Gaussian Core Model Research Articles

Glass Transition of the Monodisperse Gaussian Core Model

We numerically investigate the dynamical properties of the one-component Gaussian core model in supercooled states. We find that nucleation is increasingly suppressed with increasing density. The system concomitantly exhibits glassy, slow dynamics characterized by the two-step stretched exponential relaxation of the density correlation and a drastic increase of the relaxation time. We also find a weaker violation of the Stokes-Einstein relation and a smaller non-Gaussian parameter than in typical model glass formers, implying weaker dynamic heterogeneities. Additionally, the agreement of the simulation data with the prediction of mode-coupling theory is exceptionally good, indicating that the nature of the slow dynamics of this ultrasoft particle fluid is mean-field-like. This fact may be understood as a consequence of the long-range nature of the interaction.

Reentrant and Isostructural Transitions in a Cluster-Crystal Former

We study the low-temperature behavior of a simple cluster-crystal forming system through simulation. We find the phase diagram to be hybrid between the Gaussian core model and the penetrable sphere model. The system additionally exhibits S-shaped doubly reentrant phase sequences as well as critical isostructural transitions between crystals of different average lattice site occupancy. Because of the possible annihilation of lattice sites and accompanying clustering, the system moreover shows an unusual softening upon compression.

Pressure and energy behavior of the Gaussian core model fluid under shear

The pressure and energy behavior of the Gaussian core model (GCM) fluid as a function of strain-rate are obtained from nonequilibrium molecular dynamics simulations for a wide range of thermodynamic state points. An analytical dependence of pressure on strain-rate is observed which is in agreement with a Taylor series expansion of pressure in terms of the strain-rate tensor. In contrast, the energy as a function of strain rate is found to be dependent on temperature and density. The different behavior of pressure and energy contradicts mode-coupling theory, which requires the same variation of pressure and energy with respect to the strain-rate. The results for the GCM fluid do not support the hypothesis that the strain-rate exponent for both pressure and energy can be universally represented by a simple linear function of temperature and density.

Layering Transitions in a Gaussian-Core Model Under Geometrical Confinement

The order-disorder transition of a Gaussian-core model confined between parallel walls was investigated by a Monte Carlo simulation. When the density of the system is changed, the system shows successive layering transitions. It was also confirmed that there are ordered structures with a square lattice symmetry and with hexagonal lattice symmetry in the direction parallel to the walls. Such positional order remains beyond the critical temperature Tc 3d , at which ordered states disappear at all densities in a three-dimensional system without confinement. Different from hard-sphere suspensions, the positional order of this model remains relatively stable, despite the polydispersity of the system.

Simple relationship between the virial-route hypernetted-chain and the compressibility-route Percus–Yevick values of the fourth virial coefficient

As is well known, approximate integral equations for liquids, such as the hypernetted chain (HNC) and Percus-Yevick (PY) theories, are in general thermodynamically inconsistent in the sense that the macroscopic properties obtained from the spatial correlation functions depend on the route followed. In particular, the values of the fourth virial coefficient B(4) predicted by the HNC and PY approximations via the virial route differ from those obtained via the compressibility route. Despite this, it is shown in this paper that the value of B(4) obtained from the virial route in the HNC theory is exactly three halves the value obtained from the compressibility route in the PY theory, irrespective of the interaction potential (whether isotropic or not), the number of components, and the dimensionality of the system. This simple relationship is confirmed in one-component systems by analytical results for the one-dimensional penetrable-square-well model and the three-dimensional penetrable-sphere model, as well as by numerical results for the one-dimensional Lennard-Jones model, the one-dimensional Gaussian core model, and the three-dimensional square-well model.

Ground states and formal duality relations in the Gaussian core model

We study dimensional trends in ground states for soft-matter systems. Specifically, using a high-dimensional version of Parrinello-Rahman dynamics, we investigate the behavior of the Gaussian core model in up to eight dimensions. The results include unexpected geometric structures, with surprising anisotropy as well as formal duality relations. These duality relations suggest that the Gaussian core model possesses unexplored symmetries, and they have implications for a broad range of soft-core potentials.

Strain-rate dependent shear viscosity of the Gaussian core model fluid

Nonequilibrium molecular dynamics simulations are reported for the shear viscosity of the Gaussian core model (GCM) fluid over a wide range of densities, temperatures and strain rates. A transition from Newtonian and non-Newtonian behavior is observed in all cases for sufficiently high strain rates. On the high-density side of the solid region where re-entrant melting occurs, the shear viscosity decreases significantly when the density is increased at constant temperature and Newtonian behavior persists until very high strain rates. This behavior, which is attributed to particle overlap, is in contrast to the monotonic increase in shear viscosity with density observed for the Lennard-Jones potential. Contrary to the behavior of normal fluids, the viscosity is observed to increase with increasing temperatures at high densities. This reflects a peculiarity of the GCM, namely the approach to the "infinite-density ideal-gas limit." The behavior is also consistent with viscosity measurements of cationic surfactant solutions. In contrast to other potentials, the shear viscosities for the Gaussian core potential at low to moderate strain rates are obtained with modest statistical uncertainties. Zero shear viscosities extrapolated from the nonequilibrium simulations are in good agreement with equilibrium Green-Kubo calculations.

