Scaling of the dynamics of flexible Lennard-Jones chains

Modulating Coarse-Grained Dynamics by Perturbing Free Energy Landscapes

We introduce an approach to describe the long-time dynamics of multiatomic molecules by modulating the free energy landscape (FEL) to capture dominant features of the energy-barrier crossing dynamics of the all-atom (AA) system. Notably, we establish that the self-diffusion coefficient of coarse-grained (CG) systems can be accurately delineated by enhancing conservative force fields with high-frequency perturbations. Using theoretical arguments, we show that these perturbations do not alter the lower-order distribution functions, thereby preserving the structure of the AA system after coarse-graining. We demonstrate the utility of this approach using molecular dynamics simulations of simple molecules in bulk with distinct dynamical characteristics with and without time scale separations as well as for inhomogeneous systems where a fluid is confined in a slit-like nanochannel. Additionally, we also apply our approach to more powerful many-body potentials optimized by using machine learning (ML).

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.

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.

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.

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.

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.

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.

Isochronal superpositioning of the caged dynamics, the α, and the Johari-Goldstein β relaxations in metallic glasses

The superposition of the frequency dispersions of the structural α relaxation determined at different combinations of temperature T and pressure P while maintaining its relaxation time τ_α(T, P) constant (i.e., isochronal superpositioning) has been well established in molecular and polymeric glass-formers. Not known is whether the frequency dispersion or time dependence of the faster processes including the caged molecule dynamics and the Johari-Goldstein (JG) β relaxation possesses the same property. Experimental investigation of this issue is hindered by the lack of an instrument that can cover all three processes. Herein, we report the results from the study of the problem utilizing molecular dynamics simulations of two different glass-forming metallic alloys. The mean square displacement 〈Δr²t〉, the non-Gaussian parameter α₂t, and the self-intermediate scattering function F_sq,t at various combinations of T and P were obtained over broad time range covering the three processes. Isochronal superpositioning of 〈Δr²t〉, α₂t, and F_sq,t was observed over the entire time range, verifying that the property holds not only for the α relaxation but also for the caged dynamics and the JG β relaxation. Moreover, we successfully performed density ρ scaling of the time τ_α2,maxT,P at the peak of α₂t and the diffusion coefficient D(T, P) to show both are functions of ρ^γ/T with the same γ. It follows that the JG β relaxation time τ_β(T, P) is also a function of ρ^γ/T since τ_α2,maxT,P corresponds to τ_β(T, P).

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.

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.

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.

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.

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.

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.

Recent Progress towards Chemically-Specific Coarse-Grained Simulation Models with Consistent Dynamical Properties

Coarse-grained (CG) models can provide computationally efficient and conceptually simple characterizations of soft matter systems. While generic models probe the underlying physics governing an entire family of free-energy landscapes, bottom-up CG models are systematically constructed from a higher-resolution model to retain a high level of chemical specificity. The removal of degrees of freedom from the system modifies the relationship between the relative time scales of distinct dynamical processes through both a loss of friction and a “smoothing” of the free-energy landscape. While these effects typically result in faster dynamics, decreasing the computational expense of the model, they also obscure the connection to the true dynamics of the system. The lack of consistent dynamics is a serious limitation for CG models, which not only prevents quantitatively accurate predictions of dynamical observables but can also lead to qualitatively incorrect descriptions of the characteristic dynamical processes. With many methods available for optimizing the structural and thermodynamic properties of chemically-specific CG models, recent years have seen a stark increase in investigations addressing the accurate description of dynamical properties generated from CG simulations. In this review, we present an overview of these efforts, ranging from bottom-up parameterizations of generalized Langevin equations to refinements of the CG force field based on a Markov state modeling framework. We aim to make connections between seemingly disparate approaches, while laying out some of the major challenges as well as potential directions for future efforts.

Perspective: Excess-entropy scaling

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

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

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

Communication: Simple liquids' high-density viscosity

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

Isomorph theory of physical aging

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

Thermodynamic scaling of relaxation: insights from anharmonic elasticity

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

Communication: Polymer entanglement dynamics: Role of attractive interactions

The coupled dynamics of entangled polymers, which span broad time and length scales, govern their unique viscoelastic properties. To follow chain mobility by numerical simulations from the intermediate Rouse and reptation regimes to the late time diffusive regime, highly coarse grained models with purely repulsive interactions between monomers are widely used since they are computationally the most efficient. Here using large scale molecular dynamics simulations, the effect of including the attractive interaction between monomers on the dynamics of entangled polymer melts is explored for the first time over a wide temperature range. Attractive interactions have little effect on the local packing for all temperatures T and on the chain mobility for T higher than about twice the glass transition T_g. These results, across a broad range of molecular weight, show that to study the dynamics of entangled polymer melts, the interactions can be treated as pure repulsive, confirming a posteriori the validity of previous studies and opening the way to new large scale numerical simulations.

Pair Potential That Reproduces the Shape of Isochrones in Molecular Liquids

Many liquids have curves (isomorphs) in their phase diagrams along which structure, dynamics, and some thermodynamic quantities are invariant in reduced units. A substantial part of their phase diagrams is thus effectively one dimensional. The shapes of these isomorphs are described by a material-dependent function of density, h(ρ), which for real liquids is well approximated by a power law, ρ(γ). However, in simulations, a power law is not adequate when density changes are large; typical models, such as Lennard-Jones liquids, show that γ(ρ) ≡ d ln h(ρ)/d ln ρ is a decreasing function of density. This article presents results from computer simulations using a new pair potential that diverges at a nonzero distance and can be tuned to give a more realistic shape of γ(ρ). Our results indicate that the finite size of molecules is an important factor to take into account when modeling liquids over a large density range.

