Properties of square-well fluids

A perturbed virial expansion (expansion in powers of density about a suitable reference fluid) is used to locate the fluid critical point. It is shown that, unlike the case for the usual virial expansion, knowledge of the second virial coefficient alone is sufficient to obtain a reasonably accurate estimate for the critical temperature of both model and real fluids.

A perturbed virial expansion (expansion in powers of density about a suitable reference fluid) is used to locate the fluid critical point. It is shown that, unlike the case for the usual virial expansion, knowledge of the second virial coefficient alone is sufficient to obtain a reasonably accurate estimate for the critical temperature of both model and real fluids.

The condition under which certain systems may not have a stable liquid phase, instead, sublime from the solid to the vapor phase has been the subject of investigations by many. Until recently, it used to be thought that any amount of attraction added to a short ranged repulsion would give rise to a liquid phase. However, computer simulations, theoretical, as well as experimental studies have showed that this is not the case. By use of Hyper-parallel tempering Monte Carlo (HPTMC) simulation, computer simulations were performed to obtain the liquid-vapor coexistence data for square-well (SW) fluid with variable interaction range with the view of determining the conditions where the liquid state will simply squeeze out. The interaction range (λ) which plays a significant role in giving rise to a liquid phase in the phase diagram was varied from 1.21 to 3.0. The results of the work clearly indicate that the range of temperatures for which the liquid is stable shrinks as the interaction range decreases. And for sufficiently short interaction ranges, the square-well fluid has no stable liquid phase with a threshold value of λ = 1.24.

The high-temperature expansion of the free energy of a fluid of square wells, SW, is considered. The first four terms in this expansion are calculated for SW systems of variable range λσ, where σ is the diameter of the spherical hard-core. The properties were calculated via molecular dynamics, MD, for ranges 1≤λ≤2.5 with special emphasis on the region of shorter ranges: λ= 1.025, 1.050, 1.075, 1.100, 1.125 and 1.150. The principal aims are to compare these results with the previous ones obtained using the Monte Carlo, MC, method (Espíndola-Heredia et al. J. Chem. Phys. 130, 024509 (2009)) that showed large statistical noise in the higher-order terms at high densities, and to provide a benchmark to check the theoretical Short-Range Expansion of the free energy of these systems. The results have been corrected to obtain the thermodynamic limit via a change of ensemble algorithm and by simulating systems with 125, 200, 500 and 1000 particles. The MD results are much smoother that the corresponding MC data and their precision allow to determine the behavior of the series for high densities. The simulation results are used to test a theory built to write the free energy for short ranges. The position of the critical point is calculated with this theory for very short ranges.

The high-temperature expansion of the free energy of a fluid of square wells, SW, is considered. The first four terms in this expansion are calculated for SW systems of variable range λσ, where σ is the diameter of the spherical hard-core. The properties were calculated via molecular dynamics, MD, for ranges 1≤λ≤2.5 with special emphasis on the region of shorter ranges: λ= 1.025, 1.050, 1.075, 1.100, 1.125 and 1.150. The principal aims are to compare these results with the previous ones obtained using the Monte Carlo, MC, method (Espíndola-Heredia et al. J. Chem. Phys. 130, 024509 ( )) that showed large statistical noise in the higher-order terms at high densities, and to provide a benchmark to check the theoretical Short-Range Expansion of the free energy of these systems. The results have been corrected to obtain the thermodynamic limit via a change of ensemble algorithm and by simulating systems with 125, 200, 500 and 1000 particles. The MD results are much smoother that the corresponding MC data and their precision allow to determine the behavior of the series for high densities. The simulation results are used to test a theory built to write the free energy for short ranges. The position of the critical point is calculated with this theory for very short ranges.

The high-temperature expansion of the free energy of a fluid of square wells, SW, is considered. The first four terms in this expansion are calculated for SW systems of variable range λσ, where σ is the diameter of the spherical hard-core. The properties were calculated via molecular dynamics, MD, for ranges 1≤λ≤2.5 with special emphasis on the region of shorter ranges: λ= 1.025, 1.050, 1.075, 1.100, 1.125 and 1.150. The principal aims are to compare these results with the previous ones obtained using the Monte Carlo, MC, method (Espíndola-Heredia et al. J. Chem. Phys. 130, 024509 ( )) that showed large statistical noise in the higher-order terms at high densities, and to provide a benchmark to check the theoretical Short-Range Expansion of the free energy of these systems. The results have been corrected to obtain the thermodynamic limit via a change of ensemble algorithm and by simulating systems with 125, 200, 500 and 1000 particles. The MD results are much smoother that the corresponding MC data and their precision allow to determine the behavior of the series for high densities. The simulation results are used to test a theory built to write the free energy for short ranges. The position of the critical point is calculated with this theory for very short ranges.

