Enrique de Miguel

Phase equilibria and critical behavior of square‐well fluids of variable width by Gibbs ensemble Monte Carlo simulation

The vapor–liquid phase equilibria of square‐well systems with hard‐sphere diameters σ, well‐depths e, and ranges λ=1.25, 1.375, 1.5, 1.75, and 2 are determined by Monte Carlo simulation. The two bulk phases in coexistence are simulated simultaneously using the Gibbs ensemble technique. Vapor–liquid coexistence curves are obtained for a series of reduced temperatures between about Tr=T/Tc=0.8 and 1, where Tc is the critical temperature. The radial pair distribution functions g(r) of the two phases are calculated during the simulation, and the results extrapolated to give the appropriate contact values g(σ), g(λσ−), and g(λσ+). These are used to calculate the vapor‐pressure curves of each system and to test for equality of pressure in the coexisting vapor and liquid phases. The critical points of the square‐well fluids are determined by analyzing the density‐temperature coexistence data using the first term of a Wegner expansion. The dependence of the reduced critical temperature T*c=kTc/e, pressure P*c=Pcσ3/e, number density ρ*c=ρcσ3, and compressibility factor Z=P/(ρkT), on the potential range λ, is established. These results are compared with existing data obtained from perturbation theories. The shapes of the coexistence curves and the approach to criticality are described in terms of an apparent critical exponent β. The curves for the square‐well systems with λ=1.25, 1.375, 1.5, and 1.75 are very nearly cubic in shape corresponding to near‐universal values of β (β≊0.325). This is not the case for the system with a longer potential range; when λ=2, the coexistence curve is closer to quadratic in shape with a near‐classical value of β (β≊0.5). These results seem to confirm the view that the departure of β from a mean‐field or classical value for temperatures well below critical is unrelated to long‐range, near‐critical fluctuations.The vapor–liquid phase equilibria of square‐well systems with hard‐sphere diameters σ, well‐depths e, and ranges λ=1.25, 1.375, 1.5, 1.75, and 2 are determined by Monte Carlo simulation. The two bulk phases in coexistence are simulated simultaneously using the Gibbs ensemble technique. Vapor–liquid coexistence curves are obtained for a series of reduced temperatures between about Tr=T/Tc=0.8 and 1, where Tc is the critical temperature. The radial pair distribution functions g(r) of the two phases are calculated during the simulation, and the results extrapolated to give the appropriate contact values g(σ), g(λσ−), and g(λσ+). These are used to calculate the vapor‐pressure curves of each system and to test for equality of pressure in the coexisting vapor and liquid phases. The critical points of the square‐well fluids are determined by analyzing the density‐temperature coexistence data using the first term of a Wegner expansion. The dependence of the reduced critical temperature T*c=kTc/e, pressure P*c=Pcσ...

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.

Liquid crystal phase diagram of the Gay-Berne fluid

In this paper we report computer simulation results for bulk Gay-Berne fluids with anisotropy parameters κ = 3 and κ′ = 5. Using molecular dynamics simulations in the NVT ensemble, we identify isotropic fluid, nematic and smectic B phases. We observe that the nematic phase is only stable for reduced temperatures T* > 0·80. At lower temperatures, the isotropic phase directly evolves to the smectic B phase via a first order transition. We also give evidence of a weakly first order transition which involves a tilt of the molecular orientations with respect to the smectic planes. The effect of the attractive anisotropic forces in stabilizing the orientationally ordered phases is also studied by performing simulations for a WCA-type Gay-Berne fluid. When combined with previous studies of the vapour-liquid transition by Gibbs ensemble Monte Carlo simulations, and of the isotropic-nematic transition by thermodynamic integration, the results presented here provide quite a complete picture of the phase diagram for...

