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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.

THE THERMODYNAMICS OF HETERONUCLEAR MOLECULES FORMED FROM BONDED SQUARE-WELL (BSW) SEGMENTS USING THE SAFT-VR APPROACH

We broaden the scope of the statistical associating fluid theory for potentials of variable attractive range (SAFT-VR) to treat heteron uclear chain molecules formed from bonded square-well (BSW) segments. The ideas of the bonded hard sphere (BHS) treatment for distributed-site models composed of hard-sphere segments are applied to square-well sites with the SAFT-VR approach. The results of isothermal—isobaric Monte Carlo simulations are reported for heteronuclear square-well diatomics with different sets of energy and range parameters. The SAFT-VR approach provides an excellent description of the equation of state of the diatomic systems for a wide range of densities. The goal of the work is to provide a rigorous treatment of distributed-site models of fluids, and to establish a framework for a group contribution approach with SAFT-VR.

Deviations from corresponding-states behavior in the vapor-liquid equilibrium of the square-well fluid

The vapor-liquid equilibrium of the square-well (SW) fluid of variable range is studied. The analysis focuses on the dependence on the SW range, which exhibits deviations from corresponding-states behavior. The study is based on a new, compact and accurate equation for the SW Helmholtz free-energy. This equation relies on the mean-field approximation and a scaled-particle theory of Boublik, and agrees well with available computer simulations. The position of the critical point, the vapor pressures and the width of the orthobaric curve are obtained in terms of the width of the well. They show non-trivial oscillatory departures from corresponding-states behavior as given by the augmented van der Waals theory.

Optimized equation of the state of the square-well fluid of variable range based on a fourth-order free-energy expansion

The free energy of square-well (SW) systems of hard-core diameter sigma with ranges 1 < or = lambda < or = 3 is expanded in a perturbation series. This interval covers most ranges of interest, from short-ranged SW fluids (lambda approximately 1.2) used in modeling colloids to long ranges (lambda approximately 3) where the van der Waals classic approximation holds. The first four terms are evaluated by means of extensive Monte Carlo simulations. The calculations are corrected for the thermodynamic limit and care is taken to evaluate and to control the various sources of error. The results for the first two terms in the series confirm well-known independent results but have an increased estimated accuracy and cover a wider set of well ranges. The results for the third- and fourth-order terms are novel. The free-energy expansion for systems with short and intermediate ranges, 1 < or = lambda < or = 2, is seen to have properties similar to those of systems with longer ranges, 2 < or = lambda < or = 3. An equation of state (EOS) is built to represent the free-energy data. The thermodynamics given by this EOS, confronted against independent computer simulations, is shown to predict accurately the internal energy, pressure, specific heat, and chemical potential of the SW fluids considered and for densities 0 < or = rho sigma(3) < or = 0.9 including subcritical temperatures. This fourth-order theory is estimated to be accurate except for a small region at high density, rho sigma(3) approximately 0.9, and low temperature where terms of still higher order might be needed.

Properties of the square‐well fluid of variable width. II. The mean field term

The perturbation expansion of the Helmholtz free energy of a square‐well fluid is analyzed. A closed‐form expression is found for the first‐order term in that expansion as a function of the density and of the attractive range of the well. The procedure is based on the interpolation of the extreme cases of long and short ranges, for which exact asymptotic results are known. The proposed interpolation formula is tested against Monte Carlo calculations of the same first‐order term for different values of the range and the density, obtaining a root‐mean‐square deviation of 2.2%. Previous analytic approximations as that of van der Waals are discussed.

