Critical-point and coexistence-curve properties of the Lennard-Jones fluid: A finite-size scaling study

A molecular-dynamics simulation study on the dependence of Lennard-Jones gas-liquid phase diagram on the long-range part of the interactions

The particle-transfer molecular-dynamics technique is adopted to construct the Lennard-Jones fluid gas-liquid phase diagram. Detailed study of the dependence of the simulation results on the system size and the cutoff distance is performed to test the validity of the simulation technique. Both the traditional cutoff plus long-range correction (CPC) and Ewald summation methods are used in the simulations to calculate the interactions. In the intermediate range of temperatures, the results with the Ewald summation method are almost the same as those with the CPC method. However, in the range close to the critical point, the results with the CPC method deviate from those with the Ewald summation. Compared with the results obtained via the Ewald summation in a smaller system, simply increasing the system size in the CPC scheme may not give better results.

Monte Carlo study of the vector Blume-Emery-Griffiths model for 3He--4He mixtures in three dimensions

A version of the Vector Blume-Emery-Griffiths model with three-dimensional spins was studied on a simple cubic lattice by Monte Carlo simulations. We obtained the phase diagram, which reproduces, for a range of the parameters of the model, the topology of the one observed for bulk mixtures of 3He--4He. The phase diagram displays a superfluid, 4He-rich phase which undergoes a phase transition to a normal phase. This transition is first or second order, depending on the region of the phase diagram examined. One of the main features of this diagram is the existence of a tricritical point, which, for some values of the parameters of the model, decomposes into a critical endpoint and a double critical endpoint. These points were located with reasonable precision. This study provides the basis for the subsequent study of dynamic properties of 3He--4He mixtures.

Unravelling the Peculiar Nucleation Mechanisms for Non-Ideal Binary Mixtures with Atomistic Simulations

Recent experiments reveal unusual nucleation behavior for seemingly simple mixtures that cannot be described by the classical theory. Molecular simulations using a combination of aggregation-volume-bias Monte Carlo, umbrella sampling, and histogram reweighting methods were carried out to study the nucleation events involved in the water/ethanol, water/n-nonane, and n-nonane/ethanol mixtures. These simulations reproduced their different nonideal behaviors observed by the experiments. Furthermore, the finding of their strikingly distinct mechanisms, as implied from the calculated free-energy maps, challenges the current theoretical description of this phenomenon.

Oscillatory instabilities in phase separation of binary mixtures: Fixing the thermodynamic driving

Binary liquid mixtures can show pronounced oscillations in the differential scanning calorimeter signal for the specific heat and in the turbidity when phase separation is induced by continuously ramping the temperature. For a fixed ramp rate, i.e., a linear temporal drift of temperature, only a small number of oscillations have been observed. In the present manuscript we describe an experimental setup where simultaneous video-microscopy and shadow-graph measurements can be performed on mixtures subjected to an arbitrary temporal temperature evolution. In particular, it can be adjusted to fix the thermodynamic driving force, which characterizes the rate of change of the composition of the coexisting phases. With this novel technique both the number of oscillations and the temperature interval where oscillations are observed increase significantly. This technique can easily be applied to a great variety of binary mixtures, permitting detailed investigations of their phase-separation kinetics under slowly ramping temperature.

Test-area simulation method for the direct determination of the interfacial tension of systems with continuous or discontinuous potentials

A novel test-area (TA) technique for the direct simulation of the interfacial tension of systems interacting through arbitrary intermolecular potentials is presented in this paper. The most commonly used method invokes the mechanical relation for the interfacial tension in terms of the tangential and normal components of the pressure tensor relative to the interface (the relation of Kirkwood and Buff [J. Chem. Phys. 17, 338 (1949)]). For particles interacting through discontinuous intermolecular potentials (e.g., hard-core fluids) this involves the determination of delta functions which are impractical to evaluate, particularly in the case of nonspherical molecules. By contrast we employ a thermodynamic route to determine the surface tension from a free-energy perturbation due to a test change in the surface area. There are important distinctions between our test-area approach and the computation of a free-energy difference of two (or more) systems with different interfacial areas (the method of Bennett [J. Comput. Phys. 22, 245 (1976)]), which can also be used to determine the surface tension. In order to demonstrate the adequacy of the method, the surface tension computed from test-area Monte Carlo (TAMC) simulations are compared with the data obtained with other techniques (e.g., mechanical and free-energy differences) for the vapor-liquid interface of Lennard-Jones and square-well fluids; the latter corresponds to a discontinuous potential which is difficult to treat with standard methods. Our thermodynamic test-area approach offers advantages over existing techniques of computational efficiency, ease of implementation, and generality. The TA method can easily be implemented within either Monte Carlo (TAMC) or molecular-dynamics (TAMD) algorithms for different types of interfaces (vapor-liquid, liquid-liquid, fluid-solid, etc.) of pure systems and mixtures consisting of complex polyatomic molecules.

