Entropy, local order, and the freezing transition in Morse liquids

Hierarchy of anomalies in the simple rose model of water

The density, diffusion, and structural anomalies of the simple two-dimensional model of water were determined by Monte Carlo simulations. The rose model was used which is a very simple model for explaining the origin of water properties. Rose water molecules are modelled as two-dimensional Lennard-Jones disks with rose potentials for orientation dependent pairwise interactions mimicking formations of hydrogen bonds. The model can be seen also as a variance of silica-like models. Two parameters of potential in this work were selected in a way that (1) the model exhibits similar properties to Mercedes-Benz (MB) water model; and (2) that the model has real-like properties of water. Beside the known thermodynamic anomaly for the model we also found diffusion and structural anomalies. The orientational order parameters were calculated and maximum encountered for three and six-fold symmetry. For the MB parametrization, the anomalies occur in hierarchy order, which is a slight variation of the hierarchy order in real water. The diffusion anomaly region is the innermost in the hierarchy while for water it is the density anomaly region. In case of real water parametrization the most inner is the structural anomaly.

Hidden Scale Invariance in Polydisperse Mixtures of Exponential Repulsive Particles

Polydisperse systems of particles interacting by the purely repulsive exponential (EXP) pair potential are studied in regard to how structure and dynamics vary along isotherms, isochores, and isomorphs. The sizable size polydispersities of 23%, 29%, 35%, and 40%, as well as energy polydispersity 35%, were considered. For each system an isomorph was traced out covering about one decade in density. For all systems studied, the structure and dynamics vary significantly along the isotherms and isochores but are invariant to a good approximation along the isomorphs. We conclude that the single-component EXP system's hidden scale invariance (implying isomorph invariance of structure and dynamics) is maintained even when a sizable polydispersity is introduced into the system.

The EXP pair-potential system. III. Thermodynamic phase diagram

This paper determines the thermodynamic phase diagram of the EXP system of particles interacting by the purely repulsive exponential pair potential. The solid phase is face-centered cubic (fcc) at low densities and pressures. At higher densities and pressures, the solid phase is body-centered cubic (bcc) with a re-entrant liquid phase at the highest pressures simulated. The investigation first identifies the phase diagram at zero temperature at which the following four crystal structures are considered: fcc, bcc, hexagonal close packed, and cubic diamond. There is a T = 0 phase transition at pressure 2.651 × 10^-3 with the thermodynamically stable structure being fcc below and bcc above this pressure. The densities of the two crystal structures at the phase transition are 1.7469 × 10^-2 (fcc) and 1.7471 × 10^-2 (bcc). At finite temperatures, the fcc-bcc, fcc-liquid, and bcc-liquid coexistence lines are determined by numerical integration of the Clausius-Clapeyron equation and validated by interface-pinning simulations at selected state points. The bcc-fcc phase transition is a weak first-order transition. The liquid-fcc-bcc triple point, which is determined by the interface-pinning method, has temperature 5.9 × 10^-5 and pressure 2.5 × 10^-6; the triple-point densities are 1.556 × 10^-3 (liquid), 1.583 × 10^-3 (bcc), and 1.587 × 10^-3 (fcc).

Hierarchy of anomalies in the two-dimensional Mercedes-Benz model of water

We investigate by Monte Carlo simulations density, diffusion, and structural anomalies of the simple two-dimensional Mercedes-Benz (MB) model of water, which is a very simple toy model for explaining the origin of water properties. MB water molecules are modeled as two-dimensional Lennard-Jones disks, with three orientation-dependent hydrogen-bonding arms, arranged as in the MB logo. The model is in a way also a variance of silica-like models. Beside the known thermodynamic anomaly for the model we also found diffusion and structural anomalies and map out the cascade of density, structural, pair entropy, and diffusivity anomalies for MB model. The orientational order parameters with three and six-fold symmetry were determined and maximum for each one observed. The anomalies occur in hierarchy order, which is a slight variation of the hierarchy order in real water. The diffusion anomaly region is the innermost in the hierarchy while for water it is the density anomaly region.

Liquid state isomorphism, Rosenfeld-Tarazona temperature scaling, and Riemannian thermodynamic geometry

Aspects of isomorph theory, Rosenfeld-Tarazona temperature scaling, and thermodynamic geometry are comparatively discussed on the basis of the Lennard-Jones potential. The first two approaches approximate the high-density fluid state well when the repulsive interparticle interactions become dominant, which is typically the case close to the freezing line. However, previous studies of Rosenfeld-Tarazona scaling for the isochoric heat capacity and its relation to isomorph theory reveal deviations for the temperature dependence. It turns out that a definition of a state region in which repulsive interactions dominate is required for achieving consistent results. The Riemannian thermodynamic scalar curvature R allows for such a classification, indicating predominantly repulsive interactions by R>0. An analysis of the isomorphic character of the freezing line and the validity of Rosenfeld-Tarazona temperature scaling show that these approaches are consistent only in a small state region.

