Density minimum and liquid-liquid phase transition

We present a high-resolution computer simulation study of the equation of state of ST2 water, evaluating the liquid-state properties at 2718 state points, and precisely locating the liquid-liquid critical point (LLCP) occurring in this model. We are thereby able to reveal the interconnected set of density anomalies, spinodal instabilities and response function extrema that occur in the vicinity of a LLCP for the case of a realistic, off-lattice model of a liquid with local tetrahedral order. In particular, we unambiguously identify a density minimum in the liquid state, define its relationship to other anomalies, and show that it arises due to the approach of the liquid structure to a defect-free random tetrahedral network of hydrogen bonds.Comment: 5 pages, 4 figure

Molecular structural order and anomalies in liquid silica

The present investigation examines the relationship between structural order, diffusivity anomalies, and density anomalies in liquid silica by means of molecular dynamics simulations. We use previously defined orientational and translational order parameters to quantify local structural order in atomic configurations. Extensive simulations are performed at different state points to measure structural order, diffusivity, and thermodynamic properties. It is found that silica shares many trends recently reported for water [J. R. Errington and P. G. Debenedetti, Nature 409, 318 (2001)]. At intermediate densities, the distribution of local orientational order is bimodal. At fixed temperature, order parameter extrema occur upon compression: a maximum in orientational order followed by a minimum in translational order. Unlike water, however, silica's translational order parameter minimum is broad, and there is no range of thermodynamic conditions where both parameters are strictly coupled. Furthermore, the temperature-density regime where both structural order parameters decrease upon isothermal compression (the structurally anomalous regime) does not encompass the region of diffusivity anomalies, as was the case for water.Comment: 30 pages, 8 figure

Intra-molecular coupling as a mechanism for a liquid-liquid phase transition

We study a model for water with a tunable intra-molecular interaction $J_\sigma$, using mean field theory and off-lattice Monte Carlo simulations. For all $J_\sigma\geq 0$, the model displays a temperature of maximum density.For a finite intra-molecular interaction $J_\sigma > 0$,our calculations support the presence of a liquid-liquid phase transition with a possible liquid-liquid critical point for water, likely pre-empted by inevitable freezing. For J=0 the liquid-liquid critical point disappears at T=0.Comment: 8 pages, 4 figure

Generic mechanism for generating a liquid-liquid phase transition

Recent experimental results indicate that phosphorus, a single-component system, can have two liquid phases: a high-density liquid (HDL) and a low-density liquid (LDL) phase. A first-order transition between two liquids of different densities is consistent with experimental data for a variety of materials, including single-component systems such as water, silica and carbon. Molecular dynamics simulations of very specific models for supercooled water, liquid carbon and supercooled silica, predict a LDL-HDL critical point, but a coherent and general interpretation of the LDL-HDL transition is lacking. Here we show that the presence of a LDL and a HDL can be directly related to an interaction potential with an attractive part and two characteristic short-range repulsive distances. This kind of interaction is common to other single-component materials in the liquid state (in particular liquid metals), and such potentials are often used to decribe systems that exhibit a density anomaly. However, our results show that the LDL and HDL phases can occur in systems with no density anomaly. Our results therefore present an experimental challenge to uncover a liquid-liquid transition in systems like liquid metals, regardless of the presence of the density anomaly.Comment: 5 pages, 3 ps Fig

Metastable liquid-liquid phase transition in a single-component system with only one crystal phase and no density anomaly

We investigate the phase behavior of a single-component system in 3 dimensions with spherically-symmetric, pairwise-additive, soft-core interactions with an attractive well at a long distance, a repulsive soft-core shoulder at an intermediate distance, and a hard-core repulsion at a short distance, similar to potentials used to describe liquid systems such as colloids, protein solutions, or liquid metals. We showed [Nature {\bf 409}, 692 (2001)] that, even with no evidences of the density anomaly, the phase diagram has two first-order fluid-fluid phase transitions, one ending in a gas--low-density liquid (LDL) critical point, and the other in a gas--high-density liquid (HDL) critical point, with a LDL-HDL phase transition at low temperatures. Here we use integral equation calculations to explore the 3-parameter space of the soft-core potential and we perform molecular dynamics simulations in the interesting region of parameters. For the equilibrium phase diagram we analyze the structure of the crystal phase and find that, within the considered range of densities, the structure is independent of the density. Then, we analyze in detail the fluid metastable phases and, by explicit thermodynamic calculation in the supercooled phase, we show the absence of the density anomaly. We suggest that this absence is related to the presence of only one stable crystal structure.Comment: 15 pages, 21 figure

