Van Der Waals Approximation Research Articles

Thermodynamic equations for a confined fluid at nanometric scale

From the study of a confined fluid, using van der Waals approximations for the Helmholtz energy, the enthalpy of vaporization, Boyle temperature, specific heat, Gay–Lussac cooling effect and Joule–Thomson inversion temperature are derived. The particles interact via a Lennard–Jones potential and the wall of the nanometric capillar is neutral. It is shown that the confinement gives lower values of those quantities, when comparison is done with the bulk properties.

Structure of Polyelectrolyte Solutions at a Charged Surface

The structure of polyelectrolyte solutions at a charged surface is studied using density functional theory and Monte Carlo simulations. The polymer molecules are modeled as freely jointed chains of charged hard spheres, the counterions and co-ions as charged hard spheres, and the surface is a planar, impenetrable hard wall with a uniform surface charge density. The density functional theory treats the ideal gas contribution exactly, uses a weighted density approximation for the hard sphere contribution, and a generalized van der Waals approximation for the electrostatic contribution. At a fixed surface charge density, with increasing concentration of the polyion, the simulations show layering as well as charge inversion phenomena resulting from an interplay between excluded volume and electrostatic interactions. The integrated surface excess is a monotonically decreasing function of polymer concentration at high surface charge densities, but a nonmonotonic function of polymer concentration at lower surfac...

Effect of the incomplete interaction on the nematic–isotropic transition at the nematic–wall interface

The nematic–isotropic phase transition is investigated for a sample in the shape of a slab of thickness d, by means of a local self-consistent model. The effective interaction is written as the sum of the direct interaction of a given nematic molecule with the substrate and of its incomplete interaction with the other nematic molecules due to the presence of the limiting surface. In the van der Waals approximation both contributions depends on the power −3 of the distance of the considered molecules from the substrate. In this framework we show the existence of a boundary layer in which the order parameter can be greater or smaller than the one in the bulk, according to the strength of the surface potential with respect to the nematic one. The model can provide a simple molecular framework to interpret characteristics of nematic liquid crystal confined in small-scale structures.

A new model for brown dwarf spectra including accurate unified line shape theory for the Na I and K I resonance line profiles

We present the first brown dwarf atmosphere models based on theoretical calculations of absorption profiles of sodium and potassium perturbed by helium and molecular hydrogen. The synthetic spectra have been compared to previous calculations with Lorentz profiles and the classic van der Waals approximation, and to the observed spectrum of the T dwarf SDSS 1624. The new profiles provide increased opacities in the optical spectra of methane brown dwarfs. However, the potassium and sodium far wings alone cannot explain the missing opacity in the 0.85 to 1.1 μm range.

Phase behavior and structure of Janus fluids.

The equilibrium phase behavior of Janus fluids is examined based on a model potential for the interaction between their constituents. Janus fluids consist of axisymmetric particles possessing two different "faces," e.g., one hydrophobic and one hydrophilic surface, and the interaction depends on the relative orientation. Starting from a short range, isotropic potential we make an ansatz for an anisotropic model interaction potential. Two types of symmetries of the particles are considered. One leads to a polar phase. The Helmholtz free energy and the pressure are calculated by the help of an augmented van der Waals approximation. A qualitative phase diagram is obtained. The appearance of a polar phase and the corresponding transition temperature are examined adapting a Landau-de Gennes expansion of the orientational part of the free energy. Monte Carlo simulations are performed and the results are compared with the ones obtained by the analytical description.

On correlated heterogeneities of glass-forming liquids

The thermodynamics and structure of glass-forming liquids are considered within the framework of the heterophase fluctuation (HPF) model. The main goal of the theory developed is to find a description for the long-range correlations (LRC) of the density fluctuations known as the Fischer cluster. The van der Waals approximation of the HPF model shows that the liquid can have an isolated solid–fluid critical point analogous to the critical point of a gas–liquid system. Heterophase fluctuations in the form of solidlike noncrystalline and fluidlike clusters can have LRC in a narrow vicinity of the critical point. An analysis shows that the properties of the conventional critical fluctuations differ from those of the Fisher cluster. This forces one to look for another explanation of the observed LRC in glass-forming liquids. Large configurational entropy of liquids and glasses is a manifestation of multiplicity of the short-range ordering of molecules in the amorphous solidlike and fluidlike clusters. The multiplicity of short-range order results in structural heterogeneities. Random-field Ginzburg–Landau equations for the HPFs are deduced taking into account the structural heterogeneities. The random field is generated by these heterogeneities. It is found that at least three characteristic correlation scales are inherent to the HPFs: the radius of local order, r0, which is comparable with the radius of the first coordination sphere; the random-field-controlled radius of critical fluctuations, Rc; the average correlation length ξav of fractal aggregations formed by the correlated domains (the domains have size ∼Rc). The length ξav is the characteristic size of the Fischer cluster. The conditions for the appearance of the listed correlations are deduced by requiring that they provide minimization of the free energy of the system. The annealing kinetics and dynamics (the ultraslow modes) of the Fischer cluster are described.

