Consequences of an Equation of State in the Thermodynamic Scaling Regime

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.

The behavior of conductivity dynamic modulus and its connection to thermodynamic bulk modulus in ionic liquids

In this paper, we investigate the interplay between the dynamics and thermodynamics of aprotic ionic liquids in the supercooled and normal liquid states. For this purpose, the conductivity dynamic modulus Mσp-T, being defined as the ratio of activation energy (Ep) and activation volume (VT), and its relation to bulk modulus BT under isobaric and isothermal conditions is examined. We found that both isobaric cooling and isothermal compression lead to an increase in Mσp-T. Specifically, Mσp-T(P)T rises linearly similar to BT. Consequently, a direct linear relationship between Mσp-T(P)T and BT is established under isothermal conditions.

The effect of molecular architecture on the physical properties of supercooled liquids studied by MD simulations: Density scaling and its relation to the equation of state

Theoretical concepts in condensed matter physics are typically verified and also developed by exploiting computer simulations mostly in simple models. Predictions based on these usually isotropic models are often at odds with measurement results obtained for real materials. One of the examples is an intriguing problem within the density scaling idea that has attracted attention in recent decades due to its hallmarks of universality, i.e., the fact that the difference between the density scaling exponent and the exponent of the equation of state is observed for real materials, whereas it has not been reported for the model system. In this paper, we use new model molecules of simple but anisotropic architecture to study the effect of molecular anisotropy on the dynamic and thermodynamic properties of the system. We identify the applicable range of intermolecular interactions for a given physical process, and then we explain the reason for observed differences between the behavior of the model and real systems. It demonstrates that the new model systems open broad perspectives for simulation and theoretical research, for example, into unifying concepts in the glass transition physics.

In search of invariants for viscous liquids in the density scaling regime: investigations of dynamic and thermodynamic moduli

In this paper, we report the nontrivial results of our investigations of dynamic and thermodynamic moduli in search of invariants for viscous liquids in the density scaling regime by using selected supercooled van der Waals liquids as representative materials. Previously, the dynamic modulus M_p-T (defined in the pressure-temperature representation by the ratio of isobaric activation energy and activation volume) as well as the ratio B_T/M_p-T (where B_T is the thermodynamic modulus defined as the inverse isothermal compressibility) have been suggested as some kinds of material constants. We have established that they are not valid in the explored wide range of temperatures T over a dozen decades of structural relaxation times τ. The temperature dependences of M_p-T and B_T/M_p-T have been elucidated by comparison with the well-known measure of the relative contribution of temperature and density fluctuations to molecular dynamics near the glass transition, i.e., the ratio of isochoric and isobaric activation energies. Then, we have implemented an idea to transform the definition of the dynamic modulus M_p-T from the p-T representation to the V-T one. This idea relied on the disentanglement of combined temperature and density fluctuations involved in isobaric parameters and has resulted in finding an invariant for viscous liquids in the density scaling regime, which is the ratio of thermodynamic and dynamic moduli, B_T/M_V-T. In this way, we have constituted a characteristic of thermodynamics and molecular dynamics, which remains unchanged in the supercooled liquid state for a given material, the molecular dynamics of which obeys the power density scaling law.

Activation volume of selected liquid crystals in the density scaling regime

In this paper, we demonstrate and thoroughly analyze the activation volumetric properties of selected liquid crystals in the nematic and crystalline E phases in comparison with those reported for glass-forming liquids. In the analysis, we have employed and evaluated two entropic models (based on either total or configurational entropies) to describe the longitudinal relaxation times of the liquid crystals in the density scaling regime. In this study, we have also exploited two equations of state: volumetric and activation volumetric ones. As a result, we have established that the activation volumetric properties of the selected liquid crystals are quite opposite to such typical properties of glass-forming materials, i.e., the activation volume decreases and the isothermal bulk modulus increases when a liquid crystal is isothermally compressed. Using the model based on the configurational entropy, we suggest that the increasing pressure dependences of the activation volume in isothermal conditions and the negative curvature of the pressure dependences of isothermal longitudinal relaxation times can be related to the formation of antiparallel doublets in the examined liquid crystals. A similar pressure effect on relaxation dynamics may be also observed for other material groups in case of systems, the molecules of which form some supramolecular structures.

