Perturbed hard-sphere equations of state of real fluids. II. Effective hard-sphere diameters and residual properties

Effective hard-sphere diameters for argon, krypton and xenon have been calculated from the currently most accurate perturbation theories using accurate pair-potential models. Based on the theoretical diameters and on pressure—volumes—temperature data for the real fluids, the van der Waals parameter a_p is examined and two conjectures generalizing the behavior of a_p are formulated. These conjectures make it possible to evaluate the effective hard-sphere diameters of simple liquids at the triple-point temperature from data for a few low-temperature pressure—volume isotherms. This fact, together with a corresponding-states principle that emerges from results for the theoretical diameters, forms the basis of a simple method which we propose for evaluating temperature-dependent effective hard-sphere diameters of a perturbed hard-sphere equation of state, independently of any pair-potential model and any perturbation theory. The applicability of the method is demonstrated for methane and its extension to nonsimple liquids is discussed. It is also shown that the use of an approximate theory and/or approximate pair-potential model may often result in a qualitatively misleading picture of a_p behavior.     

Thermodynamic properties of lattice hard-sphere models

Thermodynamic properties of several lattice hard-sphere models were obtained from grand canonical histogram- reweighting Monte Carlo simulations. Sphere centers occupy positions on a simple cubic lattice of unit spacing and exclude neighboring sites up to a distance sigma. The nearestneighbor exclusion model, sigma = radical2, was previously found to have a second-order transition. Models with integer values of sigma = 1 or 2 do not have any transitions. Models with sigma = radical3 and sigma = 3 have weak first-order fluid-solid transitions while those with sigma = 2 radical2, 2 radical3, and 3 radical2 have strong fluid-solid transitions. Pressure, chemical potential, and density are reported for all models and compared to the results for the continuum, theoretical predictions, and prior simulations when available.     

Pair correlation function of soft-sphere fluids

A closed-form analytic formula for the radial distribution function (RDF) or g(r) of inverse power fluids is proposed. The RDF is expressed as a sum of separate component functions, one monotonic and a series of exponentially damped oscillatory functions. Unlike previous treatments in the literature, this formula does not rely on patching different functional forms at arbitrary crossover distances. This expression, which we refer to as g(M)(r), yields the expected asymptotic behavior at large distance and reproduces the main features of the RDF generated by molecular dynamics (MD) simulations. The g(M) is applied to the soft n = 4 inverse power fluid, and it is shown that in this case seven or fewer terms are sufficient to represent accurately the MD-generated RDF over the entire fluid domain. The relative contributions of the separate terms of the g(M) as a function of density are analyzed and discussed. The key role played by the monotonic component function and two oscillatory terms is demonstrated. The origin of the crossover from the oscillatory to the monotonic behavior is shown to be the same as that recently proposed by Evans and Henderson [R. Evans and J. R. Henderson, J. Phys.: Condens. Matter 21, 474220 (2009)] for the dispersion interactions.     

Thermodynamic and structural properties of confined discrete-potential fluids

The thermodynamic and structural behaviors of confined discrete-potential fluids are analyzed by computer simulations, studying in a systematic way the effects observed by varying the density, temperature, and parameters of the potentials that characterize the molecule-molecule interactions. The Gibbs ensemble simulation technique for confined fluids [A. Z. Panagiotopoulos, Mol. Phys. 62, 701 (1987)] is applied to a fluid confined between two parallel hard walls. Two different systems have been considered, both formed by spherical particles that differ by the interparticle pair potential: a square well plus square shoulder or a square shoulder plus square well interaction. These model interactions can describe in an effective way pair potentials of real molecular and colloidal systems. Results are compared with the simpler reference systems of square-shoulder and square-well fluids, both under confinement. From the adsorption characterization through the use of density profiles, it is possible to obtain specific values of the interparticle potential parameters that result in a positive to negative adsorption transition.     

Equations of state for tetra-dimensional hard-sphere fluids

An equation of state, a kind of generalised Padé approximants, first proposed for the hard-sphere fluid in cases of two, three, four and five dimensions is extended for the tetra-dimensional case with new simulation data available. The corresponding equations of state show good to excellent agreement with the above-mentioned data.     

Equation of state of simple dense fluids. Thermal pressure coefficients and effective hard sphere diameters

The thermal pressure coefficient of a fluid may be simply related to the hard sphere term in a van der Waals type of equation of state. Experimental data for liquid argon and simulation results for a Lennard-Jones 12-6 fluid have been used to give information about the temperature dependence of the hard sphere diameter. The implications of this behaviour have been briefly discussed.     

