An improved Monte Carlo method for direct calculation of the density of states

We present an efficient Monte Carlo algorithm for determining the density of states which is based on the statistics of transition probabilities between states. By measuring the infinite temperature transition probabilities--that is, the probabilities associated with move proposal only--we are able to extract excellent estimates of the density of states. When this estimator is used in conjunction with a Wang-Landau sampling scheme [F. Wang and D. P. Landau, Phys. Rev. Lett. 86, 2050 (2001)], we quickly achieve uniform sampling of macrostates (e.g., energies) and systematically refine the calculated density of states. This approach requires only potential energy evaluations, continues to improve the statistical quality of its results as the simulation time is extended, and is applicable to both lattice and continuum systems. We test the algorithm on the Lennard-Jones liquid and demonstrate good statistical convergence properties.Comment: 7 pages, 4 figures. to appear in Journal of Chemical Physic

Structural Order in Glassy Water

We investigate structural order in glassy water by performing classical molecular dynamics simulations using the extended simple point charge (SPC/E) model of water. We perform isochoric cooling simulations across the glass transition temperature at different cooling rates and densities. We quantify structural order by orientational and translational order metrics. Upon cooling the liquid into the glassy state, both the orientational order parameter $Q$ and translational order parameter $\tau$ increase. At T=0 K, the glasses fall on a line in the $Q$-$\tau$ plane or {\it order map}. The position of this line depends only on density and coincides with the location in the order map of the inherent structures (IS) sampled upon cooling. We evaluate the energy of the IS, $e_{IS}(T)$, and find that both order parameters for the IS are proportional to $e_{IS}$. We also study the structural order during the transformation of low-density amorphous ice (LDA) to high-density amorphous ice (HDA) upon isothermal compression and are able to identify distinct regions in the order map corresponding to these glasses. Comparison of the order parameters for LDA and HDA with those obtained upon isochoric cooling indicates major structural differences between glasses obtained by cooling and glasses obtained by compression. These structural differences are only weakly reflected in the pair correlation function. We also characterize the evolution of structural order upon isobaric annealing, leading at high pressure to very-high density amorphous ice (VHDA).Comment: submitte

Spinodal of supercooled polarizable water

We develop a series of molecular dynamics computer simulations of liquid water, performed with a polarizable potential model, to calculate the spinodal line and the curve of maximum density inside the metastable supercooled region. After analysing the structural properties,the liquid spinodal line is followed down to T=210 K. A monotonic decrease is found in the explored region. The curve of maximum density bends on approaching the spinodal line. These results, in agreement with similar studies on non polarizable models of water, are consistent with the existence of a second critical point for water.Comment: 8 pages, 5 figures, 2 tables. To be published in Phys. Re

Softness dependence of the Anomalies for the Continuous Shouldered Well potential

By molecular dynamic simulations we study a system of particles interacting through a continuous isotropic pairwise core-softened potential consisting of a repulsive shoulder and an attractive well. The model displays a phase diagram with three fluid phases, a gas-liquid critical point, a liquid-liquid critical point, and anomalies in density, diffusion and structure. The hierarchy of the anomalies is the same as for water. We study the effect on the anomalies of varying the softness of the potential. We find that, making the soft-core steeper, the regions of density and diffusion anomalies contract in the T - {\rho} plane, while the region of structural anomaly is weakly affected. Therefore, a liquid can have anomalous structural behavior without density or diffusion anomalies. We show that, by considering as effective distances those corresponding to the maxima of the first two peaks of the radial distribution function g(r) in the high-density liquid, we can generalize to continuous two-scales potentials a criterion for the occurrence of the anomalies of density and diffusion, originally proposed for discontinuous potentials. We observe that the knowledge of the structural behavior within the first two coordination shells of the liquid is not enough to establish the occurrence of the anomalies. By introducing the density derivative of the the cumulative order integral of the excess entropy we show that the anomalous behavior is regulated by the structural order at distances as large as the fourth coordination shell. By comparing the results for different softness of the potential, we conclude that the disappearing of the density and diffusion anomalies for the steeper potentials is due to a more structured short-range order. All these results increase our understanding on how, knowing the interaction potential, we can evaluate the possible presence of anomalies for a liquid

