Athanassios Z. Panagiotopoulos

Critical point and phase behavior of the pure fluid and a Lennard-Jones mixture

Monte Carlo simulations in the grand canonical ensemble were used to obtain liquid-vapor coexistence curves and critical points of the pure fluid and a binary mixture of Lennard-Jones particles. Critical parameters were obtained from mixed-field finite-size scaling analysis and subcritical coexistence data from histogram reweighting methods. The critical parameters of the untruncated Lennard-Jones potential were obtained as Tc*=1.3120±0.0007, ρc*=0.316±0.001 and pc*=0.1279±0.0006. Our results for the critical temperature and pressure are not in agreement with the recent study of Caillol [J. Chem. Phys. 109, 4885 (1998)] on a four-dimensional hypersphere. Mixture parameters were e1=2e2 and σ1=σ2, with Lorentz–Berthelot combining rules for the unlike-pair interactions. We determined the critical point at T*=1.0 and pressure-composition diagrams at three temperatures. Our results have much smaller statistical uncertainties relative to comparable Gibbs ensemble simulations.

Direct Determination of Fluid Phase Equilibria by Simulation in the Gibbs Ensemble: A Review

Abstract This paper provides an extensive review of the literature on the Gibbs ensemble Monte Carlo method for direct determination of phase coexistence in fluids. The Gibbs ensemble technique is based on performing a simulation in two distinct regions in a way that ensures that the conditions of phase coexistence are satisfied in a statistical sense. Contrary to most other available techniques for this purpose, such as thermodynamic integration, grand canonical Monte Carlo or Widom test particle insertions, the Gibbs ensemble technique involves only a single simulation per coexistence point. A significant body of literature now exists on the method, its theoretical foundations, and proposed modifications for efficient determination of equilibria involving dense fluids and complex intermolecular potentials. Some practical aspects of Gibbs ensemble simulation are also discussed in this review. Applications of the technique to date range from studies of simple model potentials (for example Lennard–Jones, s...

Metastable liquid-liquid transition in a molecular model of water

Liquid water’s isothermal compressibility and isobaric heat capacity, and the magnitude of its thermal expansion coefficient, increase sharply on cooling below the equilibrium freezing point. Many experimental, theoretical and computational studies have sought to understand the molecular origin and implications of this anomalous behaviour. Of the different theoretical scenarios put forward, one posits the existence of a first-order phase transition that involves two forms of liquid water and terminates at a critical point located at deeply supercooled conditions. Some experimental evidence is consistent with this hypothesis, but no definitive proof of a liquid–liquid transition in water has been obtained to date: rapid ice crystallization has so far prevented decisive measurements on deeply supercooled water, although this challenge has been overcome recently. Computer simulations are therefore crucial for exploring water’s structure and behaviour in this regime, and have shown that some water models exhibit liquid–liquid transitions and others do not. However, recent work has argued that the liquid–liquid transition has been mistakenly interpreted, and is in fact a liquid–crystal transition in all atomistic models of water. Here we show, by studying the liquid–liquid transition in the ST2 model of water with the use of six advanced sampling methods to compute the free-energy surface, that two metastable liquid phases and a stable crystal phase exist at the same deeply supercooled thermodynamic condition, and that the transition between the two liquids satisfies the thermodynamic criteria of a first-order transition. We follow the rearrangement of water’s coordination shell and topological ring structure along a thermodynamically reversible path from the low-density liquid to cubic ice. We also show that the system fluctuates freely between the two liquid phases rather than crystallizing. These findings provide unambiguous evidence for a liquid–liquid transition in the ST2 model of water, and point to the separation of time scales between crystallization and relaxation as being crucial for enabling it.

Monte Carlo methods for phase equilibria of fluids

This article presents an overview of Monte Carlo methods for simulations of the phase behaviour of fluids. The Gibbs ensemble method and histogram-reweighting Monte Carlo techniques are described in detail. The Gibbs ensemble method is based on simulations of two regions coupled via volume change and particle transfer moves so that the conditions for phase coexistence are satisfied in a statistical sense. Histogram-reweighting methods obtain the free energy of a system over a broad range of conditions from a small set of grand canonical Monte Carlo calculations. The histogram methods can produce highly accurate data, especially in the vicinity of critical points. Other methods described briefly include interfacial simulations, the NPT + test particle method, Gibbs-Duhem integration and pseudo-ensembles. Configurational-bias sampling techniques and expanded ensembles can be used for multisegment molecules to increase the efficiency of the simulations. The last section of the review covers applications to both model and realistic systems that have appeared since 1995.

