Hidden scale invariance in condensed matter

Hidden Scale Invariance in Polydisperse Mixtures of Exponential Repulsive Particles

Polydisperse systems of particles interacting by the purely repulsive exponential (EXP) pair potential are studied in regard to how structure and dynamics vary along isotherms, isochores, and isomorphs. The sizable size polydispersities of 23%, 29%, 35%, and 40%, as well as energy polydispersity 35%, were considered. For each system an isomorph was traced out covering about one decade in density. For all systems studied, the structure and dynamics vary significantly along the isotherms and isochores but are invariant to a good approximation along the isomorphs. We conclude that the single-component EXP system's hidden scale invariance (implying isomorph invariance of structure and dynamics) is maintained even when a sizable polydispersity is introduced into the system.

Structure of the Lennard-Jones liquid estimated from a single simulation

Combining the recent Piskulich-Thompson approach [Z. A. Piskulich and W. H. Thompson, J. Chem. Phys. 152, 011102 (2020)JCPSA60021-960610.1063/1.5135932] with isomorph theory, from a single simulation the structure of a single-component Lennard-Jones (LJ) system is obtained at an arbitrary state point in almost the whole liquid region of the temperature-density phase diagram. The LJ system exhibits two temperature ranges where the van't Hoff assumption that energetic and entropic forces are temperature independent is valid to a good approximation. A method to evaluate the structure at an arbitrary state point along an isochore from the knowledge of structures at two temperatures on the isochore is also discussed. We argue that, in general, the structure of any hidden scale-invariant system obeying the van't Hoff assumption in the whole range of temperatures can be determined in the whole liquid region of the phase diagram from a single simulation.

Reentrant melting and multiple occupancy crystals of bounded potentials: Simple theory and direct observation by molecular dynamics simulations

Aspects of the phase coexistence behavior of the generalized exponential model (GEM-m) and bounded versions of inverse power potentials based on theory and molecular dynamics (MD) simulation data are reported. The GEM-m potential is ϕ(r)=exp(-r^{m}), where r is the pair separation and m is an adjustable exponent. A simple analytic formula for the fluid-solid envelope of the Gaussian core model which takes account of the known low- and high-density limiting forms is proposed and shown to represent the simulation data well. The bounded inverse power (BIP) potential is ϕ(r)=1/(a^{q}+r^{q})^{n/q}, where a, n, and q are positive constants. The BIP potential multiple occupancy crystal or cluster crystals are predicted to form when q>2 and a>0, for n>3, which compares with the corresponding GEM-m condition of m>2. Reentrant melting should occur for the BIP potential when q≤2 and a>0. MD simulations in which the system was gradually compressed at constant temperature using the BIP potential produced cluster states in the parameter domain expected but it was not possible to establish conclusively whether a multiply occupied crystal or a cluster fluid had formed owing to assembly structural fluctuations. The random phase approximation reproduces very well the BIP MD energy per particle without any discontinuities at the phase boundaries. The Lindemann melting rule is shown analytically to give a more rapidly decaying reentrant melting curve boundary than the so-called melting indicator (MI) empirical melting criterion which has also been investigated in this study. The MI model gives a better match to the high-density phase boundary for small m and q values.

Key role of retardation and non-locality in sound propagation in amorphous solids as evidenced by a projection formalism

We investigate acoustic propagation in amorphous solids by constructing a projection formalism based on separating atomic vibrations into two, "phonon" (P) and "non-phonon" (NP), subspaces corresponding to large and small wavelengths. For a pairwise interaction model, we show the existence of a "natural" separation lengthscale, determined by structural disorder, for which the isolated P subspace presents the acoustic properties of a nearly homogenous (Debye-like) elastic continuum, while the NP one encapsulates all small scale non-affinity effects. The NP eigenstates then play the role of dynamical scatterers for the phonons. However, at variance with a conjecture of defect theories, their spectra present a finite low frequency gap, which turns out to lie around the Boson peak frequency, and only a small fraction of them are highly localized. We then show that small scale disorder effects can be rigorously reduced to the existence, in the Navier-like wave equation of the continuum, of a generalized elasticity tensor, which is not only retarded, since scatterers are dynamical, but also non-local. The full neglect of both retardation and non-locality suffices to account for most of the corrections to Born macroscopic moduli. However, these two features are responsible for sound speed dispersion and have quite a significant effect on the magnitude of sound attenuation. Although it remains open how they impact the asymptotic, large wavelength scaling of sound damping, our findings rule out the possibility of representing an amorphous solid by an inhomogeneous elastic continuum with the standard (i.e., local and static) elastic moduli.

