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A perturbation correction term for the effect of attraction forces on the equation of state is calculated and combined with previous statistical-mechanical analytical equations of state proposed by Song and Mason and by Ihm, Song, and Mason. The major effect of the correction on the p–v isotherms occurs in the metastable and unstable regions (the ‘‘van der Waals loops’’), with the result that the vapor pressures and orthobaric densities predicted from the Maxwell equal-area construction are greatly improved in accuracy. Comparison is made with experimental data for 13 selected nonpolar fluids (Ar, Kr, Xe, N2, O2, CO2, CH4, C2H6, C3H8, n-C4H10, i-C4H10, C2H4, and benzene) and one slightly polar fluid (toluene). Densities in the stable region of the p–v–T surface are accurate to about 1%–2% in the dense fluid region, and to better than 1% in the low-density gas region; the accuracy is slightly better than that achieved without the perturbation correction. Vapor pressures are predicted with an accuracy of about 2%, with orthobaric densities that are accurate to about 2% for the saturated vapor and to better than 1% for the saturated liquid. As usual for analytical equations of state, the critical region is described less accurately. In principle, the entire fluid equation of state and its vapor–liquid phase boundaries can be calculated from the intermolecular potential plus a few liquid densities. If the potential is not known, measurements of the second virial coefficient as a function of temperature can be used instead; in the absence of any such measurements, the calculation can use as input only the critical temperature, the critical pressure, and the Pitzer acentric factor, with only slight loss of accuracy. Comparison is also made with several widely used empirical equations of state. The present equation of state can be extended to include mixtures, but numerical computations on mixtures are... [ABSTRACT FROM AUTHOR]

Potential energy curves for the three lowest states of HeNe+(X 2Σ1/2+,A1 2Π3/2,A2 2Π1/2) are determined from a combination of mobility and spectroscopic measurements, in conjunction with a theoretical expression giving the A1 curve in terms of the X and A2 curves plus the energy splitting between the 2P3/2 and 2P1/2 states of Ne+. The results are also consistent with measurements of the scattering of beams of fast Ne+ ions by He gas. The best available ab initio potentials give mobilities in poor agreement with experiment, largely because of poor predictions of the positions of the potential minima. It is also shown that, contrary to initial expectations, mixture formulas for mobility based on simple momentum-transfer theory are valid for open-shell systems with multiple interaction potentials. Illustrative calculations are given for the mobility of Ne+ in a He+Ne mixture; both HeNe+ and Ne2+ have multiple potentials. [ABSTRACT FROM AUTHOR]

A universal scaling scheme is developed for closed-shell interactions. The exchange energies (total energies minus the Coulombic energies) are found to scale with two parameters to universal interaction curves for noble gas–noble gas, alkali ion–noble gas, and halogen ion–noble gas interactions. The interaction potentials constructed from the universal interaction curves agree well with experimentally determined potentials, and also successfully reproduce measured ion mobilities and diffusion coefficients. The universal interactions can be viewed not just as a correlation scheme, but also as operating to extend the range of the potentials for a number of ion–atom systems to both larger and smaller distances than are presently probed by direct measurements. They also provide the basis for predictions of potentials for systems lacking experimental measurements. In the case of the noble gases, they reduce by two the number of parameters required for the formulation of an accurate extended principle of corresponding states. [ABSTRACT FROM AUTHOR]

We present an analytical equation of state based on statistical-mechanical perturbation theory for hard spheres, using the Weeks–Chandler–Andersen decomposition of the potential and the Carnahan–Starling formula for the pair distribution function at contact, g(d+), but with a different algorithm for calculating the effective hard-sphere diameter. The second virial coefficient is calculated exactly. Two temperature-dependent quantities in addition to the second virial coefficient arise, an effective hard-sphere diameter or van der Waals covolume, and a scaling factor for g(d+). Both can be calculated by simple quadrature from the intermolecular potential. If the potential is not known, they can be determined from the experimental second virial coefficient because they are insensitive to the shape of the potential. Two scaling constants suffice for this purpose, the Boyle temperature and the Boyle volume. These could also be determined from analysis of a number of properties other than the second virial coefficient. Thus the second virial coefficient serves to predict the entire equation of state in terms of two scaling parameters, and hence a number of other thermodynamic properties including the Helmholtz free energy, the internal energy, the vapor pressure curve and the orthobaric liquid and vapor densities, and the Joule–Thomson inversion curve, among others. Since it is effectively a two-parameter equation, the equation of state implies a principle of corresponding states. Agreement with computer-simulated results for a Lennard-Jones (12,6) fluid, and with experimental p–v–T data on the noble gases (except He) is quite good, extending up to the limit of available data, which is ten times the critical density for the (12,6) fluid and about three times the critical density for the noble gases.As expected for a mean-field theory, the prediction of the critical constants is only fair, and of the critical exponents is... [ABSTRACT FROM AUTHOR]