Phase behavior of the restricted primitive model and square-well fluids from Monte Carlo simulations in the grand canonical ensemble

Coexistence curves of square-well fluids with variable interaction width and of the restricted primitive model for ionic solutions have been investigated by means of grand canonical Monte Carlo simulations aided by histogram reweighting and multicanonical sampling techniques. It is demonstrated that this approach results in efficient data collection. The shape of the coexistence curve of the square-well fluid with short potential range is nearly cubic. In contrast, for a system with a longer potential range, the coexistence curve closely resembles a parabola, except near the critical point. The critical compressibility factor for the square-well fluids increases with increasing range. The critical behavior of the restricted primitive model was found to be consistent with the Ising universality class. The critical temperature was obtained as Tc=0.0490±0.0003 and the critical density ρc=0.070±0.005, both in reduced units. The critical temperature estimate is consistent with the recent calculation of Caillol...

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, silicas 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.

Free energy and phase equilibria for the restricted primitive model of ionic fluids from Monte Carlo simulations

In this work, we investigate the liquid–vapor phase transition of the restricted primitive model of ionic fluids. We show that at the low temperatures where the phase transition occurs, the system cannot be studied by conventional molecular simulation methods because convergence to equilibrium is slow. To accelerate convergence, we propose cluster Monte Carlo moves capable of moving more than one particle at a time. We then address the issue of charged particle transfers in grand canonical and Gibbs ensemble Monte Carlo simulations, for which we propose a biased particle insertion/destruction scheme capable of sampling short interparticle distances. We compute the chemical potential for the restricted primitive model as a function of temperature and density from grand canonical Monte Carlo simulations and the phase envelope from Gibbs Monte Carlo simulations. Our calculated phase coexistence curve is in agreement with recent results of Caillol obtained on the four‐dimensional hypersphere and our own earli...

Reactive canonical Monte Carlo A new simulation technique for reacting or associating fluids

A new simulation technique is developed for calculating the properties of chemically reactive and associating (hydrogen bonding, charge transfer) systems. We call this new method reactive canonical Monte Carlo (RCMC). In contrast to previous methods for treating chemical reactions, this algorithm is applicable to reactions involving a change in mole number. Stoichiometrically balanced reactions are attempted in the forward and reverse directions to achieve chemical equilibrium. The transition probabilities do not depend on the chemical potentials or chemical potential differences of any of the components. We also extend RCMC to work in concert with the isothermal-isobaric ensemble for simulating chemical reactions at constant pressure, and with the Gibbs ensemble for simultaneous calculation of phase and chemical equilibria. Association is treated as a chemical reaction in the RCMC formalism. Results are presented for dimerization of simple model associating fluids. In contrast to previous methods, the re...

Water: A Tale of Two Liquids

Water is the most abundant liquid on earth and also the substance with the largest number of anomalies in its properties. It is a prerequisite for life and as such a most important subject of current research in chemical physics and physical chemistry. In spite of its simplicity as a liquid, it has an enormously rich phase diagram where different types of ices, amorphous phases, and anomalies disclose a path that points to unique thermodynamics of its supercooled liquid state that still hides many unraveled secrets. In this review we describe the behavior of water in the regime from ambient conditions to the deeply supercooled region. The review describes simulations and experiments on this anomalous liquid. Several scenarios have been proposed to explain the anomalous properties that become strongly enhanced in the supercooled region. Among those, the second critical-point scenario has been investigated extensively, and at present most experimental evidence point to this scenario. Starting from very low temperatures, a coexistence line between a high-density amorphous phase and a low-density amorphous phase would continue in a coexistence line between a high-density and a low-density liquid phase terminating in a liquid–liquid critical point, LLCP. On approaching this LLCP from the one-phase region, a crossover in thermodynamics and dynamics can be found. This is discussed based on a picture of a temperature-dependent balance between a high-density liquid and a low-density liquid favored by, respectively, entropy and enthalpy, leading to a consistent picture of the thermodynamics of bulk water. Ice nucleation is also discussed, since this is what severely impedes experimental investigation of the vicinity of the proposed LLCP. Experimental investigation of stretched water, i.e., water at negative pressure, gives access to a different regime of the complex water diagram. Different ways to inhibit crystallization through confinement and aqueous solutions are discussed through results from experiments and simulations using the most sophisticated and advanced techniques. These findings represent tiles of a global picture that still needs to be completed. Some of the possible experimental lines of research that are essential to complete this picture are explored.

Universality class of criticality in the restricted primitive model electrolyte.

The 1:1 equisized hard-sphere electrolyte or restricted primitive model has been simulated via grand-canonical fine-discretization Monte Carlo. Newly devised unbiased finite-size extrapolation methods using loci in the temperature-density or (T,rho) plane of isothermal rho(2-k) vs pressure inflections, of Q identical with(2)/ maxima, and of canonical and C(V) criticality, yield estimates of (T(c),rho(c)) to +/-(0.04,3)%. Extrapolated exponents and Q ratio are (gamma,nu,Q(c)) = [1.24(3), 0.63(3); 0.624(2)], which support Ising (n = 1) behavior with (1.23(9), 0.630(3); 0.623(6)), but exclude classical, XY (n = 2), self-avoiding walk (n = 0), and n = 1 criticality with potentials varphi(r)>Phi/r(4.9) when r-->infinity.