Simplicity of condensed matter at its core: generic definition of a Roskilde-simple system

Models to predict configurational adiabats of Lennard-Jones fluids and their transport coefficients

A comparison is made between three simple approximate formulas for the configurational adiabat (i.e., constant excess entropy, sex) lines in a Lennard-Jones (LJ) fluid, one of which is an analytic formula based on a harmonic approximation, which was derived by Heyes et al. [J. Chem. Phys. 159, 224504 (2023)] (analytic isomorph line, AIL). Another is where the density is normalized by the freezing density at that temperature (freezing isomorph line, FIL). It is found that the AIL formula and the average of the freezing density and the melting density ("FMIL") are configurational adiabats at all densities essentially down to the liquid-vapor binodal. The FIL approximation departs from a configurational adiabat in the vicinity of the liquid-vapor binodal close to the freezing line. The self-diffusion coefficient, D, shear viscosity, ηs, and thermal conductivity, λ, in macroscopic reduced units are essentially constant along the AIL and FMIL at all fluid densities and temperatures, but departures from this trend are found along the FIL at high liquid state densities near the liquid-vapor binodal. This supports growing evidence that for simple model systems with no or few internal degrees of freedom, isodynes are lines of constant excess entropy. It is shown that for the LJ fluid, ηs and D can be predicted accurately by an essentially analytic procedure from the high temperature limiting inverse power fluid values (apart from at very low densities), and this is demonstrated quite well also for the experimental argon viscosity.

Scaling Properties of Liquid Dynamics Predicted from a Single Configuration: Pseudoisomorphs for Harmonic-Bonded Molecules

Isomorphs are curves in the thermodynamic phase diagram of invariant excess entropy, structure, and dynamics, while pseudoisomorphs are curves of invariant structure and dynamics, but not of the excess entropy. The latter curves have been shown to exist in molecular models with flexible bonds [Olsen, A. E. J. Chem. Phys. 2016, 145, 241103]. We here present three force-based methods to trace out pseudoisomorphs based on a single configuration and test them on the asymmetric dumbbell and 10-bead Lennard-Jones chain models with bonds modeled as harmonic springs. The three methods are based on requiring that particle forces, center-of-mass forces, and torques, respectively, are invariant in reduced units. For each of the two investigated models we identify a method that works well for tracing out pseudoisomorphs, but these methods are not the same. Overall, we find that the more internal degrees of freedom there are in the molecule studied, the less they appear to affect the gross dynamical behavior. Moreover, the "internal" degrees of freedom (including rotation) do not significantly affect the scaling behavior of the dynamical/transport coefficients provided some 'quenching' is performed.

Thermodynamics and simulation of 3D crystals and phase transitions under external fields

A field-supported multiphase kinetic Monte Carlo method previously applied to self-assembled trimesic acid molecular layers [Ustinov et al., Phys. Chem. Chem. Phys. 24, 26111 (2022)] was generalized to three-dimensional gas-liquid and gas-solid systems. This method allows us to calculate the thermodynamic potentials of the liquid and solid phases and then determine the parameters of the liquid-solid phase transition. In this study, the requirement that the gas phase be ideal was introduced as an additional condition. It was shown that in a two-phase system, the sum of the analytical expression for the chemical potential of an ideal gas and the external potential imposed on the gas phase exactly equals the chemical potential of the equilibrium crystal or liquid phase. For example, the coexistence of crystalline/liquid krypton and ideal gas has been considered. A comparison with previously published data has shown that the proposed approach provides the most accurate results for determining the parameters of phase transitions and fully satisfies the Gibbs-Duhem equation. This method does not impose any restrictions on the complexity or hardness of dense phases.