Isomorph theory beyond thermal equilibrium

This paper generalizes isomorph theory to systems that are not in thermal equilibrium. The systems are assumed to be R-simple, i.e., to have a potential energy that as a function of all particle coordinates R obeys the hidden-scale-invariance condition U(R_a) < U(R_b) ⇒ U(λR_a) < U(λR_b). "Systemic isomorphs" are introduced as lines of constant excess entropy in the phase diagram defined by density and systemic temperature, which is the temperature of the equilibrium state point with the average potential energy equal to U(R). The dynamics is invariant along a systemic isomorph if there is a constant ratio between the systemic and the bath temperature. In thermal equilibrium, the systemic temperature is equal to the bath temperature and the original isomorph formalism is recovered. The new approach rationalizes within a consistent framework previously published observations of isomorph invariance in simulations involving nonlinear steady-state shear flows, zero-temperature plastic flows, and glass-state isomorphs. This paper relates briefly to granular media, physical aging, and active matter. Finally, we discuss the possibility that the energy unit defining the reduced quantities should be based on the systemic rather than the bath temperature.

Thermodynamic or density scaling of the thermal conductivity of liquids

Thermodynamic or density scaling is applied to thermal conductivity (λ) data from the literature for the model Lennard-Jones (12-6) fluid; the noble gases neon to xenon; nitrogen, ethene, and carbon dioxide as examples of linear molecules; the quasi-spherical molecules methane and carbon tetrachloride; the flexible chain molecules n-hexane and n-octane; the planar toluene and m-xylene; the cyclic methylcyclohexane; the polar R132a and chlorobenzene; and ammonia and methanol as H-bonded fluids. Only data expressed as Rosenfeld reduced properties could be scaled successfully. Two different methods were used to obtain the scaling parameter γ, one based on polynomial fits to the group (TV^γ) and the other based on the Avramov equation. The two methods agree well, except for λ of CCl₄. γ for the thermal conductivity is similar to those for the viscosity and self-diffusion coefficient for the smaller molecules. It is significantly larger for the Lennard-Jones fluid, possibly due to a different dependence on packing fraction, and much larger for polyatomic molecules where heat transfer through internal modes may have an additional effect. Methanol and ammonia, where energy can be transmitted through intermolecular hydrogen bonding, could not be scaled. This work is intended as a practical attempt to examine thermodynamic scaling of the thermal conductivity of real fluids. The divergence of the scaling parameters for different properties is unexpected, suggesting that refinement of theory is required to rationalize this result. For the Lennard-Jones fluid, the Ohtori-Iishi version of the Stokes-Einstein-Sutherland relation applies at high densities in the liquid and supercritical region.

Excess-entropy scaling in supercooled binary mixtures

Transport coefficients, such as viscosity or diffusion coefficient, show significant dependence on density or temperature near the glass transition. Although several theories have been proposed for explaining this dynamical slowdown, the origin remains to date elusive. We apply here an excess-entropy scaling strategy using molecular dynamics computer simulations and find a quasiuniversal, almost composition-independent, relation for binary mixtures, extending eight orders of magnitude in viscosity or diffusion coefficient. Metallic alloys are also well captured by this relation. The excess-entropy scaling predicts a quasiuniversal breakdown of the Stokes-Einstein relation between viscosity and diffusion coefficient in the supercooled regime. Additionally, we find evidence that quasiuniversality extends beyond binary mixtures, and that the origin is difficult to explain using existing arguments for single-component quasiuniversality.

Sound Velocities of Lennard-Jones Systems Near the Liquid-Solid Phase Transition

Longitudinal and transverse sound velocities of Lennard-Jones systems are calculated at the liquid-solid coexistence using the additivity principle. The results are shown to agree well with the "exact" values obtained from their relations to excess energy and pressure. Some consequences, in particular in the context of the Lindemann's melting rule and Stokes-Einstein relation between the self-diffusion and viscosity coefficients, are discussed. Comparison with available experimental data on the sound velocities of solid argon at melting conditions is provided.

