Search

Lennard-Jones (LJ) systems exhibit strikingly invariant structure and dynamics when energy polydispersity is introduced [Ingebrigtsen and Dyre, J. Phys. Chem. B 127, 2837 (2023)]. For instance, at a given state point the radial distribution function and the mean-square displacement as a function of time are virtually unaffected by energy polydispersity, which is in contrast to what happens when size polydispersity is introduced. We here argue - and validate by simulations of up to 30% polydispersity - that this invariance reflects an approximate invariance of the constant-potential-energy surface. $NVU$ dynamics is defined as geodesic motion at constant potential energy; because this dynamics is equivalent to Newtonian dynamics in the thermodynamic limit, the approximate invariance of the constant-potential-energy surface implies virtually the same structure and dynamics of energy polydisperse LJ systems as for the single-component version. In contrast, the constant-potential-energy surface is shown to be significantly affected by the introduction of size polydispersity.

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); Martiniani et al., Phys. Rev. X 9, 011031 (2019)], 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.

We clarify the relationship between freezing, melting and the onset of glassy dynamics in the prototypical glass-forming Kob-Andersen mixture. Our starting point is a precise definition of the onset of glassiness, as expressed by the emergence of an inflection in the time-dependent correlation functions. By scanning the temperature-composition phase diagram of the model, we find that the onset temperature barely varies with concentration, unlike the freezing temperature, which shows a marked drop at the eutectic point. We observe, however, a surprising correspondence between the onset of glassiness and the solidus line, along which the underlying crystalline phases melt. At fixed concentration, the freezing and onset temperatures display similar pressure dependencies, which are very well predicted by the isomorph theory and are encoded in the variation of the excess entropy. While our results rule out a general connection between thermodynamic metastability and glassiness, they call for a careful assessment of the role of crystalline precursors in glass-forming liquids., Comment: 6 pages, 4 figures, supplemental material available as ancillary file

Physical ageing is the generic term for irreversible processes in glassy materials resulting from molecular rearrangements. One formalism for describing such ageing processes involves the concept of material time, which may be thought of as time measured on a clock whose rate changes as the glass ages. Experimental determination of material time has so far not been realized, however. Here, we show how dynamic light-scattering measurements provide a way forward. We determined the material time for an ageing sample of the glass-former 1-phenyl-1-propanol after temperature jumps close to the glass transition from the time-autocorrelation function of the intensity fluctuations probed by multispeckle dynamic light scattering. These fluctuations are shown to be stationary and reversible when regarded as a function of the material time. The glass-forming colloidal synthetic clay Laponite and a chemically ageing curing epoxy are also shown to display material-time-reversible scattered-light intensity fluctuations, and simulations of an ageing binary system monitoring the potential energy confirm material-time reversibility. In addition to demonstrating direct measurements of the material time, our findings identify a fundamental property of ageing in quite different contexts that presents a challenge to the current theories of ageing.

In both experiments and simulations the most commonly studied kind of parameter polydispersity is that of varying particles size. This paper investigates by simulations the effects of introducing polydispersity in other parameters for two-dimensional Active Brownian Particles with Yukawa pair interactions. Polydispersity is studied separately in the translational and rotational diffusion coefficients, as well as in the swim velocity $v_0$. Uniform and binary parameter distributions are considered in both the homogeneous and the motility-induced phase-separation (MIPS) phases. We find only minute changes in structure and dynamics upon the introduction of parameter polydispersity, even for situations involving 50% polydispersity. The reason for this is not clear. An exception is the case of $v_0$ polydispersity for which the average radial distribution function with changing polydispersity shows significant variations in the MIPS phase. Even in this case, however, the dynamics is only modestly affected. As a possible application of our findings, we suggest that a temporary introduction of polydispersity into a single-component active-matter model characterized by a very long equilibration time, i.e., a glass-forming active system, may be used to equilibrate the system efficiently by particle swaps.