Complexity Scaling of Liquid Dynamics

According to excess-entropy scaling, dynamic properties of liquids like viscosity and diffusion coefficient are determined by the entropy. This link between dynamics and thermodynamics is increasingly studied and of interest also for industrial applications, but hampered by the challenge of calculating entropy efficiently. Utilizing the fact that entropy is basically the Kolmogorov complexity, which can be estimated from optimal compression algorithms [Avinery et al., Phys. Rev. Lett. 123, 178102 (2019)PRLTAO0031-900710.1103/PhysRevLett.123.178102; Martiniani et al., Phys. Rev. X 9, 011031 (2019)PRXHAE2160-330810.1103/PhysRevX.9.011031], we here demonstrate that the diffusion coefficients of four simple liquids follow a quasiuniversal exponential function of the optimal compression length of a single equilibrium configuration. We conclude that "complexity scaling" has the potential to become a useful tool for estimating dynamic properties of any liquid from a single configuration.

Melting curve of two-dimensional Yukawa systems predicted by isomorph theory

The analytical expression for the conditions of the solid-fluid phase transition, i.e., the melting curve, for two-dimensional (2D) Yukawa systems is derived theoretically from the isomorph theory. To demonstrate that the isomorph theory is applicable to 2D Yukawa systems, molecular dynamical simulations are performed under various conditions. Based on the isomorph theory, the analytical isomorphic curves of 2D Yukawa systems are derived using the local effective power-law exponent of the Yukawa potential. From the obtained analytical isomorphic curves, the melting curve of 2D Yukawa systems is directly determined using only two known melting points. The determined melting curve of 2D Yukawa systems well agrees with the previous obtained melting results using completely different approaches.

Universal scaling of transverse sound speed and its isomorphic property in Yukawa fluids

Molecular dynamical simulations are performed to investigate the scaling of the transverse sound speed in two-dimensional (2D) and 3D Yukawa fluids. From the calculated diagnostics of the radial distribution function, the mean-squared displacement, and the Pearson correlation coefficient, the approximate isomorphic curves for 2D and 3D liquidlike Yukawa systems are obtained. It is found that the structure and dynamics of 2D and 3D liquidlike Yukawa systems exhibit the isomorphic property under the conditions of the same relative coupling parameter Γ/Γ_{m}=const. It is demonstrated that the reduced transverse sound speed, i.e., the ratio of the transverse sound speed to the thermal speed, is an isomorph invariant, which is a quasiuniversal function of Γ/Γ_{m}. The obtained isomorph invariant of the reduced transverse sound speed can be useful to estimate the transverse sound speed, or determine the coupling strength, with applications to dusty (complex) plasma or colloidal systems.

Invariant dynamics in a united-atom model of an ionic liquid

We study a united-atom model of the ionic liquid 1-butyl-1-methylpyrrolidinium bis(trifluoromethyl)sulfonylamide to determine to what extent there exist curves in the phase diagram along which the microscopic dynamics are invariant when expressed in dimensionless, or reduced, form. The initial identification of these curves, termed isodynes, is made by noting that contours of reduced shear viscosity and reduced self-diffusion coefficient coincide to a good approximation. Choosing specifically the contours of reduced viscosity as nominal isodynes, further simulations were carried out for state points on these, and other aspects of dynamics were investigated to study their degree of invariance. These include the mean-squared displacement, shear-stress autocorrelation function, and various rotational correlation functions. These were invariant to a good approximation, with the main exception being rotations of the anion about its long axis. The dynamical features that are invariant have in common that they are aspects that would be relevant for a coarse-grained description of the system; specifically, removing the most microscopic degrees of freedom in principle leads to a simplification of the potential energy landscape, which allows for the existence of isodynes.

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.

Scaling Properties of Liquid Dynamics Predicted from a Single Configuration: Small Rigid Molecules

Isomorphs are curves in the thermodynamic phase diagram along which structure and dynamics are invariant to a good approximation. There are two main ways to trace out isomorphs, the configurational-adiabat method and the direct-isomorph-check method. Recently a new method based on the scaling properties of forces was introduced and shown to work very well for atomic systems [T. B. Schrøder, Phys. Rev. Lett. 2022, 129, 245501]. A unique feature of this method is that it only requires a single equilibrium configuration for tracing out an isomorph. We here test generalizations of this method to molecular systems and compare to simulations of three simple molecular models: the asymmetric dumbbell model of two Lennard-Jones spheres, the symmetric inverse-power-law dumbbell model, and the Lewis-Wahnström o-terphenyl model. We introduce and test two force-based and one torque-based methods, all of which require just a single configuration for tracing out an isomorph. Overall, the method based on requiring invariant center-of-mass reduced forces works best.

