Hidden scale invariance in condensed matter

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.

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

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

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.

Observation of liquid glass in molecular dynamics simulations

Molecular anisotropy plays an important role in the glass transition of a liquid. Recently, a novel bulk glass state has been discovered by optical microscopy experiments on suspensions of ellipsoidal colloids. "Liquid glass" is a disordered analog of a nematic liquid crystal, in which rotation motion is hindered but particles diffuse freely. Global nematic order is suppressed as clusters of aligned particles intertwine. We perform Brownian dynamics simulations to test the structure and dynamics of a dense system of soft ellipsoidal particles. As seen in the experiments and in accordance with predictions from the mode coupling theory, on the time scale of our simulations, rotation motion is frozen but translation motion persists in liquid glass. Analyses of the dynamic structure functions for translation and rotation corroborates the presence of two separate glass transitions for rotation and translation, respectively. Even though the equilibrium state should be nematic, aligned structures remain small and orientational order rapidly decays with increasing size. Long-wavelength fluctuations are remnants of the isotropic-nematic transition.

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.

Simulation and Data-Driven Modeling of the Transport Properties of the Mie Fluid

This work reports the computation and modeling of the self-diffusivity (D*), shear viscosity (η*), and thermal conductivity (κ*) of the Mie fluid. The transport properties were computed using equilibrium molecular dynamics simulations for the Mie fluid with repulsive exponents (λr) ranging from 7 to 34 and at a fixed attractive exponent (λa) of 6 over the whole fluid density (ρ*) range and over a wide temperature (T*) range. The computed database consists of 17,212, 14,288, and 13,099 data points for self-diffusivity, shear viscosity, and thermal conductivity, respectively. The database is successfully validated against published simulation data. The above-mentioned transport properties are correlated using artificial neural networks (ANNs). Two modeling approaches were tested: a semiempirical formulation based on entropy scaling and an empirical formulation based on density and temperature as input variables. For the former, it was found that a unique formulation based on entropy scaling does not yield satisfactory results over the entire density range due to a divergent and incorrect scaling of the transport properties at low densities. For the latter empirical modeling approach, it was found that regularizing the data, e.g., modeling ρ*D* instead of D*, ln η* instead of η*, and ln κ* instead of κ*, as well as using the inverse of the temperature as an input feature, helps to ease the interpolation efforts of the artificial neural networks. The trained ANNs can model seen and unseen data over a wide range of density and temperature. Ultimately, the ANNs can be used alongside equations of state to regress effective force field parameters from volumetric and transport data.

Melting Is Well-Known, but Is It Also Well-Understood?

Contrary to continuous phase transitions, where renormalization group theory provides a general framework, for discontinuous phase transitions such a framework seems to be absent. Although the thermodynamics of the latter type of transitions is well-known and requires input from two phases, for melting a variety of one-phase theories and models based on solids has been proposed, as a generally accepted theory for liquids is (yet) missing. Each theory or model deals with a specific mechanism using typically one of the various defects (vacancies, interstitials, dislocations, interstitialcies) present in solids. Furthermore, recognizing that surfaces are often present, one distinguishes between mechanical or bulk melting and thermodynamic or surface-mediated melting. After providing the necessary preliminaries, we discuss both types of melting in relation to the various defects. Thereafter we deal with the effect of pressure on the melting process, followed by a discussion along the line of type of materials. Subsequently, some other aspects and approaches are dealt with. An attempt to put melting in perspective concludes this review.