Thermodynamic and orientational properties of two-dimensional multicomponent hard rectangle fluids

A molecular statistical model is developed for a two-dimensional multicomponent fluid composed of hard rectangles. The configurational partition function of such a system on a square lattice is evaluated by applying the orientation dependent version of the Flory-Huggins probability method. Unlike earlier treatments of similar problems, the final result for the configurational entropy is independent of the order of placement of the rectangular plate-like particles. The present approach has been extended to enable an analysis of both facewise and edgewise modes of adsorption of rectangular molecules on a planar surface. Further, the limit of infinitesimal lattice size has been considered as the generalized continuous version of the corresponding lattice model. The results obtained within the present continuous approach are compared with those of studies of related one-component hard body fluids.     

Thermodynamic and orientational properties of two-dimensional multicomponent hard rectangle fluids

A molecular statistical model is developed for a two-dimensional multicomponent fluid composed of hard rectangles. The configurational partition function of such a system on a square lattice is evaluated by applying the orientation dependent version of the Flory-Huggins probability method. Unlike earlier treatments of similar problems, the final result for the configurational entropy is independent of the order of placement of the rectangular plate-like particles. The present approach has been extended to enable an analysis of both facewise and edgewise modes of adsorption of rectangular molecules on a planar surface. Further, the limit of infinitesimal lattice size has been considered as the generalized continuous version of the corresponding lattice model. The results obtained within the present continuous approach are compared with those of studies of related one-component hard body fluids.     

Mean-field cage theory for the freezing of hard-sphere fluids

Using some observations and some mean-field approximations, we develop a mean-field cage theory for the freezing of hard-sphere fluids with v(f) > or =a(d) and obtain the freezing densities as functions of the closest-packing densities and the spatial densities, which are in good agreement with the experimental and simulation results.     

The decay of pair correlations in quantum hard-sphere fluids

A study of the asymptotic decay of the pair radial correlations in the bare quantum hard-sphere (QHS) fluid and in the quantum hard-sphere Yukawa (QHSY) fluid is presented. The conditions explored are far from quantum exchange and are contained within the region (0.1相似文献   

Thermodynamic properties of polar fluids from a perturbed-dipolar-hard-sphere equation of state

Based on theoretical results for a system of hard spheres with dipoles, a new equation of state is applied to the correlation of thermodynamic properties for four fluids: argon, ammonia, water and acetonitrile. The reference system has the same dependence on density as that given by the Carnahan-Starling equation, but the coefficients are now functions of temperature through the reduced dipole moment. These coefficients are chosen to match the Padé approximant developed by Rushbrooke, Stell and Hoye for the Helmholtz energy of dipolar hard spheres. The reference system proposed here shows a phase transition for reduced dipole moments greater than 1.9. A simple, empirical perturbation term is added to the reference system to account for induction and dispersion forces. For polar fluids, the equation gives results significantly better than those obtained from conventional cubic equations of state, when using the same limited experimental data for determining equation-of-state parameters.     

Thermodynamic properties of nitrogen from a perturbation theory for ISM fluids

A first-order Barker-Henderson perturbation theory for interaction-site model (ISM) fluids has been applied to calculate the Helmholtz free energy, entropy and internal energy of liquid nitrogen. Comparison with experiment reinforces the idea that the theory is accurate over a wide range of temperatures and densities corresponding to the liquid state, except for the critical region.     

Geometrical properties of the potential energy of the soft-sphere binary mixture

We report a detailed study of the stationary points (zero-force points) of the potential energy surface (PES) of a model structural glassformer. We compare stationary points found with two different algorithms (eigenvector following and square gradient minimization), and show that the mapping between instantaneous configuration and stationary points defined by those algorithms is as different as to strongly influence the instability index K versus temperature plot, which relevance in analyzing the liquid dynamics is thus questioned. On the other hand, the plot of K versus energy is much less sensitive to the algorithm employed, showing that the energy is the good variable to discuss geometric properties of the PES. We find new evidence of a geometric transition between a minima-dominated phase and a saddle-point-dominated one. We analyze the distances between instantaneous configurations and stationary points, and find that above the glass transition, the system is closer to saddle points than to minima.     

Structural properties of a model system with effective interparticle interaction potential applicable in modeling of complex fluids

We report grand canonical ensemble Monte Carlo (MC) simulation and theoretical studies of the structural properties of a model system described by an effective interparticle interaction potential, which incorporates basic interaction terms used in modeling of various complex fluids composed of mesoscopic particles dispersed in a solvent bath. The MC results for the bulk radial distribution function are employed to test the validity of the hard-sphere bridge function in combination with a modified hypernetted chain approximation (MHNC) in closing the Ornstein-Zernike (OZ) integral equation, while the MC data for the density profiles in different inhomogeneous environments are used to assess the validity of the third-order+second-order perturbation density functional theory (DFT). We found satisfactory agreement between the results predicted by the pure theories and simulation data, which classifies the proposed theoretical approaches as convenient tools for the investigation of complex fluids. The present investigation indicates that the bridge function approximation and density functional approximation, which are traditionally used for the study of neutral atomic fluids, also perform well for complex fluids only on condition that the underlying effective potentials include a highly repulsive core as an ingredient.     

