Ulf R. Pedersen

Pressure-energy correlations in liquids. I. Results from computer simulations

We show that a number of model liquids at fixed volume exhibit strong correlations between equilibrium fluctuations of the configurational parts of (instantaneous) pressure and energy. We present detailed results for 13 systems, showing in which systems these correlations are significant. These include Lennard-Jones liquids (both single- and two-component) and several other simple liquids, neither hydrogen-bonding liquids such as methanol and water, nor the Dzugutov liquid, which has significant contributions to pressure at the second nearest neighbor distance. The pressure-energy correlations, which for the Lennard-Jones case are shown to also be present in the crystal and glass phases, reflect an effective inverse power-law potential dominating fluctuations, even at zero and slightly negative pressure. An exception to the inverse power-law explanation is a liquid with hard-sphere repulsion and a square-well attractive part, where a strong correlation is observed, but only after time averaging. The companion paper [N. P. Bailey et al., J. Chem. Phys. 129, 184508 (2008)] gives a thorough analysis of the correlations, with a focus on the Lennard-Jones liquid, and a discussion of some experimental and theoretical consequences.

Pressure-energy correlations in liquids. II. Analysis and consequences

We present a detailed analysis and discuss consequences of the strong correlations of the configurational parts of pressure and energy in their equilibrium fluctuations at fixed volume reported for simulations of several liquids in the previous paper [N. P. Bailey et al., J. Chem. Phys. 129, 184507 (2008)]. The analysis concentrates specifically on the single-component Lennard-Jones system. We demonstrate that the potential may be replaced, at fixed volume, by an effective power law but not simply because only short-distance encounters dominate the fluctuations. Indeed, contributions to the fluctuations are associated with the whole first peak of the radial distribution function, as we demonstrate by an eigenvector analysis of the spatially resolved covariance matrix. The reason the effective power law works so well depends crucially on going beyond single-pair effects and on the constraint of fixed volume. In particular, a better approximation to the potential includes a linear term, which contributes to the mean values of potential energy and virial, but little to their fluctuations, for density fluctuations which conserve volume. We also study in detail the zero temperature limit of the (classical) crystalline phase, where the correlation coefficient becomes very close, but not equal, to unity, in more than one dimension; in one dimension the limiting value is exactly unity. In the second half of the paper we consider four consequences of strong pressure-energy correlations: (1) analyzing experimental data for supercritical argon we find 96% correlation; (2) we discuss the particular significance acquired by the correlations for viscous van der Waals liquids approaching the glass transition: For strongly correlating viscous liquids knowledge of just one of the eight frequency-dependent thermoviscoelastic response functions basically implies knowledge of them all; (3) we reinterpret aging simulations of ortho-terphenyl carried out by Mossa et al. [Eur. Phys. J. B 30, 351 (2002)], showing their conclusions follow from the strongly correlating property; and (4) we briefly discuss the presence of the correlations (after appropriate time averaging) in model biomembranes, showing that significant correlations may be present even in quite complex systems.

Strong Pressure-Energy Correlations in van der Waals Liquids

Strong correlations between equilibrium fluctuations of the configurational parts of pressure and energy are found in computer simulations of the Lennard-Jones liquid and other simple liquids, but not for hydrogen-bonding liquids such as methanol and water. The correlations that are present also in the crystal and glass phases reflect an effective inverse power-law repulsive potential dominating fluctuations, even at zero and slightly negative pressure. In experimental data for supercritical argon, the correlations are found to be approximately 96%. Consequences for viscous liquid dynamics are discussed.

Pressure-energy correlations in liquids. III. Statistical mechanics and thermodynamics of liquids with hidden scale invariance

Computer simulations recently revealed that several liquids exhibit strong correlations between virial and potential energy equilibrium fluctuations in the NVT ensemble (U. R. Pedersen et al., Phys. Rev. Lett. 100, 015701 (2008)). In order to investigate whether these correlations are present also far from equilibrium constant-volume aging following a temperature down jump from equilibrium was simulated for two strongly correlating liquids, an asymmetric dumbbell model and Lewis-Wahnstrom OTP, as well as for SPC water that is not strongly correlating. For the two strongly correlating liquids virial and potential energy follow each other closely during the aging towards equilibrium. For SPC water, on the other hand, virial and potential energy vary with little correlation as the system ages towards equilibrium. Further proof that strong pressure-energy correlations express a configuration space property comes from monitoring pressure and energy during the crystallization (reported here for the first time) of supercooled Lewis-Wahnstrom OTP at constant temperature.

Geometry of slow structural fluctuations in a supercooled binary alloy.