Dynamics and local ordering of pentachloronitrobenzene: a molecular-dynamics investigation

Plastic phases are constituted by molecules whose centers of mass form a long range ordered crystalline lattice, but rotate in a more or less constrained way. Pentachloronitrobenzene (PCNB) is a quasi-planar hexa-substituted benzene formed by a benzene ring decorated with a -NO2 group and five chlorine atoms that displays below the melting point a layered structure of rhombohedral (R3̄) planes in which the molecules can rotate around a six-fold-like axis. Dielectric spectroscopy [Romanini et al., The Journal of Physical Chemistry C, 2016, 120, 10614] of this highly anisotropic phase revealed a complex relaxation dynamics with two coupled primary α processes, initially ascribed to the in-plane and out-of-plane components of the molecular dipole. In this work, we perform a series of molecular dynamics simulations together with single crystal X-ray synchrotron diffraction experiments to investigate the puzzling dynamics of PCNB. We conclude that the molecule undergoes very fast movements due to the high flexibility of the -NO2 group, and two slower movements in which only the in-plane rotation of the whole ring is involved. These two movements are related to fast attempts to perform a 60° in-plane rotation, and a diffusive motion that involves the rotation of the molecule completely decorrelating the dipole orientation. We have also investigated whether a homogeneous or a heterogeneous scenario is better suited to describe the restricted orientational disorder of this anisotropic phase both from a structural and dynamical point of view.

The receding contact line cools down during dynamic wetting

When a contact line (CL)-where a liquid-vapor interface meets a substrate-is put into motion, it is well known that the contact angle differs between advancing and receding CLs. Using non-equilibrium molecular dynamics simulations, we reveal another intriguing distinction between advancing and receding CLs: while temperature increases at an advancing CL-as expected from viscous dissipation, we show that temperature can drop at a receding CL. Detailed quantitative analysis based on the macroscopic energy balance around the dynamic CL showed that the internal energy change of the fluid due to the change of the potential field along the pathline out of the solid-liquid interface induced a remarkable temperature drop around the receding CL, in a manner similar to latent heat upon phase changes. This result provides new insights for modeling the dynamic CL, and the framework for heat transport analysis introduced here can be applied to a wide range of nanofluidic systems.

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

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

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.

Departures from perfect isomorph behavior in Lennard-Jones fluids and solids

Isomorphs are lines on a fluid or solid phase diagram along which the microstructure is invariant on affine density scaling of the molecular coordinates. Only inverse power (IP) and hard sphere potential systems are perfectly isomorphic. This work provides new theoretical tools and criteria to determine the extent of deviation from perfect isomorphicity for other pair potentials using the Lennard-Jones (LJ) system as a test case. A simple prescription for predicting isomorphs in the fluid range using the freezing line as a reference is shown to be quite accurate for the LJ system. The shear viscosity and self-diffusion coefficient scale well are calculated using this method, which enables comments on the physical significance of the correlations found previously in the literature to be made. The virial–potential energy fluctuation and the concept of an effective IPL system and exponent, n′, are investigated, particularly with reference to the LJ freezing and melting lines. It is shown that the exponent, n′, converges to the value 12 at a high temperature as ∼ T−1/2, where T is the temperature. Analytic expressions are derived for the density, temperature, and radius derivatives of the radial distribution function along an isomorph that can be used in molecular simulation. The variance of the radial distribution function and radial fluctuation function are shown to be isomorph invariant.

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.

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.

Microscopic Origins of the Viscosity of a Lennard-Jones Liquid

Unlike crystalline solids or ideal gases, transport properties remain difficult to describe from a microscopic point of view in liquids, whose dynamics result from complex energetic and entropic contributions at the atomic scale. Two scenarios are generally proposed: one represents the dynamics in a fluid as a series of energy-barrier crossings, leading to Arrhenius-like laws, while the other assumes that atoms rearrange themselves by collisions, as exemplified by the free volume model. To assess the validity of these two views, we computed, using molecular dynamics simulations, the transport properties of the Lennard-Jones fluid and tested to what extent the Arrhenius equation and the free volume model describe the temperature dependence of the viscosity and of the diffusion coefficient at fixed pressure. Although both models reproduce the simulation results over a wide range of pressure and temperature covering the liquid and supercritical states of the Lennard-Jones fluid, we found that the parameters of the free volume model can be estimated directly from local structural parameters, also obtained in the simulations. This consistency of the results gives more credibility to the free volume description of transport properties in liquids.