Hidden scale invariance in the Gay-Berne model. II. Smectic-B phase

This paper complements a previous study of the isotropic and nematic phases of the Gay-Berne liquid-crystal model [Mehri et al., Phys. Rev. E 105, 064703 (2022)2470-004510.1103/PhysRevE.105.064703] with a study of its smectic-B phase found at high density and low temperatures. We find also in this phase strong correlations between the virial and potential-energy thermal fluctuations, reflecting hidden scale invariance and implying the existence of isomorphs. The predicted approximate isomorph invariance of the physics is confirmed by simulations of the standard and orientational radial distribution functions, the mean-square displacement as a function of time, and the force, torque, velocity, angular velocity, and orientational time-autocorrelation functions. The regions of the Gay-Berne model that are relevant for liquid-crystal experiments can thus fully be simplified via the isomorph theory.

Configurational temperature in active matter. II. Quantifying the deviation from thermal equilibrium

This paper proposes using the configurational temperature T_{conf} for quantifying how far an active-matter system is from thermal equilibrium. We measure this "distance" by the ratio of the systemic temperature T_{s} to T_{conf}, where T_{s} is the canonical-ensemble temperature for which the average potential energy is equal to that of the active-matter system. T_{conf} is "local" in the sense that it is the average of a function, which depends only on how the potential energy varies in the vicinity of a given configuration. In contrast, T_{s} is a global quantity. The quantity T_{s}/T_{conf} is straightforward to evaluate in a computer simulation; equilibrium simulations in conjunction with a single steady-state active-matter configuration are enough to determine T_{s}/T_{conf}. We validate the suggestion that T_{s}/T_{conf} quantifies the deviation from thermal equilibrium by data for the radial distribution function of the 3D Kob-Andersen and 2D Yukawa active-matter models with active Ornstein-Uhlenbeck and active Brownian Particle dynamics. Moreover, we show that T_{s}/T_{conf}, structure, and dynamics of the homogeneous phase are all approximately invariant along the motility-induced phase separation boundary in the phase diagram of the 2D Yukawa model. The measure T_{s}/T_{conf} is not limited to active matter and can be used for quantifying how far any system involving a potential-energy function, e.g., a driven Hamiltonian system, is from thermal equilibrium.

Configurational temperature in active matter. I. Lines of invariant physics in the phase diagram of the Ornstein-Uhlenbeck model

This paper shows that the configurational temperature of liquid-state theory, T_{conf}, defines an energy scale, which can be used for adjusting model parameters of active Ornstein-Uhlenbeck particle (AOUP) models in order to achieve approximately invariant structure and dynamics upon a density change. The required parameter changes are calculated from the variation of a single configuration's T_{conf} for a uniform scaling of all particle coordinates. The resulting equations are justified theoretically for models involving a potential-energy function with hidden scale invariance. The validity of the procedure is illustrated by computer simulations of the Kob-Andersen binary Lennard-Jones AOUP model, showing the existence of lines of approximate invariance of the reduced-unit radial distribution function and time-dependent mean-square displacement.

Entropy scaling of viscosity for molecular models of molten salts

Entropy scaling relates dynamic and thermodynamic properties by reducing the viscosity to a function of only the residual entropy. Molecular simulations are used to investigate the entropy scaling of the viscosity of three models of sodium chloride and five monovalent salts. Even though the correlation between the potential energy and the virial is weak, entropy scaling applies at liquid densities for all models and salts investigated. At lower densities, entropy scaling breaks down due to the formation of ion pairs and chains. Entropy scaling can be used to develop more extendable correlations for the dynamic properties of molten salts.

