Determination of the thermodynamic scaling exponent for relaxation in liquids from static ambient-pressure quantities

Modeling the structure and relaxation in glycerol-silica nanocomposites

The relationship between the dynamics and structure of amorphous thin films and nanocomposites near their glass transition is an important problem in soft-matter physics. Here, we develop a simple theoretical approach to describe the density profile and the α-relaxation time of a glycerol-silica nanocomposite (S. Cheng et al., J. Chem. Phys., 2015, 143, 194704). We begin by applying the Derjaguin approximation, where we replace the curved surface of the particle with the planar one; thus, modeling the nanocomposite is reduced to that of a confined thin film. Subsequently, by employing the molecular dynamics (MD) simulation data of Cheng et al., we approximate the density profile of a supported liquid thin film as a stationary solution of a fourth-order partial differential equation (PDE). We then construct an appropriate density functional, from which the density profile emerges through the minimization of free energy. Our final assumption is that of a consistent, temperature-independent scaled density profile, ensuring that the free volume throughout the entire nanocomposite increases with temperature in a smooth, monotonic fashion. Considering the established relationship between glycerol relaxation time and temperature, we can employ Doolittle-type analysis ("naïve" free-volume model), to calculate the relaxation time based on temperature and film thickness. We then convert the film thickness into the interparticle distance and subsequently the filler volume fraction for the nanocomposites and compare our model predictions with experimental data, resulting in a good agreement. The proposed approach can be easily extended to other nanocomposite and film systems.

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.

Why Volume and Dynamics Decouple in Nanocomposite Matrices: Space that Cannot Be Accessed is Not Free

Polymer nanocomposites have important material applications and are an ongoing focus of many molecular level investigations, however, puzzling experimental results exist. For example, specific volumes for some polymer nanocomposite matrices are 2% to 4% higher than for the neat polymer; in a pure polymer melt this would correspond to a pressure change of 40 to 100 MPa, and a decrease in isothermal segmental relaxation times of 3 to 5 orders of magnitude. However, the nanocomposite segmental dynamics do not show any speed up. We can explain this apparent uncoupling of dynamics from specific volume, and the key is to consider the system expansivity, i.e., the temperature dependence of the volumetric data, together with the concept of limiting volume at close liquid packing. Using pressure, volume, temperature data as a path to both, we are able to predict the effect of nanoadditives on the accessible, i.e., free, space in the material, which is critical for facilitating molecular rearrangements in dense systems. Our analysis explains why an increase in specific volume in a material may not always lead to faster segmental dynamics.

The origin of the density scaling exponent for polyatomic molecules and the estimation of its value from the liquid structure

In this article, we unravel the problem of interpreting the density scaling exponent for the polyatomic molecules representing the real van der Waals liquids. Our studies show that the density scaling exponent is a weighted average of the exponents of the repulsive terms of all interatomic interactions that occur between molecules, where the potential energy of a given interaction represents its weight. It implies that potential energy is a key quantity required to calculate the density scaling exponent value for real molecules. Finally, we use the well-known method for potential energy estimation and show that the density scaling exponent could be successfully predicted from the liquid structure for fair representatives of the real systems.

Combined description of pressure-volume-temperature and dielectric relaxation of several polymeric and low-molecular-weight organic glass-formers using SL-TS2 approach

We apply our recently-developed mean-field "SL-TS2" (two-state Sanchez-Lacombe) model to simultaneously describe dielectric α-relaxation time, τ_α, and pressure-volume-temperature (PVT) data in four polymers (polystyrene, poly(methylmethacrylate), poly(vinyl acetate) and poly(cyclohexane methyl acrylate)) and four organic molecular glass formers (ortho-terphenyl, glycerol, PCB-62, and PDE). Previously, it has been shown that for all eight materials, the Casalini-Roland thermodynamical scaling, τ_α = f(Tvγsp) (where T is temperature and v_sp is specific volume) is satisfied (R. Casalini and C. M. Roland, Phys. Rev. E, 2004, 69(6), 62501). It has also been previously shown that the same scaling emerges naturally (for sufficiently low pressures) within the "SL-TS2" framework (V. V. Ginzburg, Soft Matter, 2021, 17, 9094-9106). Here, we fit the ambient pressure curves for the relaxation time and the specific volume as functions of temperature for the eight materials and observe a good agreement between theory and experiment. We then use the Casalini-Roland scaling to convert those results into "master curves", thus enabling predictions of relaxation times and specific volumes at elevated pressures. The proposed approach can be used to describe other glass-forming materials, both low-molecular-weight and polymeric.