The Analysis of WJ Distribution as an Extended Gaussian Function: Case Study

The double exponential WJ distribution has been shown to competently describe extreme events and critical phenomena, while the Gaussian function has celebrated rich applications in many other fields. Here we present the analysis that the WJ distribution may be properly treated as an extended Gaussian function. Based on the Taylor expansion, we propose three methods to formulate the WJ distribution in the form of Gaussian functions, with Method I and Method III being accurate and self-consistent, and elaborate the relationship among the parameters of the functions. Moreover, we derive the parameter scaling formula of the WJ distribution to express a general Gaussian function, with the work illustrated by a classical case of extreme events and critical phenomena and application to topical medical image processing to prove the effectiveness of the WJ distribution rather than the Gaussian function. Our results sturdily advocate that the WJ distribution can elegantly represent a Gaussian function of arbitrary parameters, whereas the latter usually is not able to satisfactorily describe the former except for specific parameter sets. Thus, it is conclusive that the WJ distribution offers applicability in extreme events and critical phenomena as well as processes describable by the Gaussian function, namely, implying plausibly a unifying approach to the pertinent data processing of those quite distinct areas and establishing a link between relevant extreme value theories and Gaussian processes.

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.

A density scaling conjecture for aging glasses

The aging rate of glasses has traditionally been modeled as a function of temperature, T , andfictive temperature, while density, ρ, is not explicitly included as a parameter. However, this de-scription does not naturally connect to the modern understanding of what governs the relaxationrate in equilibrium. In equilibrium it is well known that the relaxation rate, γeq , depends on tem-perature and density. In addition a large class of systems obey density scaling which means therate specifically depends on the scaling parameter, Γ = e(ρ)/T , where e(ρ) is a system specificfunction. This paper present a generalization of the fictive temperature concept in terms of a fic-tive scaling paramter, Γfic , and a density scaling conjecture for aging glasses in which the agingrate depends on Γ and Γfic .

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.

Freezing Temperature and Density Scaling of Transport Coefficients

It is demonstrated that the freezing density scaling of transport coefficients in fluids, similar to the freezing temperature scaling, originates from the quasi-universal excess entropy scaling approach proposed by Rosenfeld. The freezing density scaling has a considerably wider applicability domain on the phase diagram of Lennard-Jones and related systems. As an illustration of its predictive power, we show that it reproduces with an excellent accuracy the shear viscosity coefficients of saturated liquid argon, krypton, xenon, and methane.

Gas–liquid crossover in the Lennard-Jones system

It is demonstrated that the crossover between gas- and liquid-like regions on the phase diagram of the Lennard-Jones system occurs at a fixed value of the density divided by its value at the freezing point, ρ/ ρfr ≃ 0.35. This definition is consistent with other definitions proposed recently. As a result, a very simple practical expression for the gas-to-liquid crossover line emerges.

Experimental and Modeling Comparison of the Dynamics of Capped and Freestanding Poly(2-chlorostyrene) Films

Proximity to a nonrepulsive wall is commonly considered to cause slower dynamics, which should lead to greater relaxation times for capped thin polymer films than for bulk melts. To the contrary, here we demonstrate that Al-capped films of poly(2-chlorostyrene) exhibit enhanced dynamics with respect to the bulk, similar to analogous freestanding films. To quantitatively resolve the impact of interfaces on whole film dynamics, we analyzed the experimental data via the Cooperative Free Volume rate model. We found that the interfacial region adjacent to a cap contains an excess of free volume (relative to the bulk) about half of that proximate to a free surface. Employing a useful analogy between confinement and pressure effects, we estimated that the effect of capping an 18 nm freestanding film would be equivalent to applying a pressure increase of 19 MPa.

