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Solubility parameters such as Hildebrand's solubility parameter or its square, the cohesive energy density ced are often not able to predict solubilities of organic compounds in ionic liquids accurately. It has been suggested that this is an effect of the structural heterogeneity that many ionic liquids exhibit due to the non-polar alkyl chains forming separate domains from the charged parts of the cation and the anion. We here calculated the partial volumes of the polar and non-polar domains in Molecular Dynamics simulations of several 1-alkyl-3-methylimidazolium nitrates and 1-octyl-3-methylimidazolium hexafluorophosphate. We used these partial volumes to calculate the ced of the polar and non-polar domains. For 1-octyl-3-methylimidazolium nitrate the internal pressures Pi of the domains were also calculated. Our results show that ced and Pi are indeed very different in the domains, and that the domains containing the hydrophobic alkyl chains have solvent parameters similar to alkanes. For the domains that contain the charged part of the ions, ced and Pi are much higher, and Pi is comparable to what is found for high temperature molten salts. The results provide a possible explanation why solubility parameters seem incorrect for many ionic liquids, and may be useful in estimating more useful values using computer simulations.

Molecular dynamics (MD) simulations of five ionic liquids based on 1-alkyl-3-methylimidazolium cations, [CnC1im]+, have been performed in order to calculate high-frequency elastic moduli and to evaluate heterogeneity of local elastic moduli. The MD simulations of [CnC1im][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 shea...

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 shape of these isomorphs is described by a material-dependent function of density $h(\rho)$, which for real liquids is well approximated by a power law $\rho^\gamma$. However, in simulations, a power law is not adequate when density changes are large; typical models such as the Lennard-Jones liquid show that $\gamma(\rho) \equiv \mathrm{d} \ln h(\rho)/\mathrm{d} \ln \rho$ is a decreasing function of density. This paper 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 $\gamma(\rho)$. 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., Comment: 5 pages, 4 figures

We derive exact results for the rate of change of thermodynamic quantities, in particular the configurational specific heat at constant volume, $C_V$, along configurational adiabats (curves of constant excess entropy $S_{\textrm{ex}}$). Such curves are designated isomorphs for so-called Roskilde liquids, in view of the invariance of various structural and dynamical quantities along them. Their slope in a double logarithmic representation of the density-temperature phase diagram, $\gamma$ can be interpreted as one third of an effective inverse power-law potential exponent. We show that in liquids where $\gamma$ increases (decreases) with density, the contours of $C_V$ have smaller (larger) slope than configurational adiabats. We clarify also the connection between $\gamma$ and the pair potential. A fluctuation formula for the slope of the $C_V$-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 $d\gamma/d\rho$ is thus a third key parameter in characterizing Roskilde liquids, after $\gamma$ 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 $C_V$-contours, finding it more invariant along adiabats.

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 $\rho^{\gamma_S}/T$, where $\rho$ is density, $T$ is temperature, and $\gamma_S$ 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 a empirical scaling parameter., Comment: 9 pages, 10 figures

It is demonstrated by molecular dynamics simulations that liquids interacting via the Buckingham potential are strongly correlating, i.e., have regions of their phase diagram where constant-volume equilibrium fluctuations in the virial and potential energy are strongly correlated. A binary Buckingham liquid is cooled to a viscous phase and shown to have isomorphs, which are curves in the phase diagram along which structure and dynamics in appropriate units are invariant to a good approximation. To test this, the radial distribution function, and both the incoherent and coherent intermediate scattering function are calculated. The results are shown to reflect a hidden scale invariance; despite its exponential repulsion the Buckingham potential is well approximated by an inverse power-law plus a linear term in the region of the first peak of the radial distribution function. As a consequence the dynamics of the viscous Buckingham liquid is mimicked by a corresponding model with purely repulsive inverse-power-law interactions. The results presented here closely resemble earlier results for Lennard-Jones type liquids, demonstrating that the existence of strong correlations and isomorphs does not depend critically on the mathematical form of the repulsion being an inverse power law., Comment: 7 pages, 9 figures

The previous paper [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., 11 pages, 11 figures

This paper shows that several known properties of the Yukawa system can be derived from the isomorph theory, which applies to any system that has strong correlations between its virial and potential-energy equilibrium fluctuations. Such "Roskilde-simple" systems have a simplified thermodynamic phase diagram deriving from the fact that they have curves (isomorphs) along which structure and dynamics in reduced units are invariant to a good approximation. We show that the Yukawa system has strong virial potential-energy correlations and identify its isomorphs by two different methods. One method, the so-called direct isomorph check, identifies isomorphs numerically from jumps of relatively small density changes (here 10%). The second method identifies isomorphs analytically from the pair potential. The curves obtained by the two methods are close to each other; these curves are confirmed to be isomorphs by demonstrating the invariance of the radial distribution function, the static structure factor, the mean-square displacement as a function of time, and the incoherent intermediate scattering function. Since the melting line is predicted to be an isomorph, the theory provides a derivation of a known approximate analytical expression for this line in the temperature-density phase diagram. The paper's results give the first demonstration that the isomorph theory can be applied to systems like dense colloidal suspensions and strongly coupled dusty plasmas., Comment: 12 pages, 12 figures

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.