The liquid structure of a glass-forming binary alloy is studied using molecular dynamics simulations. The analysis employs the geometrical approach of Frank and Kasper to establish that the supercooled liquid contains extended clusters characterized by the same short range order as the crystal. The steep increase in the heat capacity on cooling is directly coupled to the growing fluctuations of the Frank-Kasper clusters. The relaxation of particles in the clusters dominates the slow tail of the self-intermediate scattering function.

Hidden scale invariance in molecular van der Waals liquids: A simulation study

We address a recent conjecture according to which the relaxation time τ of a viscous liquid obeys density scaling (τ = F (ρ/T ) where ρ is density) if the liquid is “strongly correlating,” i.e., has almost 100% correlation between equilibrium virial and potential-energy fluctuations [Pedersen et al., PRL 100, 011201 (2008)]. Computer simulations of two model liquids an asymmetric dumbbell model and the Lewis-Wahnström OTP model confirm the conjecture and demonstrate that the scaling exponent γ can be accurately predicted from equilibrium fluctuations.

Repulsive Reference Potential Reproducing the Dynamics of a Liquid with Attractions

A well-known result of liquid state theory is that the structure of dense fluids is mainly determined by their repulsive forces. The Weeks-Chandler-Andersen potential, which cuts intermolecular potentials at their minima, is therefore often used as a reference. However, this cannot reproduce the viscous dynamics of the Kob-Andersen binary Lennard-Jones liquid [Berthier and Tarjus, Phys. Rev. Lett. 103, 170601 (2009)]. This paper shows that repulsive inverse-power-law potentials provide a reference for this liquid that reproduces its structure, dynamics, and isochoric heat capacity.

Stability of supercooled binary liquid mixtures

Recently, the supercooled Wahnstrom binary Lennard-Jones mixture was partially crystallized into MgZn(2) phase crystals in lengthy molecular dynamics simulations. We present molecular dynamics simulations of a modified Kob-Andersen binary Lennard-Jones mixture that also crystallizes in lengthy simulations here, however, by forming pure fcc crystals of the majority component. The two findings motivate this paper that gives a general thermodynamic and kinetic treatment of the stability of supercooled binary mixtures, emphasizing the importance of negative mixing enthalpy whenever present. The theory is used to estimate the crystallization time in a Kob-Andersen mixture from the crystallization time in a series of related systems. At T=0.40 we estimate this time to be 5x10(7) time units ( approximately 0.1 ms). A new binary Lennard-Jones mixture is proposed that is not prone to crystallization and faster to simulate than the two standard binary Lennard-Jones mixtures. This is obtained by removing the like-particle attractions by switching to Weeks-Chandler-Andersen type potentials, while maintaining the unlike-particle attraction.At density 1.2 the Kob-Andersen binary Lennard-Jones liquid partly crystallizes in the temperature interval [0.39, 0.44] after typically 10-100 microseconds (Argon units). The crystallization is initiated by a phase separation where the large (A) particles cluster in a volume void of B particles. We investigate a modification of the Kob-Andersen system where the attraction between particles of the same type is removed, thus disfavoring phase separation. We have not been able to crystallize this new system.

Direct calculation of the solid-liquid Gibbs free energy difference in a single equilibrium simulation

Computing phase diagrams of model systems is an essential part of computational condensed matter physics. In this paper, we discuss in detail the interface pinning (IP) method for calculation of the Gibbs free energy difference between a solid and a liquid. This is done in a single equilibrium simulation by applying a harmonic field that biases the system towards two-phase configurations. The Gibbs free energy difference between the phases is determined from the average force that the applied field exerts on the system. As a test system, we study the Lennard-Jones model. It is shown that the coexistence line can be computed efficiently to a high precision when the IP method is combined with the Newton-Raphson method for finding roots. Statistical and systematic errors are investigated. Advantages and drawbacks of the IP method are discussed. The high pressure part of the temperature-density coexistence region is outlined by isomorphs.

Feasibility of a single-parameter description of equilibrium viscous liquid dynamics

Molecular dynamics results for the dynamic Prigogine-Defay ratio are presented for two glass-forming liquids, thus evaluating the experimentally relevant quantity for testing whether metastable-equilibrium liquid dynamics is described by a single parameter to a good approximation. For the Kob-Andersen binary Lennard-Jones mixture as well as for an asymmetric dumbbell model liquid, a single-parameter description works quite well. This is confirmed by time-domain results where it is found that energy and pressure fluctuations are strongly correlated on the alpha time scale in the constant-volume, constant-temperature ensemble; similarly, energy and volume fluctuations correlate strongly in the constant-pressure, constant-temperature ensemble.