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.

Density scaling of structure and dynamics of an ionic liquid

The lines in the pressure–temperature phase diagram with constant conductivity are found to be lines where other dynamic variables as well as the molecular structure factor peak are constant, while charge ordering changes.

Structural order as a genuine control parameter of dynamics in simple glass formers

Glass transition is characterised by drastic dynamical slowing down upon cooling, accompanied by growing spatial heterogeneity. Its rationalisation by subtle changes in the liquid structure has been long debated but remains elusive, due to intrinsic difficulty in detecting the underlying complex structural ordering. Here we report that structural order parameter characterising local packing capability can well describe the glassy dynamics not only macroscopically but also microscopically, no matter whether it is driven by temperature or density. A Vogel-Fulcher-Tammann (VFT)-like relation is universally identified between the structural relaxation time and the order parameter for supercooled liquids with isotropic interactions. More importantly, we find such an intriguing VFT-like relation to be statistically valid even at a particle level, between spatially coarse-grained structural order and microscopic particle-level dynamics. Such a unified description of glassy dynamics based solely on structural order is expected to contribute to the ultimate understanding of the long-standing glass-transition problem.

The glass-forming materials exhibit dynamical slowing down together with spatial heterogeneity at microscales, but their origin remains debated. Tong and Tanaka show that this phenomenon can be unified based on a structural order parameter capable of detecting subtle ordering in instantaneous liquid states.

Dynamic Equivalence between Soft Star Polymers and Hard Spheres

Understanding the dynamics of soft colloids, such as star polymers, dendrimers, and microgels, is of scientific and practical importance. It is known that the excluded volume effect plays a key role in colloidal dynamics. Here, we propose a condition of compressibility equivalence that provides a simple method to experimentally evaluate the excluded volume of soft colloids from a thermodynamic view. We apply this condition to survey the dynamics of a series of star polymer dispersions. It is found that, as the concentration increases, the slowing of the long-time self-diffusivity of the star polymer, normalized by the short-time self-diffusivity, can be mapped onto the hard-sphere behavior. This phenomenon reveals the dynamic equivalence between soft colloids and hard spheres, despite the apparent complexity of the interparticle interaction of the soft colloids. The methods for measuring the osmotic compressibility and the self-diffusivities of soft colloidal dispersions are also presented.

Isomorph invariance of dynamics of sheared glassy systems

We study hidden scale invariance in the glassy phase of the Kob-Andersen binary Lennard-Jones system. After cooling below the glass transition, we generate a so-called isomorph from the fluctuations of potential energy and virial in the NVT ensemble: a set of density, temperature pairs for which structure and dynamics are identical when expressed in appropriate reduced units. To access dynamical features, we shear the system using the SLLOD algorithm coupled with Lees-Edwards boundary conditions and study the statistics of stress fluctuations and the particle displacements transverse to the shearing direction. We find good collapse of the statistical data, showing that isomorph theory works well in this regime. The analysis of stress fluctuations, in particular the distribution of stress changes over a given strain interval, allows us to identify a clear signature of avalanche behavior in the form of an exponential tail on the negative side. This feature is also isomorph invariant. The implications of isomorphs for theories of plasticity are discussed briefly.

Elastic properties of dense hard-sphere fluids

A new analysis of elastic properties of dense hard-sphere (HS) fluids is presented, based on the expressions derived by Miller [J. Chem. Phys. 50, 2733 (1969)JCPSA60021-960610.1063/1.1671437]. Important consequences for HS fluids in terms of sound waves propagation, Poisson's ratio, Stokes-Einstein relation, and generalized Cauchy identity are explored. Conventional expressions for high-frequency elastic moduli for simple systems with continuous and differentiable interatomic interaction potentials are known to diverge when approaching the HS repulsive limit. The origin of this divergence is identified here. It is demonstrated that these conventional expressions are only applicable for sufficiently soft interactions and should not be applied to HS systems. The reported results can be of interest in the context of statistical physics, physics of fluids, soft condensed matter, and granular materials.