Location of the isotropic-nematic transition in the Gay-Berne model

Molecular dynamics computer simulations have been carried out on a system consisting of cylindrically symmetric molecules with length-to-breadth ratio k = 3 and well depth ratio k′ = 5 interacting through the Gay-Berne potential. For this system we have located the coexistence points corresponding to the isotropic-nematic transition by calculating the absolute free energy of each phase. Two temperatures, T* = 1·25 and 0·95, have been studied. In each case a weak first-order phase transition has been found, with a density change close to 2·5%. The isotropic-nematic coexistence densities are found to increase with increasing temperature.

Effect of the attractive interactions on the phase behavior of the Gay–Berne liquid crystal model

We present in this paper a computer simulation study of the phase behavior of the Gay–Berne liquid crystal model. The effect of the anisotropic attractive interactions on stabilizing orientationally ordered phases is analyzed by varying the anisotropy parameter κ′ at fixed values of the molecular elongation parameter κ. Molecular dynamics simulations have been performed at constant density and temperature along several isotherms and approximate transition densities are reported. It is found that, for a given value of the molecular elongation κ=3, smectic order is favored at lower densities as κ′ increases. When κ′ is lowered, the smectic phase is preempted by the nematic phase. As a result, the nematic phase becomes increasingly stable at lower temperatures as κ′ is decreased. Additionally, we have studied the liquid–vapor coexistence region for different values of κ′ by using Gibbs ensemble and Gibbs–Duhem Monte Carlo techniques. We have found evidence of a vapor–isotropic–nematic triple point for κ′=1 a...

The nature of the calculation of the pressure in molecular simulations of continuous models from volume perturbations

We consider some fundamental aspects of the calculation of the pressure from simulations by performing volume perturbations. The method, initially proposed for hard-core potentials by Eppenga and Frenkel [Mol. Phys.52, 1303 (1984)] and then extended to continuous potentials by Harismiadis et al. [J. Chem. Phys. 105, 8469 (1996)], is based on the numerical estimate of the change in Helmholtz free energy associated with the perturbation which, in turn, can be expressed as an ensemble average of the corresponding Boltzmann factor. The approach can be easily generalized to the calculation of components of the pressure tensor and also to ensembles other than the canonical ensemble. The accuracy of the method is assessed by comparing simulation results obtained from the volume-perturbation route with those obtained from the usual virial expression for several prototype fluid models. Monte Carlo simulation data are reported for bulk fluids and for inhomogeneous systems containing a vapor-liquid interface.

A SAFT-DFT approach for the vapour-liquid interface of associating fluids

Abstract We present a density functional theory (DFT) based on the statistical associating fluid theory (SAFT) bulk free energy to describe the behaviour of inhomogeneous associating molecular fluids, with a special emphasis on the vapour–liquid interface. The molecules are described in terms of hard-sphere (HS) segments which interact through an arbitrary intermolecular potential. Off-centre square-well bonding sites are incorporated to mediate the association between molecules. The approach presented here is based on a perturbation theory about a HS reference fluid under the local density approximation (LDA); the contributions due to chain formation and association are also considered at the local density level. The Helmholtz free energy functional due to the dispersive attractive interactions is treated at the mean-field level by ignoring the correlations. This description is essentially a ‘van der Waals’ theory of non-uniform fluids. The incorporation of a SAFT free energy of the bulk associating fluid represents the simplest extension of the theory to deal with inhomogeneous associating systems (SAFT–DFT). The resulting functional is used to investigate the effect of the range of the attractive interactions on the interfacial properties, such as the density profile and surface tension, for two different intermolecular potential models, namely the Yukawa and square-well. This simple SAFT–DFT approach is also used to make quantitative comparisons with the experimental surface tension for water.