Long Wavelength Thermal Density Fluctuations in Molecular and Polymer Glass-Forming Liquids: Experimental and Theoretical Analysis under Isobaric Conditions

We establish via an in-depth analysis of experimental data that the dimensionless compressibility (proportional to the dimensionless amplitude of long wavelength thermal density fluctuations) of one-component normal and supercooled liquids of chemically complex nonpolar and weakly polar molecules and polymers follows extremely well a surprisingly simple and general temperature dependence over an exceptionally wide range of pressures and temperatures. A theoretical basis for this behavior is shown to exist in the venerable van der Waals model and its more modern interpretations. Although associated hydrogen-bonding (and to a lesser degree strongly polar) liquids display modestly more complex behavior, rather simple temperature and pressure dependences are also discovered. A new approach to collapse the temperature- and pressure-dependent dimensionless compressibility data onto a master curve is formulated that differs from the empirical thermodynamic scaling approach. As a practical matter, we also find that the dimensionless compressibility scales well as an inverse power law with temperature with an exponent that is system dependent and decreases with pressure. At very high pressures and low temperatures, the thermal liquid behavior appears to approach (but not reach) a repulsion-dominated random close packing limit. All these findings are relevant to our recent theoretical work on the problem of activated relaxation and vitrification of supercooled molecular and polymeric liquids.

The dynamics of freestanding films: predictions for poly(2-chlorostyrene) based on bulk pressure dependence and thoughtful sample averaging

In this paper we model the segmental relaxation in poly(2-chlorostyrene) 18 nm freestanding films, using only data on bulk samples to characterize the system, and predict film relaxation times (τ) as a function of temperature that are in semi-quantitative agreement with film data. The ability to translate bulk characterization into film predictions is a direct result of our previous work connecting the effects of free surfaces in films with those of changing pressure in the bulk. Our approach combines the Locally Correlated Lattice (LCL) equation of state for prediction of free volume values (V_free) at any given density (ρ), which are then used in the Cooperative Free Volume (CFV) rate model to predict τ(T, V_free). A key feature of this work is that we calculate the locally averaged density profile as a function of distance from the surface, ρ_av(z), using the CFV-predicted lengthscale, L_coop(z), over which rearranging molecular segments cooperate. As we have shown in the past, ρ_av(z) is significantly broader than the localized profile, ρ(z), which translates into a relaxation profile, τ(z), exhibiting a breadth that mirrors experimental and simulated results. In addition, we discuss the importance of averaging the log of position dependent relaxation times across a film sample (〈log τ(z)〉), as opposed to averaging the relaxation times, themselves, in order to best approximate a whole sample-averaged value that can be directly compared to experiment.

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.

How attractive and repulsive interactions affect structure ordering and dynamics of glass-forming liquids

The theory developed in our previous papers [Phys. Rev. E 99, 030101(R) (2019)10.1103/PhysRevE.99.030101; Phys. Rev. E 103, 032611 (2021)10.1103/PhysRevE.103.032611] is applied in this paper to investigate the dependence of slowing down of dynamics of glass-forming liquids on the attractive and repulsive parts of intermolecular interactions. Through an extensive comparison of the behavior of a Lennard-Jones glass-forming liquid and that of its WCA reduction to a model with truncated pair potential without attractive tail, we demonstrate why the two systems exhibit very different dynamics despite having nearly identical pair correlation functions. In particular, we show that local structures characterized by the number of mobile and immobile particles around a central particle markedly differ in the two systems at densities and temperatures where their dynamics show large difference and nearly identical where dynamics nearly overlap. We also show how the parameter ψ(T) that measures the role of fluctuations embedded in the system on size of the cooperatively reorganizing cluster (CRC) and the crossover temperature T_{a} depend on the intermolecular interactions. These parameters stemming from the intermolecular interactions characterize the temperature and density dependence of structural relaxation time τ_{α}. The quantitative and qualitative agreements found with simulation results for the two systems suggest that our theory brings out the underlying features that determine the dynamics of glass-forming liquids.