COOPERATIVE FREE VOLUME RATE MODEL APPLIED TO THE PRESSURE-DEPENDENT SEGMENTAL DYNAMICS OF NATURAL RUBBER AND POLYUREA

We apply the cooperative free volume (CFV) rate model for pressure-dependent dynamics of glass-forming liquids and polymer melts, focusing on two new applications of the model, to natural rubber and to polyurea. In CFV, segmental relaxation times, τ, are analyzed as a function of temperature (T) and free volume (Vfree), where the latter provides an insightful route to expressing dynamics relative to using the system's overall total volume (V). Vfree is defined as the difference between the total volume and the volume at close packing and is predicted independently of the dynamics for any temperature and pressure using the locally correlated lattice equation-of-state analysis of characteristic thermodynamic data. The new results for natural rubber and polyurea are discussed in the context of results on a set of polymeric and small-molecule glass formers that had previously been modeled with CFV. We also discuss the results in the context of recent connections that we have made with the density-scaling approach.

Fast contribution to the activation energy of a glass-forming liquid

This paper presents physical-aging data for the silicone oil tetramethyl-tetraphenyl trisiloxane. The density and the high-frequency plateau shear modulus [Formula: see text] were monitored following temperature jumps starting from fully equilibrated conditions. Both quantities exhibit a fast change immediately after a temperature jump. Adopting the material-time formalism of Narayanaswamy, we determine from the dielectric loss at 0.178 Hz the time evolution of the aging-rate activation energy. The relative magnitude of the fast change of the activation energy differs from that of the density, but is identical to that of [Formula: see text] In fact, the activation energy is proportional to [Formula: see text] throughout the aging process, with minor deviations at the shortest times. This shows that for the silicone oil in question the dynamics are determined by [Formula: see text] in-as well as out of-equilibrium.

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.

Modified Entropy Scaling of the Transport Properties of the Lennard-Jones Fluid

Rosenfeld proposed two different scaling approaches to model the transport properties of fluids, separated by 22 years, one valid in the dilute gas, and another in the liquid phase. In this work, we demonstrate that these two limiting cases can be connected through the use of a novel approach to scaling transport properties and a bridging function. This approach, which is empirical and not derived from theory, is used to generate reference correlations for the transport properties of the Lennard-Jones 12-6 fluid of viscosity, thermal conductivity, and self-diffusion. This approach, with a very simple functional form, allows for the reproduction of the most accurate simulation data to within nearly their statistical uncertainty. The correlations are used to confirm that for the Lennard-Jones fluid the appropriately scaled transport properties are nearly monovariate functions of the excess entropy from low-density gases into the supercooled phase and up to extreme temperatures. This study represents the most comprehensive metastudy of the transport properties of the Lennard-Jones fluid to date.

Chain Flexibility and the Segmental Dynamics of Polymers

Using molecular dynamics simulations, we examine the dynamics of a family of model polymers with varying chain length and torsional potential barriers. We focus on features of the dynamics of polymers that are seen experimentally but absent in simulations of freely rotating and freely jointed chains. The reduced effect of volume on the segmental dynamics with increasing chain length, a capacity for pressure densification, and the deviation from constant Johari-Goldstein relaxation time at a constant segmental relaxation time all have a common origin, torsional rigidity, and these effects become increasingly apparent for more rigid chains.

The EXP pair-potential system. III. Thermodynamic phase diagram

This paper determines the thermodynamic phase diagram of the EXP system of particles interacting by the purely repulsive exponential pair potential. The solid phase is face-centered cubic (fcc) at low densities and pressures. At higher densities and pressures, the solid phase is body-centered cubic (bcc) with a re-entrant liquid phase at the highest pressures simulated. The investigation first identifies the phase diagram at zero temperature at which the following four crystal structures are considered: fcc, bcc, hexagonal close packed, and cubic diamond. There is a T = 0 phase transition at pressure 2.651 × 10^-3 with the thermodynamically stable structure being fcc below and bcc above this pressure. The densities of the two crystal structures at the phase transition are 1.7469 × 10^-2 (fcc) and 1.7471 × 10^-2 (bcc). At finite temperatures, the fcc-bcc, fcc-liquid, and bcc-liquid coexistence lines are determined by numerical integration of the Clausius-Clapeyron equation and validated by interface-pinning simulations at selected state points. The bcc-fcc phase transition is a weak first-order transition. The liquid-fcc-bcc triple point, which is determined by the interface-pinning method, has temperature 5.9 × 10^-5 and pressure 2.5 × 10^-6; the triple-point densities are 1.556 × 10^-3 (liquid), 1.583 × 10^-3 (bcc), and 1.587 × 10^-3 (fcc).

