Volume 22, Issue 10, 01 October 1954

A Proposal for Fundamental Equations of Dynamics of Gases under High Stress (A Proposal for Statistical Mechanical Treatment of Systems Not in Thermal Equilibrium Associated with Transport Phenomena)
View Description Hide DescriptionIn order to derive the fundamental equations of gas dynamics which are valid for the flow at high shearing stress and low gas pressure, an attempt was made to eliminate the assumption that the state concerned departs only slightly from thermal equilibrium, as we frequently find phenomena which cannot be treated under this assumption.
First, the state of gas in an intermediate volume element was microscopically represented in terms of the quantities of transport. Considering their averages over an intermediate time interval, an attempt was made to find the statistical character of the system. In other words, under the assumption that the macroscopic observation is possible or that the macroscopic law can be established, it was shown that the Boltzmann‐Planck method in a new sense is applicable to the present systems. The new distribution function thus derived, (where c denotes the velocity of a particle), should satisfy the Boltzmann‐Maxwell equation. This can be shown by means of Kirkwood's verification accepted in some extended meaning.
In solving the B‐M equation (hereafter, the B‐M equation is the abbreviation of the Boltzmann‐Maxwell equation) from this new standpoint, the stress components were taken together with mass density and velocity of mass motion as the independent variables in the zeroth approximation, although usually temperature is taken in place of stress. This method of treatment is analogous to that of Enskog and Chapman, although some important modifications are found in the latter half of the treatment. The fundamental equations of gas dynamics have been derived. Instead of viscosity and thermal conductivity, a new conception arises in the equations. That conception is conductivity of stress.

Thermodynamics of Adsorption
View Description Hide DescriptionThe thermodynamics of the adsorption of gases on solids is developed in terms of a two‐component system. It is shown that all solids swell during the adsorption process, and that spontaneous first‐order phase changes in the adsorbed layer are unlikely. The ideal process: i(gas) → i(adsorbed)—constant environment—is introduced and discussed; thermodynamic functions appropriate to the process are defined. Two types of heat capacity of the adsorbed layer are defined and discussed. The chemical potential of a solid is treated at some length.

Electronic Structure of Disordered One‐Dimensional Chains
View Description Hide DescriptionThe positions of the electronic levels in a variety of finite one‐dimensional models of disordered alloys and of liquids have been evaluated numerically over a wide range of energies. The disordered alloys consist of two types of potential wells thrown together in a random sequence, but in equal proportions. In the disordered case the tightly bound states give rise to narrow bands in which the distribution of states cannot be described by a smooth function. The distribution of states can be interpreted in terms of an approximation in which each electron is confined to its own group of adjacent identical atoms. At high energy levels the disordered alloys obey perturbation theory, at least in a qualitative fashion, and the ordered alloy differs from the disordered one because of the effect of Bragg reflections from the superlattice. At high energies the distribution of states can be described by a reasonably smooth density function. Between the high energy range and the tightly bound levels, in some of the cases a transition region occurs, in which the levels are distributed irregularly, but without well‐defined gaps and without being susceptible to the simple explanation of localized states. The total number of states (not counting the two spin possibilities as separate states) up to a well‐pronounced energy gap is always an integral multiple of one‐half the total number of atoms in the chain.
The liquids consist of a series of identical wells separated by a variable well‐to‐well space. In a liquid the forbidden energy ranges are either smaller than in the strictly periodic crystal, or else nonexistent. The extent to which an energy gap in the strictly periodic crystal will be affected by the introduction of dispersion in the spacing depends on the original gap width as well as on the sensitivity of the gap position, in the strictly periodic case, to uniform dilations. In both the liquid cases and the disordered alloy models a distinction must be made between energy ranges in which the density of states is very low and ranges in which it is strictly zero.

Neutron Diffraction Study of Liquid Mercury
View Description Hide DescriptionThe neutron diffraction pattern of liquid mercury at 23°C has been measured. The pattern has general resemblance to the x‐ray patterns obtained by Debye and Menke and by Jennings, although the angular resolution is not quite as good. The inner peak which has been reported by several investigators is not seen. The radial density function has been calculated from the data.

Excited States of the Naphthalene Molecule. I. Symmetry Properties of the First Two Excited Singlet States
View Description Hide DescriptionThe detailed polarizationproperties of the bands in absorption and fluorescence spectra of the naphthalene molecule have been determined by a method which makes use of a substitutional solid solution of naphthalene in durene. A single crystal of about 0.1 percent naphthalene in durene was cut so that the short axes of the naphthalenes lie strictly parallel to the surface and in one direction. The spectra were then determined in polarized light at 20°K under moderately high dispersion. The results clearly indicate that the first state is ^{1} B _{3u } (the transition from the ground state is long‐axis polarized) and the second ^{1} B _{2u }. Vibrational‐electronic interaction involving b _{1g } vibrations apparently couples the first state with the second, and this results in a large short‐axis polarized transition moment. This fact has been at the root of most of the previous difficulties with analysis of the spectra.