A simple model is presented that describes the complex behavior of the magnetic field dependence of the thermal conductivity of a polyatomic gas as a function of the Knudsen number. The model treats the solid surface as one component of a gas mixture, and a first-order Chapman–Enskog solution is adequate to account for the thermomagnetic effects in single gases. The results provide an interpolation scheme between the continuum and Knudsen regimes, in the form of scaling rules in which the Knudsen number appears in the coefficients and arguments of the functions that describe the limiting cases. Good agreement is obtained with the available experimental data, and leads to the conclusion that different surface accommodation coefficients are needed for the translational and internal energies of the gas molecules. This conclusion is consistent with analysis of independent field-free conductivity data, and with independent vibrating-surface measurements. [ABSTRACT FROM AUTHOR]

Combination rules for dispersion coefficients are greatly extended by way of a parameter corresponding to an effective number of equivalent electrons, the same parameter N that appears in the Slater–Kirkwood formula for the dipole–dipole coefficient. The same N can be used for all members of an isoelectronic sequence, and new formulas are given for higher-order two-body dispersion coefficients and three-body nonadditive coefficients, in which the same N can also be used. The only additional input data needed are static multipole polarizabilities. A theoretical justification is given using screening-constant wave functions. Extensive empirical testing suggests that the results are usually accurate within about 5% for dipole coefficients and about 5%–10% for higher coefficients. The results apply only to S-state atoms and ions, but should be capable of extension to other systems. [ABSTRACT FROM AUTHOR]

Mobilities of O+ and O- ions in He gas have been measured as a function of electric field strength at temperatures from 93 to 568 K. The results are compared with previous work, and analyzed in terms of a temperature-field strength scaling rule and the O+–He and O-–He potentials. Emphasis is placed on how much information on the potentials can be obtained from simple features of the mobility curve without extensive numerical computation. [ABSTRACT FROM AUTHOR]

Ab initio potentials for the X 2Σ+1/2, A1 2Π3/2, and A2 2Π1/2 states of ArHe+ are tested as to their ability to describe swarm measurements of gaseous ion transport coefficients. Also tested are potentials based on spectroscopic measurements and model potentials chosen specifically so as to match the transport data. Ar+-ion velocity distributions in a drift tube containing a helium buffer are calculated from the potentials that best match the mobility data, by solution of the Boltzmann kinetic equation. The velocity distributions are used with estimated cross sections for the charge-transfer reaction Ar++N2 to calculate the effects upon the rate coefficients when the distribution differs from a Maxwell–Boltzmann form. The results indicate that the corrections are small at high buffer gas temperatures (293 K and above) and low to moderate electric-field strengths, but become larger at low temperature (82 K) and high fields. The smallness of the corrections confirms that previous rate coefficient measurements in a drift tube show a dependence of the Ar++N2 reaction upon the rotational temperature of N2. [ABSTRACT FROM AUTHOR]

We present a new strong principle of corresponding states that reduces the entire pressure–volume–temperature (p–v–T) surface of a nonpolar fluid to a single curve; this curve corresponds to an effective pair distribution function at contact as a function of reduced density. This reduction of a surface to a curve is based on statistical-mechanical theory, which also furnishes the algorithms for calculating, from the intermolecular pair potential, the three temperature-dependent parameters needed for the reduction. If the pair potential is not known, data on the second virial coefficient as a function of temperature can be used instead. The principle is tested on a computer-simulated Lennard-Jones (12,6) fluid, on the noble-gas fluids (except He), on N2, CO2, CF4, SF6, and on the first four alkanes. A suitable reciprocal plot yields virtual straight lines for all the real fluids, which differ in shape from the expected Carnahan–Starling curve that describes the (12,6) fluid; we suggest that these shape differences are caused by many-body forces in the real fluids. By curve fitting straight lines to the empirical data for the real fluids, we obtain a simple analytic equation of state, cubic in the density, that can be characterized by three constants: the Boyle temperature, the Boyle volume, and a slope constant. This equation is not accurate in the nonanalytic critical and two-phase regions, but otherwise describes the volumetric behavior of nonpolar fluids very accurately over the entire range from the dilute gas to the dense liquid. It has considerable predictive power, since it permits the construction of the entire p–v–T surface from just the second virial coefficient plus a few liquid densities. [ABSTRACT FROM AUTHOR]

Data on the internal pressure of hard-sphere and hard-disk fluids have been available for some time from computer simulations, even at densities above the freezing density. These results for the metastable fluids suggest that the pressure diverges at the density of random closest packing. However, our examinations of these data indicates that the divergence is characterized by a fractional exponent. We show that incorporating this nonanalyticity not only enables us to construct a semiempirical equation of state which is accurate at densities well beyond that of the Carnahan–Starling equation of state, but it enables us to predict a finite entropy at random closest packing. We also show that this kind of thermodynamic singularity implies that the direct correlation function becomes infinitely long ranged with a critical exponent remarkably similar to the percolation exponent. Given the difficulties inherent in simulating hard spheres at such densities, however, we do suggest that these findings be regarded with some caution. [ABSTRACT FROM AUTHOR]