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.

Revisiting the Stokes-Einstein relation without a hydrodynamic diameter

We present diffusion coefficient and shear viscosity data for the Lennard-Jones fluid along nine isochores above the critical density, each involving a temperature variation of roughly two orders of magnitude. The data are analyzed with respect to the Stokes-Einstein (SE) relation, which breaks down gradually at high temperatures. This is rationalized in terms of the fact that the reduced diffusion coefficient D ̃ and the reduced viscosity η ̃ are both constant along the system's lines of constant excess entropy (the isomorphs). As a consequence, D ̃ η ̃ is a function of T/T _Ref(ρ) in which T is the temperature, ρ is the density, and T _Ref(ρ) is the temperature as a function of the density along a reference isomorph. This allows one to successfully predict the viscosity from the diffusion coefficient in the studied region of the thermodynamic phase diagram.

The quasi-low temperature behaviour of specific heat

A new mathematical approach to condensed matter physics, based on the finite temperature field theory, was recently proposed. The field theory is a scale-free formalism; thus, it denies absolute values of thermodynamic temperature and uses dimensionless thermal variables, which are obtained with the group velocities of sound and the interatomic distance. This formalism was previously applied to the specific heat of condensed matter and predicted its fourth power of temperature behaviour at sufficiently low temperatures, which was tested by experimental data for diamond lattice materials. The range of temperatures with the quartic law varies for different materials; therefore, it is called the quasi-low temperature regime. The quasi-low temperature behaviour of specific heat is verified here with experimental data for the fcc lattice materials, silver chloride and lithium iodide. The conjecture that the fourth order behaviour is universal for all condensed matter systems has also supported the data for glassy matter: vitreous silica. This law is long known to hold for the bcc solid helium-4. The characteristic temperatures of the threshold of the quasi-low temperature regime are found for the studied materials. The scaling in the specific heat of condensed matter is expressed by the dimensionless parameter, which is explored with the data for several glasses. The explanation of the correlation of the 'boson peak' temperature with the shear velocity is proposed. The critique of the Debye theory of specific heat and the Born-von Karman model of the lattice dynamics is given.

Perspective: Excess-entropy scaling

This article gives an overview of excess-entropy scaling, the 1977 discovery by Rosenfeld that entropy determines properties of liquids like viscosity, diffusion constant, and heat conductivity. We give examples from computer simulations confirming this intriguing connection between dynamics and thermodynamics, counterexamples, and experimental validations. Recent uses in application-related contexts are reviewed, and theories proposed for the origin of excess-entropy scaling are briefly summarized. It is shown that if two thermodynamic state points of a liquid have the same microscopic dynamics, they must have the same excess entropy. In this case, the potential-energy function exhibits a symmetry termed hidden scale invariance, stating that the ordering of the potential energies of configurations is maintained if these are scaled uniformly to a different density. This property leads to the isomorph theory, which provides a general framework for excess-entropy scaling and illuminates, in particular, why this does not apply rigorously and universally. It remains an open question whether all aspects of excess-entropy scaling and related regularities reflect hidden scale invariance in one form or other.

The EXP pair-potential system. II. Fluid phase isomorphs

This paper continues the investigation of the exponentially repulsive EXP pair-potential system of Paper I [A. K. Bacher et al., J. Chem. Phys. 149, 114501 (2018)] with a focus on isomorphs in the low-temperature gas and liquid phases. As expected from the EXP system's strong virial potential-energy correlations, the reduced-unit structure and dynamics are isomorph invariant to a good approximation. Three methods for generating isomorphs are compared: the small-step method that is exact in the limit of small density changes and two versions of the direct-isomorph-check method that allows for much larger density changes. Results from the latter two approximate methods are compared to those of the small-step method for each of the three isomorphs generated by 230 one percent density changes, covering one decade of density variation. Both approximate methods work well.