Understanding simple liquids through statistical and deep learning approaches

Statistical and deep learning-based methods are employed to obtain insights into the quasi-universal properties of simple liquids. In the first part, a statistical model is employed to provide a probabilistic explanation for the similarity in the structure of simple liquids interacting with different pair potential forms, collectively known as simple liquids. The methodology works by sampling the radial distribution function and the number of interacting particles within the cutoff distance, and it produces the probability density function of the net force. We show that matching the probability distribution of the net force can be a direct route to parameterize simple liquid pair potentials with a similar structure, as the net force is the main component of the Newtonian equations of motion. The statistical model is assessed and validated against various cases. In the second part, we exploit DeepILST [A. Moradzadeh and N. R. Aluru, J. Phys. Chem. Lett. 10, 1242-1250 (2019)], a data-driven and deep-learning assisted framework to parameterize the standard 12-6 Lennard-Jones (LJ) pair potential, to find structurally equivalent/isomorphic LJ liquids that identify constant order parameter [τ=∫₀ ^ξ_cf gξ-1ξ²dξ, where gξ and ξ(=rρ¹³) are the reduced radial distribution function and radial distance, respectively] systems in the space of non-dimensional temperature and density of the LJ liquids. We also investigate the consistency of DeepILST in reproducibility of radial distribution functions of various quasi-universal potentials, e.g., exponential, inverse-power-law, and Yukawa pair potentials, quantified based on the radial distribution functions and Kullback-Leibler errors. Our results provide insights into the quasi-universality of simple liquids using the statistical and deep learning methods.

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

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

Relaxation dynamics of Pd-Ni-P metallic glass: decoupling of anelastic and viscous processes

The stress relaxation dynamics of metallic glass Pd₄₀Ni₄₀P₂₀was studied in both supercooled liquid and glassy states. Time-temperature superposition was found in the metastable liquid, implying an invariant shape of the distribution of times involved in the relaxation. Once in the glass state, the distribution of relaxation times broadens as temperature and fictive temperature decrease, eventually leading to a decoupling of the relaxation in two processes. While the slow one keeps a viscous behavior, the fast one shows an anelastic nature and a time scale similar to that of the collective atomic motion measured by x-ray photon correlation spectroscopy (XPCS). These results suggest that the atomic dynamics of metallic glasses, as determined by XPCS at low temperatures in the glass state, can be related to the rearrangements of particles responsible of the macroscopically reversible anelastic behavior.

Transport properties of Lennard-Jones fluids: Freezing density scaling along isotherms

It is demonstrated that properly reduced transport coefficients (self-diffusion, shear viscosity, and thermal conductivity) of Lennard-Jones fluids along isotherms exhibit quasi-universal scaling on the density divided by its value at the freezing point. Moreover, this scaling is closely related to the density scaling of transport coefficients of hard-sphere fluids. The Stokes-Einstein relation without the hydrodynamic diameter is valid in the dense fluid regime. The lower density boundary of its validity can serve as a practical demarcation line between gaslike and liquidlike regimes.

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.

Pressure and Temperature Dependence of Local Structure and Dynamics in an Ionic Liquid

A detailed understanding of the local dynamics in ionic liquids remains an important aspect in the design of new ionic liquids as advanced functional fluids. Here, we use small-angle X-ray scattering and quasi-elastic neutron spectroscopy to investigate the local structure and dynamics in a model ionic liquid as a function of temperature and pressure, with a particular focus on state points (P,T) where the macroscopic dynamics, i.e., conductivity, is the same. Our results suggest that the initial step of ion transport is a confined diffusion process, on the nanosecond timescale, where the motion is restricted by a cage of nearest neighbors. This process is invariant considering timescale, geometry, and the participation ratio, at state points of constant conductivity, i.e., state points of isoconductivity. The connection to the nearest-neighbor structure is underlined by the invariance of the peak in the structure factor corresponding to nearest-neighbor correlations. At shorter timescales, picoseconds, two localized relaxation processes of the cation can be observed, which are not directly linked to ion transport. However, these processes also show invariance at isoconductivity. This points to that the overall energy landscape in ionic liquids responds in the same way to density changes and is mainly governed by the nearest-neighbor interactions.

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.

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.