We present new molecular dynamics results for the pressure of the pure hard disk fluid up to the hexatic transition (reduced density about 0.9). The data, combined with the known virial coefficients (up to B10), are used to build an equation of state, to estimate higher-order virial coefficients, and also to obtain a better value of B10. Finite size effects

The high-temperature expansion of the free energy of a fluid of square wells, SW, is considered. The first four terms in this expansion are calculated for SW systems of variable range λσ, where σ is the diameter of the spherical hard-core. The properties were calculated via molecular dynamics, MD, for ranges 1≤λ≤2.5 with special emphasis on the region of shorter ranges: λ= 1.025, 1.050, 1.075, 1.100, 1.125 and 1.150. The principal aims are to compare these results with the previous ones obtained using the Monte Carlo, MC, method (Espíndola-Heredia et al. J. Chem. Phys. 130, 024509 (2009)) that showed large statistical noise in the higher-order terms at high densities, and to provide a benchmark to check the theoretical Short-Range Expansion of the free energy of these systems. The results have been corrected to obtain the thermodynamic limit via a change of ensemble algorithm and by simulating systems with 125, 200, 500 and 1000 particles. The MD results are much smoother that the corresponding MC data and their precision allow to determine the behavior of the series for high densities. The simulation results are used to test a theory built to write the free energy for short ranges. The position of the critical point is calculated with this theory for very short ranges.

A bridge theory between Boublik and Fischer thermodynamic perturbation theories is proposed. The fluid models studied here are composed of linear particles interacting through a pair potential depending on the shortest distance between cores, modelled as rods. This perturbation scheme has been used to predict the thermodynamic properties of two pure fluid models composed by particles of quite different anisotropy. In general, the quality of the theoretical predictions for thermodynamic properties are better for the less anisotropic model. The larger the anisotropy and the packing fraction, the greater are the discrepancies between theory and simulation. The results shown here seem, however, to be less dependent on the elongation than those of the previous perturbation theories, and the theory works better when the temperature increases. Results for spherical harmonic components of the reference system pair correlation function are compared with available Monte Carlo (MC) simulation data. The discrepancies between theory and simulation increase with the packing fraction and the anisotropy of the model.

The recently reported two-dimensional discrete perturbation theory for soft atomic fluids has been extended here for molecular fluids. In particular, the analytical expression for the Helmholtz free energy of intermolecular potentials of arbitrary profile is built within a discrete perturbation theory constructed with a sequence of two-dimensional (2D) square-well and square-shoulder potentials of variable effective widths and ranges. Fluids that comprised both convex and dumbbell particles have been considered. For the former ones, the equation of state was obtained as a function of density, temperature and intermolecular parameters with implicit shape dependence evaluated by a virial rescaling procedure from the compressibility factor of effective hard-disk and two-dimensional square-well/square-shoulder discrete potentials. By varying the intermolecular parameters through their geometrical dependence, some illustrative cases of 2D-square-well and Kihara spherocylinder fluids are explored, and their vapor-liquid phase diagrams and equations of state are tested against new simulation data. For the latter one, an available hard-dumbbell equation of state constitutes the reference term of the perturbation expansion. It is found that these theoretical approaches are able to reproduce the equations of state of the selected fluids quantitatively, but the vapor-liquid equilibrium is only grasped in a qualitative way. Reasons for this drawback are also discussed.

The high-temperature expansion of the free energy of a fluid of square wells, SW, is considered. The first four terms in this expansion are calculated for SW systems of variable range λσ, where σ is the diameter of the spherical hard-core. The properties were calculated via molecular dynamics, MD, for ranges 1≤λ≤2.5 with special emphasis on the region of shorter ranges: λ= 1.025, 1.050, 1.075, 1.100, 1.125 and 1.150. The principal aims are to compare these results with the previous ones obtained using the Monte Carlo, MC, method (Espíndola-Heredia et al. J. Chem. Phys. 130, 024509 (2009)) that showed large statistical noise in the higher-order terms at high densities, and to provide a benchmark to check the theoretical Short-Range Expansion of the free energy of these systems. The results have been corrected to obtain the thermodynamic limit via a change of ensemble algorithm and by simulating systems with 125, 200, 500 and 1000 particles. The MD results are much smoother that the corresponding MC data and their precision allow to determine the behavior of the series for high densities. The simulation results are used to test a theory built to write the free energy for short ranges. The position of the critical point is calculated with this theory for very short ranges.

The efficient recently proposed SP-MC method for calculating the chemical potential of hard-body fluids at very high densities by computer simulation is extended to the case of the square-well fluid. Results are obtained for the square-well fluid with energy width parameter X = 1.5. The implementation of the method takes into account a discontinuity in the third derivative with respect to core size of the chemical potential at infinite dilution of a test particle in the fluid. We note the implications of this discontinuity for the SP-MC method for larger values of X and for equations of state for square-well fluid mixtures. Chemical potentials have been simulated at two high densities over a range of temperatures. We additionally present new simulation results for the compressibility factor and the internal energies of the fluid at these state points, and perform thermodynamic consistency calculations involving these quantities and the chemical potentials. The results are also compared with those of a recently-published equation of state.