Generalized geometric cluster algorithm for fluid simulation

We present a detailed description of the generalized geometric cluster algorithm for the efficient simulation of continuum fluids. The connection with well-known cluster algorithms for lattice spin models is discussed, and an explicit full cluster decomposition is derived for a particle configuration in a fluid. We investigate a number of basic properties of the geometric cluster algorithm, including the dependence of the cluster-size distribution on density and temperature. Practical aspects of its implementation and possible extensions are discussed. The capabilities and efficiency of our approach are illustrated by means of two example studies.

Liquid-vapor interface of a polydisperse fluid

We report a grand canonical Monte Carlo simulation study of the liquid-vapor interface of a model fluid exhibiting polydispersity in terms of the particle size sigma. The bulk density distribution, rho0(sigma), of the system is controlled by the imposed chemical potential distribution mu(sigma), the form of which is specified such that rho0(sigma) assumes a Schulz form with associated degree of polydispersity approximately = 14%. By introducing a smooth attractive wall, a planar liquid-vapor interface is formed for bulk state points within the region of liquid-vapor coexistence. Owing to fractionation, the pure liquid phase is enriched in large particles, with respect to the coexisting vapor. We investigate how the spatial variation of the density near the liquid-vapor interface affects the evolution of the local distribution of particle sizes between the limiting pure phase forms. We find [as previously predicted by density-functional theory, Bellier-Castella, Phys. Rev. E 65, 021503 (2002)] a segregation of smaller particles to the interface. The magnitude of this effect as a function of sigma is quantified via measurements of the relative adsorption. Additionally, we consider the utility of various estimators for the interfacial width and highlight the difficulty of isolating the intrinsic contribution of polydispersity to this width.

Stochastic potential switching algorithm for Monte Carlo simulations of complex systems

This paper describes a new Monte Carlo method based on a novel stochastic potential switching algorithm. This algorithm enables the equilibrium properties of a system with potential V to be computed using a Monte Carlo simulation for a system with a possibly less complex stochastically altered potential V. By proper choices of the stochastic switching and transition probabilities, it is shown that detailed balance can be strictly maintained with respect to the original potential V. The validity of the method is illustrated with a simple one-dimensional example. The method is then generalized to multidimensional systems with any additive potential, providing a framework for the design of more efficient algorithms to simulate complex systems. A near-critical Lennard-Jones fluid with more than 20,000 particles is used to illustrate the method. The new algorithm produced a much smaller dynamic scaling exponent compared to the Metropolis method and improved sampling efficiency by over an order of magnitude.

Simulation study of the phase behavior of a planar Maier-Saupe nematogenic liquid

Using extensive Monte Carlo simulations and a simple approximation in density functional theory, we study the phase behavior of a fluid of nematogenic molecules with centers of mass constrained to lie in a plane but with axes free to rotate in any direction, both with and without an external disorienting field perpendicular to the plane. We find that simulation predicts the existence of an order-disorder phase transition belonging to the Berezinskii-Kosterlitz-Thouless type, along with a low temperature gas-liquid transition. In contrast to the simulation results, density functional theory predicts a first-order orientational phase transition coupled continuously with a first-order gas-liquid transition. The approximate theoretical approach qualitatively reproduces the field dependence of the order-disorder and gas-liquid transitions but is far from quantitative.

Phase separation of the Widom–Rowlinson mixture in confined geometry

The behavior of binary Widom-Rowlinson [J. Chem. Phys. 52, 1670 (1970)] mixture in confined geometry is investigated. The influence of confinement on phase separation is examined. Coexistence curves for the mixture in slitlike pores and pores of complex geometry are calculated in Monte Carlo simulations. Finite size scaling analysis is used to determine precisely the location of critical point for the bulk mixture.