Isomorphs in sheared binary Lennard-Jones glass: Transient response

We have studied shear deformation of binary Lennard-Jones glasses to investigate the extent to which the transient part of the stress strain curves is invariant when the thermodynamic state point is varied along an isomorph. Shear deformations were carried out on glass samples of varying stability, determined by cooling rate, and at varying strain rates, at state points deep in the glass. Density changes up to and exceeding a factor of two were made. We investigated several different methods for generating isomorphs but none of the previously developed methods could generate sufficiently precise isomorphs given the large density changes and nonequilibrium situation. Instead, the temperatures for these higher densities were chosen to give state points isomorphic to the starting state point by requiring the steady-state flow stress for isomorphic state points to be invariant in reduced units. In contrast to the steady-state flow stress, we find that the peak stress on the stress strain curve is not invariant. The peak stress decreases by a few percent for each ten percent increase in density, although the differences decrease with increasing density. Analysis of strain profiles and nonaffine motion during the transient phase suggests that the root of the changes in peak stress is a varying tendency to form shear bands, with the largest tendency occurring at the lowest densities. We suggest that this reflects the effective steepness of the potential; a higher effective steepness gives a greater tendency to form shear bands.

Predicting Scaling Properties from a Single Fluid Configuration

Time-dependent dynamical properties of a fluid cannot be estimated directly from a single configuration without performing a simulation. Here, however, we present a method that predicts the scaling properties of both structure and dynamics from a single configuration. The method is demonstrated to work well for the Lennard-Jones fluid as well as the viscous Kob-Andersen Lennard-Jones mixture, both in and out of equilibrium. The method is conceptually simple and easy to implement and, thus, should become a standard tool in the study of scaling properties of fluids and liquids.

Comparing four hard-sphere approximations for the low-temperature WCA melting line

By combining interface-pinning simulations with numerical integration of the Clausius–Clapeyron equation, we accurately determine the melting-line coexistence pressure and fluid/crystal densities of the Weeks–Chandler–Andersen system, covering four decades of temperature. The data are used for comparing the melting-line predictions of the Boltzmann, Andersen–Weeks–Chandler, Barker–Henderson, and Stillinger hard-sphere approximations. The Andersen–Weeks–Chandler and Barker–Henderson theories give the most accurate predictions, and they both work excellently in the zero-temperature limit for which analytical expressions are derived here.

Freezing density scaling of fluid transport properties: Application to liquified noble gases

A freezing density scaling of transport properties of the Lennard-Jones fluid is rationalized in terms of the Rosenfeld's excess entropy scaling and isomorph theory of Roskilde-simple systems. Then, it is demonstrated that the freezing density scaling operates reasonably well for viscosity and thermal conductivity coefficients of liquid argon, krypton, and xenon. Quasi-universality of the reduced transport coefficients at their minima and at freezing conditions is discussed. The magnitude of the thermal conductivity coefficient at the freezing point is shown to agree remarkably well with the prediction of the vibrational model of thermal transport in dense fluids.

Hidden scale invariance in the Gay-Berne model

This paper presents a numerical study of the Gay-Berne liquid crystal model with parameters corresponding to calamitic (rod-shaped) molecules. The focus is on the isotropic and nematic phases at temperatures above unity, where we find strong correlations between the virial and potential-energy thermal fluctuations, reflecting the hidden scale invariance symmetry. This implies the existence of isomorphs, which are curves in the thermodynamic phase diagram of approximately invariant physics. We study numerically one isomorph in the isotropic phase and one in the nematic phase. In both cases, good invariance of the dynamics is demonstrated via data for the mean-square displacement and the reduced-unit time-autocorrelation functions of the velocity, angular velocity, force, torque, and first- and second-order Legendre polynomial orientational order parameters. Deviations from isomorph invariance are observed at short times for the orientational time-autocorrelation functions, which reflects the fact that the moment of inertia is assumed to be constant and thus not isomorph-invariant in reduced units. Structural isomorph invariance is demonstrated from data for the radial distribution functions of the molecules and their orientations. For comparison, all quantities were also simulated along an isochore of similar temperature variation, in which case invariance is not observed. We conclude that the thermodynamic phase diagram of the calamitic Gay-Berne model is essentially one-dimensional in the studied regions as predicted by isomorph theory, a fact that potentially allows for simplifications of future theories and numerical studies.