Local self-consistent approach to the phase transition at the nematic liquid-crystal-wall interface.

The nematic-isotropic transition for a semi-infinite sample is analyzed by means of the Maier-Saupe theory. The effect of a delocalized surface field acting on the nematic molecules, and of the incomplete interaction between the nematic molecules, are taken into account in the van der Waals approximation. We show that the existence of a surface transition is governed by the strength of the surface potential. The spatial profile of the order parameter and the degree of extra order near the walls are determined for different temperatures. The surface tension of nematic origin is calculated near the bulk transition temperature. It is estimated to be one order of magnitude smaller than the total surface tension experimentally detected with standard techniques.

Wigner crystallization in a magnetic field: single electrons versus electron pairs at the lattice sites

The ground state energy of a two-dimensional Wigner crystal in a perpendicular magnetic field with one and two electrons per cell is investigated. The electron–electron interaction between the cells is treated in second-order (dipole) van der Waals approximation. In case of two electrons per lattice site, the interaction of the electrons within each cell is taken into account exactly (including exchange and correlation effects). No further approximations are made, in particular Landau level mixing and incomplete spin polarization are accounted for. The phase diagram shows that the paired phase is energetically more favorable than the single electron phase for large filling factors and high densities.

Wigner crystallization of a two-dimensional electron gas in a magnetic field: Single electrons versus electron pairs at the lattice sites

The ground state energy and the lowest excitations of a two dimensional Wigner crystal in a perpendicular magnetic field with one and two electrons per cell is investigated. In case of two electrons per lattice site, the interaction of the electrons {\em within} each cell is taken into account exactly (including exchange and correlation effects), and the interaction {\em between} the cells is in second order (dipole) van der Waals approximation. No further approximations are made, in particular Landau level mixing and {\em in}complete spin polarization are accounted for. Therefore, our calculation comprises a, roughly speaking, complementary description of the bubble phase (in the special case of one and two electrons per bubble), which was proposed by Koulakov, Fogler and Shklovskii on the basis of a Hartree Fock calculation. The phase diagram shows that in GaAs the paired phase is energetically more favorable than the single electron phase for, roughly speaking, filling factor $f$ larger than 0.3 and density parameter $r_s$ smaller than 19 effective Bohr radii (for a more precise statement see Fig.s 4 and 5). If we start within the paired phase and increase magnetic field or decrease density, the pairs first undergo some singlet- triplet transitions before they break.

Phase diagrams of polydisperse van der Waals fluids

The phase behavior of a system composed of spherical particles with a monomodal size distribution is investigated theoretically within the context of the van der Waals approximation for polydisperse fluids. It is shown how the binodals, spinodals, cloud-point and shadow curves as well as all the (polydispersity induced) critical points can be obtained for a variety of interaction potentials. The polydispersity induced modifications of the phase diagram (even for a polydispersity index I as small as I≈1.01) should be observable in some colloidal dispersions.

Effects of molecular geometry on liquid crystalline phase behaviour: isotropic-nematic transition

The effects of range and geometry of a simple attractive square-well on the phase diagram of hard ellipsoids and hard spherocylinders is systematically studied using a simple van der Waals type theory. The orientational single particle distribution function is approximated using the Onsager trial function. The quantitative errors introduced by this are thought to be considerably smaller than the use of the van der Waals approximation, which has been shown to give qualitatively correct phase diagrams for similar models. The phase diagrams obtained for hard ellipsoids and hard spherocylinders of aspect ratios ranging between 3 and 10 with a variety of square-well attractions are found to fall into three general types. The first type shows liquid-vapour coexistence and an isotropic-nematic transition, which meet at a liquid-vapour-nematic triple point. The second type shows a marked widening of the isotropic-nematic biphasic region which pre-empts the liquid-vapour coexistence. The final phase diagram shows a strong destabilization of the nematic phase with respect to the isotropic, which results in a shift of the phase transition to higher densities and pressures as the temperature is lowered.

Generalized van der Waals density functional theory for nonuniform polymers

A density functional theory is presented for the effect of attractions on the structure of polymers at surfaces. The theory treats the ideal gas functional exactly, and uses a weighted density approximation for the hard chain contribution to the excess free energy functional. The attractive interactions are treated using a van der Waals approximation. The theory is in good agreement with computer simulations for the density profiles at surfaces for a wide range of densities and temperatures, except for low polymer densities at low temperatures where it overestimates the depletion of chains from the surface. This deficiency is attributed to the neglect of liquid state correlations in the van der Waals term of the free energy functional.

One-fluid theory of liquid-vapor surface tension in simple multi-component mixtures

We propose a theory of surface tension in multi-component mixtures of simple fluids far from critical conditions based on the one-fluid van der Waals approximation and statistical mechanical perturbation approach. The theory contains no adjustable parameters. By comparison with molecular dynamics simulation of binary Lennard-Jones mixtures it is shown that the theory provides a quantitative (within a tolerance of ∼15%–20%) description of surface tension.

