Square-well Fluids Of Variable Width Research Articles

A new coordination number model and heat capacity of square-well fluids of variable width

A new coordination number model for square-well fluid is proposed in this work. The model modifies the theory previously developed for the coordination number of square-well fluids derived on the basis of the generalized van der Waals theory by Largo and Solana. In the present work, we have calculated the co-ordination number of a square-well fluid on the basis of high temperature expansion (HTE) approach along with the modified formula of the maximum reduced density and a novel approach to derive the coordination number of hard sphere fluids. We have also performed the theoretical predictions of constant-volume excess heat capacity of the square-well fluids. It is shown that the theoretical predictions of the constant-volume excess heat capacity determined by second-order perturbation term are in much better agreement with simulation data than to the values of C V E / N K obtained by other workers due to the better description of the second-order term.

Heat capacity of square-well fluids of variable width

We have obtained by Monte Carlo NVT simulations the constant-volume excess heat capacity of square-well fluids for several temperatures, densities and potential widths. Heat capacity is a thermodynamic property much more sensitive to the accuracy of a theory than other thermodynamic quantities, such as the compressibility factor. This is illustrated by comparing the reported simulation data for the heat capacity with the theoretical predictions given by the Barker-Henderson perturbation theory as well as with those given by a non-perturbative theoretical model based on Baxter's solution of the Percus-Yevick integral equation for sticky hard spheres. Both theories give accurate predictions for the equation of state. By contrast, it is found that the Barker-Henderson theory strongly underestimates the excess heat capacity for low to moderate temperatures, whereas a much better agreement between theory and simulation is achieved with the non-perturbative theoretical model, particularly for small well widths, although the accuracy of the latter worsens for high densities and low temperatures, as the well width increases.

Theory and computer simulation of the coordination number of square-well fluids of variable width

Computer simulations have been performed to determine the coordination number of square-well (SW) fluids for wide ranges of densities, temperatures, and potential widths. These data are used to test the performance of a new coordination number model derived on the basis of the quasi-chemical approximation. The model presents a considerable improvement over other previously reported theoretical models based on similar grounds.

A square-well model for the structural and thermodynamic properties of simple colloidal systems

A model for the radial distribution function g(r) of a square-well fluid of variable width previously proposed [Yuste and Santos, J. Chem. Phys. 101, 2355 (1994)] is revisited and simplified. The model provides an explicit expression for the Laplace transform of rg(r), the coefficients being given as explicit functions of the density, the temperature, and the interaction range. In the limits corresponding to hard spheres and sticky hard spheres, the model reduces to the analytical solutions of the Percus–Yevick equation for those potentials. The results can be useful to describe in a fully analytical way the structural and thermodynamic behavior of colloidal suspensions modeled as hard-core particles with a short-range attraction. Comparison with computer simulation data shows a general good agreement, even for relatively wide wells.

Analytical expressions for the thermodynamic properties of square-well fluids of variable width

Simple analytical expressions are derived for the thermodynamic properties of square-well fluids of variable width. In this derivation we use an expression previously developed for the first coordination shell of the radial distribution function. This expression was, in turn, derived as a double series expansion, in terms of both the radial distance and the packing fraction, from the Percus-Yevick theory. Then, on the basis of the Barker - Henderson perturbation theory, thermodynamic properties for square-well fluids are expressed as series expansions of the inverse of the reduced temperature. The coefficients in these expansions are functions of the packing fraction and the range of the potential well. In general the results show good agreement with simulation data.

A perturbed hard-sphere-chain equation of state for normal fluids and polymers using the square-well potential of variable width

A perturbed hard-sphere-chain (PHSC) equation of state is developed for normal fluids and polymers, including mixtures. The new PHSC equation of state for pure fluids uses a perturbation term based on the analytic solution by Chang and Sandler to the second-order perturbation theory of Barker and Henderson for the square-well fluid of variable width. The reference equation of state is the modified Chiew equation of state for athermal mixtures of hard-sphere chains as used in the original PHSC equation of state. The analytic solution by Chang and Sandler is simplified such that theory is readily extended to mixtures by conventional mixing rules. Using an optimum system-independent reduced well width, the new PHSC equation of state correlates the vapor pressures and liquid densities of saturated liquids with good accuracy. Combined with one-fluid type mixing rules for the perturbation term, theory is applied to liquid-liquid and vapor-liquid equilibria for binary mixtures where all components have the same reduced well width. Calculations were also made for a polymer solution where each component has a different reduced well width. In solvent/polymer systems, calculated liquid-liquid equilibria are sensitive to the reduced well width. The perturbation term, however, neglects chain connectivity.

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 ε, 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/ε, pressure P*c=Pcσ3/ε, 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.

Properties of the square-well fluid of variable width

Simulation results for a square-well (SW) fluid of range λ = 3 are presented and used to test the long-range (LR) theory recently developed for SW systems. The discontinuous molecular dynamics methods was used to obtain values of internal energies, pressures and orthobaric densities. The predictions of the second-order LR theory are in excellent agreement with the simulated results, showing that the LR approximation is highly accurate for ranges λ ⩾ 3. The accuracy of the van der Waals, mean-field and LR approximations is established in terms of the temperature of the system and the range of the well.

Properties of the square-well fluid of variable width

The Helmholtz free-energy of a square-well fluid is studied as a function of the range of the well. A high-temperature perturbation expansion is carried out to second order, which is necessary to obtain accurate thermodynamic properties. The second-order term is expanded in powers of the range λ of the well, plus a short-range term that tends to zero when λ → ∞. In the long-range approximation (LRA) the short-range term is neglected and the remaining coefficients are obtained explicitly as functions of density. This LRA is asymptotically exact for large λ, has an estimated error of a few percent for λ = 3 (in units of the hard-sphere diameter), and provides a correction to the van der Waals limit. Also, for λ ≥ 3, its low density expansion is exact to the order of the fourth virial coefficient. It is compared with available Monte Carlo results for λ ˇ- 2 and with alternative approximations.

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.

Properties of the square-well fluid of variable width

Etude de la variation de l'energie libre de Helmholtz d'un tel fluide en fonction de la largeur du puits de potentiel, λ, par un developpement de perturbation a haute temperature jusqu'au 2eme ordre en puissance de λ, dans l'approximation a longue portee: les resultats sont asymptotiquement exacts pour λ eleve, donnent une correction a la limite de van der Waals; pour λ≥3, le developpement a basse densite exact jusqu'a l'ordre du 4eme coefficient viriel