Simple liquids' quasiuniversality and the hard-sphere paradigm

This topical review discusses the quasiuniversality of simple liquids' structure and dynamics and two possible justifications of it. The traditional one is based on the van der Waals picture of liquids in which the hard-sphere system reflects the basic physics. An alternative explanation argues that all quasiuniversal liquids to a good approximation conform to the same equation of motion, referring to the exponentially repulsive pair-potential system as the basic reference system. The paper, which is aimed at non-experts, ends by listing a number of open problems in the field.

Effect of Energy Polydispersity on the Nature of Lennard-Jones Liquids

In the companion paper [ Ingebrigtsen , T. S. ; Tanaka , H. J. Phys. Chem. B 2015 , 119 , 11052 ] the effect of size polydispersity on the nature of Lennard-Jones (LJ) liquids, which represent most molecular liquids without hydrogen bonds, was studied. More specifically, it was shown that even highly size polydisperse LJ liquids are Roskilde-simple (RS) liquids. RS liquids are liquids with strong correlation between constant volume equilibrium fluctuations of virial and potential energy and are simpler than other types of liquids. Moreover, it was shown that size polydisperse LJ liquids have isomorphs to a good approximation. Isomorphs are curves in the phase diagram of RS liquids along which structure, dynamics, and some thermodynamic quantities are invariant in dimensionless (reduced) units. In this paper, we study the effect of energy polydispersity on the nature of LJ liquids. We show that energy polydisperse LJ liquids are RS liquids. However, a tendency of particle segregation, which increases with the degree of polydispersity, leads to a loss of strong virial-potential energy correlation but is mitigated by increasing temperature and/or density. Isomorphs are a good approximation also for energy polydisperse LJ liquids, although particle-resolved quantities display a somewhat poorer scaling compared to the mean quantities along the isomorph.

Freezing and melting line invariants of the Lennard-Jones system

The invariance of several structural and dynamical properties of the Lennard-Jones (LJ) system along the freezing and melting lines is interpreted in terms of isomorph theory. First the freezing/melting lines of the LJ system are shown to be approximated by isomorphs. Then we show that the invariants observed along the freezing and melting isomorphs are also observed on other isomorphs in the liquid and crystalline phases. The structure is probed by the radial distribution function and the structure factor and dynamics are probed by the mean-square displacement, the intermediate scattering function, and the shear viscosity. Studying these properties with reference to isomorph theory explains why the known single-phase melting criteria hold, e.g., the Hansen-Verlet and the Lindemann criteria, and why the Andrade equation for the viscosity at freezing applies, e.g., for most liquid metals. Our conclusion is that these empirical rules and invariants can all be understood from isomorph theory and that the invariants are not peculiar to the freezing and melting lines, but hold along all isomorphs.

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

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

Effect of Size Polydispersity on the Nature of Lennard-Jones Liquids

Polydisperse fluids are encountered everywhere in biological and industrial processes. These fluids naturally show a rich phenomenology exhibiting fractionation and shifts in critical point and freezing temperatures. We study here the effect of size polydispersity on the basic nature of Lennard-Jones (LJ) liquids, which represent most molecular liquids without hydrogen bonds, via two- and three-dimensional molecular dynamics computer simulations. A single-component liquid constituting spherical particles and interacting via the LJ potential is known to exhibit strong correlations between virial and potential energy equilibrium fluctuations at constant volume. This correlation significantly simplifies the physical description of the liquid, and these liquids are now known as Roskilde-simple (RS) liquids. We show that this simple nature of the single-component LJ liquid is preserved even for very high polydispersities (above 40% polydispersity for the studied uniform distribution). We also investigate isomorphs of moderately polydisperse LJ liquids. Isomorphs are curves in the phase diagram of RS liquids along which structure, dynamics, and some thermodynamic quantities are invariant in dimensionless units. We find that isomorphs are a good approximation even for polydisperse LJ liquids. The theory of isomorphs thus extends readily to size polydisperse fluids and can be used to improve even further the understanding of these intriguing systems.

Variation of the dynamic susceptibility along an isochrone

Koperwas et al. showed in a recent paper [Phys. Rev. Lett. 111, 125701 (2013)] that the dynamic susceptibility χ4 as estimated by dielectric measurements for certain glass-forming liquids decreases substantially with increasing pressure along a curve of constant relaxation time. This observation is at odds with other measures of dynamics being invariant and seems to pose a problem for theories of glass formation. We show that this variation is in fact consistent with predictions for liquids with hidden scale invariance: Measures of dynamics at constant volume are invariant along isochrones, called isomorphs in such liquids, but contributions to fluctuations from long-wavelength fluctuations can vary. This is related to the known noninvariance of the isothermal bulk modulus. Considering the version of χ4 defined for the NVT ensemble, data from simulations of a binary Lennard-Jones liquid show in fact a slight increase with increasing density. This is a true departure from the formal invariance expected for this quantity.

Hidden scale invariance in condensed matter

Recent developments show that many liquids and solids have an approximate "hidden" scale invariance that implies the existence of lines in the thermodynamic phase diagram, so-called isomorphs, along which structure and dynamics in properly reduced units are invariant to a good approximation. This means that the phase diagram becomes effectively one-dimensional with regard to several physical properties. Liquids and solids with isomorphs include most or all van der Waals bonded systems and metals, as well as weakly ionic or dipolar systems. On the other hand, systems with directional bonding (hydrogen bonds or covalent bonds) or strong Coulomb forces generally do not exhibit hidden scale invariance. The article reviews the theory behind this picture of condensed matter and the evidence for it coming from computer simulations and experiments.