Recent developments in the experimental investigations of relaxations in pharmaceuticals by dielectric techniques at ambient and elevated pressure

In recent years, there is a growing interest in improving the physicochemical stability of amorphous pharmaceutical solids due to their very promising applications to manufacture medicines characterized by a better water solubility, and consequently by a higher dissolution rate than those of their crystalline counterparts. In this review article, we show that the molecular mobility investigated both in the supercooled liquid and glassy states is the crucial factor required to understand molecular mechanisms that govern the physical stability of amorphous drugs. We demonstrate that pharmaceuticals can be thoroughly examined by means of the broadband dielectric spectroscopy, which is a very useful experimental technique to explore different relaxation processes and crystallization kinetics as well. Such studies conducted in the wide temperature and pressure ranges provide data needed in searching correlations between properties of molecular dynamics and crystallization process, which are aimed at developing effective and efficient methods for stabilizing amorphous drugs.

Adam-Gibbs model in the density scaling regime and its implications for the configurational entropy scaling

To solve a long-standing problem of condensed matter physics with determining a proper description of the thermodynamic evolution of the time scale of molecular dynamics near the glass transition, we have extended the well-known Adam-Gibbs model to describe the temperature-volume dependence of structural relaxation times, τ_α(T, V). We also employ the thermodynamic scaling idea reflected in the density scaling power law, τ_α = f(T⁻¹V^−γ), recently acknowledged as a valid unifying concept in the glass transition physics, to differentiate between physically relevant and irrelevant attempts at formulating the temperature-volume representations of the Adam-Gibbs model. As a consequence, we determine a straightforward relation between the structural relaxation time τ_α and the configurational entropy S_C, giving evidence that also S_C(T, V) = g(T⁻¹V^−γ) with the exponent γ that enables to scale τ_α(T, V). This important findings have meaningful implications for the connection between thermodynamics and molecular dynamics near the glass transition, because it implies that τ_α can be scaled with S_C.

Can the scaling behavior of electric conductivity be used to probe the self-organizational changes in solution with respect to the ionic liquid structure? The case of [C8MIM][NTf2]

Electrical conductivity of the supercooled ionic liquid [C8MIM][NTf2], determined as a function of temperature and pressure, highlights strong differences in its ionic transport behavior between low and high temperature regions. To date, the crossover effect which is very well known for low molecular van der Waals liquids has been rarely described for classical ionic liquids. This finding highlights that the thermal fluctuations could be dominant mechanisms driving the dramatic slowing down of ion motions near Tg. An alternative way to analyze separately low and high temperature dc-conductivity data using a density scaling approach was then proposed. Based on which a common value of the scaling exponent γ = 2.4 was obtained, indicating that the applied density scaling is insensitive to the crossover effect. By comparing the scaling exponent γ reported herein along with literature data for other ionic liquids, it appears that γ decreases by increasing the alkyl chain length on the 1-alkyl-3-methylimidazolium-based ionic liquids. This observation may be related to changes in the interaction between ions in solution driven by an increase in the van der Waals type interaction by increasing the alkyl chain length on the cation. This effect may be related to changes in the ionic liquid nanostructural organization with the alkyl chain length on the cation as previously reported in the literature based on molecular dynamic simulations. In other words, the calculated scaling exponent γ may be then used as a key parameter to probe the interaction and/or self-organizational changes in solution with respect to the ionic liquid structure.

