Transport coefficients of dense fluids of molecules interacting according to a square well potential

A simplified kinetic theory is described for spherical molecules interacting according to a square well potential. The statistical premises of this theory correspond closely to those of Longuet-Higgins' and Pople's theory of dense fluids of rigid spheres. The thermal conductivity λ, shear viscosity η and bulk viscosity κ are predicted to be in the ratio where k is Boltzmann's constant and m the mass of a molecule. To calculate any of these coefficients absolutely requires independent information about the equilibrium pair distribution. This may be obtained from the self-diffusion constant D, whose value is also given by the theory. For argon the measured value of D leads to a theoretical value for η which is in good agreement with experiment; for this liquid however the observed ratio κ:η is very much smaller than predicted.     

Fluid mechanics revisited

Öttinger's recent nontraditional incorporation of fluctuations into the formulation of the friction matrix appearing in the phenomenological GENERIC theory of nonequilibrium irreversible processes is shown to furnish transport equations for single-component gases and liquids undergoing heat transfer which support the view that revisions to the Navier–Stokes–Fourier (N–S–F) momentum/energy equation set are necessary, as empirically proposed by the author on the basis of an experimentally supported theory of diffuse volume transport. The hypothesis that the conventional N–S–F equations prevail without modification only in the case of “incompressible” fluids, where the density ρ of the fluid is uniform throughout, serves to determine the new phenomenological parameter α^′ appearing in the GENERIC friction matrix. In the case of ideal gases the consequences of this constitutive hypothesis are shown to yield results identical to those derived theoretically by Öttinger on the basis of a “proper” coarse-graining of Boltzmann's kinetic equation. A major consequence of the present work is that the fluid's specific momentum density v is equal to its volume velocity v_v, rather than to its mass velocity v_m, contrary to current views dating back 250 years to Euler. In the case of rarefied gases the proposed modifications are also observed to agree with those resulting from Klimontovich's molecularly based, albeit ad hoc, self-diffusion addendum to Boltzmann's collision integral. Despite the differences in their respective physical models—molecular vs. phenomenological—the role played by Klimontovich's collisional addition to Boltzmann's equation in modifying the N–S–F equations is noted to constitute a molecular counterpart of Öttinger's phenomenological fluctuation addition to the GENERIC friction matrix. Together, these two theories collectively recognize the need to address multiple- rather than single-encounter collisions between a test molecule and its neighbors when formulating physically satisfactory statistical–mechanical theories of irreversible transport processes in gases. Overall, the results of the present work implicitly support the unorthodox view, implicit in the GENERIC scheme, that the translation of Newton's discrete mass-point molecular mechanics into continuum mechanics, the latter as embodied in the Cauchy linear momentum equation of fluid mechanics, cannot be correctly effected independently of the laws of thermodynamics. While Öttinger's modification of GENERIC necessitates fundamental changes in the foundations of fluid mechanics in regard to momentum transport, no basic changes are required in the foundations of linear irreversible thermodynamics (LIT) beyond recognizing the need to add volume to the usual list of extensive physical properties undergoing transport in single-species fluid continua, namely mass, momentum and energy. An alternative, nonGENERICally based approach to LIT, derived from our findings, is outlined at the conclusion of the paper. Finally, our proposed modifications of both Cauchy's linear momentum equation and Newton's rheological constitutive law for fluid-phase continua are noted to be mirrored by counterparts in the literature for solid-phase continua dating back to the classical interdiffusion experiments of Kirkendall and their subsequent interpretation by Darken in terms of diffuse volume transport.     

Vibronic interaction in the lower electronic states of benzene

Results of further calculations on the dynamic coupling between the lower B _1u and E _1u electronic states of benzene via a single e _2g mode are presented. In part I we gave the ‘pseudo-cylindrical’ solutions that result when the leading coupling term, linear in the nuclear displacements, is considered (cylindrical Born-Oppenheimer potential). Here we investigate the effect of

1. (1) the next higher terms in the expansion of the coupling hamiltonian for the free molecule (hexagonal Born-Oppenheimer potential);

2. (2) a crystal field anisotropy.

From the scanty data on the coupling constants available a priori it would follow that the refinement introduced by (1) is small for benzene. On the contrary, the effect of even a small crystal field anisotropy is predicted to be appreciable.

The results of the calculations are analysed by comparison with experimental data on the benzene crystal at low temperature. A consistent interpretation of both magnetic resonance results and the triplet ← singlet absorption spectrum is obtained.     

Theory of melting,vacancy model

A theory of melting based on vacancy model is formulated. The polymer solution theory is used for derivation of the melting equation for a two-species model of melting solid. Under simplifying assumptions the analysis leads to a simple correlation betweenT _m and 〈v〉, the average energy of interaction between the vibrating atoms. Pseudopotential method is used for calculating 〈v〉 for the alkali metals lithium, sodium, potassium and rubidium at temperatureT _m. The calculated values ofT _m〈v〉 are in accord with those expected from our model. Application to the high pressure melting curves of solids is also discussed.     

Pair exchange interaction in a crystalline nitroxide radical ESR study of dimers in the triplet state

The dimerization of the 9-aza-bicyclo (3,3,1) nonan-3-one-9-oxyl in the solid state is investigated by use of ESR spectroscopy. The ESR spectrum of a single crystal is characteristic of symmetric pairs of exchange-coupled radicals in a thermally accessible triplet state. The presence of well-resolved hyperfine structure is evidence for strongly localized excitations with a jumping rate lower than 10⁷ Hz.

The ESR spectrum is well described by the spin hamiltonian

At 35 GHz the observed splitting of the m _s=+ 1?0 transition has been found to be slightly different from that of the m _s=0?-1 one; this anomaly is explained by the mixing of the m _s electronic states.

The parameters and the principal directions of the zero-field splitting, spectroscopic and hyperfine tensors are determined and discussed. The principal directions of the dipolar tensor indicate a nearly equal spin density on the nitrogen and oxygen atoms; from the fine structure parameters D and E, determined to be (-0·0723 ± 0·0005) cm^-1 and (-0·0044±0·0003) cm^-1 at T=293 K respectively, it is suggested that the unpaired electron is partly delocalized on the molecule.

The singlet-triplet energy gap (J) and the zero-field splitting parameters are shown to be linearly temperature-dependent. These variations with temperature are attributed to the thermal expansion of the crystal lattice.     

Predissociation and photodissociation of IBr

The observed predominance of excited Br(² P _1/2) atoms in the nearultra-violet photodissociation products of IBr is shown to be quantitatively consistent with an intermediate coupling regime in the visible absorption region, which invalidates the traditional interpretation of the B′(O ⁺) state as a new Born-Oppenheimer state arising from a strongly avoided potential curve crossing. A general theory of predissociation at intermediate coupling, covering the positions, intensities and widths of the spectral lines, shows that both diabatic and adiabatic characteristics must be taken into account. The presence of a sharp level is predicted at any coincidence between an adiabatic and a diabatic term value with the same J value, and the spacing between neighbouring lines is shown to depend on an average between the diabatic and adiabatic rotational constants. The theory is successfully applied to the B(³Π _{o ⁺} ) and B′(O ⁺) states of IBr, and potential curves for the two states are reported. The analysis is consistent with the following curve crossing parameters r_x = 3·220 Å, E_x = 16 915 cm^-1, V ₁₂ = 170 cm^-1, and ΔF = 9178 cm^-1 Å^-1, and with the following spectroscopic constants for the B′(O ⁺) state of IBr⁷⁹: