L. Monchick

Transport Properties of Polar Gases

A model is proposed for the calculation of viscosity, diffusion, thermal diffusion, and the translational part of the heat conductivity of dilute polar gases. It is assumed that the molecular‐collision trajectories are negligibly distorted by transfer of internal rotational energy, and that the relative orientation of two colliding dipoles remains fixed throughout the significant portion of the collision trajectory around the distance of closest approach. For this model, the Chapman‐Enskog theory retains its usual form, but the collision integrals which appear must be averaged over all possible relative orientations occurring in collisions. Collision integrals have been calculated for the Stockmayer (12–6–3) potential, [open phi](r)=4e0[(σ0/r)12−(σ0/r)6+δ(σ0/r)3], for kT/e0 from zero to 100 and for δ from —2.5 to +2.5, and averaged over all orientations (assumed equally probable). Sufficient collision integrals are tabulated that the convergence error of the Chapman‐Enskog theoretical expressions is not a...

Heat Conductivity of Polyatomic and Polar Gases

The formal kinetic theory of Wang Chang and Uhlenbeck and of Taxman has been used to derive explicit expressions for the heat conductivity of polyatomic and polar gases. By systematic inclusion of terms involving inelastic collisions the usual modified Eucken expression is derived as a first approximation, and as a second approximation an expression involving the relaxation times for various internal degrees of freedom (as well as the viscosity, diffusion coefficients, and heat capacity). For polar gases a second effect is often important in that a resonant exchange of rotational energy is possible.The comparison of experimental results with those calculated using empirical values of relaxation times is generally satisfactory, and most of the previously noted anomalies in the ratio f=λM/ηCv are accounted for quantitatively.

FORMAL KINETIC THEORY OF TRANSPORT PHENOMENA IN POLYATOMIC GAS MIXTURES

A rigorous formal kinetic theory of multicomponent polyatomic gas mixtures is derived. The methods are essentially a combination of those used by Chapman and Enskog for monatomic gases (as extended to multicomponent mixtures by Curtiss and Hirschfelder), and those used by Wang Chang and Uhlenbeck for a single polyatomic gas for the case where the equilibration between internal and translational degrees of freedom is easy. The calculations correspond to the first approximation in the classical Chapman—Enskog theory. Expressions are derived for the coefficients of shear viscosity, volume viscosity (which is proportional to a relaxation time), ordinary diffusion, translational and internal thermal conductivity, and thermal diffusion. Although the results are rather formal, a number of useful conclusions about the effects of inelastic collisions can be drawn without the necessity of detailed calculations. For instance, it is comparatively simple to show that inelastic collisions have very little effect on she...

Collision Integrals for the Exponential Repulsive Potential

The exponential potential function, Ae−r/ρ long has been regarded as the true qualitative form of the repulsive intermolecular potential at moderately small internuclear distances (or equivalently, high temperatures). Because of the increasing interest in gases at high temperatures it has become desirable to be able to evaluate the transport properties under these conditions. The calculation of integrals related to the usual collision integrals Ω(l,s) and cross sections Q(l) have been carried out for the exponential repulsive potential. Some high‐temperature viscosities have been calculated and compared to the calculated results of Amdur and Mason which are based on an experimental scattering potential.

Transport Properties of Polar‐Gas Mixtures

A previously proposed model for the calculation of viscosity, diffusion, and thermal diffusion in dilute polar gases is extended to mixtures. A simple set of combination rules for the potential parameters is discussed. Available data limit the comparison of calculation and experiment to binary mixtures of a polar and a nonpolar gas. The agreement exhibits a success comparable to that obtained for models and combination rules involving only nonpolar gases. It is concluded that the present model and combination rules can be used to describe the transport properties of mixtures with a fair measure of success, and that any attempts to refine the combination rules should await more experimental results of high accuracy, especially results on thermal diffusion and diffusion.

