Crystallization of the Wahnstr\"om Binary Lennard-Jones Liquid

We report observation of crystallization of the glass-forming binary Lennard-Jones liquid first used by Wahnstr\"om [G. Wahnstr\"om, Phys. Rev. A 44, 3752 (1991)]. Molecular dynamics simulations of the metastable liquid on a timescale of microseconds were performed. The liquid crystallized spontaneously. The crystal structure was identified as MgZn_2. Formation of transient crystallites is observed in the liquid. The crystallization is investigate at different temperatures and compositions. At high temperature the rate of crystallite formation is the limiting factor, while at low temperature the limiting factor is growth rate. The melting temperature of the crystal is estimated to be T_m=0.93 at rho=0.82. The maximum crystallization rate of the A_2B composition is T=0.60+/-0.02.Comment: 4 pages, 4 figures; corrected typo

Strong pressure-energy correlations in liquids as a configuration space property: Simulations of temperature down jumps and crystallization

Computer simulations recently revealed that several liquids exhibit strong correlations between virial and potential energy equilibrium fluctuations in the NVT ensemble [U. R. Pedersen {\it et al.}, Phys. Rev. Lett. {\bf 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-Wahnstr{\"o}m 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-Wahnstr{\"o}m OTP at constant temperature

Estimating the density scaling exponent of viscous liquids from specific heat and bulk modulus data

It was recently shown by computer simulations that a large class of liquids exhibits strong correlations in their thermal fluctuations of virial and potential energy [Pedersen et al., Phys. Rev. Lett. 100, 015701 (2008)]. Among organic liquids the class of strongly correlating liquids includes van der Waals liquids, but excludes ionic and hydrogen-bonding liquids. The present note focuses on the density scaling of strongly correlating liquids, i.e., the fact their relaxation time tau at different densities rho and temperatures T collapses to a master curve according to the expression tau propto F(rho^gamma/T) [Schroder et al., arXiv:0803.2199]. We here show how to calculate the exponent gamma from bulk modulus and specific heat data, either measured as functions of frequency in the metastable liquid or extrapolated from the glass and liquid phases to a common temperature (close to the glass transition temperature). Thus an exponent defined from the response to highly nonlinear parameter changes may be determined from linear response measurements

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

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 NVT ensemble. Paper IV [N. Gnan et al., J. Chem. Phys. v131, 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 to a single curve. Two applications are given. One is testing the prediction that the solid-liquid coexistence curve follows an isomorph by comparing to recent simulations by Ahmed and Sadus [J. Chem. Phys. v131, 174504 (2009)]. Excellent agreement is found on the liquid side of the coexistence, whereas the agreement is worse 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 potential energy on isochores. It is shown that the new equation of state agrees well with simulations.Comment: 12 pages, 14 figures, Section on solid-liquid coexistence expande

Strongly correlating liquids and their isomorphs

This paper summarizes the properties of strongly correlating liquids, i.e., liquids with strong correlations between virial and potential energy equilibrium fluctuations at constant volume. We proceed to focus on the experimental predictions for strongly correlating glass-forming liquids. These predictions include i) density scaling, ii) isochronal superposition, iii) that there is a single function from which all frequency-dependent viscoelastic response functions may be calculated, iv) that strongly correlating liquids are approximately single-parameter liquids with close to unity Prigogine-Defay ratio, and v) that the fictive temperature initially decreases for an isobaric temperature up jump. The "isomorph filter", which allows one to test for universality of theories for the non-Arrhenius temperature dependence of the relaxation time, is also briefly discussed

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 the Lennard-Jones liquid and other simple liquids, but not in hydrogen-bonding liquids like 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.Comment: Phys. Rev. Lett., in pres

Pressure-energy correlations in liquids. IV. "Isomorphs" in liquid state diagrams

This paper is the fourth in a series devoted to identifying and explaining the properties of strongly correlating liquids, i.e., liquids where virial and potential energy correlate better than 90% in their thermal equilibrium fluctuations in the NVT ensemble. For such liquids we here introduce the concept of "isomorphic" curves in the state diagram. A number of thermodynamic, static, and dynamic isomorph invariants are identified. These include the excess entropy, the isochoric specific heat, reduced-unit static and dynamic correlation functions, as well as reduced-unit transport coefficients. The dynamic invariants apply for both Newtonian and Brownian dynamics. It is shown that after a jump between isomorphic state points the system is instantaneously in thermal equilibrium; consequences of this for generic aging experiments are discussed. Selected isomorph predictions are validated by computer simulations of the Kob-Andersen binary Lennard-Jones mixture, which is a strongly correlating liquid. The final section of the paper relates the isomorph concept to phenomenological melting rules, Rosenfeld's excess entropy scaling, Young and Andersen's approximate scaling principle, and the two-order parameter maps of Debenedetti and coworkers. This section also shows how the existence of isomorphs implies an "isomorph filter" for theories for the non-Arrhenius temperature dependence of viscous liquids' relaxation time, as well as explains isochronal superposition for strongly correlating viscous liquids

TVA’s Brief in Reply to Plaintiffs’ Post-Trial Brief, \u3cem\u3eTVA v. Hill et al\u3c/em\u3e, Civil Action No. 3-76-48

Brief for the defendants in response to the plaintiffs\u27 post-trial brief in the case of TVA v. Hill et al in the United States District Court for the Eastern District of Tennessee, Northern Division

Post-Trial Brief of Tennessee Valley Authority, \u3cem\u3eTVA v. Hill et al\u3c/em\u3e, Civil Action No. 3-76-48

Post-trial brief for the defendants in the case of TVA v. Hill et al in the United States District Court for the Eastern District of Tennessee, Northern Division