Bridge functions of classical one-component plasmas

In a recent paper, Lucco Castello et al. [arXiv:2107.03537] performed systematic extractions of classical one-component plasma bridge functions from molecular dynamics simulations and provided an accurate parametrization that was incorporated in their isomorph-based empirically modified hypernetted chain approach for Yukawa one-component plasmas. Here the extraction technique and parametrization strategy are described in detail, while the deficiencies of earlier efforts are discussed. The structural and thermodynamic predictions of the updated version of the integral equation theory approach are compared with extensive available simulation results revealing a truly unprecedented level of accuracy in the entire dense liquid region of the Yukawa phase diagram.

Generalized hydrodynamics of the Lennard-Jones liquid in view of hidden scale invariance

In recent years lines along which structure and dynamics are invariant to a good approximation, so-called isomorphs, have been identified in the thermodynamic phase diagrams of several model liquids and solids. This paper reports computer simulation data of the transverse and longitudinal collective dynamics at different length scales along an isomorph of the Lennard-Jones system. Our findings are compared to corresponding results along an isotherm and an isochore. Confirming the theoretical prediction, the reduced-unit dynamics of the transverse momentum density is invariant to a good approximation along the isomorph on all time and length scales. Likewise, the wave-vector dependent shear-stress autocorrelation function is found to be isomorph invariant (with minor deviations at very short times). A similar invariance is not seen along the isotherm or the isochore. Using a spatially nonlocal hydrodynamic model for the transverse momentum-density time-autocorrelation function, the macroscopic shear viscosity and its wave dependence are determined, demonstrating that the shear viscosity is isomorphic invariant on all length scales studied. This analysis implies the existence of a length scale that is isomorph invariant in reduced units, i.e., which characterizes each isomorph. The transverse sound-wave velocity, the Maxwell relaxation time, and the rigidity shear modulus are also isomorph invariant. In contrast to the isomorph invariance of all aspects of the transverse dynamics, the reduced-unit dynamics of the mass density is not invariant on length scales longer than the interparticle distance. By fitting to a generalized hydrodynamic model, we extract values for the wave-vector-dependent thermal diffusion coefficient, sound attenuation coefficient, and adiabatic sound velocity. The isomorph variation of these quantities in reduced units on long length scales can be eliminated by scaling with the density-scaling exponent, a fundamental quantity in the isomorph theory framework; this is an empirical observation that remains to be explained theoretically.

Isomorphs in nanoconfined liquids

We study in this paper the possible existence of Roskilde-simple liquids and their isomorphs in a rough-wall nanoconfinement. Isomorphs are curves in the thermodynamic phase diagram along which structure and dynamics are invariant in suitable nondimensionalized units. Two model liquids using molecular dynamics computer simulations are considered: the single-component Lennard-Jones (LJ) liquid and the Kob-Andersen binary LJ mixture, both of which in the bulk phases are known to have good isomorphs. Nanoconfinement is implemented by adopting a slit-pore geometry with fcc crystalline walls; this implies inhomogenous density profiles both parallel and perpendicular to the confining walls. Despite this fact and consistent with an earlier study [Ingebrigtsen et al., Phys. Rev. Lett., 2013, 111, 235901] we find that these two nanoconfined liquids have isomorphs to a good approximation. More specifically, we show good invariance along the isomorphs of inhomogenous density profiles, mean-square displacements, and higher-order structures probed using the topological cluster classification algorithm. Our study thus provides an alternative framework for understanding nanoconfined liquids.

