Volume 45, Issue 10, 15 November 1966
Index of content:
Transport Properties of Polyatomic Fluids. IV. The Kinetic Theory of a Dense Gas of Perfectly Rough Spheres45(1966); http://dx.doi.org/10.1063/1.1727365View Description Hide Description
The Enskog theory of transport in a dense gas is applied to the rough‐sphere model. A formal analog of the Chapman—Enskog method is developed in order to construct the normal solution of the corresponding kinetic equation. Accurate estimates are given for the coefficients of shear and bulk viscosity and of thermal conductivity. A procedure is provided for computing the coefficient which characterizes the antisymmetric portion of the stress tensor and also for estimating the coefficients of proportionality between the flux of spin angular momentum and the gradient of the local spin velocity. Numerical values are given for these and other transport coefficients and characteristic relaxation times. A study is provided of the hydrodynamical significance of antisymmetric stress and of spin flux. Finally, the theory of this paper is compared with other, rather more heuristic, methods.
45(1966); http://dx.doi.org/10.1063/1.1727366View Description Hide Description
The melting curves of the sodium halides have been determined to 40 kbar. The present curves for NaCl and NaF are in agreement with Clark's corrected curves to 17 kbar, but the agreement for the other sodium halides is less good. There are no triple points on the melting curves to 40 kbar and it is concluded that the transitions found previously in NaF and NaCl near ∼20 kbar, if real, are metastable and shear induced.
45(1966); http://dx.doi.org/10.1063/1.1727367View Description Hide Description
EPR studies at X‐band frequencies have been carried out between 300° and 77°K on amorphous and crystalline selenium. Dominating the spectra of the amorphous material were a large number of paramagnetic centers ∼1019/cc which contribute to an unusually broad and inhomogeneous line of width, ΔHp p ∼3Kg and g=2.3 to 2.8±0.01. The linewidths and g values were very sensitive to heat treatments. This broad line is attributed to electrons at chain ends in a highly disordered region of the solid. A different species was also present in much lower concentrations ∼1013/cc, as observed by a sharp resonance with peak‐to‐peak linewidth, ΔHp p ∼6 G and g=2.0039±0.0006, which is close to the g value of 2.0023 for a free electron.Heat treatments altered the magnitude of the signal in an erratic manner and up to ∼1016/cc spins were observed with no changes in ΔHp p or g value. The identification is rather uncertain. Theoretical considerations of the g value and linewidth favor a center associated with an impurity (i.e., oxygen) at the end of the selenium chain but have shown that a chain end interacting with a neighboring chain cannot be ruled out. Experimental results tending to minimize the role of oxygen were that no conclusive differences were observed when samples were heat treated in air or vacuum or prepared by evaporation, and the appearance of a virtually identical resonance when single crystals of hexagonal selenium were damaged (mechanically and by electron bombardment).
No resonances were found in pure ``as grown'' monoclinic or hexagonal selenium. This result was unexpected for the latter material, and chemisorption of oxygen on the surface is thought to be the explanation.
45(1966); http://dx.doi.org/10.1063/1.1727368View Description Hide Description
The electronic structures of various sulfur and selenium radicals were studied by semiempirical molecular orbital theory in the form of a parameter theory. The ESR data (g values) were used to determine the actual value of the parameter α, which is the coefficient of the s orbital in the bonding hybrid of the S(Se) atom in the radical. The physical significance of α so determined was studied by investigating some quantum chemical quantities such as valence state energies Ev and bond strengths B as functions of α. As a result, a criterion for the determination of the parameter value was deduced, namely, the selection of that value of α which maximizes B 2 | Ev |.
From theoretical considerations and experimental data in the literature, the relative signs of the principal values of the hyperfine‐structure tensor of selenium were determined, and the magnitudes of the isotropic and anisotropic components were evaluated.
45(1966); http://dx.doi.org/10.1063/1.1727369View Description Hide Description
The g values of several possible models for paramagnetic centers in amorphous selenium are calculated by the method described in the preceding paper. The results of that paper show that the electron spin resonance lines of amorphous selenium reported to date cannot be attributed to free chain ends because of the disagreement in the calculated and observed g values. In this paper, we invoke interaction between the chain end and other atoms, including those in the same chain and in a neighboring chain, as well as impurities. The results show that the most probable source of the sharp line with g=2.0039±0.0006 is an oxygen impurity terminating the chain; the broad line with larger g values (2.3 to 2.8±0.01) can be interpreted as inhomogeneously broadened by pairs of interacting chain ends.