Temperature Dependence of Structural Relaxation in Glass-Forming Liquids and Polymers

Understanding the microscopic mechanism of the transition of glass remains one of the most challenging topics in Condensed Matter Physics. What controls the sharp slowing down of molecular motion upon approaching the glass transition temperature Tg, whether there is an underlying thermodynamic transition at some finite temperature below Tg, what the role of cooperativity and heterogeneity are, and many other questions continue to be topics of active discussions. This review focuses on the mechanisms that control the steepness of the temperature dependence of structural relaxation (fragility) in glass-forming liquids. We present a brief overview of the basic theoretical models and their experimental tests, analyzing their predictions for fragility and emphasizing the successes and failures of the models. Special attention is focused on the connection of fast dynamics on picosecond time scales to the behavior of structural relaxation on much longer time scales. A separate section discusses the specific case of polymeric glass-forming liquids, which usually have extremely high fragility. We emphasize the apparent difference between the glass transitions in polymers and small molecules. We also discuss the possible role of quantum effects in the glass transition of light molecules and highlight the recent discovery of the unusually low fragility of water. At the end, we formulate the major challenges and questions remaining in this field.

A Simple New Way To Account for Free Volume in Glassy Dynamics: Model-Free Estimation of the Close-Packed Volume from PVT Data

In this article we focus on the important role of well-defined free volume (V_free) in dictating the structural relaxation times, τ, of glass-forming liquids and polymer melts. Our definition of V_free = V - V_hc, where V is the total system volume, means the use of V_free depends on determination of V_hc, the system's volume in the limiting closely packed state. Rejecting the historically compromised use of V_free as a dynamics-dependent fitting function, we have successfully applied a clear thermodynamics-based route to V_hc using the locally correlated lattice (LCL) model equation of state (EOS). However, in this work we go further and show that V_hc can be defined without the use of an equation of state by direct linear extrapolation of a V(T) high-pressure isobar down to zero temperature (T). The results from this route, tested on a dozen experimental systems, yield ln τ vs 1/V_free isotherms that are linear with T-dependent slopes, consistent with the general ln τ ∼ f(T) × (1/V_free) form of behavior we have previously described. This functional form also results by implementing a simple mechanistic explanation via the cooperative free volume (CFV) rate model, which assumes that dynamic relaxation is both thermally activated and that it requires molecular segmental cooperativity. With the degree of the latter, and thus the activation energy, being determined by the availability of free volume, the new route we demonstrate here for determination of V_free expands the potential for understanding and predicting local dynamic relaxation in glass-forming materials.

To Understand Film Dynamics Look to the Bulk

We show that shifts in dynamics of confined systems relative to that of the bulk material originate in the properties of bulk alone, and exhibit the same form of behavior as when different bulk isobars are compared. For bulk material, pressure-dependent structural relaxation times follow τ(T,V)∝exp[f(T)×g(V)]. When two states (isobars) of the material, "1" and "2", are compared at the same temperature this leads to a form τ_{2}∝τ_{1}^{c}, where c=g[V_{2}(T)]/g[V_{1}(T)]. Using equation of state analysis and two models for P-dependent dynamics, we show that c is approximately T independent, and that it can be very simply expressed in terms of either the (free) volume above the close packed state (V_{free}) or the activation energy for cooperative motion. The effect of changing state through a shift in pressure (P_{1} to P_{2}) is thus mechanistically traceable to cooperativity changing with density, through V_{free}. The connection with confined dynamics follows when 1 and 2 are taken as bulk and film at ambient P, differing in density only due to the film surface. The general form for τ(T,V) also illuminates why samples in different states (film vs bulk, high P vs low) trend toward the same relaxation behavior at high T.