The free energy of square-well SW systems of hard-core diameter with ranges 1 3 is expanded in a perturbation series. This interval covers most ranges of interest, from short-ranged SW fluids 1.2 used in modeling colloids to long ranges 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 2, is seen to have properties similar to those of systems with longer ranges, 2 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 3 0.9 including subcritical temperatures. This fourth-order theory is estimated to be accurate except for a small region at high density, 3 0.9, and low temperature where terms of still higher order might be needed.

In a recent article [G. A. Chapela and J. Alejandre, J. Chem. Phys., 132(10), 104704 (2010)], it is shown that heteronuclear vibrating square-well dumbbells with a diameter ratio between particles of 1/2 and interacting potential ratio of 4 form micelles of different sizes and shapes which manifest themselves in both the liquid and vapor phases, up to and above the critical point. This means that micellization and phase separation are present simultaneously in this simple model. These systems present a maximum in the critical temperature when plotted against the potential well depth of the second particle 2. In the same publication, it was speculated that the formation of micelles was responsible for the appearance of the maximum. A thorough study on this phenomena is presented here and it is found that there is a threshold on the size of the second particle and its corresponding depth of interaction potential, where the micelles are formed. If the diameter and well depth of the second particle are small enough for the first and deep enough for the second, micelles are formed. For σ 2 /σ 1 between 0.25 and 0.65 and 2 // 1 larger than 5.7, micelles are formed up to and above the critical temperature. Outside these ranges micelles appear only at temperatures lower than the critical point. There is a strong temperature dependence on the formation and persistence of the aggregates. For the deepest wells and large enough second particles, a gel interconnected aggregate is obtained. In this work, the micelles are formed at temperatures as low as the triple point and as high as the critical point and, in some cases, persist well above it. The presence of these maxima in critical temperatures T c when plotted against 2 as follows. At lower values of 2 , an increase of T c is obtained as is expected by the increase of the attractive volume as indicated by the principle of corresponding states. As 2 increases further, the formation of molecular aggregates produce a saturation effect of the deepening of the potential well by encapsulating the particles of the second kind inside the micelles, so the resulting T c represents a new poly disperse system of molecular aggregates and not the original het-eronuclear vibrating square-well dumbbells. The surface tension is also analyzed for these systems, and it is shown that decreases with increasing attraction due to the formation of molecular aggregates.

This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and education use, including for instruction at the authors institution and sharing with colleagues. Other uses, including reproduction and distribution, or selling or licensing copies, or posting to personal, institutional or third party websites are prohibited. In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier's archiving and manuscript policies are encouraged to visit: http://www.elsevier.com/authorsrights The high-temperature expansion of the free energy of a fluid of square wells, SW, is considered. The first four terms in this expansion are calculated for SW systems of variable range λσ, where σ is the diameter of the spherical hard-core. The properties were calculated via molecular dynamics, MD, for ranges 1≤λ≤2.5 with special emphasis on the region of shorter ranges: λ= 1.025, 1.050, 1.075, 1.100, 1.125 and 1.150. The principal aims are to compare these results with the previous ones obtained using the Monte Carlo, MC, method (Espíndola-Heredia et al. J. Chem. Phys. 130, 024509 (2009)) that showed large statistical noise in the higher-order terms at high densities , and to provide a benchmark to check the theoretical Short-Range Expansion of the free energy of these systems. The results have been corrected to obtain the thermodynamic limit via a change of ensemble algorithm and by simulating systems with 125, 200, 500 and 1000 particles. The MD results are much smoother that the corresponding MC data and their precision allow to determine the behavior of the series for high densities. The simulation results are used to test a theory built to write the free energy for short ranges. The position of the critical point is calculated with this theory for very short ranges.

We have recently investigated the phase behaviour of model colloidal dumbbells constituted by two identical tangent hard spheres, with the first one being surrounded by an attractive square-well interaction (Janus dumbbells, Munaò G et al 2014 Soft Matter 10 5269). Here we extend our previous analysis by introducing in the model the size asymmetry of the hard-core diameters, and study the enriched phase
scenario thereby obtained. By employing standard Monte Carlo simulations we show that in such “heteronuclear Janus dumbbells” a larger hard-sphere site promotes the
formation of clusters, whereas in the opposite condition a gas-liquid phase separation takes place, with a narrow interval of intermediate asymmetries wherein the two phase
behaviours may compete. In addition, some peculiar geometrical arrangements, such as lamellæ, are observed only around the perfectly symmetric case. A qualitative
agreement is found with recent experimental results, where it is shown that the roughness of molecular surfaces in heterogeneous dimers leads to the formation of colloidal micelles.