Grand canonical ensemble simulation studies of polydisperse uids

We describe a Monte Carlo scheme for simulating polydisperse fluids within the grand canonical ensemble. Given some polydisperse attribute σ, the state of the system is described by a density distribution ρ(σ) whose form is controlled by the imposed chemical potential distribution µ(σ). We detail how histogram extrapolation techniques can be employed to tune µ(σ) such as to traverse some particular desired path in the space of ρ(σ). The method is applied in simulations of size-disperse hard spheres with densities distributed according to Schulz and log-normal forms. In each case, the equation of state is obtained along the dilution line, i.e. the path along which the scale of ρ(σ) changes but not its shape. The results are compared with the moment-based expressions of Boublik et al (J. Chem. Phys. 54, 1523) and Salacuse and Stell (J. Chem. Phys. 77, 3714 (1982)). It is found that for high degrees of polydispersity, both expressions fail to give a quantitatively accurate description of the equation of state when the overall volume fraction is large.

The Journal of Chemical Physics, 2008

We present two efficient iterative Monte Carlo algorithms in the grand canonical ensemble with which the chemical potentials corresponding to prescribed ͑targeted͒ partial densities can be determined. The first algorithm works by always using the targeted densities in the kT log͑ i ͒ ͑ideal gas͒ terms and updating the excess chemical potentials from the previous iteration. The second algorithm extrapolates the chemical potentials in the next iteration from the results of the previous iteration using a first order series expansion of the densities. The coefficients of the series, the derivatives of the densities with respect to the chemical potentials, are obtained from the simulations by fluctuation formulas. The convergence of this procedure is shown for the examples of a homogeneous Lennard-Jones mixture and a NaCl-CaCl 2 electrolyte mixture in the primitive model. The methods are quite robust under the conditions investigated. The first algorithm is less sensitive to initial conditions.

Journal of Chemical Theory and Computation, 2006

We present automated methods for determining the value of Adams' B parameter corresponding to a target solvent density in grand canonical ensemble Monte Carlo simulations. The method found to work best employs a proportional-integral control equation commonly used in industrial process control applications. We show here that simulations employing this method rapidly converge to the desired target density. We further show that this method is robust over a wide range of system sizes. This advance reduces the overall CPU time and user effort in determining the equilibrium excess chemical potential in these systems.

The Journal of Chemical Physics, 1996

I. INTRODUCTION Insertion-type methods are ubiquitous in molecular simulations of phase equilibria. 1–4 Unfortunately, such meth- ods tend to be inefficient for dense systems and for large, complex molecules. Development of more ...

Journal of Statistical Physics, 1985

We apply a technique to simulate the canonical ensemble, mixing molecular dynamics and Monte Carlo techniques, in which particles suffer virtual hard shocks. In the limit of infinite time the system approaches a Boltzmann distribution. A good approximation to the Boltzmann distribution is achieved in computationally accessible time for some model systems including the onedimensional jellium.

The Journal of Chemical Physics, 1995

A new method is proposed for calculation of the chemical potential of macromolecules by computer simulation. Simulations are performed in an expanded ensemble whose states are defined by the length of a tagged molecule of ...

Physical review. E, 2021

The unconstrained ensemble describes completely open systems whose control parameters are the chemical potential, pressure, and temperature. For macroscopic systems with short-range interactions, thermodynamics prevents the simultaneous use of these intensive variables as control parameters, because they are not independent and cannot account for the system size. When the range of the interactions is comparable with the size of the system, however, these variables are not truly intensive and may become independent, so equilibrium states defined by the values of these parameters may exist. Here, we derive a Monte Carlo algorithm for the unconstrained ensemble and show that simulations can be performed using the chemical potential, pressure, and temperature as control parameters. We illustrate the algorithm by applying it to physical systems where either the system has long-range interactions or is confined by external conditions. The method opens up an avenue for the simulation of co...

The Journal of Chemical Physics, 2005

We present a modification of the gauge cell Monte Carlo simulation method ͓A. V. Neimark and A. Vishnyakov, Phys. Rev. E 62, 4611 ͑2000͔͒ designed for chemical potential calculations in small confined inhomogeneous systems. To measure the chemical potential, the system under study is set in chemical equilibrium with the gauge cell, which represents a finite volume reservoir of ideal particles. The system and the gauge cell are immersed into the thermal bath of a given temperature. The size of the gauge cell controls the level of density fluctuations in the system. The chemical potential is rigorously calculated from the equilibrium distribution of particles between the system cell and the gauge cell and does not depend on the gauge cell size. This scheme, which we call a mesoscopic canonical ensemble, bridges the gap between the canonical and the grand canonical ensembles, which are known to be inconsistent for small systems. The ideal gas gauge cell method is illustrated with Monte Carlo simulations of Lennard-Jones fluid confined to spherical pores of different sizes. Special attention is paid to the case of extreme confinement of several molecular diameters in cross section where the inconsistency between the canonical ensemble and the grand canonical ensemble is most pronounced. For sufficiently large systems, the chemical potential can be reliably determined from the mean density in the gauge cell as it was implied in the original gauge cell method. The method is applied to study the transition from supercritical adsorption to subcritical capillary condensation, which is observed in nanoporous materials as the pore size increases.

Computer Physics Communications, 2002

The most efficient MC weights for the calculation of physical, canonical expectation values are not necessarily those of the canonical ensemble. The use of suitably generalized ensembles can lead to a much faster convergence of the simulation. Although not realized by nature, these ensembles can be implemented on computers. In recent years generalized ensembles have in particular been studied for the simulation of complex systems. For these systems it is typical that conflicting constraints lead to free energy barriers, which fragment the configuration space. Examples of major interest are spin glasses and proteins. In my overview I first comment on the strengths and weaknesses of a few major approaches, multicanonical simulations, transition variable methods, and parallel tempering. Subsequently, two applications are presented: a new analysis of the Parisi overlap distribution for the 3d Edwards-Anderson Ising spin glass and the helix-coil transition of amino-acid homo-oligomers.

2001