Statistical thermodynamics and dielectric properties of dipole-quadrupole hard-sphere fluid

Within a hindered rotation model, approximate analytical expressions have been obtained for thermodynamic functions and the Kirkwood factor of the model polar fluid of dipole-quadrupole hard spheres in the nearest neighbor approximation. A peculiarity of the considered system from the viewpoint of the hindered rotation model is the ability to generate a three-dimensional grid of quadrupole-bonded molecules, as indicated by the behavior of quadrupole hard-sphere fluid at large values of the quadrupole moment.     

Thermodynamic properties of van der Waals fluids from Monte Carlo simulations and perturbative Monte Carlo theory

Computer simulations have been performed for fluids with van der Waals potential, that is, hard spheres with attractive inverse power tails, to determine the equation of state and the excess energy. On the other hand, the first- and second-order perturbative contributions to the energy and the zero- and first-order perturbative contributions to the compressibility factor have been determined too from Monte Carlo simulations performed on the reference hard-sphere system. The aim was to test the reliability of this "exact" perturbation theory. It has been found that the results obtained from the Monte Carlo perturbation theory for these two thermodynamic properties agree well with the direct Monte Carlo simulations. Moreover, it has been found that results from the Barker-Henderson [J. Chem. Phys. 47, 2856 (1967)] perturbation theory are in good agreement with those from the exact perturbation theory.     

Thermal properties of bi nanowire arrays with different orientations and diameters

The thermal properties of single-crystalline Bi nanowire arrays with different orientations and diameters were studied by differential scanning calorimeter and in situ high-temperature X-ray diffraction. Bi nanowires were fabricated by a pulsed electrodeposition technique within the porous anodic alumina membrane. The relationships between the orientation and diameter of Bi nanowires and the corresponding thermal properties are deduced solely from experimental results. It is shown that the melting point decreases with decreasing nanowire diameter, and there is an anisotropic thermal expansion property of Bi nanowires with different orientations and diameters. The transition of the thermal expansion coefficient from positive at low temperature to negative at high temperature for Bi nanowire arrays was analyzed and discussed.     

Computational studies on thermodynamic properties, effective diameters, and free volume of argon using an ab initio potential

A quantum mechanical derived ab initio interaction potential for the argon dimer was tested in molecular simulations to reproduce the thermophysical properties of the vapor-liquid phase equilibria using the Gibbs ensemble Monte Carlo simulations as well as the liquid and supercritical equation of state using the NVT Monte Carlo simulations. The ab initio interaction potential was taken from the literature. A recently developed theory [R. Laghaei et al., J. Chem. Phys. 124, 154502 (2006)] was used to compute the effective diameters of argon in fluid phases and the results were subsequently applied in the generic van der Waals theory to compute the free volume of argon. The calculated densities of the coexisting phases, the vapor pressure, and the equation of state show excellent agreement with experimental values. The effective diameters and free volumes of argon are given over a wide range of densities and temperatures. An empirical formula was used to fit the effective diameters as a function of density and temperature. The computed free volume will be used in future investigations to calculate the transport properties of argon.     

Thermodynamic properties of tetrachlorocyclopropene

A facility is described which incorporates the use of electronic microbalances to follow gravimetric changes due to the formation or spallation of surface oxides on metals or alloys during high temperature oxidation. The outputs from the balances are fed into a data acquisition system which allows easy collection and analysis of the data from more than one microbalance.The sensitivity of the technique is illustrated by reference to the measurements of oxidation and spallation on a 20Cr/25Ni/Nb stabilised stainless steel oxidised in flowing CO₂ based gas at 1 atmosphere pressure and 850°C.     

Thermodynamic properties of methylvinylsulphide

Enthalpies of the overall decomposition reactions MX₂L₂(c) → MX₂(c) + 2L(g) and of the intermediate stepwise loss of ligand, L, where X is Cl or Br; L is 3-chloropyridine, 3-bromopyridine, 2-chloropyridine, 2-bromopyridine, or 2-methoxypyridine; and M is Mn, Ni, Cu, or Cd have been measured by use of a differential scanning calorimeter. Enthalpies of sublimation of NiCl₂(3-chloropyridine)₂, NiCl₂(3-bromopyridine)₂ and CuCl₂(3-bromopyridine)₂ have been determined. Values of the metal—nitrogen bond dissociation energies in these compounds have been calculated. A value for the specific heat of CuCl₂(2-chloropyridine)₂ is reported.