Mechanical heterogeneity in ionic liquids.

Molecular dynamics (MD) simulations of five ionic liquids based on 1-alkyl-3-methylimidazolium cations, [C n C1im]+, have been performed in order to calculate high-frequency elastic moduli and to evaluate heterogeneity of local elastic moduli. The MD simulations of [C n C1im][NO3], n = 2, 4, 6, and 8, assessed the effect of domain segregation when the alkyl chain length increases, and [C8C1im][PF6] assessed the effect of strength of anion-cation interaction. Dispersion curves of excitation energies of longitudinal and transverse acoustic, LA and TA, modes were obtained from time correlation functions of mass currents at different wavevectors. High-frequency sound velocity of LA modes depends on the alkyl chain length, but sound velocity for TA modes does not. High-frequency bulk and shear moduli, K ∞ and G ∞ , depend on the alkyl chain length because of a density effect. Both K ∞ and G ∞ are strongly dependent on the anion. The calculation of local bulk and shear moduli was accomplished by performing bulk and shear deformations of the systems cooled to 0 K. The simulations showed a clear connection between structural and elastic modulus heterogeneities. The development of nano-heterogeneous structure with increasing length of the alkyl chain in [C n C1im][NO3] implies lower values for local bulk and shear moduli in the non-polar domains. The mean value and the standard deviations of distributions of local elastic moduli decrease when [NO3]- is replaced by the less coordinating [PF6]- anion.

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.

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.

Scaling of the dynamics of flexible Lennard-Jones chains.

The isomorph theory provides an explanation for the so-called power law density scaling which has been observed in many molecular and polymeric glass formers, both experimentally and in simulations. Power law density scaling (relaxation times and transport coefficients being functions of ρ(γ(S)), where ρ is density, T is temperature, and γ(S) is a material specific scaling exponent) is an approximation to a more general scaling predicted by the isomorph theory. Furthermore, the isomorph theory provides an explanation for Rosenfeld scaling (relaxation times and transport coefficients being functions of excess entropy) which has been observed in simulations of both molecular and polymeric systems. Doing molecular dynamics simulations of flexible Lennard-Jones chains (LJC) with rigid bonds, we here provide the first detailed test of the isomorph theory applied to flexible chain molecules. We confirm the existence of isomorphs, which are curves in the phase diagram along which the dynamics is invariant in the appropriate reduced units. This holds not only for the relaxation times but also for the full time dependence of the dynamics, including chain specific dynamics such as the end-to-end vector autocorrelation function and the relaxation of the Rouse modes. As predicted by the isomorph theory, jumps between different state points on the same isomorph happen instantaneously without any slow relaxation. Since the LJC is a simple coarse-grained model for alkanes and polymers, our results provide a possible explanation for why power-law density scaling is observed experimentally in alkanes and many polymeric systems. The theory provides an independent method of determining the scaling exponent, which is usually treated as an empirical scaling parameter.

Statistical mechanics of Roskilde liquids: configurational adiabats, specific heat contours, and density dependence of the scaling exponent.

We derive exact results for the rate of change of thermodynamic quantities, in particular, the configurational specific heat at constant volume, CV, along configurational adiabats (curves of constant excess entropy Sex). Such curves are designated isomorphs for so-called Roskilde liquids, in view of the invariance of various structural and dynamical quantities along them. The slope of the isomorphs in a double logarithmic representation of the density-temperature phase diagram, γ, can be interpreted as one third of an effective inverse power-law potential exponent. We show that in liquids where γ increases (decreases) with density, the contours of CV have smaller (larger) slope than configurational adiabats. We clarify also the connection between γ and the pair potential. A fluctuation formula for the slope of the CV-contours is derived. The theoretical results are supported with data from computer simulations of two systems, the Lennard-Jones fluid, and the Girifalco fluid. The sign of dγ∕dρ is thus a third key parameter in characterizing Roskilde liquids, after γ and the virial-potential energy correlation coefficient R. To go beyond isomorph theory we compare invariance of a dynamical quantity, the self-diffusion coefficient, along adiabats and CV-contours, finding it more invariant along adiabats.

Communication: The Rosenfeld-Tarazona expression for liquids' specific heat: a numerical investigation of eighteen systems.

We investigate the accuracy of the expression of Rosenfeld and Tarazona (RT) for the excess isochoric heat capacity, C(V)(ex)∝T(-2/5), for 18 model liquids. Previous investigations have reported no unifying features of breakdown for the RT expression. Here, liquids with different stoichiometric composition, molecular topology, chemical interactions, degree of undercooling, and environment are investigated. The RT expression is a better approximation for liquids with strong correlations between equilibrium fluctuations of virial and potential energy, i.e., "Roskilde-simple" liquids [T. S. Ingebrigtsen, T. B. Schrøder, and J. C. Dyre, Phys. Rev. X 2, 011011 (2012)]. This observation holds even for molecular liquids under severe nanoscale confinement which does not follow from the original RT bulk hard-sphere fluid perturbation theory arguments. The density dependence of the specific heat is predicted from the isomorph theory for Roskilde-simple liquids, which in combination with the RT expression provides a complete description of the specific heat's density and temperature dependence.

Do the repulsive and attractive pair forces play separate roles for the physics of liquids?

According to standard liquid-state theory repulsive and attractive pair forces play distinct roles for the physics of liquids. This paradigm is put into perspective here by demonstrating a continuous series of pair potentials that have virtually the same structure and dynamics, although only some of them have attractive forces of significance. Our findings reflect the fact that the motion of a given particle is determined by the total force on it, whereas the quantity usually discussed in liquid-state theory is the individual pair force.