Simple pair potential model for real fluids

Simple pair potential accounting realistically for both the short-range repulsions and long-range attractions is proposed and its main properties are discussed. It is shown that for simple fluids (i) its attractive force constant, C₆, corresponds to that found experimentally and (ii) it gives perfect agreement of the second virial coefficient over the entire temperature ranges for which experimental data are known.     

Simple pair potential model for real fluids. III. Parameter determination and a revised model for spherical molecules

A method combining macroscopic data with atomic structure constants for determination of the parameters of simple potential models is discussed. A revised hybrid potential model, MMH, whose hard core diameter and location of the potential minimum are determined a priori from the atomic structure is proposed. Calculations of the second and third virial coefficients and the viscosity coefficient indicate that the MMH model may be a reliable potential superior to all other simple potential models.     

Ab initio potential energy curve for the helium atom pair and thermophysical properties of the dilute helium gas. II. Thermophysical standard values for low-density helium

A helium–helium interatomic potential energy curve determined from quantum-mechanical ab initio calculations and described with an analytical representation considering relativistic retardation effects (R. Hellmann, E. Bich, and E. Vogel, Molec. Phys. (in press)) was used in the framework of the quantum-statistical mechanics and of the corresponding kinetic theory to calculate the most important thermophysical properties of helium governed by two-body and three-body interactions. The second pressure virial coefficient as well as the viscosity and thermal conductivity coefficients, the last two in the so-called limit of zero density, were calculated for ³He and ⁴He from 1 to 10 000 K and the third pressure virial coefficient for ⁴He from 20 to 10 000 K. The transport property values can be applied as standard values for the complete temperature range of the calculations characterized by an uncertainty of ±0.02% for temperatures above 15 K. This uncertainty is superior to the best experimental measurements at ambient temperature.     

Transport properties of diatomic gases

The coefficients of shear viscosity and self-diffusion for nitrogen in the dilute gas limit have been calculated within the Mason-Monchick approximation using the intermolecular potential surfaces of Berns and van der Avoird and van Hemert and Berns. The same potentials had previously been used in transport property calculations using the classical limit of the Wang Chang, Uhlenbeck and de Boer theory. Comparisons between the results for each potential surface using the different transport theories reveal surprising discrepancies which increase with increasing temperature. Possible causes of this behaviour are considered.     

Transport properties of dilute magnetic alloys

The electrical resistivity, thermopower, and the electronic part of the thermal resistivity of dilute magnetic alloys are calculated in the framework of the Suhl-Nagoaka theory. Using Bloomfield's and Hamann's solution of the Nagaoka equations, we derive expressions for the transport quantities in the limitT? ¯ T_K andT?¯ T_K to order (In ¯T _K /T)^?4 where ¯T _K is the Kondo temperature which may depend on the spin independent scattering. We find that the thermopower and deviations from the Wiedemann-Franz law in this limit decrease as ¦In ¯T_K/T¦^?3 if one neglects a trivial temperature dependence of the thermopower due to the electron-phonon interaction.     

Particle densities for dilute hard-sphere Bose or Fermi gases in an external potential

We prove that if the diameter of a hard-sphere is much smaller than the size of an external potential, the s-wave pseudopotential reduces to the Huang-Yang s-wave pseudopotential. We obtain the first-order virial expansions of particle densities for dilute hard-sphere Bose or Fermi gases in an arbitrary external potential. In the absence of an external potential, the results reduce to the Huang-Yang-Luttinger and Lee-Yang virial expansions. In the quasi-classical limit, the results reduce to the results of the local density approximation.     

Effective pair potentials in fluids in the presence of three-body forces. II

Earlier calculations are extended to the second order in density thus providing the non-additive contributions to the fourth virial coefficient in the presence of a weak three-body force given by the triple-dipole dispersion potential of Axilrod and Teller. We compare the Percus-Yevick approximations of Rushbrooke and Silbert and of Rowlinson at the level of the fourth virial coefficient and find that the former is more accurate. We also compare our calculations of the effective pair potential of liquid argon with the results of Mikolaj and Pings obtained from X-ray diffraction measurements.     

The interpretation of transport coefficients on the basis of the Van der Waals model: II. Extension to dilute gases

The Van der Waals model for transport properties which forms a very satisfactory basis for the interpretation of dense-gas transport-coefficient data, is applied to dilute gases to determine the effect of attractive forces between real molecules on the values of transport coefficients. It is found that experimental viscosity coefficient and thermal-conductivity coefficient data are lower than the values calculated by up to 40%. For the rare gases these differences are found to be related simply to the temperature and molar volume and expressions are given which reproduce the available experimental data generally to better than 2% over the whole density range.     

Existence of Green's functions for dilute Bose gases

Some properties of finite volume Green's functions are obtained, and the infinite volume limit is shown to exist for the multi-time Green's functions of a dilute Bose gas, constructed with the operators of the quasi-local algebra (see Theorem IV.5).     

