass transition, the growth of dynamic heterogeneity has long been thought to play a key role in explaining the abrupt slowdown of structural relaxation. However, it still remains elusive whether there is an underlying link between structural relaxation and dynamic heterogeneity. Here, we unravel the link by introducing a characteristic time scale hiding behind an identical dynamic heterogeneity for various model glass-forming liquids. We find that the time scale corresponds to the kinetic fragility of liquids. Moreover, it leads to scaling collapse of both the structural relaxation time and dynamic heterogeneity for all liquids studied, together with a characteristic temperature associated with the same dynamic heterogeneity. Our findings imply that studying the glass transition from the viewpoint of dynamic heterogeneity is more informative than expected.

Cage Size and Jump Precursors in Glass-Forming Liquids: Experiment and Simulations

Glassy dynamics is intermittent, as particles suddenly jump out of the cage formed by their neighbors, and heterogeneous, as these jumps are not uniformly distributed across the system. Relating these features of the dynamics to the diverse local environments explored by the particles is essential to rationalize the relaxation process. Here we investigate this issue characterizing the local environment of a particle with the amplitude of its short time vibrational motion, as determined by segmenting in cages and jumps the particle trajectories. Both simulations of supercooled liquids and experiments on colloidal suspensions show that particles in large cages are likely to jump after a small time-lag, and that, on average, the cage enlarges shortly before the particle jumps. At large time-lags, the cage has essentially a constant size, which is smaller for longer-lasting cages. Finally, we clarify how this coupling between cage size and duration controls the average behavior and opens the way to a better understanding of the relaxation process in glass-forming liquids.

Ionic liquids and their bases: Striking differences in the dynamic heterogeneity near the glass transition

Ionic liquids (ILs) constitute an active field of research due to their important applications. A challenge for these investigations is to explore properties of ILs near the glass transition temperature Tg, which still require our better understanding. To shed a new light on the issues, we measured ILs and their base counterparts using the temperature modulated calorimetry. We performed a comparative analysis of the dynamic heterogeneity at Tg for bases and their salts with a simple monoatomic anion (Cl(-)). Each pair of ionic and non-ionic liquids is characterized by nearly the same chemical structure but their intermolecular interactions are completely different. We found that the size of the dynamic heterogeneity of ILs near Tg is considerably smaller than that established for their dipolar counterparts. Further results obtained for several other ILs near Tg additionally strengthen the conclusion about the relatively small size of the dynamic heterogeneity of molecular systems dominated by electrostatic interactions. Our finding opens up new perspectives on designing different material properties depending on intermolecular interaction types.

Role of entropy in the thermodynamic evolution of the time scale of molecular dynamics near the glass transition

In this paper, we investigate how changes in the system entropy influence the characteristic time scale of the system molecular dynamics near the glass transition. Independently of any model of thermodynamic evolution of the time scale, against some previous suppositions, we show that the system entropy S is not sufficient to govern the time scale defined by structural relaxation time τ. In the density scaling regime, we argue that the decoupling between τ and S is a consequence of different values of the scaling exponents γ and γ(S) in the density scaling laws, τ=f(ρ(γ)/T) and S=h(ρ(γ(S))/T), where ρ and T denote density and temperature, respectively. It implies that the proper relation between τ and S requires supplementing with a density factor, u(ρ), i.e., τ=g(u(ρ)w(S)). This meaningful finding additionally demonstrates that the density scaling idea can be successfully used to separate physically relevant contributions to the time scale of molecular dynamics near the glass transition. The relation reported by us between τ and S constitutes a general pattern based on nonconfigurational quantities for describing the thermodynamic evolution of the characteristic time scale of molecular dynamics near the glass transition in the density scaling regime, which is a promising alternative to the approaches based as the Adam-Gibbs model on the configurational entropy that is difficult to evaluate in the entire thermodynamic space. As an example, we revise the Avramov entropic model of the dependence τ(T,ρ), giving evidence that its entropic basis has to be extended by the density dependence of the maximal energy barrier for structural relaxation. We also discuss the excess entropy S(ex), the density scaling of which is found to mimic the density scaling of the total system entropy S.

Variation of the dynamic susceptibility along an isochrone

Koperwas et al. showed in a recent paper [Phys. Rev. Lett. 111, 125701 (2013)] that the dynamic susceptibility χ4 as estimated by dielectric measurements for certain glass-forming liquids decreases substantially with increasing pressure along a curve of constant relaxation time. This observation is at odds with other measures of dynamics being invariant and seems to pose a problem for theories of glass formation. We show that this variation is in fact consistent with predictions for liquids with hidden scale invariance: Measures of dynamics at constant volume are invariant along isochrones, called isomorphs in such liquids, but contributions to fluctuations from long-wavelength fluctuations can vary. This is related to the known noninvariance of the isothermal bulk modulus. Considering the version of χ4 defined for the NVT ensemble, data from simulations of a binary Lennard-Jones liquid show in fact a slight increase with increasing density. This is a true departure from the formal invariance expected for this quantity.

Hidden scale invariance in condensed matter

Recent developments show that many liquids and solids have an approximate "hidden" scale invariance that implies the existence of lines in the thermodynamic phase diagram, so-called isomorphs, along which structure and dynamics in properly reduced units are invariant to a good approximation. This means that the phase diagram becomes effectively one-dimensional with regard to several physical properties. Liquids and solids with isomorphs include most or all van der Waals bonded systems and metals, as well as weakly ionic or dipolar systems. On the other hand, systems with directional bonding (hydrogen bonds or covalent bonds) or strong Coulomb forces generally do not exhibit hidden scale invariance. The article reviews the theory behind this picture of condensed matter and the evidence for it coming from computer simulations and experiments.