An examination of the vapour-liquid interface of associating fluids using a SAFT-DFT approach

With a realistic description of the free energy of bulk fluids, it is now possible to make accurate predictions at the molecular level for the phase behaviour of systems as complex as aqueous solutions of amphiphiles, reacting and associating fluids, polymers, and electrolytes (e.g. using the statistical associating fluid theory SAFT). A quantitative molecular description of the interfacial properties of inhomogeneous fluids, including surface tension and adsorption is much less common. In this work we first hope to improve the general understanding of the effect of association on the vapour-liquid interface. The vapour-liquid interface of the inhomogenous associating fluid is examined by combining the SAFT and density functional theory (DFT) approaches. A simple SAFT-HS representation is employed as it incorporates all of the essential physics of associating fluids and provides a good representation of the vapour pressure and coexisting phases. In this simplified SAFT approach the bulk fluid is represented as a hard-core reference, the association is treated with Wertheims first order perturbation theory (TPTI), and a van der Waals mean-field approximation is used for the dispersive attractive interactions. In order to keep the representation of the bulk fluid and interface at the same level of approximation we use the van der Waals theory for non-uniform fluids, which is a DFT at the level of a local density approximation (LDA); the correlations are neglected in the attractive non-local term. The vapour-liquid interface of model systems with one, two and four bonding sites are examined for varying degrees of association. As expected, a stronger site-site interaction is generally found to sharpen the interface (decrease the interfacial thickness) and increase the surface tension. In the case of a dimerizing (single site) fluid a limiting behaviour is reached for full association (saturation) where the molecular species are dimers. After an in depth analysis of the effect of association on the vapour-liquid interface, we highlight the strengths of our simple SAFT-DFT approach by making some quantitative comparisons with experimental surface tensions for selected systems including water and replacement refrigerants.

A Molecular Simulation of A Liquid-crystal Model

Abstract A Gay-Berne fluid of prolate molecules with length-to-breadth ratio 3 is studied using molecular dynamics simulations. This fluid exhibits vapor, isotropic liquid, nematic, and smectic-B mesophases. For the bulk fluid we report new results along isochores that further delineate the smectic and nematic regions of the phase diagram; the effect of system size is also discussed. These studies lead to a rather complete description of the fluid part of the phase diagram. We have also studied the changes that occur when such a fluid is confined in a pore with parallel, homeotropic walls. Our molecular dynamics results show that the isotropic-nematic transition shifts to higher temperatures, or lower densities, i.e., the liquid crystal phase is stabilized relative to the bulk flild.

Determination of the melting point of hard spheres from direct coexistence simulation methods

We consider the computation of the coexistence pressure of the liquid-solid transition of a system of hard spheres from direct simulation of the inhomogeneous system formed from liquid and solid phases separated by an interface. Monte Carlo simulations of the interfacial system are performed in three different ensembles. In a first approach, a series of simulations is carried out in the isothermal-isobaric ensemble, where the solid is allowed to relax to its equilibrium crystalline structure, thus avoiding the appearance of artificial stress in the system. Here, the total volume of the system fluctuates due to changes in the three dimensions of the simulation box. In a second approach, we consider simulations of the inhomogeneous system in an isothermal-isobaric ensemble where the normal pressure, as well as the area of the (planar) fluid-solid interface, are kept constant. Now, the total volume of the system fluctuates due to changes in the longitudinal dimension of the simulation box. In both approaches, the coexistence pressure is estimated by monitoring the evolution of the density along several simulations carried out at different pressures. Both routes are seen to provide consistent values of the fluid-solid coexistence pressure, p=11.54(4)k(B)T/sigma(3), which indicates that the error introduced by the use of the standard constant-pressure ensemble for this particular problem is small, provided the systems are sufficiently large. An additional simulation of the interfacial system is conducted in a canonical ensemble where the dimensions of the simulation box are allowed to change subject to the constraint that the total volume is kept fixed. In this approach, the coexistence pressure corresponds to the normal component of the pressure tensor, which can be computed as an appropriate ensemble average in a single simulation. This route yields a value of p=11.54(4)k(B)T/sigma(3). We conclude that the results obtained for the coexistence pressure from direct simulations of the liquid and solid phases in coexistence using different ensembles are mutually consistent and are in excellent agreement with the values obtained from free energy calculations.