Quantifying dynamical and structural invariance in a simple molten salt model

Recent experimental results for the structure in the ionic liquid PYR₁₄ ⁺TFSI^- have shown invariance in the main structure factor peak along curves of equal electrical conductivity [Hansen et al., Phys. Chem. Chem. Phys. 22, 14169 (2020)]. The charge peak decreases slightly with increasing temperature at fixed conductivity, however. For simple liquids, curves with invariant dynamics and structure, known as isomorphs, can be identified as configurational adiabats. While liquids with strong-Coulomb interactions do not have good isomorphs, ionic liquids could be an intermediate case with approximate isomorphs along which some aspects of structure and dynamics are invariant. We study a simple molten salt model using molecular dynamics simulations to test this hypothesis. Simple measures of structure and dynamics are investigated along with one transport property, the shear viscosity. We find that there is a substantial degree of invariance of the self-intermediate scattering function, the mean square displacement, and the viscosity along configurational adiabats over a wide range of densities for the three adiabats simulated. The density range studied is more than a factor of two and extends from the strong-Coulomb regime at low densities to the weak-Coulomb regime at high densities. The structure is not invariant over the full range of density, but in the weak-Coulomb regime, we see behavior similar to that seen experimentally over density changes of order 15%. In view of the limited structural invariance but substantial dynamical invariance, we designate the configurational adiabats as isodynes.

Extreme case of density scaling: The Weeks-Chandler-Andersen system at low temperatures

This paper studies numerically the Weeks-Chandler-Andersen system, which is shown to obey hidden scale invariance with a density-scaling exponent that varies from below 5 to above 500. This unprecedented variation makes it advantageous to use the fourth-order Runge-Kutta algorithm for tracing out isomorphs. Good isomorph invariance of structure and dynamics is observed over more than three orders of magnitude temperature variation. For all state points studied, the virial potential-energy correlation coefficient and the density-scaling exponent are controlled mainly by the temperature. Based on the assumption of statistically independent pair interactions, a mean-field theory is developed that rationalizes this finding and provides an excellent fit to data at low temperatures.

Isomorph Invariance of Higher-Order Structural Measures in Four Lennard-Jones Systems

In the condensed liquid phase, both single- and multicomponent Lennard-Jones (LJ) systems obey the "hidden-scale-invariance" symmetry to a good approximation. Defining an isomorph as a line of constant excess entropy in the thermodynamic phase diagram, the consequent approximate isomorph invariance of structure and dynamics in appropriate units is well documented. However, although all measures of the structure are predicted to be isomorph invariant, with few exceptions only the radial distribution function (RDF) has been investigated. This paper studies the variation along isomorphs of the nearest-neighbor geometry quantified by the occurrence of Voronoi structures, Frank-Kasper bonds, icosahedral local order, and bond-orientational order. Data are presented for the standard LJ system and for three binary LJ mixtures (Kob-Andersen, Wahnström, NiY2). We find that, while the nearest-neighbor geometry generally varies significantly throughout the phase diagram, good invariance is observed along the isomorphs. We conclude that higher-order structural correlations are no less isomorph invariant than is the RDF.

Theoretical Estimate of the Glass Transition Line of Yukawa One-Component Plasmas

The mode coupling theory of supercooled liquids is combined with advanced closures to the integral equation theory of liquids in order to estimate the glass transition line of Yukawa one-component plasmas from the unscreened Coulomb limit up to the strong screening regime. The present predictions constitute a major improvement over the current literature predictions. The calculations confirm the validity of an existing analytical parameterization of the glass transition line. It is verified that the glass transition line is an approximate isomorphic curve and the value of the corresponding reduced excess entropy is estimated. Capitalizing on the isomorphic nature of the glass transition line, two structural vitrification indicators are identified that allow a rough estimate of the glass transition point only through simple curve metrics of the static properties of supercooled liquids. The vitrification indicators are demonstrated to be quasi-universal by an investigation of hard sphere and inverse power law supercooled liquids. The straightforward extension of the present results to bi-Yukawa systems is also discussed.

Testing the isomorph invariance of the bridge functions of Yukawa one-component plasmas

It has been recently conjectured that bridge functions remain nearly invariant along phase diagram lines of constant excess entropy for the broad class of R-simple liquids. To test this hypothesis, the bridge functions of Yukawa systems are computed outside the correlation void with the Ornstein-Zernike inversion method employing structural input from ultra-accurate molecular dynamics simulations and inside the correlation void with the cavity distribution method employing structural input from ultra-long specially designed molecular dynamics simulations featuring a tagged particle pair. Yukawa bridge functions are revealed to be isomorph invariant to a very high degree. The observed invariance is not exact, however, since isomorphic deviations exceed the overall uncertainties.