Determination of fluid-phase behavior using transition-matrix Monte Carlo: Binary Lennard-Jones mixtures

We present a novel computational methodology for determining fluid-phase equilibria in binary mixtures. The method is based on a combination of highly efficient transition-matrix Monte Carlo and histogram reweighting. In particular, a directed grand-canonical transition-matrix Monte Carlo scheme is used to calculate the particle-number probability distribution, after which histogram reweighting is used as a postprocessing procedure to determine the conditions of phase equilibria. To validate the methodology, we have applied it to a number of model binary Lennard-Jones systems known to exhibit nontrivial fluid-phase behavior. Although we have focused on monatomic fluids in this work, the method presented here is general and can be easily extended to more complex molecular fluids. Finally, an important feature of this method is the capability to predict the entire fluid-phase diagram of a binary mixture at fixed temperature in a single simulation.

Simulating Vapor−Liquid Nucleation of Water: A Combined Histogram-Reweighting and Aggregation-Volume-Bias Monte Carlo Investigation for Fixed-Charge and Polarizable Models

The method of histogram-reweighting was integrated with a recently developed approach using aggregation-volume-bias Monte Carlo and self-adaptive umbrella sampling to develop the AVUS-HR algorithm that allows for exceedingly efficient calculations of nucleation properties over a wide range of thermodynamic conditions. Simulations were carried out for water using both fixed-charge and polarizable force fields belonging to the TIP4P family (namely, TIP4P, TIP4P-FQ, TIP4P-pol2, and TIP4P-pol3) to investigate the nucleation of water over a temperature range from 200 to 300 K and the concentration of water clusters in the atmosphere at elevations up to 15 km. It was found that the nucleation free energy barriers and atmospheric concentrations are extremely sensitive to the force field, albeit all of the models investigated in this study support the following general conclusions: (i) ice nucleation is not present under the thermodynamic conditions and cluster-size range investigated here, i.e., the critical nuclei possess liquidlike structures, and (ii) the atmospheric concentrations of water clusters under homogeneous conditions are very low with the mole fraction of hexamers being about 10(-10), a number probably too low to influence the solar radiation balance. Compared to the experimental data, the TIP4P-pol3 model yields the most accurate nucleation results, consistent with its excellent performance for the second virial coefficient and the minimum cluster energies.

Computer simulation of the phase diagram for a fluid confined in a fractal and disordered porous material

We present a grand canonical Monte Carlo simulation study of the phase diagram of a Lennard-Jones fluid adsorbed in a fractal and highly porous aerogel. The gel environment is generated from an off-lattice diffusion limited cluster-cluster aggregation process. Simulations have been performed with the multicanonical ensemble sampling technique. The biased sampling function has been obtained by histogram reweighting calculations. Comparing the confined and the bulk system liquid-vapor coexistence curves we observe a decrease of both the critical temperature and density in qualitative agreement with experiments and other Monte Carlo studies on Lennard-Jones fluids confined in random matrices of spheres. At variance with these numerical studies we do not observe upon confinement a peak on the liquid side of the coexistence curve associated with a liquid-liquid phase coexistence. In our case only a shouldering of the coexistence curve appears upon confinement. This shoulder can be associated with high density fluctuations in the liquid phase. The coexisting vapor and liquid phases in our system show a high degree of spatial disorder and inhomogeneity.

Designing specificity of protein-substrate interactions

One of the key properties of biological molecules is that they can bind strongly to certain substrates yet interact only weakly with the very large number of other molecules that they encounter. Using a simple lattice model, we test several methods to design molecule-substrate binding specificity. We characterize the binding free energy and binding energy as a function of the size of the interacting units. Our simulations indicate that there exists a temperature window where specific binding is possible. Binding sites that have been designed to interact quite strongly with specific substrates are unlikely to bind nonspecifically to other substrates. In other words, the conflict between specific interactions between small numbers of biomolecules and weak, nonspecific interaction with the rest need not be a very serious design constraint.

