Excess entropy, Diffusivity and Structural Order in liquids with water-like anomalies

The excess entropy, Se, defined as the difference between the entropies of the liquid and the ideal gas under identical density and temperature conditions, is shown to be the critical quantity connecting the structural, diffusional and density anomalies in water-like liquids. Based on simulations of silica and the two-scale ramp liquids, water-like density and diffusional anomalies can be seen as consequences of a characteristic non-monotonic density dependence of Se. The relationship between excess entropy, the order metrics and the structural anomaly can be understood using a pair correlation approximation to Se.Comment: 9 pages, 5 figues in ps forma

Diffusivity, excess entropy, and the potential-energy landscape of monatomic liquids

The connection between thermodynamic, transport, and potential-energy landscape features is studied for liquids with Lennard-Jones-type pair interactions using both microcanonical molecular-dynamics and isothermal-isobaric ensemble Monte Carlo simulations. Instantaneous normal-mode and saddle-point analyses of two variants of the monatomic Lennard-Jones liquid have been performed. The diffusivity is shown to depend linearly on several key properties of instantaneous and saddle configurations-the energy, the fraction of negative curvature directions, and the mean, maximum, and minimum eigenvalues of the Hessian. Since the Dzugutov scaling relationship also holds for such systems [ Nature (London) 381, 137 (1996) ], the exponential of the excess entropy, within the two-particle approximation, displays the same linear dependence on energy landscape properties as the diffusivity

Determining landscape-based criteria for freezing of liquids

The correlation between statistical properties of the energy landscape and the number of accessible configurational states, as measured by the exponential of the excess entropy (e<SUP>S<SUB>e</SUB></SUP>), are studied in the case of a simple Lennard-Jones-type liquid in the neighborhood of the thermodynamic freezing transition. The excess entropy S<SUB>e</SUB> is defined as the difference between the entropy of the liquid and that of the ideal gas under identical temperature and pressure conditions and is estimated using the pair correlation contribution, S<SUB>2</SUB>. Landscape properties associated with three categories of configurations are considered: instantaneous configurations, inherent saddles, and inherent minima. Landscape properties studied include the energy and the key parameters of the Hessian eigenvalue distribution as well as the mean distances between instantaneous configurations and the corresponding inherent saddles and minima. The signatures of the thermodynamic freezing transition are clearest in the case of inherent structure properties which show, as a function of e<SUP>S<SUB>e</SUB></SUP>, a pronounced change in slope in the vicinity of the solid-liquid coexistence. The mean distance between instantaneous and saddle configurations also shows a similar change in slope when the system crosses from the stable to the supercooled regime. In the case of inherent saddles, the minimum eigenvalue acts as a similar indicator of the thermodynamic freezing transition but the average and maximum eigenvalues do not carry similar signatures. In the case of instantaneous configurations, a weak indicator of the thermodynamic freezing transition is seen in the behavior of the fraction of negative curvature directions as a function of the exponential of the excess entropy

A Monte Carlo Simulation Study of Methane Clathrate Hydrates Confined in Slit-Shaped Pores

Monte Carlo simulations are used to study the structure, stability, and dissociation mechanisms of methane hydrate crystals inside carbon-like slit-shaped pores. The simulation conditions used mimic experimental studies of the dissociation of methane and propane hydrates in mesoporous silica gels (Handa, Y. P.; Stupin, D. <i>J. Phys. Chem. </i><b>1992</b>, <i>96</i>, 8599). Simulations are performed under conditions of fixed methane pressure and fixed water loading, with the temperature increased in steps, with long equilibrations at each temperature. The initial structures of the confined hydrates are taken to be bulk-like, and pore widths chosen to accommodate integer or half-integer numbers of hydrate unit cells. Density profiles and orientational order parameter profiles are obtained and used to understand the structural changes associated with hydrate dissociation. Three different common water models, SPC/E, TIP4P, and TIP4P/2005, are used and the results compared. For water modeled using either the TIP4P or TIP4P/2005 potentials, dissociation temperatures are depressed proportionally to the inverse pore width, as predicted by the macroscopic Gibbs–Thomson equation. This behavior is observed for pores small enough that only half-cages of the clathrate structure are present. Experimental work has verified Gibbs–Thomson behavior for pores as small as 2 nm (Seshadri, K.; Wilder, J. W.; Smith, D. H. <i>J. Phys. Chem. B</i> <b>2001</b>, <i>105</i>, 2627); micropores of the size studied here have not yet been studied by experiment. Interestingly, the dissociation of hydrates modeled using the SPC/E water potential does not display the predicted pore-size dependence, and the dissociation mechanisms in this model seem to be quite different than those in the TIP4P-type models. In the SPC/E hydrates, with increasing temperature, cage dissocation occurs before methane desorption. In TIP4P-type hydrates, these processes occur either at the same temperature (to within the resolution of this study) or with dissociation occurring at higher temperatures than desorption. These simulations show that a variety of interesting clathrate structures and phase behaviors may be accessed in suitably designed microporous materials, with potentially useful applications in gas storage or separations

Melting of atomic solids: effect of range and softness of interaction potentials

The relationship between the behaviour at melting and the range and softness of interatomic potentials is explored using Monte Carlo simulations of bulk Morse and Lennard-Jones systems. The range parameter of the Morse interaction is tuned to mimic the variation seen in atomic systems, from metallic systems with soft, long-range interactions to van der Waals solids with short-range, strongly repulsive potentials. An umbrella sampling procedure is used to determine the melting point by constructing Landau free energy curves; the accuracy and finite-size effects associated with this approach are estimated for the Lennard-Jones system by comparison with existing results in the literature. The melting temperature as well as the strength of the first-order transition for Morse solids is shown to increase as the range and softness of the interatomic interactions decrease. The phase transition properties are largely determined by the behaviour of the pair interaction near equilibrium separation. The height of the barrier separating the two phases, as determined from the Landau free energy curve, is shown to be correlated with the crystal-liquid interfacial free energy

Understanding melting of Ti crystal with spherical voids from molecular dynamics simulations

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