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

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114

115

This series of papers is devoted to identifying and explaining the properties of strongly correlating liquids, i.e., liquids with more than 90% correlation between their virial W and potential energy U fluctuations in the N V T ensemble. Paper IV [N. Gnan et al., J. Chem. Phys. 131, 234504 (2009)] showed that strongly correlating liquids have "isomorphs," which are curves in the phase diagram along which structure, dynamics, and some thermodynamic properties are invariant in reduced units. In the present paper, using the fact that reduced-unit radial distribution functions are isomorph invariant, we derive an expression for the shapes of isomorphs in the WU phase diagram of generalized Lennard-Jones systems of one or more types of particles. The isomorph shape depends only on the Lennard-Jones exponents; thus all isomorphs of standard Lennard-Jones systems (with exponents 12 and 6) can be scaled onto a single curve. Two applications are given. One tests the prediction that the solid-liquid coexistence curve follows an isomorph by comparing to recent simulations by Ahmed and Sadus [J. Chem. Phys. 131, 174504 (2009)]. Excellent agreement is found on the liquid side of the coexistence curve, whereas the agreement is less convincing on the solid side. A second application is the derivation of an approximate equation of state for generalized Lennard-Jones systems by combining the isomorph theory with the Rosenfeld-Tarazona expression for the temperature dependence of the potential energy on isochores. It is shown that the new equation of state agrees well with simulations.

Section: Introductionmentioning

confidence: 87%

Section: Introductionmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

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

Schrøder

Gnan

Pedersen

et al. 2011

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114

115

“…The study of thermodynamic scaling has triggered the proposal of several novel concepts by Dyre and coworkers, such as that of "strongly correlating liquids" (i.e., liquids with strong correlations between equilibrium fluctuations of the potential energy and the virial in a canonical ensemble) and "isomorphs" (i.e., curves in the phase diagram along which structure, dynamics, and some thermodynamic properties are invariant in reduced units) . [23][24][25][26][27][28] The isomorph theory indicates that the scaling exponent γ is not constant, but depends on density, [27][28][29][30] and the power-law form ρ γ is only a special case. However, the power-law density scaling is a useful approximation to the isomorph scaling since a number of experiments find a weak dependence of γ on density under certain thermodynamic conditions [4][5][6] and since using a constant value of γ leads to collapse onto a master curve of the dynamics in glass-forming liquids.…”

Section: Introductionmentioning

confidence: 99%

Thermodynamic scaling of dynamics in polymer melts: Predictions from the generalized entropy theory

Freed

2013

Many glass-forming fluids exhibit a remarkable thermodynamic scaling in which dynamic properties, such as the viscosity, the relaxation time, and the diffusion constant, can be described under different thermodynamic conditions in terms of a unique scaling function of the ratio ρ γ /T , where ρ is the density, T is the temperature, and γ is a material dependent constant. Interest in the scaling is also heightened because the exponent γ enters prominently into considerations of the relative contributions to the dynamics from pressure effects (e.g., activation barriers) vs. volume effects (e.g., free volume). Although this scaling is clearly of great practical use, a molecular understanding of the scaling remains elusive. Providing this molecular understanding would greatly enhance the utility of the empirically observed scaling in assisting the rational design of materials by describing how controllable molecular factors, such as monomer structures, interactions, flexibility, etc., influence the scaling exponent γ and, hence, the dynamics. Given the successes of the generalized entropy theory in elucidating the influence of molecular details on the universal properties of glass-forming polymers, this theory is extended here to investigate the thermodynamic scaling in polymer melts. The predictions of theory are in accord with the appearance of thermodynamic scaling for pressures not in excess of ∼ 50 MPa. (The failure at higher pressures arises due to inherent limitations of a lattice model.) In line with arguments relating the magnitude of γ to the steepness of the repulsive part of the intermolecular potential, the abrupt, square-well nature of the lattice model interactions lead, as expected, to much larger values of the scaling exponent. Nevertheless, the theory is employed to study how individual molecular parameters affect the scaling exponent in order to extract a molecular understanding of the information content contained in the exponent. The chain rigidity, cohesive energy, chain length, and the side group length are all found to significantly affect the magnitude of the scaling exponent, and the computed trends agree well with available experiments. The variations of γ with these molecular parameters are explained by establishing a correlation between the computed molecular dependence of the scaling exponent and the fragility. Thus, the efficiency of packing the polymers is established as the universal physical mechanism determining both the fragility and the scaling exponent γ.

“…According to the isomorph theory [7][8][9][10][11], the class of socalled strongly correlating liquids have isomorphs, which are curves in the phase diagram along which structural, dynamical, and some thermodynamic properties are invariant when expressed in reduced units. This theory has been tested successfully experimentally [12] and numerically [13][14][15].…”

Section: Introductionmentioning

confidence: 99%

Isomorph invariance of Couette shear flows simulated by the SLLOD equations of motion

Separdar

Bailey²,

Schrøder³

et al. 2013

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Non-equilibrium molecular dynamics simulations were performed to study the thermodynamic, structural, and dynamical properties of the single-component Lennard-Jones and the Kob-Andersen binary Lennard-Jones liquids. Both systems are known to have strong correlations between equilibrium thermal fluctuations of virial and potential energy. Such systems have good isomorphs (curves in the thermodynamic phase diagram along which structural, dynamical, and some thermodynamic quantities are invariant when expressed in reduced units). The SLLOD equations of motion were used to simulate Couette shear flows of the two systems. We show analytically that these equations are isomorph invariant provided the reduced strain rate is fixed along the isomorph. Since isomorph invariance is generally only approximate, a range of shear rates were simulated to test for the predicted invariance, covering both the linear and non-linear regimes. For both systems, when represented in reduced units the radial distribution function and the intermediate scattering function are identical for state points that are isomorphic. The strain-rate dependence of the viscosity, which exhibits shear thinning, is also invariant along an isomorph. Our results extend the isomorph concept to the non-equilibrium situation of a shear flow, in which the phase diagram is three dimensional because the shear rate defines a third dimension.