Exploring the connection between the density-scaling exponent and the intermolecular potential for liquids on the basis of computer simulations of quasireal model systems

In this paper, based on the molecular dynamics simulations of quasireal model systems, we propose a method for determination of the effective intermolecular potential for real materials. We show that in contrast to the simple liquids, the effective intermolecular potential for the studied systems depends on the thermodynamic conditions. Nevertheless, the previously established relationship for simple liquids between the exponent of the inverse power law approximation of intermolecular potential and the density-scaling exponent is still preserved when small enough intermolecular distances are considered. However, our studies show that molecules approach each other at these very short distances relatively rarely. Consequently, only sparse interactions between extremely close molecules determine the value of the scaling exponent and then strongly influence the connection between dynamics and thermodynamics of the whole system.

Experimental Evidence for a State-Point-Independent Density-Scaling Exponent in Ionic Liquids

This Letter addresses a fundamental issue of condensed-matter physics, which is the validity of the density-scaling concept. For this purpose, the ambient and high-pressure conductivity measurements of two selected ionic liquids (ILs), with the different contribution of H-bonding interactions, were performed in the dynamic range of 13 orders of magnitude and corresponding to the density changes as large as 20%. All experimental data obtained within one compound are shown to superimpose each other when plotted as a function of ρ^{γ}/T. These results clearly show that for studied ILs the scaling exponent is a state-point-independent parameter that is in odds with the recent findings for van der Waals liquid [Sanz et al., Phys. Rev. Lett. 122, 055501 (2019)PRLTAO0031-900710.1103/PhysRevLett.122.055501].

The cooperative free volume rate model for segmental dynamics: Application to glass-forming liquids and connections with the density scaling approach⋆

In this paper, we apply the cooperative free volume (CFV) rate model for pressure-dependent dynamics of glass-forming liquids and polymer melts. We analyze segmental relaxation times, [Formula: see text] , as a function of temperature (T and free volume ( [Formula: see text] , and make substantive comparisons with the density scaling approach. [Formula: see text] , the difference between the total volume (V and the volume at close-packing, is predicted independently of the dynamics for any temperature and pressure using the locally correlated lattice (LCL) equation-of-state (EOS) analysis of characteristic thermodynamic data. We discuss the underlying physical motivation in the CFV and density scaling models, and show that their key, respective, material parameters are connected, where the CFV b parameter and the density scaling [Formula: see text] parameter each characterize the relative sensitivity of dynamics to changes in T , vs. changes in V . We find [Formula: see text] , where [Formula: see text] is the value predicted by the LCL EOS at the ambient [Formula: see text] . In comparing the predictive power of the two models we highlight the CFV advantage in yielding a universal linear collapse of relaxation data using a minimal set of parameters, compared to the same parameter space yielding a changing functional form in the density scaling approach. Further, we demonstrate that in the low data limit, where there is not enough data to characterize the density scaling model, the CFV model may still be successfully applied, and we even use it to predict the correct [Formula: see text] parameter.

Experimental Evidence for a State-Point-Dependent Density-Scaling Exponent of Liquid Dynamics

A large class of liquids obey density scaling characterized by an exponent, which quantifies the relative roles of temperature and density for the dynamics. We present experimental evidence that the density-scaling exponent γ is state-point dependent for the glass formers tetramethyl-tetraphenyl-trisiloxane (DC704) and 5-polyphenyl ether (5PPE). A method is proposed that from dynamic and thermodynamic properties at equilibrium estimates the value of γ. The method applies at any state point of the pressure-temperature plane, both in the supercooled and the normal liquid regimes. We find that γ is generally state-point dependent, which is confirmed by reanalyzing data for 20 metallic liquids and two model liquids.