This paper studies size-polydisperse Lennard-Jones systems described by active Ornstein-Uhlenbeck particle dynamics. The focus is on the existence of isomorphs (curves of invariant structure and dynamics) in the model's three-dimensional phase diagram. Isomorphs are traced out from a single steady-state configuration by means of the configurational-temperature method. Good invariance of the reduced-unit radial distribution function and the mean-square displacement as a function of time is demonstrated for three uniform-distribution polydispersities, 12%, 23%, and 29%. Comparing to active-matter isomorphs generated by the analytical direct-isomorph-check method, the latter give somewhat poorer invariance of the structure, but better invariance of the dynamics. We conclude that both methods can be used to quickly get an overview of the phase diagram of polydisperse AOUP models involving a potential-energy function obeying the hidden-scale-invariance property required for isomorph theory to apply.

This paper suggests using the configurational temperature $\Tc$ for quantifying how far an active-matter system is from thermal equilibrium. We measure this ``distance'' by the ratio of the systemic temperature $\Ts$ to $\Tc$, where $\Ts$ is the canonical-ensemble temperature for which the average potential energy is equal to that of the active-matter system. $\Tc$ is ``local'' in the sense that it is the average of a function, which only depends on how the potential energy varies in the vicinity of a given configuration; in contrast $\Ts$ is a global quantity. The quantity $\Ts/\Tc$ is straightforward to evaluate in a computer simulation; equilibrium simulations in conjunction with a single steady-state active-matter configuration are enough to determine $\Ts/\Tc$. We validate the suggestion that $\Ts/\Tc$ quantifies the deviation from thermal equilibrium by data for the radial distribution function of 3d Kob-Andersen and 2d Yukawa active-matter models with active Ornstein-Uhlenbeck and active Brownian Particle dynamics. Moreover, we show that $\Ts/\Tc$, structure, and dynamics of the homogeneous phase are all approximately invariant along the motility-induced phase separation (MIPS) boundary in the phase diagram of the 2d Yukawa model. The measure $\Ts/\Tc$ is not limited to active matter; it can be used for quantifying how far any system involving a potential-energy function, e.g., a driven Hamiltonian system, is from thermal equilibrium., Comment: Paper I is available at arXiv:2204.06819

Physical aging deals with slow property changes over time caused by molecular rearrangements. This is relevant for non-crystalline materials like polymers and inorganic glasses, both in production and during subsequent use. The Narayanaswamy theory from 1971 describes physical aging - an inherently nonlinear phenomenon - in terms of a linear convolution integral over the so-called material time $\xi$. The resulting "Tool-Narayanaswamy (TN) formalism" is generally recognized to provide an excellent description of physical aging for small, but still highly nonlinear temperature variations. The simplest version of the TN formalism is single-parameter aging according to which the clock rate $d\xi/dt$ is an exponential function of the property monitored [T. Hecksher et al., J. Chem. Phys. 142, 241103 (2015)]. For temperature jumps starting from thermal equilibrium, this leads to a first-order differential equation for property monitored, involving a system-specific function. The present paper shows analytically that the solution to this equation to first order in the temperature variation has a universal expression in terms of the zeroth-order solution, $R_0(t)$. Numerical data for a binary Lennard-Jones glass former probing the potential energy confirm that, in the weakly nonlinear limit, the theory predicts aging correctly from $R_0(t)$ (which by the fluctuation-dissipation theorem is the normalized equilibrium potential-energy time-autocorrelation function).

A simple model for viscous liquid dynamics is introduced. Consider the surface of the union of hyper-spheres centered at random positions inside a hypercube with periodic boundary conditions. It is argued and demonstrated by numerical simulations that at high dimensions geodetic flows on this surface is a good model for viscous liquid dynamics. It is shown that this simple model exhibits viscous dynamics for densities above the percolation threshold in $8$, $12$ and $16$ dimensions. Thus the slowing down of the dynamics, measured by the mean-squared displacement, extends to several orders of magnitude similarly to what is observed in other models for viscous dynamics. Furthermore, the shape of the mean-squared displacement is to a very good approximation the same as for the standard model in simulations of viscous liquids: the Kob-Andersen binary Lennard Jones mixture., Comment: 4 pages, 5 Figures

It is shown that the residual entropy (entropy minus that of the ideal gas at the same temperature and density) is mostly synonymous with the independent variable of density scaling, identifying a direct link between these two approaches. The two-body residual entropy is demonstrated to not be a suitable surrogate for the total residual entropy in the gas phase. The residual entropy and the effective hardness of interaction (itself a derivative at constant residual entropy) are studied for the Lennard-Jones monomer and dimer as well as a range of rigid molecular models for carbon dioxide. It is observed that the density scaling exponent is related to the two-body interactions.

