Senftleben-Beenakker Effect Research Articles

Relaxation and transport of molecular systems in the gas phase

Some of the properties of gas phase relaxation and transport are reviewed with an emphasis on those properties that are due entirely to the presence of internal states in real molecular systems. The theoretical formulations of such non-equilibrium effects is based on the quantum Boltzmann equation. The conditions for the validity and the properties of this equation are reviewed. This includes a general discussion of how the combination of free molecule motion and collisions is required for the approach to global equilibrium. It is shown how the free motion is equivalent to a phase randomization of the elements of the density operator that are off-diagonal in energy. Spin relaxation and the magnetic field dependence (Senftleben-Beenakker effects) of the viscosity for a gas of diatomics are used to illustrate these aspects of the approach to equilibrium.

Comparison of classical trajectory and quantal close-coupling calculation of generalized cross sections for N2+-He mixtures

Quantal close-coupling calculations of the energy-dependent cross sections governing relaxation phenomena in depolarized Rayleigh scattering and nuclear magnetic resonance, and the Senftleben–Beenakker effect on viscosity, diffusion, and thermal conductivity have been performed for the system N+ 2–He. The corresponding classical expressions for these cross sections have been evaluated by the classical trajectory method and compared with the quantal results in the energy range 50 cm-1 to 838⋅6 cm-1. Excellent agreement is found for all 16 cross sections at the highest energy studied. While the agreement deteriorates for most of the cross sections at lower energies, the quantization errors for the field-free viscosity and diffusion cross sections, which have non-vanishing spherical limits, are within 3% for all energies considered.

Comparison of classical trajectory and quantal close-coupling calculation of generalized cross sections for N+2-He mixtures

Quantal close-coupling calculations of the energy-dependent cross sections governing relaxation phenomena in depolarized Rayleigh scattering and nuclear magnetic resonance, and the Senftleben–Beenakker effect on viscosity, diffusion, and thermal conductivity have been performed for the system N+ 2–He. The corresponding classical expressions for these cross sections have been evaluated by the classical trajectory method and compared with the quantal results in the energy range 50 cm-1 to 838⋅6 cm-1. Excellent agreement is found for all 16 cross sections at the highest energy studied. While the agreement deteriorates for most of the cross sections at lower energies, the quantization errors for the field-free viscosity and diffusion cross sections, which have non-vanishing spherical limits, are within 3% for all energies considered.

Comparison of quantum and classical calculations of thermal-conductivity cross-sections governing the Senftleben-Beenakker effect for HD-He mixtures

The classical approximation to nine cross-sections required for evaluating the mixture thermal conductivity and its magnetic-field dependence is tested by comparison with quantal close-coupling results for the HD-He interaction. Explicit results are given for the relation between the working expressions for the classical and quantal cross-sections as a function of total energy. At the highest total energy considered, 3000 cm-1, the agreement between the quantal and classical results is found to be good for all cross-sections considered, although it deteriorates as the energy is lowered to the j = 1 threshold energy, below which all the quantal results vanish. The cross-sections are thermally averaged for temperatures between 77·3 K and 298 K, and the difference between classical and quantal results is at most 11% at 298 K, with somewhat larger errors at lower temperatures. A hybrid scheme that interpolates between classical results above 3000 cm-1 and quantal results below 516 cm-1 is shown to yield accur...

Classical limits of generalized cross-sections for atom-molecule systems

The classical limits of the quantal generalized cross-sections for transport and line-broadening phenomena have been derived using classical S-matrix theory and various semiclassical expressions for the Wigner coefficients. For transport processes, these limits are found to be in agreement with those obtained from a direct classical approach. Explicit expressions are given for the Senftleben-Beenakker effect thermal-conductivity cross-sections.

Close-coupling calculations of transport and relaxation cross sections for H2 in Ar

Close-coupling calculations of effective cross sections for transport and relaxation processes in Ar+H2 mixtures are performed, using both the recent TT3(6,8) potential of Le Roy and Hutson and the older BC3(6,8) potential of Carley and Le Roy. The cross sections calculated are those involved in sound absorption, thermal diffusion, shear viscosity, pressure broadening and shifting of rotational Raman lines, depolarized Rayleigh light scattering, nuclear magnetic relaxation, and the Senftleben–Beenakker effects. Comparisons with experimental results are made wherever possible.

Classical trajectory calculations for anisotropy-dependent cross sections for He-N2mixtures

The classical expressions for kinetic theory cross sections which are related to the Senftleben-Beenakker effect on viscosity, diffusion, conductivity and thermal diffusion are evaluated using the HFD1 surface (R. Fuchs et al. (1984)) in the temperature range 77.3-1100K. The depolarised Rayleigh scattering and rotational-relaxation cross sections are also obtained. Comparisons with experiment show that the authors' values for these cross sections are 10-80% larger than the measurements. These consistent discrepancies suggest that this potential surface is too anisotropic.