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.

Explaining the T,V-dependent dynamics of glass forming liquids: The cooperative free volume model tested against new simulation results

In this article, we derive a rate model, the "cooperative free volume" (CFV) model, to explain relaxation dynamics in terms of a system's free volume, V_free, and its temperature, T, over widely varied pressure dependent conditions. In the CFV model, the rate a molecule moves a distance on the order of its own size is dependent on the cooperation of surrounding molecules to open up enough free space. To test CFV, we have generated extensive T,V dependent simulation data for structural relaxation times, τ, on a Kob and Andersen type Lennard-Jones (KA-LJ) fluid. The V_free = V - V_hc values are obtained by estimating the limiting hard core volume, V_hc, through analysis of the KA-LJ PVT data. We provide the first simulation evidence that shows ln τ to be linearly proportional to 1/V_free on isotherms, with T-dependent slopes, thus confirming our recent analysis of experimental systems. The linear relationship exhibited by the simulation data is further shown to occur at temperatures both above and below the transition to Arrhenius behavior. We also show that the gas kinetic T-dependent contribution is important in simulation results and that there can be a significant entropic contribution from lingering molecular hard-cores at high T. A key result is that non-Arrhenius relaxation behavior is always exhibited on isobars of the KA-LJ fluid, even at high T. The CFV model predicts all of this behavior over a surprisingly wide range of the KA-LJ T,V space, fitting it with just a single set of three parameters. The CFV approach leads to a framework wherein the number of cooperating particles, and thus, the process free energy of activation, is inversely proportional to V_free, and this is the foundation for the form of the model's volume contribution, a form that we find to hold for all systems and at all temperatures.

Evidence of a one-dimensional thermodynamic phase diagram for simple glass-formers

Glass formers show motional processes over an extremely broad range of timescales, covering more than ten orders of magnitude, meaning that a full understanding of the glass transition needs to comprise this tremendous range in timescales. Here we report simultaneous dielectric and neutron spectroscopy investigations of three glass-forming liquids, probing in a single experiment the full range of dynamics. For two van der Waals liquids, we locate in the pressure-temperature phase diagram lines of identical dynamics of the molecules on both second and picosecond timescales. This confirms predictions of the isomorph theory and effectively reduces the phase diagram from two to one dimension. The implication is that dynamics on widely different timescales are governed by the same underlying mechanisms.

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/τ_ref) = (1/V_free) × 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/V_free), 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/T^b, 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/(V_freeT^b), and because it is linear, it allows us to write an explicit analytic expression for log τ that covers a broad PVT space.

Thermodynamic Scaling of the Dynamics of a Strongly Hydrogen-Bonded Glass-Former

We probe the temperature- and pressure-dependent specific volume (v) and dipolar dynamics of the amorphous phase (in both the supercooled liquid and glass states) of the ternidazole drug (TDZ). Three molecular dynamic processes are identified by means of dielectric spectroscopy, namely the α relaxation, which vitrifies at the glass transition, a Johari-Goldstein β JG relaxation, and an intramolecular process associated with the relaxation motion of the propanol chain of the TDZ molecule. The lineshapes of dielectric spectra characterized by the same relaxation time (isochronal spectra) are virtually identical, within the studied temperature and pressure ranges, so that the time-temperature-pressure superposition principle holds for TDZ. The α and β JG relaxation times fulfil the density-dependent thermodynamic scaling: master curves result when they are plotted against the thermodynamic quantity Tv γ , with thermodynamic exponent γ approximately equal to 2. These results show that the dynamics of TDZ, a system characterized by strong hydrogen bonding, is characterized by an isomorphism similar to that of van-der-Waals systems. The low value of γ can be rationalized in terms of the relatively weak density-dependence of the dynamics of hydrogen-bonded systems.