Lattice Dynamics of Body‐Centered and Face‐Centered Cubic Metallic Elements. II
View Description Hide DescriptionA numerical table is presented which permits the easy calculation of the Debye characteristic temperature of any cubic metallic element at 0°K. The use of the table presupposes a knowledge of the elastic constants, atomic volume, and density of the element at 0°K. The characteristic temperature can be evaluated for either of the theoretical cases described in an earlier paper by the author.

Microwave Spectrum and Properties of Vinylene Carbonate
View Description Hide DescriptionThe microwave spectrum of vinylene carbonate has been investigated in the region from 19 000 to 32 000 Mc/sec. Eight R‐branch transitions have been identified and fitted with the following spectroscopic parameters: a = 9346.79 Mc/sec, b = 4188.46 Mc/sec, c = 2891.54 Mc/sec, all ±0.10 Mc/sec; k = —0.59818. The dipole moment of the vapor, as determined from Stark effect studies, is 4.51±0.05D and lies in the a‐axis. The molecule has been shown to be planar. The significance of these results is discussed.

Vacuum Ultraviolet Photochemistry, Part I. Nitrous Oxide at 1470 A
View Description Hide DescriptionThe photolysis of nitrous oxide at 1470 A has been studied and the quantum yields measured for N_{2}O disappearance and NO, O_{2}, and N_{2} appearance. The average of 38 measurements gives φN_{2}O=1.7_{0}, φO_{2}=0.5_{0}, and φN_{2}=1.4_{4} with φNO being pressure dependent. The data obtained here can be explained by a mechanism involving initial dissociation of nitrous oxide into nitrogen molecules and oxygen atoms. The source of NO can be in the reaction O+N_{2}O→2NO. These results are discussed in the light of previous work.

Vacuum Ultraviolet Photochemistry, Part II. Nitrous Oxide at 1849 A
View Description Hide DescriptionThe photolysis of nitrous oxide at 1849 A has been studied and the quantum yield ratios φN_{2}O/φN_{2}, φN_{2}O/φO_{2}, and φN_{2}O/φNO measured. The former two ratios compare well with the same ratios at 1470 A and the latter ratio is pressure dependent. It appears that the photolysis mechanism at 1849 A is similar to that at 1470 A. The absorption coefficient of N_{2}O is calculated from the photolysis data and found to compare well with previous work.

Application of the Hertz Theory of Impact to Explosion Phenomena
View Description Hide DescriptionPressure and time of impact have been calculated by Hertz theory of impact, taking data from some experiments on explosion. The calculated temperature rise, by adiabatic compression of an entrapped gas bubble, is within a reasonable range of that obtained experimentally. The calculated times have been compared with experimental observations on impact explosion delays. The adiabatic compression of solids has been referred to.

Electron Trap Distributions in Phosphors
View Description Hide DescriptionThe possible interpretation of long lifetime phosphorescence decay in terms of the electron trap mechanism is briefly reviewed. It is then shown how the distribution of activation energies among filled traps may be computed from the experimentally observed decay curves. The decay curves can be expressed as a Laplace transform of the distribution density function for activation energies, and the latter can then be calculated by inversion of the transform. Several examples are given in illustration of the procedure. The limitations inherent in the procedure are briefly discussed, and it is pointed out how the method might be used to test the applicability of the simple electron‐trap model to experimental data.

Fluorescence of Nitrogen Dioxide
View Description Hide DescriptionThe mean lifetime of fluorescence of NO_{2} vapor was measured at pressures in the range 12 to 0.6 microns by a direct electronic method. A linear dependence of lifetime on pressure was found, and extrapolation to zero pressure gave 44 microseconds for the lifetime in absence of collisions. The fluorescencespectrum in the region 4600—8000 A was photographed with 4358 and 5461 A excitation, with somewhat different results. Interpretation of the results appears to require two excited electronic levels, one of which is not connected optically with the normal state and which is responsible for the long‐lived fluorescence.

Thermodynamics of Alcohol‐Hydrocarbon Mixtures
View Description Hide DescriptionThe thermodynamic properties of alcohol‐hydrocarbon mixtures are explained on the basis of association of the alcohol to form polymers of all orders from two to infinity. Our treatment differs from that of Redlich and Kister in using the Flory‐Huggins expression for free energy, and an equilibrium constant in terms of concentrations rather than mole fractions. The equations derived are in satisfactory agreement with vapor‐pressure data for several systems. They also agree with the experimental energy of mixing and excess entropy for ethanol‐methylcyclohexane solutions. For mixtures of alcohols with aromatic hydrocarbons, it is necessary to assume that each alcohol monomer or polymer can combine with one molecule of hydrocarbon.