Van der waals approximation for potassium bubbles in tungsten

The finely dispersed potassium bubbles are responsible for the high-temperature sag resistance of lamp filaments; thus, the understanding of development of bubble structure is of practical importance. Usually, the ideal gas theory is used for describing the potassium bubbles in tungsten. Instead, we used the van der Waals approximation which can account for phase changes and describes a two-phase coexistence region. It is shown theoretically that bubbles in the practically important size range (some tenth of microns) can exist in a two-phase state. Some experimental findings are also better explained by the real gas approximation.

Comment on "Relation between the electron scattering length and the van der Waals approximation to the equation of state"

In a recent paper, Reisfeld and Asaf [Phys. Rev. A 49, 348 (1994)] have undertaken an attempt to explain the linear dependence of the electron-atom scattering length on the atomic polarizability. They used the Born approximation, which is valid only for small atomic or molecular polarizabilities. Using the exact formula for the scattering length, we offer a simple expression for estimation of the scattering length by known values of the polarizability and ionization potential.

Erratum: Relation between the electron scattering length and the van der Waals approximation to the equation of state

A theoretical relation between the electron scattering length and the van der Waals approximation to the equation of state is described. The theory provides a simple calculation for the scattering length of neutral atomic scatterers such as rare gases, using two experimental parameters: the hard-core radius (calculated from the van der Waals equation of state, using critical data) and the atomic polarizability. The results for the calculated electron scattering length agree with measured values derived either from the energy shifts of highly excited molecular Rydberg states, perturbed by He, Ne, Ar, Kr, and Xe, or from swarm electron cross-section data for the same gases.

Application of generalized van der Waals theory and approximations of radial distribution functions to the development of mixing rules

Li, M.-H. and Huang, F.-N., 1994. Application of generalized van der Waals theory and approximations of radial distribution functions to the development of mixing rules. Fluid Phase Equilibria, 96: 155-172. Based on generalized van der Waals partition function theory and approximations of radial distribution functions, mixing rules for the attractive part of an equation of state have been presented for extension of an augmented hard-core equation of state to mixtures. Two approximations, the van der Waals one-fluid approximation and the mean density approximation, are applied in this study. Within the framework of the conformal solution theory, the properties of a hypothetical fluid were calculated from the attractive part of an augmented hard-core equation of state. As a preliminary test of the method, an augmented hard-sphere equation of state has been applied. For polar systems in which components do not differ appreciably in size, both the MDA and the VDW models yield satisfactory results for the vapor-liquid equilibrium calculations. However, for strongly non-ideal fluid systems, the MDA is superior to the VDW. Adopting the mixing rules for the repulsive hard-core mixtures to describe structure effects, the proposed method can, in principle, be used to extend any accurate augmented hard-core equation of state to mixtures.

Relation between the electron scattering length and the van der Waals approximation to the equation of state.

A theoretical relation between the electron scattering length and the van der Waals approximation to the equation of state is described. The theory provides a simple calculation for the scattering length of neutral atomic scatterers such as rare gases, using two experimental parameters: the hard-core radius (calculated from the van der Waals equation of state, using critical data) and the atomic polarizability. The results for the calculated electron scattering length agree with measured values derived either from the energy shifts of highly excited molecular Rydberg states, perturbed by He, Ne, Ar, Kr, and Xe, or from swarm electron cross-section data for the same gases.

Correlation of unusual phase behaviour at elevated pressure

An unusual phase behaviour is in this context a phase behaviour which can not be correlated with a PVT model and the van der Waals approximation which is the most widely used mixture model in high pressure phase equilibrium thermodynamics. The van der Waals approximation is a successful model for correlation of phase equilibria in nonpolar fluid mixtures. All PVT models for reservoir fluids and in the petroleum industry are van der Waals approximations. In the chemical industry most phase equilibria are low pressure phase equilibria of systems containing polar compounds which can be correlated by means of an activity coefficient model. However, phase equilibria in systems containing mixed polar solvents and nonpolar solutes are difficult to correlate. In the last decade models have been developed which combine the complex composition dependence of activity coefficient models with equations of state. In the first part of the paper we review some rules of model developments set by the classical thermodynamics, although elementary, these rules are often overlooked, leading to inconsistent models. In the last part of the paper we review the state of the art of model developments and identify areas where further developments are warranted.

Variational bounds for lattice fermion models. I. Spinless fermions

The authors assess the validity of mean-field theories for lattice fermion systems with attractive interactions by comparing variational upper bounds from two plausible mean-field approximations-a Van der Waals (independent particle) approximation and a pairing approximation of the BCS type-for the Helmholtz free energy of a spinless fermion model with attractive nearest-neighbour interactions. It is found that there is a crossover from the Van der Waals approximation giving the best bound to the pairing approximation giving the best bound as t, the hopping integral passes through a critical value tc. This crossover phenomenon exists in all dimensions as well as for the limiting d to infinity model. The authors conclude that there can be no simple mean-field theory which is valid for fermion systems with attractive interactions.