This paper shows that the configurational temperature of liquid-state theory, $\Tc$, 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 $\Tc$ 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, demonstrating lines of approximate reduced-unit invariance of the radial distribution function and time-dependent mean-square displacement., Comment: Paper II is available at arXiv:2212.09041

Liquids displaying strong virial-potential energy correlations conform to an approximate density scaling of their structural and dynamical observables. This scaling property does not extend to the entire phase diagram, in general. The validity of the scaling can be quantified by a correlation coefficient. In this work a simple scheme to predict the correlation coefficient and the density-scaling exponent is presented. Although this scheme is exact only in the dilute gas regime or in high dimension d, a comparison with results from molecular dynamics simulations in d = 1 to 4 shows that it reproduces well the behavior of generalized Lennard-Jones systems in a large portion of the fluid phase., Comment: Submission to SciPost

This paper investigates the relation between the density-scaling exponent $\gamma$ and the virial potential-energy correlation coefficient $R$ at several thermodynamic state points in three dimensions for the generalized $(2n,n)$ Lennard-Jones (LJ) system for $n=4, 9, 12, 18$, as well as for the standard $n=6$ LJ system in two, three, and four dimensions. The state points studied include many low-density states at which the virial potential-energy correlations are not strong. For these state points we find the roughly linear relation $\gamma\cong 3nR/d$ in $d$ dimensions. This result is discussed in light of the approximate "extended inverse power law" description of generalized LJ potentials [N. P. Bailey et al., J. Chem. Phys. 129, 184508 (2008)]. In the plot of $\gamma$ versus $R$ there is in all cases a transition around $R\approx 0.9$, above which $\gamma$ starts to decrease as $R$ approaches unity. This is consistent with the fact that $\gamma\rightarrow 2n/d$ for $R\rightarrow 1$, a limit that is approached at high densities and/or temperatures at which the repulsive $r^{-2n}$ term dominates the physics.

The recent theoretical prediction by Maimbourg and Kurchan [arXiv:1603.05023] that for regular pair-potential systems the virial potential-energy correlation coefficient increases towards unity as the dimension $d$ goes to infinity is investigated for the standard 12-6 Lennard-Jones fluid. This is done by computer simulations for $d=2,3,4$ going from the critical point along the critical isotherm/isochore to higher density/temperature. In all cases the virial potential-energy correlation coefficient increases significantly. For a given density and temperature relative to the critical point, with increasing number of dimension the Lennard-Jones system conforms better to the hidden-scale-invariance property characterized by high virial potential-energy correlations (a property that leads to the existence of isomorphs in the thermodynamic phase diagram, implying that it becomes effectively one-dimensional in regard to structure and dynamics). The present paper also gives the first numerical demonstration of isomorph invariance of structure and dynamics in four dimensions. Our findings emphasize the need for a universally applicable $1/d$ expansion in liquid-state theory; we conjecture that the systems known to obey hidden scale invariance in three dimensions are those for which the yet-to-be-developed $1/d$ expansion converges rapidly.

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 the isomorph theory. First the freezing/melting lines for 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 phase. Structure is probed by the radial distribution function and the structure factor and dynamics is probed by the mean-square displacement, the intermediate scattering function, and the shear viscosity. Studying these properties by reference to the isomorph theory explains why known single-phase melting criteria holds, e.g., the Hansen-Verlet and the Lindemann criterion, 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 the isomorph theory and that the invariants are not peculiar to the freezing and melting lines, but hold along all isomorphs., Comment: 21 pg, 12 figures Accepted from PCCP (Physical Chemistry Chemical Physics)

RUMD is a general purpose, high-performance molecular dynamics (MD) simulation package running on graphical processing units (GPU's). RUMD addresses the challenge of utilizing the many-core nature of modern GPU hardware when simulating small to medium system sizes (roughly from a few thousand up to hundred thousand particles). It has a performance that is comparable to other GPU-MD codes at large system sizes and substantially better at smaller sizes.RUMD is open-source and consists of a library written in C++ and the CUDA extension to C, an easy-to-use Python interface, and a set of tools for set-up and post-simulation data analysis. The paper describes RUMD's main features, optimizations and performance benchmarks., Comment: 22 pages. Resubmission to SciPost Physics