Thermal Diffusion in Polyatomic Gases: A Generalized Stefan—Maxwell Diffusion Equation

A study is made of the influence of inelastic processes on thermal diffusion in polyatomic gases, based on the Wang‐Chang—Uhlenbeck—deBoer treatment of the Boltzmann equation, in which it is assumed that the distribution function for molecular spins is isotropic. A generalized Stefan—Maxwell diffusion equation is obtained for multicomponent mixtures of polyatomic gases, carried to the second Chapman—Enskog approximation. The external form of this equation is the same as the well‐known result for monatomic gases, but contains higher‐order corrections for the binary diffusion coefficients (i.e., the composition dependence of these coefficients), and correction terms for the effect of inelastic collisions on the diffusion and thermal‐diffusion coefficients. Numerical calculations for several selected systems show that the effects of inelastic collisions on the thermal‐diffusion factor are not negligible and must be considered in any attempt to derive information on intermolecular forces from thermal‐diffusio...

On the theory of chemically induced electron polarization (CIDEP): Vector model and an asymptotic solution

It is shown that the stochastic–Liouville model of CIDEP can be cast into the form of a ’’Bloch‐type’’ equation with diffusion. This leads to a generalized vector model of the radical pair mechanism of chemically induced magnetic polarization, which gives a clear picture of the qualitative features of both CIDNP and CIDEP. For the case of simple Brownian motion of the two radicals the differential form of the stochastic–Liouville equations of CIDEP is readily converted into a single integral equation. In the limit of slow singlet–triplet mixing by the magnetic spin Hamiltonian, and with an exchange interaction that decays exponentially with radical separation, this integral equation may be solved exactly. The electron polarization then takes the form of a superposition of an infinite number of ’’contact exchange modes’’.

Theory of chemically induced magnetic polarization. Effects of S–T±1 mixing in strong magnetic fields

Chemically induced magnetic polarization due to mixing of the singlet and MS=±1 triplet sublevels of a diffusing radical pair in a strong magnetic field is investigated by an approximate stochastic Liouville model which considers separately the two‐level S–T−1 and S–T1 mixings. As previously found for S–T0 mixing, the stochastic Liouville equations for S–T−1 level mixing can be written as a Bloch‐type equation with diffusion, and a similar equation for the S–T1 mixing can be obtained simply by changing the sign of the magnetic field. These equations give a simple vector model of chemically induced polarization by S–T±1 mixing, including the all‐important diffusion through the S–T−1 level crossing. For simple Brownian diffusion and an exchange interaction that decays exponentially with radical separation, the stochastic Liouville equations for S–T−1 mixing can be converted to a single integral equation for the resulting polarization, and a similar equation can be derived for the S–T1 case. The polarization...

Validity of approximate methods in molecular scattering: Thermal HCl–He collisions

Accurate close coupling scattering calculations are presented for thermal energy HCl–He collisions. The interaction potential is obtained from the Gordon–Kim electron gas model, adjusted to have the correct long‐range multipole form. A variety of phenomenological cross sections are computed from the close coupling S matrix, and these are compared with results from several commonly employed approximate methods. In particular, it is found that the total integral, total differential, and gas kinetic cross sections are accurately predicted by the central field approximation which retains just the spherical average of the interaction. Integral inelastic cross sections are represented quite accurately by the coupled states approximation of McGuire and Kouri, but only qualitatively by the effective potential method of Rabitz. Pressure broadening cross sections from the close coupling calculation are in much better agreement with experiment than either Anderson theory calculations or the classical trajectory stud...

Thermal Diffusion in Polyatomic Gases: Nonspherical Interactions

The thermal‐diffusion factor αT, of polyatomic gases is reconsidered and the assumption is dropped that the differential scattering cross section is independent of the entrance and exit channels in inelastic collisions. In addition to the linear relation previously found, linking αT to the partial translational thermal conductivities of the constituents, a new term arises relating αT to the partial internal thermal conductivities. Estimates of this new coupling coefficient were made using the loaded sphere model and an approximate analysis of the thermal separation of ortho‐ and parahydrogen. They both indicate that this coefficient is very small and ordinarily does not contribute much to the total thermal‐diffusion factor. It is shown, however, that there are some situations in which this term becomes dominant. To first order in the eccentricity of isotopic series of diatomic molecules, αT turns out to be proportional to the difference of the moments of inertia, an empirical relation observed by many inv...