Triplet correlations dominate the transition from simple to tetrahedral liquids

The total, triplet, and pair contributions to the entropy with increasing tetrahedrality are mapped out for the Stillinger-Weber liquids to demonstrate the qualitative and quantitative differences between triplet-dominated, tetrahedral liquids and pair-dominated, simple liquids with regard to supercooling and crystallization. The heat capacity anomaly of tetrahedral liquids originates in local ordering due to both pair and triplet correlations. The results suggest that structural correlations can be directly related to thermodynamic anomalies, phase changes, and self-assembly in other atomic and colloidal fluids.

Isomorphs, hidden scale invariance, and quasiuniversality

This paper first establishes an approximate scaling property of the potential-energy function of a classical liquid with good isomorphs (a Roskilde-simple liquid). This "pseudohomogeneous" property makes explicit that-and in which sense-such a system has a hidden scale invariance. The second part of the paper gives a potential-energy formulation of the quasiuniversality of monatomic Roskilde-simple liquids, which was recently rationalized in terms of the existence of a quasiuniversal single-parameter family of reduced-coordinate constant-potential-energy hypersurfaces [J. C. Dyre, Phys. Rev. E 87, 022106 (2013)]. The new formulation involves a quasiuniversal reduced-coordinate potential-energy function. A few consequences of this are discussed.

NVU perspective on simple liquids' quasiuniversality

The last half-century of research into the structure, dynamics, and thermodynamics of simple liquids has revealed a number of approximate universalities. This paper argues that simple liquids' reduced-coordinate constant-potential-energy hypersurfaces constitute a quasiuniversal family of compact Riemannian manifolds parametrized by a single number; from this follows the quasiuniversalities.

Structural correlations and cooperative dynamics in supercooled liquids

The relationships between diffusivity and the excess, pair and residual multiparticle contributions to the entropy are examined for Lennard-Jones liquids and binary glassformers, in the context of approximate inverse power law mappings of simple liquids. In the dense liquid where diffusivities are controlled by collisions and cage relaxations, Rosenfeld-type excess entropy scaling of diffusivities is found to hold for both crystallizing as well as vitrifying liquids. The crucial differences between the two categories of liquids emerge only when local cooperative effects in the dynamics result in significant caging effects in the time-dependent behaviour of the single-particle mean square displacement. In the case of glassformers, onset of such local cooperativity coincides with onset of deviations from Rosenfeld-type excess entropy scaling of diffusivities and increasing spatiotemporal heterogeneity. In contrast, for two- and three-dimensional liquids with a propensity to crystallise, the onset of local cooperative dynamics is sufficient to trigger crystallization provided that the liquid is sufficiently supercooled that the free energy barrier to nucleation of the solid phase is negligible. The state points corresponding to onset of transient caging effects can be associated with typical values, within reasonable bounds, of the excess, pair, and residual multiparticle entropy as a consequence of the isomorph-invariant character of the excess entropy, diffusivity and related static and dynamic correlation functions.

Relationship between structure, entropy, and diffusivity in water and water-like liquids

Anomalous behavior of the excess entropy (S(e)) and the associated scaling relationship with diffusivity are compared in liquids with very different underlying interactions but similar water-like anomalies: water (SPC/E and TIP3P models), tetrahedral ionic melts (SiO(2) and BeF(2)), and a fluid with core-softened, two-scale ramp (2SRP) interactions. We demonstrate the presence of an excess entropy anomaly in the two water models. Using length and energy scales appropriate for onset of anomalous behavior, we show the density range of the excess entropy anomaly to be much narrower in water than in ionic melts or the 2SRP fluid. While the reduced diffusivities (D*) conform to the excess-entropy-scaling relation, D* = A exp(alphaS(e)) for all the systems (Rosenfeld, Y. Phys. Rev. A 1977, 15, 2545), the exponential scaling parameter, alpha, shows a small isochore dependence in the case of water. Replacing S(e) by pair correlation-based approximants accentuates the isochore dependence of the diffusivity scaling. Isochores with similar diffusivity-scaling parameters are shown to have the temperature dependence of the corresponding entropic contribution. The relationship between diffusivity, excess entropy, and pair correlation approximants to the excess entropy are very similar in all the tetrahedral liquids.