Simple optimized Brenner potential for thermodynamic properties of diamond

We have examined the commonly used Brenner potentials in the context of the thermodynamic properties of diamond. A simple optimized Brenner potential is proposed that provides very good predictions of the thermodynamic properties of diamond. It is shown that, compared to the experimental data, the lattice wave theory of molecular dynamics (LWT) with this optimized Brenner potential can accurately predict the temperature dependence of specific heat, lattice constant, Grüneisen parameters and coefficient of thermal expansion (CTE) of diamond.     

Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy methods for sums of Lyapunov exponents for dilute gases

We consider a general method for computing the sum of positive Lyapunov exponents for moderately dense gases. This method is based upon hierarchy techniques used previously to derive the generalized Boltzmann equation for the time-dependent spatial and velocity distribution functions for such systems. We extend the variables in the generalized Boltzmann equation to include a new set of quantities that describe the separation of trajectories in phase space needed for a calculation of the Lyapunov exponents. The method described here is especially suitable for calculating the sum of all of the positive Lyapunov exponents for the system, and may be applied to equilibrium as well as nonequilibrium situations. For low densities we obtain an extended Boltzmann equation, from which, under a simplifying approximation, we recover the sum of positive Lyapunov exponents for hard-disk and hard-sphere systems, obtained before by a simpler method. In addition we indicate how to improve these results by avoiding the simplifying approximation. The restriction to hard-sphere systems in d dimensions is made to keep the somewhat complicated formalism as clear as possible, but the method can be easily generalized to apply to gases of particles that interact with strong short-range forces. (c) 1998 American Institute of Physics.     

Transport properties of diazonium functionalized graphene: chiral two-dimensional hole gases

The electric transport properties of diazonium functionalized graphene (DFG) were investigated. The temperature dependence of the resistivity (ρ-T) and the Shubnikov-de Haas oscillation of the DFG revealed two-dimensional hole gas (2DHG) behaviors. The DFGs exhibited unusual weak localization behaviors in which both inelastic and chirality-breaking elastic scattering processes should be taken into account, meaning that graphene chirality was maintained. Because of the giant decrease in the diffusion coefficient, the scattering rates remained relatively low in the presence of suppression of the scattering lengths. The decreases of both the mean free path and the Fermi velocity were responsible for the suppression of the diffusion coefficient and hence the charge mobility.     

Radiative properties of model gases for applications in radiative energy transfer

An approximate analysis of the radiative properties of gases is presented for use in problems of fluid mechanics involving radiative transfer of energy. The analytical expressions obtained are presented in a non-dimensional form which clarifies their meaning and gives insight into the numerical magnitudes of significant radiative properties.Results are presented for line and continuum spectral absorption coefficients as functions of frequency and temperature. The corresponding emission coefficients are integrated to obtain Planck mean absorption co-efficients. It is found, for example, that for monatomic gases in the temperature range considered, T < 30 000°K, the Planck mean for atomic lines always exceeds that for the continuum. Although the absorption coefficients for continuum radiation in this temperature range are greatest for frequencies above the ground state ionization frequency, the major contribution to the Planck mean absorption coefficient comes from frequencies below the ionization frequency.Comparison of the photon mean free paths with the particle mean free paths, shows that the Planck photon mfp is much longer than the particle mfp but that the photon mfp corresponding to the peak line absorption coefficient is much shorter than the particle mfp.     

Chaotic capture of vortices by a moving body. II. Bound pair model

Previously, we have presented a simple model for the interaction of a fluid vortex structure with a moving bluff body, and demonstrated the existence of a trapping mechanism related to chaotic scattering. This single point vortex model required explicit perturbation to generate chaos and the subsequent complex dynamics. Here, we present a model which attempts to introduce internal degrees-of-freedom in the vortex structure in the simplest manner, by replacing the single vortex with a like-signed pair. We show that this model exhibits chaotic trapping without the need of explicit perturbation, however, the region of parameter space for which trapping occurs is exceedingly small due to the spatially dependent form of the perturbation. We claim that this result explains some the behavior observed in Navier-Stokes simulations of the same vortex-body system, where we find close correspondence between the dynamics of an extended vorticity distribution and the single vortex model. Finally, we generalize the model to unequal strength vortex pairs, and find more complex behavior which includes "partial" capture of the weaker vortex by the body. (c) 1994 American Institute of Physics.     

A convergent nonequilibrium statistical mechanical theory for dense gases. II. Transport coefficients to first order in the density

Using the two-body distribution function found earlier by the authors with the aid of new boundary conditions, the kinetic equation and the transport coefficients are obtained to zeroth and first order in the density. To zeroth order we recover the Boltzmann kinetic equation. To first order the resulting expressions differ from the ones obtained by Choh and Uhlenbeck, due to effects of the medium.3 Reference 2 will be referred to as I. Here we use the same notation as in I.