Nigel B. Wilding

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

Monte Carlo simulations within the grand canonical ensemble are used to explore the liquid-vapour coexistence curve and critical point properties of the Lennard-Jones fluid. Attention is focused on the joint distribution of density and energy fluctuations at coexistence. In the vicinity of the critical point, this distribution is analysed using mixed-field finite-size scaling techniques aided by histogram reweighting methods. The analysis yields highly accurate estimates of the critical point parameters, as well as exposing the size and character of corrections to scaling. In the sub-critical coexistence region the density distribution is obtained by combining multicanonical simulations with histogram reweighting techniques. It is demonstrated that this procedure permits an efficient and accurate mapping of the coexistence curve, even deep within the two phase region.

Density fluctuations and field mixing in the critical fluid

The authors develop a finite-size-scaling theory describing the joint density and energy fluctuations in a near-critical fluid. As a result of the mixing of the temperature and chemical potential in the two relevant scaling fields, the energy operator features in the critical density distribution as an antisymmetric correction to the limiting scale-invariant form. Both the limiting form and the correction are predicted to be functions that are characteristic of the Ising universality class and are independently known. The theory is tested with extensive Monte Carlo studies of the two-dimensional Lennard-Jones fluid, within the grand canonical ensemble. The simulations and scaling framework together are shown to provide a powerful way of identifying the location of the liquid-gas critical point, while confirming and clarifying its essentially Ising character. The simulations also show a clearly identifiable signature of the field-mixing responsible for the failure of the law of rectilinear diameter.

Free Energy of Crystalline Solids: A Lattice-Switch Monte Carlo Method

We present a Monte Carlo method for evaluating the difference between the free energies of two crystal structures. The method uses a biased sampling of atomic displacements to favor configurations of one structure that can be replaced by corresponding configurations of the other through a Monte Carlo switch of the lattice. The configurations of both structures can be sampled in a single process, and the difference between their free energies evaluated from their measured probabilities. The method is applied to the free energies of the fcc and hcp phases of hard spheres.

Phase behavior of a fluid with competing attractive and repulsive interactions

Fluids in which the interparticle potential has a hard core, is attractive at moderate separations, and repulsive at large separations are known to exhibit unusual phase behavior, including stable inhomogeneous phases. Here we report a joint simulation and theoretical study of such a fluid, focusing on the relationship between the liquid-vapor transition line and any new phases. The phase diagram is studied as a function of the amplitude of the attraction for a certain fixed amplitude of the long ranged repulsion. We find that the effect of the repulsion is to substitute the liquid-vapor critical point and a portion of the associated liquid-vapor transition line, by two first-order transitions. One of these transitions separates the vapor from a fluid of spherical liquidlike clusters; the other separates the liquid from a fluid of spherical voids. At low temperature, the two transition lines intersect one another and a vapor-liquid transition line at a triple point. While most integral equation theories are unable to describe the new phase transitions, the Percus-Yevick approximation does succeed in capturing the vapor-cluster transition, as well as aspects of the structure of the cluster fluid, in reasonable agreement with the simulation results.

A liquid-state theory that remains successful in the critical region

A thermodynamically self-consistent Ornstein—Zernike approximaton (SCOZA) is applied to a fluid of spherical particles with a pair potential given by a hard core repulsion and a Yukawa attractive tail w(r) =—exp[—z(r—1)]/r. This potential allows one to take advantage of the known analytical properties of the solution of the Ornstein—Zernike equation for the case in which the direct correlation function outside the repulsive core is given by a linear combination of two Yukawa tails and the radial distribution function g(r) satisfies the exact core condition g(r) = 0 for r < 1. The predictions for the thermodynamics, the critical point, and the coexistence curve are compared with other theories and with simulation results. In order to assess unambiguously the ability of the SCOZA to locate the critical point and the phase boundary of the system, a new set of simulations also has been performed. The method adopted combines Monte Carlo and finite-size scaling techniques, and is especially adapted to deal with...

Simulation studies of fluid critical behaviour

We review and discuss recent advances in the simulation of bulk critical phenomena in model fluids. In particular we emphasize the extensions to finite-size scaling theory needed to cope with the lack of symmetry between coexisting fluid phases. The consequences of this asymmetry for simulation measurements of quantities such as the particle density and the heat capacity are pointed out and the relationship to experiment is discussed. A general simulation strategy based on the finite-size scaling theory is described and its utility illustrated via Monte Carlo studies of the Lennard-Jones fluid and a two-dimensional spin-fluid model. Recent applications to critical polymer blends and solutions are also briefly reviewed. Finally we consider the outlook for future simulation work in the field.

Chain length dependence of the polymer–solvent critical point parameters

We report grand canonical Monte Carlo simulations of the critical point properties of homopolymers within the bond fluctuation model. By employing configurational bias Monte Carlo methods, chain lengths of up to N=60 monomers could be studied. For each chain length investigated, the critical point parameters were determined by matching the ordering operator distribution function to its universal fixed‐point Ising form. Histogram reweighting methods were employed to increase the efficiency of this procedure. The results indicate that the scaling of the critical temperature with chain length is relatively well described by Flory theory, i.e., Θ−Tc∼N−0.5. The critical volume fraction, on the other hand, was found to scale like φc∼N−0.37, in clear disagreement with the Flory theory prediction φc∼N−0.5, but in good agreement with experiment. Measurements of the chain length dependence of the end‐to‐end distance indicate that the chains are not collapsed at the critical point.

Computer simulation of fluid phase transitions

The goal of accurately locating fluid phase boundaries by means of computer simulation is hampered by difficulties associated with sampling both coexisting phases in a single simulation. We explain the background to these difficulties and describe how they can be tackled using a synthesis of biased Monte Carlo sampling and histogram extrapolation methods, in conjunction with a standard fluid simulation algorithm. The combined approach provides a powerful method for tracing fluid phase boundaries.

Accurate measurements of the chemical potential of polymeric systems by Monte Carlo simulation

We present a new Monte Carlo method for estimating the chemical potential of model polymer systems. The method is based on the gradual insertion of a penetrable ‘‘ghost’’ polymer into the system and is effective for large chain lengths and at high densities. Insertion of the ghost chain is facilitated by use of an expanded ensemble, in which weighted transitions are permitted between states characterizing the strength of the excluded volume and thermal interactions experienced by the ghost chain. We discuss the implementation and optimization of the method within the framework of the bond fluctuation model and demonstrate its precision by a calculation of the finite‐size corrections to the chemical potential.

Freezing by monte carlo phase switch

We describe a Monte Carlo procedure which allows sampling of the disjoint configuration spaces associated with crystalline and fluid phases, within a single simulation. The method utilizes biased sampling techniques to enhance the probabilities of gateway states (in each phase) which are such that a global switch (to the other phase) can be implemented. Equilibrium freezing-point parameters can be determined directly, statistical uncertainties prescribed transparently, and finite-size effects quantified systematically. The method is potentially quite general. We apply it to the freezing of hard spheres.