Application of the modified van der waals equation for unsaturated vapour and liquid states

The Law-Lielmezs (L-L) modification of the Van der Waals equation of state: P = RT/(V-b)-a(T)/V² where: a(T) = a(T_c)·a(T_c·a(T¹) and: a(T¹) = 1 + pT^1q has been extended to include unsaturated states in terms of a correcting function C_f(such that the α(T¹) term becomes: a(T¹) = 1 + _pC_fT^1q The proposed extension has been compared with the results obtained by the use of the original Van der Waals equation of state.     

An estimation of the critical temperatures for atoms adsorbed on fractal surfaces using the van der waals equation in non-integral dimensional space

Using a Lagrangian interpolation over the values of space occupied by a sphere in one-, two- and three-dimensional space an expression for the space occupied by a sphere in non-integral dimensional space is obtained. This is used to obtain expressions for the pressure and volume corrections to the van der Waals equation in non-integral dimensional space. An expression for the critical temperature of a gas in non-integral dimensional space is derived and its experimental implications discussed. It is shown that the value of the critical temperature is not dependent on the form of the original interpolation.     

The use of van der waals molecules to identify spectroscopic origins

A technique for identifying the origin band of an electronic transition is described. The technique utilizes the increased linewidth of helium van der Waals complexes caused by vibrational predissociation when the molecular part of the complex is vibrationally excited. The method is applied to the visible spectrum of chromyl chloride, and we conclude that the d₅ band of chromyl chloride is not a second electronic origin.     

Dipole moment functions of van der waals complexes of HF and HCl with rare gas atoms

A simple electrostatic model based on a single-centre multipole expansion is applied to derive the dipole moment functions of complexes formed by the HF (DF) and HCl (DCl) molecules with rare gas atoms. Vibrationally averaged ground state dipole moments agree quite well with the available experimental data. Some transition dipole moments for the internal modes of complexes are also estimated.     

On the interdependence of van der waals and double layer forces

We study the effect of coupling the electrostatic and low frequency electrodynamic responses of colloidal systems. Exact results are reported for the van der Waals free energy of interaction of non-uniform electrolyte across planar dielectric and planar charged dielectric across non-uniform electrolyte. In both cases, the results depend on the double layer repulsion.     

Extended equation for the coexistence curve of molecular liquids in the vicinity of a critical point

An extended equation of state for substances along a phase interface, based on the Van der Waals model of a gas with fluctuations of the order parameter is confirmed by experimental data along the coexistence curve of a wide class of homogeneous and inhomogeneous molecular liquids under the Earth’s field of gravity. It is shown that the parameters of the extended equation for the coexistence curve of homogeneous and spatially inhomogeneous molecular liquids are linear functions of the compressibility factor. This allows us to predict the parameters of the equations of state of molecular liquids that are difficult to investigate experimentally.     

On the van der waals energy of two half-spaces at small separations

It is shown that the introduction of a cut-off wavenumber corresponding to electron-hole excitations leads to a 10% reduction of the Lifshitz van der Waals attraction of low density metallic half-spaces at small separations.     

Application of 1-1 modification of van der waals equation of state for saturated binary liquid mixtures

The Law-Lielmezs (L-L) modification of Van der Waals equation of state has been extended to include four hydrocarbon-hydrocarbon binary liquid mixtures for the saturated liquid-vapour equilibrium states. The values of the characteristic mixture p_m and q_m parameters have been calculated, and a relation between the values of these parameters and the molecular weight of binary mixture has been established. The proposed relation is compared with the results obtained by the use of Lielmezs, Howell and Campbell, and Soave 1980 modifications of the Redlich-Kwong equation of state.     

Microscopic solvent shifts in the electronic spectra of large van der waals molecules

The experimental red-shifts of the electronic origins of a number of large non-polar van der Waals molecules are reported. A comparison with the theoretical red-shifts calculated by a formalism given by Longuet-Higgins and Pople yields a good correlation, reflecting the dominant role of dispersion interactions in these complexes.     

Mode-selective broadening in low-frequency vibrational modes of trans-stilbene van der waals complexes

Both RE2PI and LIF excitation spectra have been taken of several van der Waals complexes of trans-stilbene, p-methyl-, and m-methyl-trans-stilbene. The t-stilbene spectra reveal a strongly mode-dependent broadening of the van der Waals complex transitions associated with the low-frequency vibrations 82 and 95 cm⁻¹ above the origin. The fwhm of these peaks is three times as broad as any other feature in the spectrum. The source of the broadening appears to be fast vibrational relaxation from these modes to the van der Waals modes of the complex.     

Diamagnetic susceptibilities in some linear van der waals complexes using the promolecule model

The second moments and diamagnetic susceptibilities of some linear van der Waals compounds may be calculated by the simple promolecule model utilizing an atomic monopole approximation for the electronic charge distribution. The results are in good agreement with experimental data. The estimated values for a large number of van der Waals systems can aid in interpreting measured Zeeman effects in rotational spectra.     

An approach for extending van der waals equations of state for polar,hydrogen bonding fluids applied to the soave equation of state

A method is developed for extending van der Waals type equations of state to highly polar, hydrogen bonding fluids. The method uses the acentric factor of the hydrocarbon homolog as the shape parameter and an empirical polar parameter incorporated into a closed form, temperature dependent polar correction term. When the method is applied to the Soave equation of state, a three-parameter equation of state results which reduces to the Soave equation for non-polar fluids, yet fits vapor pressures for polar fluids much better than the original equation. Furthermore, unlike other extensions applicable to polar fluids, the polar parameters obtained do seem to be related to the expected strength of polar interactions for different classes of compounds.     

Thermodynamic equations for the isobaric and isochoric heat capacities of pure substances at the critical point

It was proved on the assumption of a nonzero and finite slope of the elasticity curve at the critical point that the isochoric heat capacity at this point cannot be established on the basis of thermodynamics only. The critical conditions of a pure substance were derived from the differential equations of thermodynamics using a rigorous mathematical apparatus. Several indeterminate forms containing isochoric or isobaric heat capacities or their derivatives were evaluated.     

Analytical dependences between first order derivatives at the critical point of a pure substance

The finiteness and positive value of the slope of the saturation curve at the critical point according to its location in the region of a thermodynamic surface restricted by the curves of inversion and saturation are substantiated. It is shown that any two derivatives of the first order formed with respect to volume, internal energy, entropy, enthalpy, and the Helmholtz energy, one of which is taken at a fixed value of pressure and the other at a fixed value of temperature, are equal in the critical state. New sets of the critical conditions for a pure substance are obtained.     

Determination of vibrational level spacings of van der waals molecules from the Lennard-Jones potential

An approximate expression for the eigenvalues for van der Waals molecules by use of the Lennard-Jones (12-6) potential in the WKB approximation is presented. The expression is applied to the rare gas molecules. Ar₂, Kr₂, and Xe₂ by fitting the potential function to the observed potential parameters. Calculated results of vibrational energy spacings for these molecules agree well with the experiment and other calculations which are based on numerical integration of the Schrödinger equation. For Xe₂, the energy spacing expression is used to determine the thermodynamic functions of the van der Waals bond.     

Positron annihilation in the vicinity of the critical solution point of methanol-cyclohexane mixtures

The positron annihilation method was used to investigate critical phenomena in liquid mixtures of methanol and cyclohexane. Anomalies in the annihilation parameters near the critical solution temperature were found.