Atom–diatomic molecule kinetic theory cross sections

Classical expressions for the generalized or kinetic theory cross sections for gases of diatomic molecules derived earlier are specialized to describe atom–diatomic molecules collisions and developed further. Numerical results based on parameters intended to describe Ar–N2 collisions are then presented and the resulting generalized cross sections are compared with those derived from experimental studies of the Senftleben–Beenakker effect on the viscosity of mixtures of argon and nitrogen. The results indicate that the experimental values may be reproduced using reasonable values of the anisotropy parameters.

The theory of viscous diffusion in the presence of a magnetic field

The diffusion flux occurring in an isothermal viscous flow of a rarefied binary gas mixture is studied within the framework of kinetic theory in first and second order Chapman-Enskog approximation. For polyatomic gases the diffusion flux is influenced by an external magnetic field because of the presence of angular momentum polarizations. Special attention is given to the dependence of this “viscomagnetic diffusion flux” on the orientation of the field with respect to the gas flow. As an application the field induced transverse diffusion flux in N2-He and N2-Ar mixtures at room temperature is calculated using data derived from other Senftleben-Beenakker effects. The results provide theoretical expressions for the bulk contribution of this phenomenon, to be compared with experimental results presented in a subsequent paper.

A comparison of the predictions of various model N2–He potential energy surfaces with experiment

Predictions of beam scattering and bulk gas phenomena based upon five different model potential energy surfaces for the N2–He system are compared with experiment. The surfaces considered are our recent HFD1 and HFD2 surfaces based on the Hartree–Fock plus damped dispersion (HFD) model, the surface of Habitz, Tang, and Toennies (HTT) based upon the Tang–Toennies model, the surface of Keil, Slankas, and Kuppermann (KSK) and a modification (KKM3) of the KSK surface. The physical observables against which these surfaces are tested include total differential scattering cross sections, state-to-state inelastic differential scattering cross sections, interaction second virial coefficients, shear viscosity and binary diffusion coefficients, and the relaxation cross section for the Senftleben–Beenakker effect on the shear viscosity. None of the surfaces is in complete agreement with all of these observables. For the interaction second virial coefficients, the shear viscosity and binary diffusion coefficients, the HFD1 surface is the only one to predict values within most of the experimental error bars. The relaxation cross section is correctly predicted only by the KKM3 surface which was essentially fitted to it. The HFD1, HFD2, and HTT surfaces are all in good agreement with the state-to-state inelastic cross sections. The KSK surface gives the best agreement with the total differential cross section. It appears that an accurate N2–He surface cannot be obtained from simple models, and its determination will require multiproperty fits.

Ab initio calculation of transport - orientation-phenomena (Senftleben-Beenakker effects) for HD infinitely dilute in helium

The effective kinetic cross sections governing the magnetic field influences (Senftleben-Beenakker effects) on viscosity, heat conductivity, diffusion and thermal diffusion as well as flow birefringence and the collisional broadening of the depolarized Rayleigh line have been evaluated for HD infinitely dilute in He in the temperature range between 20 K and 450 K. Starting point was a new He-HD anisotropic interaction obtained from the ab initio He-H 2 potential surface of Meyer, Hariharan and Kutzelnigg. The elements of the scattering amplitude matrix needed for the calculation of all effective cross sections have been obtained in close coupled procedures. Rotational levels of HD up to j=5 have been taken into account. As far as comparison with experiment is possible, full quantitative agreement is obtained. The inelastic contributions to the cross sections are shown to be mainly due to the strong P 1(cos θ)-anisotropy in the potential.

Theoretical studies of H2–H2 collisions. IV. Ab initio calculations of anisotropic transport phenomena in para-hydrogen gasa)

The temperature dependence of the effective Waldmann–Snider cross sections determining the Senftleben–Beenakker effects of viscosity and heat conductivity has been studied for pH2 gas between 10 and 200 K. From ab initio nonspherical potentials of H2–H2, scattering matrices have been determined in close-coupling calculations. From these, the elements of the scattering amplitude matrix have been obtained and used as input quantities for the evaluation of the various Waldmann–Snider collision integrals. The results of these first ab initio numerical calculations of anisotropic transport coefficients show excellent agreement of calculated and measured effective cross sections, especially for the most recent improved version of the interaction potential. In addition, it has been shown that the polarization production cross sections are quite sensitive to the potential anisotropy.

Classical S-matrix theory of viscomagnetic production cross section

The semiclassical theory of Marcus and Miller is applied to obtain an expression for the production cross section in the shear viscosity Senftleben-Beenakker effect, whose exact expression has been recently obtained by Liu et al. The result involves a multi-dimensional integral over a function of the orientation angles between the initial orbital angular momentum and the final rotational angular momentum, and in principle can be evaluated by a Monte Carlo procedure through the computation of classical trajectories.