45(1966); http://dx.doi.org/10.1063/1.1727370View Description Hide Description
The shape of emission bands is determined by the vibrational‐energy distribution of the luminescence centers and by the form of the potential curves. A new potential is introduced, permitting us to establish the intensity distribution within a band as a function of frequency and temperature. The calculations are based on a semiclassical approximation of the Franck—Condon factors and are worked out with the aid of the Mehler formula. The obtained expression is in close agreement with the experimental results.
45(1966); http://dx.doi.org/10.1063/1.1727371View Description Hide Description
The preparation of two types of anthracene dimer is described and their absorption and fluorescence spectra are reported. The basic spectral features of each dimer, together with a consideration of the method of formation, enable us to assign a geometry to each pair. One dimer, prepared by photolytic dissociation of dianthracene, has a symmetrical sandwich configuration. The geometry of the other dimer, prepared in solution at low temperatures, is deduced from an analysis of the vibronic structure of its first absorption band (1 A 1g →1 B 2u transition of a single molecule) using the theory of vibronic coupling in dimers. The two molecules have a configuration related to that of the two molecules in the unit cell of the crystal; one in which the short in‐plane axes make an angle of 55 deg with each other while the long axes are parallel. The resonance splittings of the 1 B 2u and 1 B 3u states in each dimer are deduced from the spectra and the results are discussed in relation to the theories of the energy levels of dimers. The fluorescence of the sandwich dimer is of the excimer type while the fluorescence from the other dimer is excited dimer emission with a vibrational intensity distribution different from that in the corresponding monomerspectrum.
45(1966); http://dx.doi.org/10.1063/1.1727372View Description Hide Description
The absorption and fluorescence spectra of seven sandwich dimers of substituted anthracenes are reported. The absorption spectra of dimers of 9‐methyl‐, 9‐chloro‐, 9‐bromo‐, and 9‐cyanoanthracene are consistent with a symmetrical sandwich configuration. The resonance splittings are about 400 cm−1 for the 1 A 1g →1 B 2u transition (of anthracene) and about 1500 cm−1 for the 1 A 1g →1 B 3u transition. The dimers of 9,10‐dichloroanthracene and 9,10‐dibromoanthracene have absorption spectra consistent with a rotated sandwich configuration; the angle between the molecular axes is 61 deg for the dichloro compound and 73 deg for the dibromo compound. The spectrum of the mixed sandwich dimer of anthracene and 9,10‐dichloroanthracene is interpreted on the basis of a ``symmetrical'' sandwich configuration. The 1 B 3u electronic states are completely mixed by orbital overlap and only one absorption band is observed. On the other hand the spectral features of both monomer transitions to the 1 B 2u state are present in the spectrum of the dimer. The fluorescence spectra of all the sandwich dimers are of the excimer type and the fluorescence yield, relative to that of the monomer, is decreased markedly by the heavy‐atom substituents. The relevance of the experimental results to the theories of the energy levels of dimers and excimers is discussed critically.
Photodimerization of Crystalline Anthracene. The Photolytic Dissociation of Crystalline Dianthracene45(1966); http://dx.doi.org/10.1063/1.1727373View Description Hide Description
The photodimerization of anthracene dispersed in potassium bromide matrix has been reinvestigated. The hydrocarbon is shown to be present as ordinary crystalline anthracene. Dianthracene, prepared in potassium bromide discs, can be photolytically dissociated at low temperatures to give a new sandwich crystal form of anthracene which has a yellow‐green excimer fluorescence. This crystal structure can also be used to explain recent studies of the fluorescence of crystalline anthracene under high pressure.
45(1966); http://dx.doi.org/10.1063/1.1727374View Description Hide Description
The McWeeny theory has been used to calculate the shielding parameters for polycyclic hydrocarbons up through four rings. These results are presented along with experimental values, some of which come from new analyses of 100‐Mc/sec NMR spectra of these compounds, and semiquantitative agreement is observed. The Jonathan—Gordon—Dailey semiempirical equation for spin—spin coupling constants is also subjected to further test by new data. Absence of inter‐ring spin—spin coupling is reconfirmed.
45(1966); http://dx.doi.org/10.1063/1.1727375View Description Hide Description
Total cross sections were calculated for collisions of polar molecules. They were found to be determined chiefly by the rotationally inelastic collisions occurring at large impact parameters and to be highly sensitive to the amount of energy transferred from translation to rotation. The calculations were done by using either the Born approximation or a semiclassical method based on time‐dependent perturbation theory to obtain the scattering matrix for large impact parameters (both methods yield the same results). Scattering at smaller impact parameters was handled using a generalized Massey—Mohr treatment. The cross sections were found to be large and strongly dependent on the rotational states. Averaged cross sections were calculated for Boltzmann distributions of rotational states. These depend, as expected, on both the rotation constants and on the rotational temperature. Cross sections for linear dipoles such as alkali halides scattered by CH3I are around 4000 Å2. Cross sections for two symmetric tops are much higher. The averaged velocity derivative is quite different from that found for atom—atom scattering. A calculation of the second‐order elastic scattering was done for the case where the rotational energy levels of the two molecules are badly mismatched. Comparison is made with several other treatments which use the sudden approximation or some sort of averaged potential. The methods developed here are also applicable to scattering of polarized beams or to the calculation of small‐angle inelastic scattering.
