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

Abstract

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.

Pressure-energy correlations in liquids. V. Isomorphs in generalized Lennard-Jones systems

“…. , r N ) is the potential energy function and it is understood that the constant C 12 depends only on the state points (1) and (2). The property of being isomorphic defines a mathematical equivalence relation on the set of state points.…”

“…This is the final paper in a series [1][2][3][4] investigating the properties of strongly correlating liquids, 5 i.e., liquids that have strong correlations between their constant-volume equilibrium fluctuations of potential energy, U (t), and virial 6,7 W (t) ≡ −1/3 i r i · ∇ r i U (r 1 , ..., r N ) where r i is the position of particle i at time t. As is well known, the average virial W gives the configurational contribution to the pressure:…”

“…The strong correlations were related to the well-known fact that an inverse power-law (IPL) pair potential, v(r ) ∝ r −n where r is the distance between two particles, [31][32][33][34][35][36][37][38][39][40][41][42] implies perfect WU correlation, 2,5 W (t) = γ U (t) ( 3 ) with γ = n/3. Around the potential energy minimum, the LJ potential is well described by an "extended" inverse powerlaw potential (eIPL), 2 v LJ (r ) ∼ = Ar −n + B + Cr. At constant volume the linear term contributes little to the virial and potential-energy fluctuations: when one nearest-neighbor distance increases, others decrease in such a way that the sum is almost constant.…”

“…[8][9][10][11][12][13][14][15][16][17][18] Thus it has been shown that strongly correlating viscous liquids to a good approximation have all eight frequency-dependent thermoviscoelastic response functions [19][20][21] given in terms of just one 22 (i.e., are single-parameter liquids in the sense of having dynamic Prigogine-Defay ratio 19 close to unity 2,20,22 ). Strongly correlating viscous liquids moreover obey density scaling [23][24][25][26][27] to a good approximation, i.e., their dimensionless relaxation timeτ ≡ τρ 1/3 √ k B T /m (where m is the average particle mass) depends on density ρ = N /V and temperature as τ = F(ρ γ /T ).…”

“…[28][29][30] Paper I 1 presented computer simulations of 13 different systems, showing that van der Waals type liquids are strongly correlating, whereas hydrogen-bonding liquids like methanol or water are not. Strongly correlating liquids include, 1,2,5,22,29 for instance, the standard Lennard-Jones (LJ) liquid, the Kob-Andersen binary LJ (KABLJ) mixture, an asymmetric rigid-bond dumbbell model, a seven-site united-atom toluene model, and the Lewis-Wahnström OTP model.…”