The isotropic–nematic phase transition in a fluid of square well spherocylinders

The isotropic–nematic phase transition in a fluid of hard spherocylinders with a spherocylindrical square-well attraction is examined using Monte Carlo simulations and two theoretical approaches. The first theory is a first-order perturbation theory which incorporates the Parsons decoupling approximation for the pair distribution function. The second theory is a simple resummation of the virial coefficients in the nematic phase which maps the thermodynamics of the nematic phase to those of the isotropic phase. In general both the theoretical approaches and the simulation results show a destabilization of the nematic phase with respect to the isotropic phase as the temperature is decreased. However, close comparison between the simulation results and the theories reveals that the Parsons approach is quantitatively deficient. On the other hand, the results for the resummation procedure are in good agreement with the simulation results over the full isotropic range and for the isotropic–nematic phase transit...

Vapor-liquid equilibrium of a multipolar square-well fluid

A simple polar fluid is modelled by square-well particles with point dipoles and quadrupoles at their centers. An equation for the free energy is derived by perturbation theory, obtaining the explicit dependence on the potential parameters, and allowing to study the effects of the strength of the multipoles on the vapor-liquid (V-L) equilibrium. It is found that the critical temperature is the property most sensitive to the values of the dipolar and quadrupolar moments, μ and Q, increasing with increasing moments although the effect of Q is much stronger. The shape of the coexistence curve is mostly affected on the liquid side and the coexistence diameters are found to be far from rectilinear. Comparison with simulation results shows that a multipolar SW fluid, for an attractive range equal to 1.5 times the diameter, is remarkably similar to the multipolar Lennard-Jones fluid.

Vapor-liquid equilibrium of a multipolar square-well fluid II. Effect of a variable square-well range

The multipolar square-well (MSW) fluid treated in part I [Physica A 202 (1994) 420] is studied in order to analyze the effect of SW range λ, which models the range of dispersion forces, on the vapor-liquid (VL) equilibrium. The model includes a simpler and more accurate treatment of the SW interactions of variable width. The MSW model covers systems ranging from a system similar to a multipolar Lennard-Jones fluid (λ = 1.5) to the multipolar van der Waals fluid (λ ⪢ 1). The relative influence of the dispersion and electrostatic forces on the critical properties and the VL phase diagram is analyzed. The critical temperature in most sensible to variations in λ, whereas the shape of the VL coexistence curve is affected more by the multipolar forces. The latter have a larger effect on the critical temperature than on the critical pressure for all ranges. A change in λ (at constant dipolar and quadrupolar moments strengths, μ∗and Q∗) and changes in μ∗and Q∗ (at λ constant) have similar effects. The electrostatic forces become systematically less important as λ increases. For μ∗and Q∗ ⩽ 1 their effect on the VL properties is almost negligible relative to that of the dispersion forces when λ ⩾ 2.5.

Square well perturbation theory of fluids

A perturbation theory for simple classical fluids that uses a square well reference system is presented. To first order, the theory expresses the free energy of a simple fluid in terms of the properties of a SW system with suitably selected hard core diameter, range and depth. These effective parameters are shown to have an interpretation as averages of microscopic quantities. The problem of handling the reference SW system is considered and the theory is tested by calculating the properties of a Lennard-Jones system. The results show the SWPT to be highly convergent, and the behaviour of the effective parameters is discussed.

Discrete perturbation theory applied to Lennard-Jones and Yukawa potentials

Discrete perturbation theory (DPT) is a powerful tool to study systems interacting with potentials that are continuous but can be approximated by a piecewise continuous function composed of horizontal segments. The main goal of this work is to analyze the effect of several variables to improve the representation of continuous potentials in order to take advantage of DPT. The main DPT parameters chosen for the purpose are the starting location and size of the horizontal segments used to divide the full range of the potential and its maximum reach. We also studied the effect of having each segment aligned to the left, to the right, or centered on the continuous function. The properties selected to asses the success of this strategy are the orthobaric densities and their corresponding critical points. Critical parameters and orthobaric densities were evaluated by DPT for each of an ample set of variables and compared with their values calculated via discontinuous molecular dynamics. The best sets of DPT parameters are chosen so as to give equations of state that represent accurately the Lennard-Jones and Yukawa fluids.