Dipole—Dipole Scattering in Molecular Beams. Variation of Total Cross Section with Velocity and Rotational Overlap45(1966); http://dx.doi.org/10.1063/1.1727376View Description Hide Description
Total cross sections were measured for scattering of velocity‐selected beams of alkali halide molecules KCl, CsCl, and CsBr by HBr and CH3I and, for comparison, for Kr and Xe. The pressure in the scattering chamber was monitored by a second crossed beam of alkali atoms, which allowed direct measurement of the ratios of cross sections for different molecules interacting with the same scattering gas. As expected from the first‐order selection rules, the results indicate that the contribution of rotationally inelastic transitions produced by the angle‐dependent dipole—dipole force depends strongly on the extent to which the rotational spectra of the two molecules overlap. Inelastic scattering appears to be dominant for the CH3I systems, where the overlap is very good. The cross sections are ∼5000 Å2 (compared with ∼1400 Å2 for elastic van der Waals scattering; both corrected for angular resolution) and the velocity dependence is much weaker than for elasticscattering. In the Appendix simple approximate formulas are derived from which the first‐order inelastic dipole—dipole cross section can be calculated without numerical integrations over impact parameters and rotational distributions.
Radiation Chemistry of Liquid Sulfur Dioxide. II. Radiation‐Induced Oxidation—Reduction Reactions in Liquid Sulfur Dioxide Solutions of Sulfur Trioxide and Potassium Iodide45(1966); http://dx.doi.org/10.1063/1.1727377View Description Hide Description
Irradiation by 60Co gamma rays of dilute solutions of sulfur trioxide in anhydrous, air‐free liquid sulfur dioxide confirms that (1) molecular oxygen is formed by attack of radicals on sulfur trioxide, most likely via O+SO3→SO2+O2, (2) no measurably significant amount of O2 is formed by radical recombination O+O→O2 in the spurs. Irradiation of air‐free anhydrous solutions of potassium iodide in liquid sulfur dioxide yields iodine and potassium bisulfate K2S2O7 at constant rates and to high percents of conversion of iodide to iodine. The data are discussed in terms of electron‐transfer reactions from the charge‐transfer complex iodide anion—sulfur dioxide to the oxygen atom. The possibility of reactions of iodide ion with ionic species which have been suggested to arise in liquid sulfur dioxide during radiolysis is considered briefly. The difference between the radiation chemistry of liquid sulfur dioxide on one hand and those of water and liquid ammonia on the other is believed to be a consequence of the radical scavenging properties of liquid sulfur dioxide.
On the Existence of Conformers of Cyclobutyl Monohalides. III. Assignments of the Fundamentals of Bromocyclobutane and Chlorocyclobutane45(1966); http://dx.doi.org/10.1063/1.1727378View Description Hide Description
The infrared spectra of the liquid and the vapor and the Raman spectra of the liquid of bromocyclobutane and chlorocyclobutane are reported. The 30 fundamentals of each halide are assigned and an approximate picture of the motions of those atoms, which are mainly involved in the fundamental modes, is given. There is one‐to‐one correlation between the fundamentals of bromocyclobutane with the fundamentals of chlorocyclobutane. This signifies that the amount of interaction between different modes is generally of the same order of magnitude in both halides, in contrast to the corresponding cyclopropyl halides. There is little symmetry correlation between the fundamentals of the cyclobutyl halides and cyclobutane; the out‐of‐plane ring‐bending (ring‐puckering) mode is an exception. In the Appendix, computer calculations of A‐ and C‐type band envelopes are presented and compared with observations; the computations include vibration—rotation interaction.