Virial-potential-energy correlation and its relation to density scaling for quasireal model systems

In this paper, we examine the virial- and the potential-energy correlation for quasireal model systems. This correlation constitutes the framework of the theory of the isomorph in the liquid phase diagram commonly examined using simple liquids. Interestingly, our results show that for the systems characterized by structural anisotropy and flexible bonds, the instantaneous values of total virial and total potential energy are entirely uncorrelated. It is due to the presence of the intramolecular interactions because the contributions to the virial and potential energy resulting from the intermolecular interactions still exhibit strong linear dependence. Interestingly, in contrast to the results reported for simple liquids, the slope of the mentioned linear dependence is different than the values of the density scaling exponent. However, our findings show that for quasireal materials, the slope of dependence between the virial and potential energy (resulting from the intermolecular interactions) strongly depends on the interval of intermolecular distances that are taken into account. Consequently, the value of the slope of the discussed relationship, which enables satisfactory density scaling, can be obtained. Interestingly, this conclusion is supported by the results obtained for analogous systems without intermolecular attraction, for which the value the slope of the virial-potential-energy correlation is independent of considered intermolecular distances, directly corresponds to the exponent of the intermolecular repulsion, and finally leads to accurate density scaling.

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.

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.

On the pressure dependence of the thermodynamical scaling exponent γ

Since its initial discovery more than fifteen years ago, the thermodynamical scaling of the dynamics of supercooled liquids has been used to provide many new important insights in the physics of liquids, particularly on the link between dynamics and intermolecular potential. A question that has long been discussed is whether the scaling exponent γ_S is a constant or does it depends on pressure. An alternative definition of the scaling parameter, γ_I = ∂ ln T/∂ ln ρ|_X has been presented in the literature, and has been erroneously considered equivalent to γ_S. Here we offer a simple method to determine the pressure dependence of γ_I using only the pressure dependence of the glass transition and the equation of state. Using this new method we find that for the six nonassociated liquids investigated, γ_I always decreases with increasing pressure. Importantly in all cases the value of γ_I remains always larger than 4. Liquids having γ_I closer to 4 at low pressure show a smaller change in γ_I with pressure. We argue that this result has very important consequences for the experimental determination of the functional form of the repulsive part of the potential in liquids. Comparing the pressure and temperature dependence of γ_S and γ_I we find, contrary to what has been assumed in the literature to date, that these two parameters are not equivalent and have very different pressure and temperature dependences.

An entropy scaling demarcation of gas- and liquid-like fluid behaviors

In this work, we propose a generic and simple definition of a line separating gas-like and liquid-like fluid behaviors from the standpoint of shear viscosity. This definition is valid even for fluids such as the hard sphere and the inverse power law that exhibit a unique fluid phase. We argue that this line is defined by the location of the minimum of the macroscopically scaled viscosity when plotted as a function of the excess entropy, which differs from the popular Widom lines. For hard sphere, Lennard-Jones, and inverse-power-law fluids, such a line is located at an excess entropy approximately equal to -2/3 times Boltzmann's constant and corresponds to points in the thermodynamic phase diagram for which the kinetic contribution to viscosity is approximately half of the total viscosity. For flexible Lennard-Jones chains, the excess entropy at the minimum is a linear function of the chain length. This definition opens a straightforward route to classify the dynamical behavior of fluids from a single thermodynamic quantity obtainable from high-accuracy thermodynamic models.

Effective hardness of interaction from thermodynamics and viscosity in dilute gases

The hardness of the effective inverse power law (IPL) potential, which can be obtained from thermodynamics or collision integrals, can be used to demonstrate similarities between thermodynamic and transport properties. This link is investigated for systems of increasing complexity (i.e., the EXP, square-well, Lennard-Jones, and Stockmayer potentials; ab initio results for small molecules; and rigid linear chains of Lennard-Jones sites). These results show that while the two approaches do not yield precisely the same values of effective IPL exponent, their qualitative behavior is intriguingly similar, offering a new way of understanding the effective interactions between molecules, especially at high temperatures. In both approaches, the effective hardness is obtained from a double-logarithmic temperature derivative of an effective area.