Close-coupled and coupled-states calculation of shear viscosity SBE cross sections for the H2–He system

Close-coupled (CC) and coupled-state (CS) calculations of kinetic theory relaxation and production cross sections are presented for the system H2 at infinite dilution in a bath of He. Performing these calculations for the same potential has allowed a test to be made of the efficacy of the CS procedure for use in calculating kinetic theory cross sections, especially those determining the Senftleben–Beenakker effects (SBE) in transport phenomena. The CS procedure is found to work extremely well (better than 1% agreement with CC results) for those cross sections that are predominantly elastic, to work rather well for relaxation cross sections determined either by reorientation of energetically inelastic collisonal events (about 10% agreement with CC results), and to work relatively poorly for production cross sections. In fact, the CS procedure for light molecules fares only marginally better than the IOS procedure for heavier molecules in the calculation of production cross sections. Finally, using only CC results, the sensitivity of the shear viscosity SBE is shown to be sufficient to distinguish easily between two recently obtained ab initio potentials for the H2–He system.

Effect of magnetic field on heat flow in a polyatomic gas in intermediate pressure range

The effect of a magnetic field, B , on heat flow in a gas in an intermediate pressure range has been studied. The ratio of the heat flow changes in the fields B ⊥ ▿T and B ‖ ▿T was found to change nonmonotonically with pressure in N 2 and CO. With the decreasing pressure, a difference is observed between the dependence of heat flow on field orientation and the corresponding angular dependence in the limiting case Kn→0 ( Kn = l/L , l is the mean free path, L is the geometric size). An expression has been obtained for the heat flow in a magnetic field for Kn ≲ 0.1 from the solution of an integral kinetic equation. In particular, it has been shown that the special features of the Senftleben-Beenakker effect observed with the decreasing pressure arise not only due to spherically symmetric molecule-surface interaction, but also to nonspherical scattering on walls.

Kinetic cross sections in the infinite order sudden approximation

The translational-internal coupling scheme allows a factorization of energy-dependent and kinetic cross sections into internal and translational parts. WKB-IOS phase shifts for the N/sub 2/-Ar potential of Kistemaker and de Vries are used to calculate the translational factors. A T-matrix version of the theory based on calculating only downward collisions is used as an attempt to lessen the effect of ignoring energy inelastic effects in the phase shift computation. All kinetic cross sections associated with the viscosity Senftleben-Beenakker effect are estimated in this manner.

Anisotropic intermolecular potentials and transport properties in polyatomic gases

It is widely accepted that the ordinary bulk transport properties of polyatomic gases, such as the shear viscosity or the thermal conductivity, are predominantly determined by the isotropic part of the intermolecular interaction, so that it is difficult to utilize them directly as sources of or tests for intermolecular anisotropies. It is also widely known that the effects of external electric and magnetic fields on these same transport properties depend critically upon the anisotropies, e.g. they are nonzero only for anisotropic potentials. Thus, external field effects on transport properties, particularly their temperature dependence, provide an important source of data for testing and/or determining intermolecular anisotropies. Before such data can be utilized, however, it is necessary to have available exact relationships between the effective cross-sections determining these phenomena and the S-matrix elements obtained from scattering calculations, together with reliable numerical procedures for calculating the S-matrix elements. An illustration of Liouville space methods for carrying out the first step of this procedure is given for one of the cross-sections occurring in the thermal conductivity. The infinite-order sudden approximation is utilized to show the importance of taking into consideration the full potential surface when analysing ordinary bulk properties of systems. Results are given for binary mixtures of N2 and Ar. The results of a full close-coupled calculation of the thermal conductivity Senftleben–Beenakker effect (SBE) for the H2–He system are presented and discussed briefly.

The Senftleben-Beenakker effect in ammonia and its mixtures with noble gases

Experimental results are presented for the influence of a magnetic field on the viscosity of NH3-He and NH3-Ar and on the thermal conductivity of NH3-Ar gas mixtures. Data are reported for various mixture compositions at room temperature. The data are analyzed in detail in an attempt to clarify the unique behavior of ammonia.

Interpretation of ES, CS, and IOS approximations within a translational-internal coupling scheme. II. Application to atom–diatom kinetic cross sections

ES, CS, and IOS approximations to atom–diatom kinetic cross sections are derived. In doing so, reduced S-matrices in a translational-internal coupling scheme are stressed. This entails the insertion of recently obtained approximate reduced S-matrices in the translational-internal coupling scheme into previously derived general expressions for the kinetic cross sections. Of special interest is the structure (rotational j quantum number dependence) of the kinetic cross sections associated with the Senftleben Beenakker effects and of pure internal state relaxation phenomena. The viscomagnetic effect is used as an illustrative example. It is found in particular that there is a great similarity of structure between the energy sudden (and IOS) approximation and the previously derived distorted wave Born results.

Effective collision cross sections governing the effect of an external magnetic field on the thermal conductivity of a pure gas of linear molecules

Using Liouville-space algebra, general expressions are derived for the independent effective collision cross sections governing the thermal conductivity Senftleben–Beenakker effect in a pure gas of linear molecules. These cross sections are presented in terms of S-matrix elements in the total-J representation since it is particularly useful for the dynamical approximation procedures in current use.