Liquid–vapor asymmetry in pure fluids: A Monte Carlo simulation study

Perturbation theories for fluids with short-ranged attractive forces: A case study of the Lennard-Jones spline fluid

It is generally not straightforward to apply molecular-thermodynamic theories to fluids with short-ranged attractive forces between their constituent molecules (or particles). This especially applies to perturbation theories, which, for short-ranged attractive fluids, typically must be extended to high order or may not converge at all. Here, we show that a recent first-order perturbation theory, the uv-theory, holds promise for describing such fluids. As a case study, we apply the uv-theory to a fluid with pair interactions defined by the Lennard-Jones spline potential, which is a short-ranged version of the LJ potential that is known to provide a challenge for equation-of-state development. The results of the uv-theory are compared to those of third-order Barker–Henderson and fourth-order Weeks–Chandler–Andersen perturbation theories, which are implemented using Monte Carlo simulation results for the respective perturbation terms. Theoretical predictions are compared to an extensive dataset of molecular simulation results from this (and previous) work, including vapor–liquid equilibria, first- and second-order derivative properties, the critical region, and metastable states. The uv-theory proves superior for all properties examined. An especially accurate description of metastable vapor and liquid states is obtained, which might prove valuable for future applications of the equation-of-state model to inhomogeneous phases or nucleation processes. Although the uv-theory is analytic, it accurately describes molecular simulation results for both the critical point and the binodal up to at least 99% of the critical temperature. This suggests that the difficulties typically encountered in describing the vapor–liquid critical region are only to a small extent caused by non-analyticity.

Accurate thermodynamics of simple fluids and chain fluids based on first-order perturbation theory and second virial coefficients: uv-theory

We develop a simplification of our recently proposed uf-theory for describing the thermodynamics of simple fluids and fluids comprising short chain molecules. In its original form, the uf-theory interpolates the Helmholtz energy between a first-order f-expansion and first-order u-expansion as (effective) lower and upper bounds. We here replace the f-bound by a new, tighter (effective) lower bound. The resulting equation of state interpolates between a first-order u-expansion at high densities and another first-order u-expansion that is modified to recover the exact second virial coefficient at low densities. The theory merely requires the Helmholtz energy of the reference fluid, the first-order u-perturbation term, and the total perturbation contribution to the second virial coefficient as input. The revised theory-referred to as uv-theory-is thus simpler than the uf-theory but leads to similar accuracy, as we show for fluids with intermolecular pair interactions governed by a Mie potential. The uv-theory is thereby easier to extend to fluid mixtures and provides more flexibility in extending the model to non-spherical or chain-like molecules. The usefulness of the uv-theory for developing equation-of-state models of non-spherical molecules is here exemplified by developing an equation of state for Lennard-Jones dimers.

Measuring the composition-curvature coupling in binary lipid membranes by computer simulations

The coupling between local composition fluctuations in binary lipid membranes and curvature affects the lateral membrane structure. We propose an efficient method to compute the composition-curvature coupling in molecular simulations and apply it to two coarse-grained membrane models-a minimal, implicit-solvent model and the MARTINI model. Both the weak-curvature behavior that is typical for thermal fluctuations of planar bilayer membranes as well as the strong-curvature regime corresponding to narrow cylindrical membrane tubes are studied by molecular dynamics simulation. The simulation results are analyzed by using a phenomenological model of the thermodynamics of curved, mixed bilayer membranes that accounts for the change of the monolayer area upon bending. Additionally the role of thermodynamic characteristics such as the incompatibility between the two lipid species and asymmetry of composition are investigated.

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.

Probability distribution of the order parameter for the three-dimensional ising-model universality class: A high-precision monte carlo study

We study the probability distribution P(M) of the order parameter (average magnetization) M, for the finite-size systems at the critical point. The systems under consideration are the 3-dimensional Ising model on a simple cubic lattice, and its 3-state generalization known to have remarkably small corrections to scaling. Both models are studied in a cubic box with periodic boundary conditions. The model with reduced corrections to scaling makes it possible to determine P(M) with unprecedented precision. We also obtain a simple, but remarkably accurate, approximate formula describing the universal shape of P(M).