Liquid-Liquid Phase Transitions for Soft-Core Attractive Potentials

Using event driven molecular dynamics simulations, we study a three dimensional one-component system of spherical particles interacting via a discontinuous potential combining a repulsive square soft core and an attractive square well. In the case of a narrow attractive well, it has been shown that this potential has two metastable gas-liquid critical points. Here we systematically investigate how the changes of the parameters of this potential affect the phase diagram of the system. We find a broad range of potential parameters for which the system has both a gas-liquid critical point and a liquid-liquid critical point. For the liquid-gas critical point we find that the derivatives of the critical temperature and pressure, with respect to the parameters of the potential, have the same signs: they are positive for increasing width of the attractive well and negative for increasing width and repulsive energy of the soft core. This result resembles the behavior of the liquid-gas critical point for standard liquids. In contrast, for the liquid-liquid critical point the critical pressure decreases as the critical temperature increases. As a consequence, the liquid-liquid critical point exists at positive pressures only in a finite range of parameters. We present a modified van der Waals equation which qualitatively reproduces the behavior of both critical points within some range of parameters, and give us insight on the mechanisms ruling the dependence of the two critical points on the potential's parameters. The soft core potential studied here resembles model potentials used for colloids, proteins, and potentials that have been related to liquid metals, raising an interesting possibility that a liquid-liquid phase transition may be present in some systems where it has not yet been observed.Comment: 29 pages, 15 figure

Mpemba effect and phase transitions in the adiabatic cooling of water before freezing

An accurate experimental investigation on the Mpemba effect (that is, the freezing of initially hot water before cold one) is carried out, showing that in the adiabatic cooling of water a relevant role is played by supercooling as well as by phase transitions taking place at 6 +/- 1 oC, 3.5 +/- 0.5 oC and 1.3 +/- 0.6 oC, respectively. The last transition, occurring with a non negligible probability of 0.21, has not been detected earlier. Supported by the experimental results achieved, a thorough theoretical analysis of supercooling and such phase transitions, which are interpreted in terms of different ordering of clusters of molecules in water, is given.Comment: revtex, 4 pages, 2 figure

Supersaturated dispersions of rod-like viruses with added attraction

The kinetics of isotropic-nematic (I-N) and nematic-isotropic (N-I) phase transitions in dispersions of rod-like {\it fd}-viruses are studied. Concentration quenches were applied using pressure jumps in combination with polarization microscopy, birefringence and turbidity measurements. The full biphasic region could be accessed, resulting in the construction of a first experimental analogue of the bifurcation diagram. The N-I spinodal points for dispersions of rods with varying concentrations of depletion agents (dextran) were obtained from orientation quenches, using cessation of shear flow in combination with small angle light scattering. We found that the location of the N-I spinodal point is independent of the attraction, which was confirmed by theoretical calculations. Surprisingly, the experiments showed that also the absolute induction time, the critical nucleus and the growth rate are insensitive of the attraction, when the concentration is scaled to the distance to the phase boundaries.Comment: 13 pages, 14 figures. accepted in Phsical Review

Non-exponential kinetic behavior of confined water

We present the results of molecular dynamics simulations of SPC/E water confined in a realistic model of a silica pore. The single-particle dynamics have been studied at ambient temperature for different hydration levels. The confinement near the hydrophilic surface makes the dynamic behaviour of the liquid strongly dependent on the hydration level. Upon decrease of the number of water molecules in the pore we observe the onset of a slow dynamics due to the ``cage effect''. The conventional picture of a stochastic single-particle diffusion process thus looses its validity

Potential Energy Landscape Equation of State

Depth, number, and shape of the basins of the potential energy landscape are the key ingredients of the inherent structure thermodynamic formalism introduced by Stillinger and Weber [F. H. Stillinger and T. A. Weber, Phys. Rev. A 25, 978 (1982)]. Within this formalism, an equation of state based only on the volume dependence of these landscape properties is derived. Vibrational and configurational contributions to pressure are sorted out in a transparent way. Predictions are successfully compared with data from extensive molecular dynamics simulations of a simple model for the fragile liquid orthoterphenyl.Comment: RevTeX4, 4 pages, 5 figure