Recent progress on dielectric properties of protic ionic liquids

Protic ionic liquids (PILs) are key materials for a wide range of emerging technologies. In particular, these systems have long been envisioned as promising candidates for fuel cells. Therefore, in recent years special attention has been devoted to thorough studies of these compounds. Amongst others, dielectric properties of PILs at ambient and elevated pressure have become the subject of intense research. The reason for this lies in the role of broadband dielectric spectroscopy in recognizing the conductivity mechanism in protic ionic systems. In this paper, we summarize the dielectric results of various PILs reflecting recent advances in this field.

The complex, non-monotonic thermal response of the volumetric space of simple liquids

We show that a non-monotonic solution of the equation ∂α_p(p,T)/∂T = 0 divides the phase diagram of simple liquids into two parts.

Scaling of volumetric data in model systems based on the Lennard-Jones potential

The crucial problem for better understanding the nature of glass transition and related relaxation phenomena is to find proper interrelations between the molecular dynamics and thermodynamics of viscous systems. To make progress towards this goal the recently observed density scaling of viscous liquid dynamics has been very intensively and successfully studied in the past few years. However, previous attempts at related scaling of volumetric data yielded results inconsistent with those found from the density scaling of molecular dynamics. In this paper, we show that volumetric data obtained from simulations in simple molecular models based on the Lennard-Jones (LJ) potential, such as the Kob-Andersen binary LJ liquid, its repulsive inverse power-law version, and the Lewis-Wahnström o-terphenyl model, can be scaled by using the same value of the exponent, which scales dynamic quantities and is directly related to the exponent of the repulsive inverse power law that underlies short-range approximations of the LJ potential.

Density scaling in viscous systems near the glass transition

In this paper, a general equation of state (EOS) valid for fluids in the vicinity of the glass transition is derived on the basis of its isothermal precursor. This EOS is able to predict the density scaling of both isobaric and isothermal PVT data and it explicitly involves the scaling exponent γ(EOS), which is most likely straightforwardly related to the exponent of the inverse power law of some effective potential valid for viscous systems. This EOS and the density scaling are very successfully tested for representatives of several material classes (van der Waals liquids, polymer melts, ionic liquids, and even strongly hydrogen-bonded systems). Additionally, if the thermodynamic scaling of primary relaxation times can be achieved with the scaling exponent γ for a given material, then the value γ(EOS) found from fitting its PVT data to the EOS enables us to evaluate the value γ, which is always considerably smaller than γ(EOS).

Comment on "Density scaling of the diffusion coefficient at various pressures in viscous liquids"

The thermodynamic scaling idea enables an elegant description of relaxation dynamics near the glass transition and provides a linkage between thermodynamics and molecular dynamics of supercooled liquids. A lot of effort has been put into finding functions, f(T(-1)V(-γ)), which can scale dynamical quantities such as relaxation time, viscosity, and diffusion coefficient. Within the trend, Papathanassiou [A. N. Papathanassiou, Phys. Rev. E 79, 032501 (2009)] has recently derived a new scaling function for the reduced diffusion coefficient. In this Comment, we report that this scaling function is not sufficiently grounded, because it is based on some scaled equation of state which predicts significantly different values of the scaling exponent γ from volumetric data in comparison with those found from the scaling of relaxation or viscosity data. Moreover, we would like to point out that any scaling function f cannot be straightforwardly formulated on the basis of any equation of state which yields the scaling exponent γ different from that used to scale the dynamic quantity.

Hidden scale invariance in molecular van der Waals liquids: a simulation study

Results from molecular dynamics simulations of two viscous molecular model liquids--the Lewis-Wahnström model of orthoterphenyl and an asymmetric dumbbell model--are reported. We demonstrate that the liquids have a "hidden" approximate scale invariance: equilibrium potential energy fluctuations are accurately described by inverse power-law (IPL) potentials, the radial distribution functions are accurately reproduced by the IPL's, and the radial distribution functions obey the IPL predicted scaling properties to a good approximation. IPL scaling of the dynamics also applies--with the scaling exponent predicted by the equilibrium fluctuations. In contrast, the equation of state does not obey the IPL scaling. We argue that our results are general for van der Waals liquids, but do not apply, e.g., for hydrogen-bonded liquids.