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.

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.

Topological extension of the isomorph theory based on the Shannon entropy

Isomorph theory is one of the promising theories for understanding the quasiuniversal relationship between thermodynamic, dynamic, and structural characteristics. Based on the hidden scale invariance of the inverse power law potentials, it rationalizes the excess entropy scaling law of dynamic properties. This work aims to show that this basic idea of isomorph theory can be extended by examining the microstructural features of the system. Using the topological framework in conjunction with the entropy calculation algorithm, we demonstrate that Voronoi entropy, a measure of the topological diversity of single atoms, provides a scaling law for the transport properties of soft-sphere fluids, which is comparable to the frequently used excess entropy scaling. By examining the relationship between the Voronoi entropy and the solidlike fraction of simple fluids, we suggest that the Frenkel line, a rigid-nonrigid crossover line, be a topological isomorphic line at which the scaling relation qualitatively changes.

Topological generalization of the rigid-nonrigid transition in soft-sphere and hard-sphere fluids

A fluid particle changes its dynamics from diffusive to oscillatory as the system density increases up to the melting density. Hence the notion of the Frenkel line was introduced to demarcate the fluid region into rigid and nonrigid liquid subregions based on the collective particle dynamics. In this work, we apply a topological framework to locate the Frenkel lines of the soft-sphere and the hard-sphere models relying on the system configurations. The topological characteristics of the ideal gas and the maximally random jammed state are first analyzed, then the classification scheme designed in our earlier work is applied to soft-sphere and hard-sphere fluids. The dependence of the classification result on the bulk density is understood based on the theory of fluid polyamorphism. The percolation behavior of solid-like clusters is described based on the fraction of solid-like molecules in an integrated manner. The crossover densities are obtained by examining the percolation of solid-like clusters. The resultant crossover densities of soft-sphere fluids converge to that of hard-sphere fluid. Hence the topological method successfully highlights the generality of the Frenkel line.

Hidden scale invariance at high pressures in gold and five other face-centered-cubic metal crystals

Recent density functional theory simulations showed that metals have a hitherto overlooked symmetry termed "hidden scale invariance" [Hummel et al., Phys. Rev. B 92, 174116 (2015)PRBMDO1098-012110.1103/PhysRevB.92.174116]. This scaling property implies the existence of lines in the thermodynamic phase diagram, so-called isomorphs, along which structure and dynamics are invariant to a good approximation when given in properly reduced units. This means that the phase diagram becomes effectively one-dimensional with regard to several physical properties. This paper investigates consequences and implications of the isomorph theory in six metallic crystals: Au, Ni, Cu, Pd, Ag, and Pt. The data are obtained from molecular dynamics simulations employing many-body effective medium theory (EMT) to model the atomic interactions realistically. We test the predictions from isomorph theory for structure and dynamics by means of the radial distribution and the velocity autocorrelation functions, as well as the prediction of instantaneous equilibration after a jump between two isomorphic state points. Many properties of crystals tend to be dominated by defects, and many of the properties associated with these defects are expected to be isomorph invariant as well. This is investigated in this paper for the case of vacancy diffusion. In regard to the perfect crystal properties, we find the predicted invariance of structure and also, though less perfectly, of dynamics. We show results on the variation of the density-scaling exponent γ, which can be related to the Grüneisen parameter, for all six metals. We consider large density changes up to a factor of two, corresponding to very high pressures. Unlike systems modeled using the Lennard-Jones potential where the density-scaling exponent γ is almost constant, this quantity varies substantially when using the EMT potential and is also strongly material dependent.

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.

Perspective: Searching for simplicity rather than universality in glass-forming liquids

This article gives an overview of experimental results on dynamics in bulk glass-forming molecular liquids. Rather than looking for phenomenology that is universal, in the sense that it is seen in all liquids, the focus is on identifying the basic characteristics, or "stylized facts," of the glass transition problem, i.e., the central observations that a theory of the physics of glass formation should aim to explain in a unified manner.

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.