Liquid state isomorphism, Rosenfeld-Tarazona temperature scaling, and Riemannian thermodynamic geometry

Aspects of isomorph theory, Rosenfeld-Tarazona temperature scaling, and thermodynamic geometry are comparatively discussed on the basis of the Lennard-Jones potential. The first two approaches approximate the high-density fluid state well when the repulsive interparticle interactions become dominant, which is typically the case close to the freezing line. However, previous studies of Rosenfeld-Tarazona scaling for the isochoric heat capacity and its relation to isomorph theory reveal deviations for the temperature dependence. It turns out that a definition of a state region in which repulsive interactions dominate is required for achieving consistent results. The Riemannian thermodynamic scalar curvature R allows for such a classification, indicating predominantly repulsive interactions by R>0. An analysis of the isomorphic character of the freezing line and the validity of Rosenfeld-Tarazona temperature scaling show that these approaches are consistent only in a small state region.

Communication: Simple liquids' high-density viscosity

This paper argues that the viscosity of simple fluids at densities above that of the triple point is a specific function of temperature relative to the freezing temperature at the density in question. The proposed viscosity expression, which is arrived at in part by reference to the isomorph theory of systems with hidden scale invariance, describes computer simulations of the Lennard-Jones system as well as argon and methane experimental data and simulation results for an effective-pair-potential model of liquid sodium.

Isomorph theory of physical aging

This paper derives and discusses the configuration-space Langevin equation describing a physically aging R-simple system and the corresponding Smoluchowski equation. Externally controlled thermodynamic variables like temperature, density, and pressure enter the description via the single parameter T_s/T, in which T is the bath temperature and T_s is the "systemic" temperature defined at any time t as the thermodynamic equilibrium temperature of the state point with density ρ(t) and potential energy U(t). In equilibrium, T_s ≅ T with fluctuations that vanish in the thermodynamic limit. In contrast to Tool's fictive temperature and other effective temperatures in glass science, the systemic temperature is defined for any configuration with a well-defined density, even if it is not close to equilibrium. Density and systemic temperature define an aging phase diagram, in which the aging system traces out a curve. Predictions are discussed for aging following various density-temperature and pressure-temperature jumps from one equilibrium state to another, as well as for a few other scenarios. The proposed theory implies that R-simple glass-forming liquids are characterized by the dynamic Prigogine-Defay ratio being equal to unity.

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.

Phase Diagram of Kob-Andersen-Type Binary Lennard-Jones Mixtures

The binary Kob-Andersen (KA) Lennard-Jones mixture is the standard model for computational studies of viscous liquids and the glass transition. For very long simulations, the viscous KA system crystallizes, however, by phase separating into a pure A particle phase forming a fcc crystal. We present the thermodynamic phase diagram for KA-type mixtures consisting of up to 50% small (B) particles showing, in particular, that the melting temperature of the standard KA system at liquid density 1.2 is 1.028(3) in A particle Lennard-Jones units. At large B particle concentrations, the system crystallizes into the CsCl crystal structure. The eutectic corresponding to the fcc and CsCl structures is cutoff in a narrow interval of B particle concentrations around 26% at which the bipyramidal orthorhombic PuBr_{3} structure is the thermodynamically stable phase. The melting temperature's variation with B particle concentration at two constant pressures, as well as at the constant density 1.2, is estimated from simulations at pressure 10.19 using isomorph theory. Our data demonstrate approximate identity between the melting temperature and the onset temperature below which viscous dynamics appears. Finally, the nature of the solid-liquid interface is briefly discussed.