Liquid-gas coexistence and critical point shifts in size-disperse fluids

Specialized Monte Carlo simulations and the moment free energy (MFE) method are employed to study liquid-gas phase equilibria in size-disperse fluids. The investigation is made subject to the constraint of fixed polydispersity, i.e., the form of the "parent" density distribution rho(0)(sigma) of the particle diameters sigma, is prescribed. This is the experimentally realistic scenario for, e.g., colloidal dispersions. The simulations are used to obtain the cloud and shadow curve properties of a Lennard-Jones fluid having diameters distributed according to a Schulz form with a large (delta approximately 40%) degree of polydispersity. Good qualitative accord is found with the results from a MFE method study of a corresponding van der Waals model that incorporates size dispersity both in the hard core reference and the attractive parts of the free energy. The results show that polydispersity engenders considerable broadening of the coexistence region between the cloud curves. The principal effect of fractionation in this region is a common overall scaling of the particle sizes and typical interparticle distances, and we discuss why this effect is rather specific to systems with Schulz diameter distributions. Next, by studying a family of such systems with distributions of various widths, we estimate the dependence of the critical point parameters on delta. In contrast to a previous theoretical prediction, size dispersity is found to raise the critical temperature above its monodisperse value. Unusually for a polydisperse system, the critical point is found to lie at or very close to the extremum of the coexistence region in all cases. We outline an argument showing that such behavior will occur whenever polydispersity affects only the range, rather than the strength of the interparticle interactions.

A finite-size scaling study of a model of globular proteins

Grand canonical Monte Carlo simulations are used to explore the metastable fluid-fluid coexistence curve of the modified Lennard-Jones model of globular proteins of ten Wolde and Frenkel [Science, 277, 1975 (1997)]. Using both mixed-field finite-size scaling and histogram-reweighting methods, the joint distribution of density and energy fluctuations is analyzed at coexistence to accurately determine the critical-point parameters. The subcritical coexistence region is explored using the recently developed hyper parallel tempering Monte Carlo simulation method along with histogram reweighting to obtain the density distributions. The phase diagram for the metastable fluid-fluid coexistence curve is calculated in close proximity to the critical point, a region previously unattained by simulations.

Prewetting transitions for a model argon on solid carbon dioxide system

Grand canonical transition matrix Monte Carlo simulations are used to investigate the phase behavior of the model argon on solid carbon dioxide system introduced by Ebner and Saam (Phys. Rev. Lett. 1977, 38, 1486). Our results indicate that the system exhibits first-order prewetting transitions at temperatures above a wetting temperature of Tw = 0.598(5) and below a critical prewetting temperature of Tpwc approximately 0.92. The wetting transition is identified by determining the temperature at which the difference between the bulk vapor-liquid and prewetting saturation chemical potentials goes to zero. Coexistence is directly located at a given temperature by obtaining a density probability distribution from simulation data and utilizing histogram reweighting to determine the conditions that satisfy phase coexistence. Structural properties of the adsorbed films are also examined.

New approach to the first-order phase transition of Lennard-Jones fluids

The multicanonical Monte Carlo method is applied to a bulk Lennard-Jones fluid system to investigate the liquid-solid phase transition. We take the example of a system of 108 argon particles. The multicanonical weight factor we determined turned out to be reliable for the energy range between -7.0 and -4.0 kJ/mol, which corresponds to the temperature range between 60 and 250 K. The expectation values of the thermodynamic quantities obtained from the multicanonical production run by the reweighting techniques exhibit the characteristics of first-order phase transitions between liquid and solid states around 150 K. The present study reveals that the multicanonical algorithm is particularly suitable for analyzing the transition state of the first-order phase transition in detail.

Simulation of phase transitions in fluids

This review provides a discussion of recent techniques for simulation of phase equilibria of complex fluids. Monte Carlo methods are emphasized over molecular dynamics methods. We describe recent developments, such as the use of expanded-ensemble, tempering, or histogram reweighting techniques. Our discussion of such developments is aimed at a general audience and is intended to provide an overview of the main advantages and limitations of each particular technique. References are provided to allow interested readers to identify and trace back most recent applications of a particular simulation technique. We conclude with general guidelines regarding selection of suitable simulation methods for particular problems and systems of interest.

Rejection-free geometric cluster algorithm for complex fluids

We present a novel, generally applicable Monte Carlo algorithm for the simulation of fluid systems. Geometric transformations are used to identify clusters of particles in such a manner that every cluster move is accepted, irrespective of the nature of the pair interactions. The rejection-free and nonlocal nature of the algorithm make it particularly suitable for the efficient simulation of complex fluids with components of widely varying size, such as colloidal mixtures. Compared to conventional simulation algorithms, typical efficiency improvements amount to several orders of magnitude.

