Luis F. Rull

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...

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.

Vapour—liquid equilibrium of the square-well fluid of variable range via a hybrid simulation approach

The equilibrium between vapour and liquid in a square-well system has been determined by a hybrid simulation approach combining chemical potentials calculated via the Gibbs ensemble Monte Carlo technique with pressures calculated by the standard NVT Monte Carlo method. The phase equilibrium was determined from the thermodynamic conditions of equality of pressure and chemical potential between the two phases. The results of this hybrid approach were tested by independent NPT and μPT calculations and are shown to be of much higher accuracy than those of conventional GEMC simulations. The coexistence curves, vapour pressures and critical points were determined for SW systems of interaction ranges λ = 1.25, 1.5, 1.75 and 2. The new results show a systematic dependence on the range λ, in agreement with results from perturbation theory where previous work had shown more erratic behaviour.

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.

Liquid-vapour coexistence of the Gay-Berne fluid by Gibbs-ensemble simulation

The Gibbs-ensemble Monte Carlo simulation method is used to predict the liquid-vapour coexistence of a fluid whose molecules interact with a cut and shifted Gay-Berne pair potential with elongation κ = 3 and well-depth ratio κ′ = 5. From these simulation results we estimate the temperature, density and pressure at the critical point to be kT c/eo = 0·489 ± 0·005, ρcσ3 o = 0·096 ± 0·004, p cσ3 o/eo = 0·0138 ± 0·0014. We also present evidence of the existence of the vapour-isotropic-liquid-solid triple point. Comparison with the density-functional approximation shows that this theoretical method predicts coexistence and critical temperatures that are too low.

Vapor–liquid and liquid–liquid phase equilibria of mixtures containing square‐well molecules by Gibbs ensemble Monte Carlo simulation

Gibbs ensemble Monte Carlo simulations are undertaken in order to determine the vapor–liquid and liquid–liquid phase equilibria for mixtures containing square‐well particles. Two types of binary systems are examined, namely, a mixture of hard spheres and square wells, and a symmetrical mixture of square wells in which the unlike interaction is purely repulsive, i.e., hard sphere like. The latter system exhibits liquid–liquid immiscibility as well as the usual vapor–liquid coexistence. Intermolecular potential ranges which are intermediate (λ=1.5) and moderately long (λ=2) are examined in order to determine the effect of range on the phase behavior. The coexistence data are also analyzed using a Wegner expansion; the differences in densities and compositions of the two coexisting phases can both be used as the order parameter. This approach enables a description of the phase equilibria over the entire fluid range. In the case of the vapor–liquid coexistence exhibited by the mixture of hard spheres and squa...

Phase diagram of a liquid crystal model: A computer simulation study

Continuous potential models used in computer simulation of liquid crystals are reviewed, paying special attention to the anisotropic Gay-Berne model. This potential model, though phenomenological in nature, has a physical background and is able to reproduce mesogenic behaviour. Results from molecular dynamics simulations are presented here showing the different phases appearing in Gay-Berne fluids made up by molecules with axial ratio 3:1. The effect of the attractive forces in stabilizing the orientationally ordered phases is also studied by performing simulations for a WCA-type Gay-Berne fluid. The dynamics of the fluid is examined, especially the process in the vicinity of the isotropic-nematic transition region.

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

A computer simulation study of the phase behavior of the dipolar Gay–Berne liquid crystal model is presented. The phase transitions are determined with isothermal–isobaric (NPT) Monte Carlo simulations, utilizing the reaction field method. The electrostatic forces are found to have a considerable effect on the nature of the observed phases, but the density at which the isotropic fluid becomes unstable with respect to partially ordered phases is seen to be remarkably insensitive to the strength of the dipole. We pay particular attention to the structure of the mesophases, combining information from several singlet and pair distribution functions to build up an accurate picture of the molecular arrangement of the systems.

Monte Carlo study of liquid crystal phases of hard and soft spherocylinders

We report on a Monte Carlo study of the liquid crystal phases of two model fluids of linear elongated molecules: (a) hard spherocylinders with an attractive square-well (SWSC) and (b) purely repulsive soft spherocylinders (SRS), in both cases for a length-to-breadth ratio L*=5. Monte Carlo simulations in the isothermal–isobaric ensemble have been performed at a reduced temperature T*=5 probing thermodynamic states within the isotropic (I), nematic (N), and smectic A (Sm A) regions exhibited by each of the models. In addition, the performance of an entropy criterion to allocate liquid crystalline phase boundaries, recently proposed for the isotropic–nematic transition of the hard spherocylinder (HSC) fluid, is successfully tested for the SWSC and the SRS fluids and furthermore extended to the study of the nematic–smectic transition. With respect to the more extensively studied HSC fluid, the introduction of the attractive square well in the SWSC model brings the I–N and N–Sm A transitions to higher pressur...