Solid-liquid phase equilibria of the Gaussian core model fluid

The solid-liquid phase equilibria of the Gaussian core model are determined using the GWTS [J. Ge, G.-W. Wu, B. D. Todd, and R. J. Sadus, J. Chem. Phys. 119, 11017 (2003)] algorithm, which combines equilibrium and nonequilibrium molecular dynamics simulations. This is the first reported use of the GWTS algorithm for a fluid system displaying a reentrant melting scenario. Using the GWTS algorithm, the phase envelope of the Gaussian core model can be calculated more precisely than previously possible. The results for the low-density and the high-density (reentrant melting) sides of the solid state are in good agreement with those obtained by Monte Carlo simulations in conjunction with calculations of the solid free energies. The common point on the Gaussian core envelope, where equal-density solid and liquid phases are in coexistence, could be determined with high precision.

Transport Anomalies in the Gaussian Core Model Fluid

Abstract In this study, we investigate the self-diffusion coefficient, the shear viscosity and the thermal conductivity of a single-component system interacting via a Gaussian core (GC) potential. The transport properties are studied by means of the Green-Kubo formulas calculated from molecular dynamics simulation. We show that, for certain state conditions, anomalous behaviour occurs for the diffusivity and the shear viscosity. Therefore, the Stokes-Einstein relation is violated for the GC fluid. We do not find anomalous behaviour for the thermal conductivity. We develop an equation of state for the deviation of the ideal gas pressure and we derive the excess entropy from this equation. Depending on the phase space region, the excess entropy also shows anomalous behaviour. We discuss recently developed scaling relationships between excess entropy and transport properties. Because the GC potential is bounded, these relationships do not work properly for the GC fluid. Using new empirical scaling relations we are able to fit the diffusion coefficient within one single master curve for the whole density and temperature range we have simulated. We were also able to find a single master curve for the viscosity, but only for state conditions where the classical Stokes-Einstein relation is valid.

Effects of porous confinement on the structural properties of the Gaussian core model

We have investigated the structural properties of a fluid in which particles, interacting via soft potentials, are imbibed into a disordered porous structure built up by soft particles. Using a Gaussian potential for all interactions involved, we determine via Monte Carlo simulations and integral-equation theory the fluid–fluid, fluid–matrix, connected, and blocked structure factors. Within the explored range of state parameters, the fluid–fluid structure factors display a distinct pre-peak, which we identify as a fingerprint of the structure of the matrix. We show that this feature at low wave-vectors arises from contributions of blocked correlations to the fluid–fluid structure factor. We argue that a similar feature may be found also in systems in which particles interact via harshly repulsive potentials. On the other hand, the variation of the main peak of the fluid–fluid structure factor resembles the behaviour of the equilibrium Gaussian core model fluid. In particular, the height of the main peak changes non-monotonically with increasing fluid density at fixed matrix density. Finally, we analyse the effect of a mismatch between the temperature of the fluid and the temperature of the matrix on the structural properties of the system.

Counterintuitive ground states in soft-core models

It is well known that statistical mechanics systems exhibit subtle behavior in high dimensions. In this paper, we show that certain natural soft-core models, such as the Gaussian core model, have unexpectedly complex ground states even in relatively low dimensions. Specifically, we disprove a conjecture of Torquato and Stillinger, who predicted that dilute ground states of the Gaussian core model in dimensions 2 through 8 would be Bravais lattices. We show that in dimensions 5 and 7, there are in fact lower-energy non-Bravais lattices. (The nearest three-dimensional analog is the hexagonal close-packing, but it has higher energy than the face-centered cubic lattice.) We believe these phenomena are in fact quite widespread, and we relate them to decorrelation in high dimensions.

Stokes‐Einstein Behaviour for Liquids with Bounded Potentials at High Densities

AbstractBy means of molecular dynamics simulations we investigate the Stokes–Einstein behaviour of the Gaussian Core Model liquid at high densities. From a recent analysis at moderately high densities, we found that the Stokes–Einstein factor grows linearly with the viscosity. We show that at high densities the behaviour is similar, but there are slight departures at lower temperatures and higher densities. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Thermodynamic and mechanical stability of many‐body systems interacting with coarse‐grained bounded potentials