Optical Spectra of Divalent Manganese Salts. I. Energy Levels for Cubic and Lower‐Symmetry Complexes45(1966); http://dx.doi.org/10.1063/1.1727379View Description Hide Description
An extensive study of the optical absorptionspectra of Mn(II) salts is introduced with a re‐examination of the nature of crystal‐field independent transitions and their dependence upon slight changes in ligand positions. Evidence for an unexpected but significant decrease in metal—ligand bond lengths for the 4 A 2 state with respect to those for 6 A 1 equilibrium ground state is obtained both from experiment, in terms of the excitation of totally symmetric displacements, and from approximate calculations. The latter involve both an extended formulation of the nephelauxetic effect and molecular orbital (MO) parameters obtained by a semiempirical LCAO MO scheme. A classification scheme for crystal‐field independent transitions, not necessarily in Mn(II) complexes, is introduced, and is based on the type of molecular orbitals, σ, π, or both, appearing in the exchange integrals associated with the transition energies. Low‐symmetry effects, especially for the 4 E states, are discussed.
45(1966); http://dx.doi.org/10.1063/1.1727380View Description Hide Description
We examine the ground‐state energy ε(λ) for two electrons bound to an infinite‐mass point nucleus regarded as a function of the complex coupling constant λ for the interelectron interaction. In the units used, the ground states of the homologous series H−, He, Li+, Be++, ···, correspond, respectively, to λ=1, ½, ⅓, ¼, ···, so the λ power‐series expansion of ε(λ) is equivalent to the familiar expansion in inverse nuclear charge Z −1. It is argued that the power series has a finite radius of convergence imposed by the existence of a branch point on the positive real axis at λ=λ*≅1.1184 with exponent approximately 6/5. Furthermore, ε(λ*) apparently lies above the continuum limit, but still corresponds to a localized wavefunction.
Determination of Hydrogen‐Atom Concentration by Lyman‐α Photometry. I. Oscillator Strength of the Hydrogen‐Atom Transition. II. Kinetics of the Reaction of Hydrogen Atoms with Acetylene and Ethylene45(1966); http://dx.doi.org/10.1063/1.1727381View Description Hide Description
A photometric method of determining hydrogen‐atom concentration in the gas phase has been developed. It consists of a hydrogen—neon lamp emitting Lyman‐α radiation at 1216 Å, and a nitric oxide‐filled ion chamber which serves as the detector. A fast‐flow system with a microwave discharge in an H2–He mixture was used as the source of hydrogen atoms. This arrangement permits the determination of H‐atom concentrations of 1011 atoms/cc. A photometric calibration curve was obtained by using titration with NO2 as an absolute measure of H‐atom concentration.
The oscillator strength of the Lyman‐α transition was determined with this apparatus. Depending on the assumed profile of the emission line and the extent of self‐reversal in the source,oscillator strengths of 0.4 to 1.1 (compared with the theoretical value of 0.8324) were obtained.
Rates of reaction of H atoms with ethylene and acetylene were determined at various total pressures and concentrations of reactants. Both reactions are first order with respect to each reactant, and the recombination of H atoms contributes very little to their rate of disappearance. The pressure effect on the reaction with ethylene depends on the formation of vibrationally excited ethyl radicals which either decompose to form reactants or are stabilized by collision. The reaction with acetylene appears to be complicated by a pressure‐independent reaction path which predominates at low pressures and is most probably the abstraction reaction H+C2H2→H2+C2H.
45(1966); http://dx.doi.org/10.1063/1.1727382View Description Hide Description
A comparison of experimental and theoretical vibrational collision numbers has been carried out for deuterium and hydrogen and also for interactions of those gases with argon and krypton. Agreement is obtained for the latter while definite discrepancies appear for the D2—D2 and H2–H2 interactions. This discrepancy is rather large at the lowest temperatures; however, extrapolation of the experimental data indicates that at temperatures of the order of 10 000°K agreement is attained.
The intermolecular interaction constants used in comparing theory and experiment are shown to be consistent with those derived from measurements on rotational relaxation times for hydrogen and hydrogen—rare‐gas mixtures. Using these interaction constants a value of 67 collisions is obtained for the rotational collision number of hydrogen in the limit of very high temperature.
45(1966); http://dx.doi.org/10.1063/1.1727383View Description Hide Description
The microwave spectrum of carbamyl fluoride, H2 14N12COF, has been studied. The rotational constants are A = 11 304.39 Mc/sec, B = 11 176.14 Mc/sec, and C = 5616.06 Mc/sec. The quadrupole coupling constants have been determined from the splittings of low‐J transitions. These are eQqm = −4.05 Mc/sec and η=−0.165. Two components of the dipole moment were determined and are μ a = 3.33 D and μ b = 2.31 D. No excited‐state spectrum was observed.
45(1966); http://dx.doi.org/10.1063/1.1727384View Description Hide Description
A simple hard‐core system is studied over the entire density range. The model embodies both the simplicity associated with a nearest‐neighbor lattice‐gas interaction and the realism of a continuous configuration space.
In two dimensions the model system shows no signs of a first‐order phase transition. In three dimensions a transition is indicated.