Excess entropy and structural transitions in a two-dimensional square-shoulder fluid

Metropolis Monte Carlo simulations on the square-shoulder fluid of Malescio and Pellicane are used to trace the temperature dependent excess entropy, the heat capacity, and configurational energy along several isochores, including those for which mechanically stable zero-temperature structures have been predicted. Thermodynamic signatures of structural phase transitions are identified along several isochores, in addition to the low-density triangular solid and stripe phase transitions identified earlier. The finite temperature phases illustrate the competition between cluster formation and stripe formation as competing mechanisms for generating minimum free energy configurations as a function of density, consistent with earlier results at zero temperature. We also critically examine the usefulness of a phase-ordering rule based on the residual multiparticle entropy (RMPE) in predicting the formation of this diverse set of ordered structures from a disordered fluid phase. For the majority of the isochores studied, the RMPE prediction and the thermodynamic evidence for a phase transition were consistent. However, this criterion fails along isochores that are in regions of coexistence. Thus, the zero-RMPE rule is only likely to be approximately predictive in systems with small phase coexistence regimes, e.g., in the case of liquid crystal forming systems.

Universality in the vibrational spectra of weakly-disordered two-dimensional clusters

We numerically investigate the vibrational spectra of single-component clusters in two dimensions. Stable configurations of clusters at local energy minima are obtained, and for each the Hessian matrix is evaluated and diagonalized to obtain eigenvalues as well as eigenvectors. We study the density of states so obtained as a function of the width of the potential well describing the two-body interaction. As the width is reduced, as in three dimensions, we find that the density of states approaches a common form but the two-peak behavior survives. Further, calculations of the participation ratio show that most states are extended, although a smaller fraction of the degrees of freedom are involved in these modes compared to three dimensions. We show that the fluctuation properties of these modes converge to those of the Gaussian orthogonal ensemble of random matrices, in common with previous results on three-dimensional amorphous clusters and molecular liquids.

Local structures of fluid with discrete spherical potential: Theory and grand canonical ensemble Monte Carlo simulation

Grand canonical Monte Carlo simulation and theoretical calculations based on Ornstein-Zernike (OZ) integral equation and third order+second order perturbation density functional theory (DFT) are performed to study a system of spherical particles interacting through a core-softened (CS) potential combining a repulsive square soft core and an attractive square well. Both theoretical predictions and simulation results reveal peculiar homogeneous and inhomogeneous local structures originating from the discontinuous nature of the CS potential. The bulk radial distribution function displays discontinuities at the distances coinciding with the ranges of the successive repulsive and attractive parts in the CS potential function. The density profiles of confined CS fluid show the shapes arising from the complex interplay among the steric effects and the competition between the repulsive and attractive parts of the CS potential. Satisfactory agreement between the theoretical results and simulation data leads to the following conclusions: (i) a modified hypernetted chain approximation combined with a hard sphere bridge function, which has been recently proposed by one of the authors of this study, is sufficiently reliable for the structural studies of CS fluid, and (ii) the third order+second order perturbation DFT, which has proven successful for the study of inhomogeneous structure of model fluids with continuous intermolecular potential function, posses a high adaptability to be applied for various types of interaction potentials and performs well also in the case of discontinuous CS model.

Monte Carlo simulation in the isobaric-multithermal ensemble of a bulk Lennard-Jones fluid system: thermodynamic quantities for pressure from P{ *}=2.42 to 7.25

A Monte Carlo (MC) simulation in the isobaric-multithermal (MuTh) ensemble has been carried out for a bulk Lennard-Jones fluid system that consists of 108 particles. The MuTh weight factor which we determined turned out to be reliable for the temperature and pressure range from (T{ *},P{ *})=(T_{0}{ *},P_{0}{ *})=(2.09,7.25) to (T{ *},P{ *})=(0.417,1.45) along P{ *}/T{ *}=P_{0}{ *}/T_{0}{ *} . Thermodynamic quantities calculated from the MuTh MC production run by the reweighting techniques showed the discontinuous change, which is the feature of the first-order phase transition. The radial distribution functions suggest that the transition takes place between liquid and solid states. Two distinct local maxima were observed in the obtained contour representations of the probability distribution at T{ *}=1.04 and P{ *}=3.63 , which is the phase transition point along P{ *}/T{ *}=P_{0}{ *}/T_{0}{ *} .

Waterlike hierarchy of anomalies in a continuous spherical shouldered potential

We investigate by molecular dynamics simulations a continuous isotropic core-softened potential with attractive well in three dimensions, introduced by Franzese [J. Mol. Liq. 136, 267 (2007)], that displays liquid-liquid coexistence with a critical point and waterlike density anomaly. Besides the thermodynamic anomalies, here we find diffusion and structural anomalies. The anomalies, not observed in the discrete version of this model, occur with the same hierarchy that characterizes water. We discuss the differences in the anomalous behavior of the continuous and the discrete model in the framework of the excess entropy, calculated within the pair correlation approximation.