Thermodynamic scaling of relaxation: insights from anharmonic elasticity

Using molecular dynamics simulations of a molecular liquid, we investigate the thermodynamic scaling (TS) of the structural relaxation time [Formula: see text] in terms of the quantity [Formula: see text], where T and ρ are the temperature and density, respectively. The liquid does not exhibit strong virial-energy correlations. We propose a method for evaluating both the characteristic exponent [Formula: see text] and the TS master curve that uses experimentally accessible quantities that characterise the anharmonic elasticity and does not use details about the microscopic interactions. In particular, we express the TS characteristic exponent [Formula: see text] in terms of the lattice Grüneisen parameter [Formula: see text] and the isochoric anharmonicity [Formula: see text]. An analytic expression of the TS master curve of [Formula: see text] with [Formula: see text] as the key adjustable parameter is found. The comparison with the experimental TS master curves and the isochoric fragilities of 34 glassformers is satisfying. In a few cases, where thermodynamic data are available, we test (i) the predicted characteristic exponent [Formula: see text] and (ii) the isochoric anharmonicity [Formula: see text], as drawn by the best fit of the TS of the structural relaxation, against the available thermodynamic data. A linear relation between the isochoric fragility and the isochoric anharmonicity [Formula: see text] is found and compared favourably with the results of experiments with no adjustable parameters. A relation between the increase of the isochoric vibrational heat capacity due to anharmonicity and the isochoric fragility is derived.

Scaling of the dynamics of flexible Lennard-Jones chains: Effects of harmonic bonds

The previous paper [A. A. Veldhorst et al., J. Chem. Phys. 141, 054904 (2014)] demonstrated that the isomorph theory explains the scaling properties of a liquid of flexible chains consisting of ten Lennard-Jones particles connected by rigid bonds. We here investigate the same model with harmonic bonds. The introduction of harmonic bonds almost completely destroys the correlations in the equilibrium fluctuations of the potential energy and the virial. According to the isomorph theory, if these correlations are strong a system has isomorphs, curves in the phase diagram along which structure, dynamics, and the excess entropy are invariant. The Lennard-Jones chain liquid with harmonic bonds does have curves in the phase diagram along which the structure and dynamics are invariant. The excess entropy is not invariant on these curves, which we refer to as "pseudoisomorphs." In particular, this means that Rosenfeld's excess-entropy scaling (the dynamics being a function of excess entropy only) does not apply for the Lennard-Jones chain with harmonic bonds.

Thermodynamic consequences of the kinetic nature of the glass transition

In this paper, we consider the glass transition as a kinetic process and establish one universal equation for the pressure coefficient of the glass transition temperature, dTg/dp, which is a thermodynamic characteristic of this process. Our findings challenge the common previous expectations concerning key characteristics of the transformation from the liquid to the glassy state, because it suggests that without employing an additional condition, met in the glass transition, derivation of the two independent equations for dTg/dp is not possible. Hence, the relation among the thermodynamic coefficients, which could be equivalent to the well-known Prigogine-Defay ratio for the process under consideration, cannot be obtained. Besides, by comparing the predictions of our universal equation for dTg/dp and Ehrenfest equations, we find the aforementioned supplementary restriction, which must be met to use the Prigogine-Defay ratio for the glass transition.

Qualitative change in structural dynamics of some glass-forming systems

Analysis of the temperature dependence of the structural relaxation time τ(α)(T) in supercooled liquids revealed a qualitatively distinct feature-a sharp, cusplike maximum in the second derivative of logτ(α)(T)at some T(max). It suggests that the super-Arrhenius temperature dependence of τ(α)(T) in glass-forming liquids eventually crosses over to an Arrhenius behavior at T<T(max), and there is no divergence of τ(α)(T) at nonzero T. T(max) can be above or below T(g), depending on the sensitivity of τ(T) to a change in the liquid's density quantified by the exponent γ in the scaling τ(α)(T)∼exp(A/Tρ(-γ)). These results might turn the discussion of the glass transition in a different direction-toward the origin of the limiting activation energy for structural relaxation at low T.

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.