A critical study of the simulation of the liquid-vapour interface of a Lennard-Jones fluid

444

426

We report a computer-simulation study of homogeneous gas-liquid nucleation in a Lennard-Jones system. Using umbrella sampling, we compute the free energy of a cluster as a function of its size. A thermodynamic integration scheme is employed to determine the height of the nucleation barrier as a function of supersaturation. Our simulations illustrate that the mechanical and the thermodynamical surfaces of tension and surface tension differ significantly. In particular, we show that the mechanical definition of the surface tension cannot be used to compute this barrier height. We find that the relations recently proposed by McGraw and Laaksonen ͓J. Chem. Phys. 106, 5284 ͑1997͔͒ for the height of the barrier and for the size of the critical nucleus are obeyed.

Section: Resultsmentioning

confidence: 99%

Section: Deviations From Classical Nucleation Theorymentioning

confidence: 99%

Computer simulation study of gas–liquid nucleation in a Lennard-Jones system

Wolde¹,

Frenkel²

1998

444

426

“…The significant discrepancies in the estimates of the vapor-liquid surface tension reported in the numerous simulation studies of LJ fluids cannot, however, all be attributed to finite-size effects. An inconsistent treatment of the long-range interactions in Monte Carlo and molecular dynamics has also led to conflicting results for the interfacial properties, 33 and great care has to be employed when using truncated potentials. The problems associated with the truncation of the potential have been very clearly illustrated by Trokhymchuk and Alejandre 34 by simulating LJ particles for various values of the potential cutoff r c .…”

Section: Simulation Of the Interfacial Tensionmentioning

confidence: 99%

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

Gloor

Jackson

Blas

et al. 2005

311

367

A novel test-area ͑TA͒ 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 ͑1949͔͒͒. For particles interacting through discontinuous intermolecular potentials ͑e.g., hard-core fluids͒ this involves the determination of ␦ 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 more͒ systems with different interfacial areas ͑the method of Bennett ͓J. Comput. Phys. 22, 245 ͑1976͔͒͒, 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 ͑TAMC͒ simulations are compared with the data obtained with other techniques ͑e.g., mechanical and free-energy differences͒ 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 ͑TAMC͒ or molecular-dynamics ͑TAMD͒ algorithms for different types of interfaces ͑vapor-liquid, liquid-liquid, fluid-solid, etc.͒ of pure systems and mixtures consisting of complex polyatomic molecules.

“…At the outset of a simulation, all values of η m are set to zero and the system preferentially visits those subensembles with the lowest free energies. After a number of simulation cycles, accumulated acceptance probabilities are used to estimate the probability distribution and weighting function using Equations (8)(9)(10)(11)(12). During the subsequent phase of the simulation, the now nonuniform weighting function encourages the system to visit a broader distribution of subensembles.…”

Section: 25mentioning

confidence: 99%

“…Perhaps the most common route to this property is through the mechanical definition. [3][4][5][6][7][8][9][10][11] For a planar interface, the surface tension is related to an integral of the difference between the normal and tangential components of the pressure tensor along the direction perpendicular to the interface. The pressure tensor is typically evaluated using the molecular virial.…”

Section: Introductionmentioning

confidence: 99%

Calculation of surface tension via area sampling

Errington

Kofke²

2007

104

We examine the performance of several molecular simulation techniques aimed at evaluation of the surface tension through its thermodynamic definition. For all methods explored, the surface tension is calculated by approximating the change in Helmholtz free energy associated with a change in interfacial area through simulation of a liquid slab at constant particle number, volume, and temperature. The methods explored fall within three general classes: free-energy perturbation, the Bennett acceptance-ratio scheme, and the expanded ensemble technique. Calculations are performed for both the truncated Lennard-Jones and square-well fluids at select temperatures spaced along their respective liquid-vapor saturation lines. Overall, we find that Bennett and expanded ensemble approaches provide the best combination of accuracy and precision. All of the methods, when applied using sufficiently small area perturbation, generate equivalent results for the Lennard-Jones fluid. However, single-stage free-energy-perturbation methods and the closely related test-area technique recently introduced by Gloor et al. [J. Chem. Phys. 123, 134703 (2005)], generate surface tension values for the square-well fluid that are not consistent with those obtained from the more robust expanded ensemble and Bennett approaches, regardless of the size of the area perturbation. Single-stage perturbation methods fail also for the Lennard-Jones system when applied using large area perturbations. Here an analysis of phase-space overlap produces a quantitative explanation of the observed inaccuracy, and shows that the satisfactory results obtained in these cases from the test-area method arise from a cancellation of errors that cannot be expected in general. We also briefly analyze the variation in method performance with respect to the adjustable parameters inherent to the techniques.