Growing length scale accompanying vitrification: A perspective based on nonsingular density fluctuations

A model for describing growing length scale accompanying the vitrification is introduced, in which we assume that in a subsystem whose density is above a certain threshold value, ρ_{c}, due to steric constraints, particle rearrangements are highly suppressed for a sufficiently long time period (∼structural relaxation time). We regard such a subsystem as a glassy cluster. With this assumption and without introducing any complicated thermodynamic arguments, we predict that with compression (increasing average density ρ) at a fixed temperature T in supercooled states, the characteristic length of the clusters, ξ, diverges as ξ∼(ρ_{c}-ρ)^{-2/d}, where d is the spatial dimensionality. This ξ measures the average persistence length of the steric constraints in blocking the rearrangement motions and is determined by the subsystem density. Additionally, with decreasing T at a fixed ρ, the length scale diverges in the same manner as ξ∼(T-T_{c})^{-2/d}, for which ρ is identical to ρ_{c} at T=T_{c}. The exponent describing the diverging length scale is the same as the one predicted by some theoretical models and indeed has been observed in some simulations and experiments. However, the basic mechanism for this divergence is different; that is, we do not invoke thermodynamic anomalies associated with the thermodynamic phase transition as the origin of the growing length scale. We further present arguements for the cooperative properties of the structural relaxation based on the clusters.

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.

High-pressure cell for simultaneous dielectric and neutron spectroscopy

In this article, we report on the design, manufacture, and testing of a high-pressure cell for simultaneous dielectric and neutron spectroscopy. This cell is a unique tool for studying dynamics on different time scales, from kilo- to picoseconds, covering universal features such as the α relaxation and fast vibrations at the same time. The cell, constructed in cylindrical geometry, is made of a high-strength aluminum alloy and operates up to 500 MPa in a temperature range between roughly 2 and 320 K. In order to measure the scattered neutron intensity and the sample capacitance simultaneously, a cylindrical capacitor is positioned within the bore of the high-pressure container. The capacitor consists of two concentric electrodes separated by insulating spacers. The performance of this setup has been successfully verified by collecting simultaneous dielectric and neutron spectroscopy data on dipropylene glycol, using both backscattering and time-of-flight instruments. We have carried out the experiments at different combinations of temperature and pressure in both the supercooled liquid and glassy state.

Determination of derived volumetric properties and heat capacities at high pressures using two density scaling based equations of state. Application to dipentaerythritol hexa(3,5,5-trimethylhexanoate)

Scaling based EoSs describe the complex behavior of derived properties for broad temperature and pressure ranges from diPEiC₉ experimental densities.

Mapping Isobaric Aging onto the Equilibrium Phase Diagram

The linear volume relaxation and the nonlinear volume aging of a glass-forming liquid are measured, directly compared, and used to extract the out-of-equilibrium relaxation time. This opens a window to investigate how the relaxation time depends on temperature, structure, and volume in parts of phase space that are not accessed by the equilibrium liquid. It is found that the temperature dependence of relaxation time is non-Arrhenius even in the isostructural case-challenging the Adam-Gibbs entropy model. Based on the presented data and the idea that aging happens through quasiequilibrium states, we suggest a mapping of the out-of-equilibrium states during isobaric aging to the equilibrium phase diagram. This mapping implies the existence of isostructural lines in the equilibrium phase diagram. The relaxation time is found to depend on the bath temperature, density, and a just single structural parameter, referred to as an effective temperature.

Communication: Effect of density on the physical aging of pressure-densified polymethylmethacrylate

The rate of physical aging of glassy polymethylmethacrylate (PMMA), followed from the change in the secondary relaxation with aging, is found to be independent of the density, the latter controlled by the pressure during glass formation. Thus, the aging behavior of the secondary relaxation is the same whether the glass is more compacted or less dense than the corresponding equilibrium liquid. This equivalence in aging of glasses formed under different pressures indicates that local packing is the dominant variable governing the glassy dynamics. The fact that pressure densification yields different glass structures is at odds with a model for non-associated materials having dynamic properties exhibited by PMMA, such as density scaling of the relaxation time and isochronal superposition of the relaxation dispersion.

A test for the existence of isomorphs in glass-forming materials

We describe a method to determine whether a material has isomorphs in its thermodynamic phase diagram. Isomorphs are state points for which various properties are invariant in reduced units. Such materials are commonly identified from strong correlation between thermal fluctuations of the potential energy, U, and the virial W, but this identification is not generally applicable to real materials. We show from molecular dynamic simulations of atomic, molecular, and polymeric materials that systems with strong U-W correlation cannot be pressure densified, that is, the density obtained on cooling to the glassy state and releasing the pressure is independent of the pressure applied during cooling.

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.