AbstractWe discuss the stability criteria of Fisher and Ruelle [J. Math. Phys. 7, 260 (1966)] which can be used to establish if a given pair potential satisfies the requirements for thermodynamic stability. The mechanical and thermodynamic stability are considered for systems composed of particles interacting with a bounded potential, which could be used to model a mesostructured material at a coarse‐grained level. The elastic moduli of fcc and bcc solids at zero temperature are calculated as a function of density for an assembly of particles interacting via the following (at r = 0 bounded potentials: (a) a Gaussian Core Model, GCM, potential, φ (r) = exp (–r2), and (b) the separation‐shifted Lennard–Jones, SSLJ, bounded potential, φ (r) = 4[1/α2 + r2)6 – 1/(α2 + r2)3], with α > 0, where in both cases the characteristic energy and lengthscale are set to unity, and r is the separation between the particles. For both potential forms, at low densities, the static fcc structure is the thermodynamically stable structural form but from above a certain density the bcc lattice becomes the stable structure. It is shown that for the SSLJ potential this transition density varies roughly as ∼α–3. In the T → 0 limit, auxetic behaviour is demonstrated to occur for both fcc and bcc structures, but at high pressure and for the bcc structural form its response to external strain can be entirely nonauxetic. A significant role of the attractive part of the interparticle interaction in enhancing auxetic behaviour is observed. The ranges of the mechanical stability are determined for both systems. At zero temperature, the lattice becomes mechanically unstable for α > αc, which appears to coincide with the value αc = (7/32)1/6 = 0.7762 proved previously to lead to thermodynamically unstable fluid states for this potential. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Preface: phys. stat. sol. (b) 245/11

Preface: phys. stat. sol. (b) 245/11

Auxeticity of cubic materials: The role of repulsive core interaction

Possible elastic response of anisotropic materials to uniaxial stretching is discussed. For cubic symmetry regions of different auxetic behavior are indicated and various solid structures located on elastic moduli maps. The elastic properties of two model molecular systems, the Gaussian-core model and soft-sphere solids are investigated. A generic mechanism leading to auxetic behavior in cubic materials is suggested.

Gaussian core model phase diagram and pair correlations in high Euclidean dimensions

The physical properties of a classical many-particle system with interactions given by a repulsive Gaussian pair potential are extended to arbitrarily high Euclidean dimensions. The goals of this paper are to characterize the behavior of the pair correlation function g(2) in various density regimes and to understand the phase properties of the Gaussian core model (GCM) as parametrized by dimension d. To this end, we explore the fluid (dilute and dense) and crystalline solid phases. For the dilute regime of the fluid phase, a cluster expansion of g(2) in reciprocal temperature beta is presented, the coefficients of which may be evaluated analytically due to the nature of the Gaussian potential. We present preliminary results concerning the convergence properties of this expansion. The analytical cluster expansion is related to numerical approximations for g(2) in the dense fluid regime by utilizing hypernetted chain, Percus-Yevick, and mean-field closures to the Ornstein-Zernike equation. Based on the results of these comparisons, we provide evidence in support of a decorrelation principle for the GCM in high Euclidean dimensions. In the solid phase, we consider the behavior of the freezing temperature T(f)(rho) in the limit rho-->+infinity and show T(f)(rho)-->0 in this limit for any d via a collective coordinate argument. Duality relations with respect to the energies of a lattice and its dual are then discussed, and these relations aid in the Maxwell double-tangent construction of phase coexistence regions between dual lattices based on lattice summation energies. The results from this analysis are used to draw conclusions about the ground-state structures of the GCM for a given dimension.

Stokes-Einstein violation for liquids with bounded potentials

The Stokes-Einstein relation between shear viscosity, diffusion constant, and temperature holds in many liquids, but there are certain examples where the relation fails. In this study, we consider liquids where the interaction potential is bounded, and we find that a different behavior of the Stokes-Einstein relation is possible, where the relation between shear viscosity, diffusion constant, and temperature grows linearly with the viscosity. This special behavior occurs when the potential is bounded and full overlap between the particles is possible. We try to show that the peculiar departure from the classical Stokes-Einstein relation can be explained by this possible overlap of particles by using a hydrodynamic model. Then we compare our result with molecular dynamics simulations for the Gaussian core model liquid.

Shear Viscosity of the Gaussian Core Model Fluid

AbstractBy means of molecular dynamics simulations we investigated the shear viscosity of the Gaussian Core Model fluid. We observed anomalous viscous behaviour for dimensionless densities greater than 0.3 and dimensionless temperatures below 0.04. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Static and dynamic anomalies in the Gaussian core model liquid

We investigated static and dynamic liquid-state anomalies of a single-component system interacting via a Gaussian core potential. Anomalies are produced due to the fact that the potential is bounded. Based on standard Monte Carlo simulations, we developed an equation of state for an extended phase space. From this, we were able to derive anomalies for the isothermal compressibility, the thermal expansion coefficient, as well as the specific heat very similar to the situation in liquid water. Using the pair correlation function, we detected structural peculiarities when the dimensionless density became greater than approximately 0.23. The self-diffusion coefficient is studied by means of the mean squared displacement and the Green–Kubo formula calculated from molecular dynamics simulation. This dynamic property again shows anomalous behaviour when the dimensionless density becomes greater than approximately 0.33. The behaviour can be explained by increased mobility of the particles.

Evaluation of phenomenological one-phase criteria for the melting and freezing of softly repulsive particles

We test the validity of some widely used phenomenological criteria for the localization of the fluid-solid transition thresholds against the phase diagrams of particles interacting through the exp-6, inverse-power-law, and Gaussian potentials. We find that one-phase rules give, on the whole, reliable estimates of freezing/melting points. The agreement is ordinarily better for a face-centered-cubic solid than for a body-centered-cubic crystal, even more so in the presence of a pressure-driven reentrant transition of the solid into a denser fluid phase, as found in the Gaussian-core model.