Phase diagram of the adhesive hard sphere fluid

The phase behavior of the Baxter adhesive hard sphere fluid has been determined using specialized Monte Carlo simulations. We give a detailed account of the techniques used and present data for the fluid-fluid coexistence curve as well as parametrized fits for the supercritical equation of state and the percolation threshold. These properties are compared with the existing results of Percus-Yevick theory for this system.

Collective dynamics near fluid phase transitions

By means of molecular dynamics simulations, we calculate the intermediate scattering function F(k(axially),t) where k(||) is the wave number and t is the time. We focus on thermodynamic states in the vicinity of a fluid phase transition in bulk and confined systems which we locate in parallel Monte Carlo simulations in the grand canonical ensemble. As one approaches the limit of stability of the fluid (i.e., its spinodal) from either low- or high-density branches of a subcritical isotherm, F(k(axially),t) becomes increasingly long-range. The apparent lack of decorrelation in the metastable regime can be understood within the framework of a simple mean-field theory that links the long-range nature of F(k(axially),t) to a divergence of the ratio of isostress and isochoric heat capacities gamma. Our results suggest that as one approaches the spinodal the dynamic structure factor S(k(axially),omega) (omega frequency), which is related to F(k(axially),t) through a Laplace transformation, should undergo a qualitative change from the usual triplet of Brillouin and Rayleigh lines to a singlet (delta-function-like peak) centered at omega=0 for states directly at the spinodal. This qualitative change in S(k(axially),omega) should be measurable in scattering experiments thereby promoting more detailed insight into the phase behavior and thermodynamic stability of confined and bulk fluids.

Continuous demixing at liquid-vapor coexistence in a symmetrical binary fluid mixture

We report a Monte Carlo finite-size scaling study of the demixing transition of a symmetrical Lennard-Jones binary fluid mixture. For equal concentration of species, and for a choice of the unlike-to-like interaction ratio delta=0.7, this transition is found to be continuous at liquid-vapor coexistence. The associated critical end point exhibits an Ising-like universality. These findings confirm those of earlier smaller scale simulation studies of the same model, but contradict the findings of recent integral equation and hierarchical reference theory investigations.

Competition of percolation and phase separation in a fluid of adhesive hard spheres

Using a combination of Monte Carlo techniques, we locate the liquid-vapor critical point of adhesive hard spheres. We find that the critical point lies deep inside the gel region of the phase diagram. The (reduced) critical temperature and density are tau(c)=0.1133+/-0.0005 and rho(c)=0.508+/-0.01. We compare these results with the available theoretical predictions. Using a finite-size scaling analysis, we verify that the critical behavior of the adhesive hard sphere model is consistent with that of the 3D Ising universality class, the default for systems with short-range attractive forces.

Phase behavior and thermodynamic anomalies of core-softened fluids

We report extensive simulation studies of phase behavior in single component systems of particles interacting via a core-softened interparticle potential. Two recently proposed examples of such potentials are considered; one in which the hard core exhibits a shoulder [Sadr-Lahijany et al., Phys. Rev. Lett. 81, 4895 (1998)], and the other in which the softening takes the form of a linear ramp [Jagla, Phys. Rev. E 63, 061501 (2001)]. Using a combination of state-of-the-art Monte Carlo methods, we obtain the gas, liquid, and solid phase behavior of the shoulder model in two dimensions. We then focus on the thermodynamic anomalies of the liquid phase, namely, maxima in the density and compressibility as a function of temperature. Analysis of the finite-size behavior of these maxima suggests that, rather than stemming from a metastable liquid-liquid critical point, as previously supposed, they are actually induced by the quasicontinuous nature of the two dimensional freezing transition. For the ramp model in three dimensions, we confirm the existence of a stable liquid-liquid ("second") critical point occurring at higher pressure and lower temperature than the liquid-gas critical point. Both these critical points and portions of their associated coexistence curves are located to high precision. In contrast to the shoulder model, the observed thermodynamic anomalies of this model are found to be authentic, i.e., they are not engendered by an incipient new phase. We trace the locus of density and compressibility maxima, the former of which appears to terminate close to the second critical point.