Equilibration times in numerical simulation of structural glasses: Comparing parallel tempering and conventional molecular dynamics

Generation of equilibrium configurations is the major obstacle for numerical investigation of the slow dynamics in supercooled liquid states. The parallel tempering (PT) technique, originally proposed for the numerical equilibration of discrete spin-glass model configurations, has recently been applied in the study of supercooled structural glasses. We present an investigation of the ability of parallel tempering to properly sample the liquid configuration space at different temperatures, by mapping the PT dynamics into the dynamics of the closest local potential energy minima (inherent structures). Comparing the PT equilibration process with the standard molecular dynamics equilibration process we find that the PT does not increase the speed of equilibration of the (slow) configurational degrees of freedom.Comment: 5 pages, 3 figure

Long-Time Tails and Anomalous Slowing Down in the Relaxation of Spatially Inhomogeneous Excitations in Quantum Spin Chains

Exact analytic calculations in spin-1/2 XY chains, show the presence of long-time tails in the asymptotic dynamics of spatially inhomogeneous excitations. The decay of inhomogeneities, for $t\to \infty$, is given in the form of a power law $$(t/\tau_{Q}) ^{-\nu_{Q}}$$ where the relaxation time $\tau_{Q}$ and the exponent $\nu_{Q}$ depend on the wave vector $Q$, characterizing the spatial modulation of the initial excitation. We consider several variants of the XY model (dimerized, with staggered magnetic field, with bond alternation, and with isotropic and uniform interactions), that are grouped into two families, whether the energy spectrum has a gap or not. Once the initial condition is given, the non-equilibrium problem for the magnetization is solved in closed form, without any other assumption. The long-time behavior for $t\to \infty$ can be obtained systematically in a form of an asymptotic series through the stationary phase method. We found that gapped models show critical behavior with respect to $Q$, in the sense that there exist critical values $Q_{c}$, where the relaxation time $\tau_{Q}$ diverges and the exponent $\nu_{Q}$ changes discontinuously. At those points, a slowing down of the relaxation process is induced, similarly to phenomena occurring near phase transitions. Long-lived excitations are identified as incommensurate spin density waves that emerge in systems undergoing the Peierls transition. In contrast, gapless models do not present the above anomalies as a function of the wave vector $Q$.Comment: 25 pages, 2 postscript figures. Manuscript submitted to Physical Review

Glass Transition Behavior of Polymer Films of Nanoscopic Dimensions

Glass transition behavior of nanoscopically thin polymer films is investigated by means of molecular dynamics simulations. A thin polymer film that is composed of bead-spring model chains and supported on an idealized, fcc lattice substrate surface is studied in this work.Comment: in review, macromolecule

Liquid-liquid critical point in supercooled silicon

A novel liquid-liquid phase transition has been proposed and investigated in a wide variety of pure substances recently, including water, silica and silicon. From computer simulations using the Stillinger-Weber classical empirical potential, Sastry and Angell [1] demonstrated a first order liquid-liquid transition in supercooled silicon, subsequently supported by experimental and simulation studies. Here, we report evidence for a liquid-liquid critical end point at negative pressures, from computer simulations using the SW potential. Compressibilities exhibit a growing maximum upon lowering temperature below 1500 K and isotherms exhibit density discontinuities below 1120 K, at negative pressure. Below 1120 K, isotherms obtained from constant volume-temperature simulations exhibit non-monotonic, van der Waals-like behavior signaling a first order transition. We identify Tc ~ 1120 +/- 12 K, Pc -0.60 +/- 0.15 GPa as the critical temperature and pressure for the liquid-liquid critical point. The structure of the liquid changes dramatically upon decreasing the temperature and pressure. Diffusivities vary over 4 orders of magnitude, and exhibit anomalous pressure dependence near the critical point. A strong relationship between local geometry quantified by the coordination number, and diffusivity, is seen, suggesting that atomic mobility in both low and high density liquids can usefully be analyzed in terms of defects in the tetrahedral network structure. We have constructed the phase diagram of supercooled silicon. We identify the lines of compressibility, density extrema (maxima and minima) and the spinodal which reveal the interconnection between thermodynamic anomalies and the phase behaviour of the system as suggested in previous works [2-9]Comment: (to be published in revised form); small corrections to previous version; Nature Physics 201