Deviations from Additivity of the Intermolecular Field at High Densities
View Description Hide DescriptionThe intermolecular field of an assembly of neutral atoms or molecules is usually assumed to be additive with respect to isolated pairs. Nonadditive effects have been calculated in the first‐order forces by Rosen and in the second‐order forces by Axilrod and Teller. For the evaluation of second‐order forces between two molecules at high densities the zero‐order wave function must be made antisymmetric with respect to nearest neighbors. It is shown that this correction results in a decrease of the second‐order forces compared to an isolated pair of molecules, and may be interpreted as a screening effect. The method is based on the model of the caged atom or molecule.

Oxidation Ions in Hydrocarbons on Ultraviolet Irradiation
View Description Hide DescriptionUltraviolet irradiation, mostly in the presence of a peroxide, increases the electrical conductivity, thus produces oxidation ions in solutions of aromatic diols, to a lesser extent in those of monohydroxyl compounds, and to a still lesser, but measurable, extent in a hydrocarbon itself, namely o‐xylene. Ultraviolet spectroscopy permits identification of the chief oxidation products: o‐phthalic aldehyde in the case of o‐xylene. The ions are probably oxidation intermediates of relative stability. Whereas the anion can be derived from the acids, the cations are probably oxonium‐type ions, derivable from the o‐aldehydes formed.

Magnetic Dipolar Interactions in MnO and in Ferrites
View Description Hide DescriptionThe magnetic dipole energies of MnO and of the normal and inverse spinel structures are calculated. It is found that with this interaction alone MnO would have its direction of spin alignment in a (111) plane, in contrast to the experimentally found [100]. The addition of a nearest neighbor quadrupole interaction is suggested as a means of making the [100] direction preferred. The normal and the inverse spinel structures are found to have zero magnetic dipole energies.

N‐Particle Distribution Functions
View Description Hide DescriptionAn investigation of a certain class of approximate solutions of the Yvon‐Born‐Green recurrence relations for the lower‐dimensional molecular distribution functions has been presented, based on a particular mechanism of exclusion of interactions among ``clusters'' composed of successively larger number of molecules. This mechanism leads to a chain of equations for the approximate distribution functions which (a) converge to the exact molecular distribution function after a finite number of approximations, (b) are linear in the dependent variable just like the Yvon‐Born‐Green recurrence relations, and (c) are time reversible. The connection between these equations and certain natural generalizations of Boltzmann's equation to other than binary collisions is obtained. Finally the application of this hierarchy to certain problems of fluids at equilibrium has been indicated.

Millimeter Wave Spectra and Centrifugal Stretching Constants of the Methyl Halides
View Description Hide DescriptionHigh J transitions of the methyl halides have been measured and have been used to calculate accurate values for the centrifugal distortion constants.
The values obtained for B_{O}, D_{JJ}, and D_{JK} are (in Mc/sec and kc/sec, respectively); CH_{3}·F^{19}, 25 536.11, 59.3, 445; CH_{3}·Cl^{35}, 13 292.86, 18.1, 198; CH_{3}·Br^{79}, 9568.20, 9.9, 128.3; CH_{3}·Br^{81}, 9531.82, 9.7, 127.4; CH_{3}·I^{127}, 7501.30, 6.28, 98.5.
The new D_{JJ} value for CH_{3}·Cl^{35} is in good agreement with the value of 18.4 kc/sec theoretically predicted by Chang and Dennison.
For all four molecules the D_{JJ} constants were found to be in good agreement with those predicted from Kratzer's formulawhere ω is the vibrational frequency corresponding to the stretching of the carbon halogen bond.

Rotational Constants of GeH_{3}D and GeHD_{3}
View Description Hide DescriptionThe analysis of the rotational structure of the Ge–D stretching fundamental of GeH_{3}D yields the following values:A similar analysis of the Ge—H stretching mode in GeD_{3}H yields for this molecule:The germanium‐hydrogen distance obtained under the assumption that it is unchanged by isotopic substitution is 1.52_{9}±0.003 and 1.52_{5}±0.005 in GeH_{3}D and GeHD_{3}, respectively.

Approximate Treatment of the Viscosity of Idealized Liquids. I. The Collisional Contribution
View Description Hide DescriptionThe instantaneous transport of momentum across the bodies of molecules occurs upon molecular collision in a rigid sphere liquid undergoing viscous flow. The contribution of this effect to the viscosity is calculated on a quasi‐equilibrium basis for a liquid consisting of hard spherical molecules. The calculation makes use of the free volume theory, a correction being introduced to take account of the blocking effect of third neighbors. The equation so obtained may be expressed in terms of the adiabatic compressibility of the liquid and its heat of vaporization. The calculated viscosity contributions are of the order of a quarter to a half of the experimental viscosities for various low molecular weight liquids investigated. The temperature coefficients of the viscosity contributions are also lower than those of the experimental viscosities.