Volume 29, Issue 4, 01 October 1958

Internal Energy‐Compressibility‐Temperature Equation for Air in Dissociative and Ionic Equilibrium
View Description Hide DescriptionBased on the real gas data of Hilsenrath and Beckett, an equationE/RT=f(Z, T) is proposed to describe air in dissociative and ionic equilibrium over wide state‐variable intervals. Used in conjunction with a suitable real gas state equation [e.g., Z=g(ρ, T)], an entropy‐compressibility‐density relation, and pertinent conservationequations, the proposed equation should complete a realistic, consistent set of dynamic and thermodynamicequations. The proposed equation exhibits excellent agreement with the data in sample calculations.

Interrelations Involving Solutions of Equations of Equalizing Processes and Oscillating Processes
View Description Hide DescriptionAssessment of the velocity of a fast chemical reaction can be made by studying the way the reaction interferes with other rapid processes. Both equalizing processes, such as diffusion, and oscillating processes, such as the passage of sound waves, can be employed. Solution of the differential equations of these processes, under a variety of conditions, is a necessary part of the background investigation of these methods and is also of importance in the study of many other physical and chemical problems. This paper shows how a wide range of these solutions can easily be obtained from simpler existing solutions. Among other results, complete resolutions of the ``age equation'' and the vibration equation have been effected for arbitrary initial conditions and a range of important boundary conditions (including those of Dirichlet and Neumann as special cases).

Free‐Convectional Heat Transfer from a Single Horizontal Wire
View Description Hide DescriptionFree‐convectional heat transfer from single, horizontal, heated, 2‐, and 3‐mil platinum wires was measured in gaseous A, N_{2}, O_{2}, CO_{2} and in liquid (CH_{3})_{2}CO, CH_{3}OH, C_{6}H_{5}CH_{3}. The measurements, extending approximately from GrPr=1 to GrPr=10^{—5}, satisfied the Senftleben correlation.

Statistical Mechanical Theory of Transport Processes in Liquids
View Description Hide DescriptionThe hydrodynamicequations of the transport processes are developed in a form in which the irreversibility appears explicitly in terms of the instantaneous time derivatives of the stresses in a molecular scale nonequilibrium region of a system otherwise at equilibrium. The time derivatives of the stresses are shown to be proportional to the gradients of the properties being transported and to the squares of the transport coefficients. The corresponding time derivatives in the statistical mechanical treatment can be expressed as ensemble averages of molecular interactions using instantaneous values of the molecular pair density functions directly without recourse to time‐smoothing with considerable gain in simplicity. Expressions for the transport coefficients are obtained by comparison of the hydrodynamic and statistical mechanical equations for the time derivatives of the dissipative stresses. The resulting hydrodynamic frictional and self‐diffusion coefficients turn out to be identical to the expressions for these quantities provisionally suggested by Kirkwood, Buff, and Green. Relatively simple expressions are also obtained for the shear and volume viscosity and thermal conductivity coefficients in terms of integrals over space derivatives of the potential energy and the molecular pair density. It is further shown that, if an inter‐molecular potential of the Lennard‐Jones and Devonshire from is assumed, the integrals may be eliminated between these equations and the corresponding statistical mechanical equations for the hydrostaticpressure and the ideal heat of vaporization. This provides simple expressions for the shear vicsosity and the thermal conductivity coefficients directly in terms of the latter equilibrium properties. The numerical values obtained for the above two transport coefficients from evaluation of the integrals in the statistical mechanical equations and from the simple expressions in terms of equilibrium properties, are each in comparatively good agreement with experiment.

Effect of Pressure on Viscosity of Higher Hydrocarbons and Their Mixtures
View Description Hide DescriptionUsing the rolling‐ball method the viscosity of seven pure hydrocarbons, having 25 or 26 carbon atoms, and three binary mixtures of them has been measured to 3450 bars at 37.8°, 60.0°, 98.8°, and 135°C. The compounds included isoparaffinic, cycloparaffinic, and aromatic types. The increase in viscosity with pressure was found to be strongly dependent on molecular structure. The viscosity‐temperature coefficient 1/η(∂η/∂T)_{ p } increased with increased pressure while the viscosity‐pressure coefficient 1/η(∂η/∂P)_{ T } decreased with increased temperature. The behavior of the binary mixtures corresponded within 5% over a range of 50–100 fold change in viscosity to that of the pure compounds equivalent to them in molecular weight and average molecular structure. This remarkable agreement is interpreted to mean that the viscosity of these compounds is some additive function of their constituent groups whether these groups are combined in the same or different molecules as long as the basic molecular symmetry is unchanged. The values of the Eyring theory ΔF _{±}, ΔH _{±} ^{ i }, ΔS _{±}, and ΔV _{±} for these data are discussed. For the saturated compounds at constant temperature, an approximately linear relation was found between log η and [(v/v _{0})^{4}—(v/v _{0})^{2}] where v is the specific volume and η the absolute viscosity.

Delayed Fluorescence in Naphthalene Crystals at 4°K
View Description Hide DescriptionThe fluorescence of naphthalene crystals has been observed through a phosphoroscope indicating that a part of this emission has a lifetime greater than 10^{—3} sec at 4.2°K. It is suggested that this phenomenon is connected with the photoconductivity observed in crystals of aromatic compounds and has its origin in the storage of energy by an electron trapping mechanism.

Delayed Singlet‐Singlet Emission from Molecular Crystals
View Description Hide DescriptionThe fluorescence emission from the molecular crystals naphthalene and phenanthrene may be observed after a delay of several milliseconds from the time of excitation. The decay time is strongly temperature dependent and the decay law is nonexponential. The delayed emission is connected with the crystalline state of the material, but is not otherwise understood.

Application of Charge‐Transfer Theory to the Heats of Adsorption of the Inert Gases on Charcoal
View Description Hide DescriptionThe adsorption of the inert gases on charcoal is considered from the viewpoint of charge‐transfer no‐bond complex formation, and interaction integrals are calculated from the heats of adsorption at effectively zero coverage. The numerical values obtained in this way are compatible with similar data in the literature. It is shown that the linear relationship previously reported between the heat of adsorption of the inert gases on charcoal and the polarizabilities of the gases can be satisfactorily derived on the basis of this theory, and arises to a large extent from the comparatively high ionization potentials of these elements.

Study of the Compressions of Several High Molecular Weight Hydrocarbons
View Description Hide DescriptionIsothermal compressions were measured for thirteen high‐purity liquid hydrocarbons and two binary mixtures of liquid hydrocarbons. These hydrocarbons have a molecular weight range of 170 to 351 and included normal paraffins, cycloparaffins, aromatics, and fused ring compounds. The pressure range for these measurements was from atmospheric to as high as 10 000 bars, being limited to lower values for some compounds to avoid possible solidification of the liquid. The volume changes due to pressure were measured at six temperatures spaced about equally in the range 37.8°C to 135.0°C. The volume changes and pressures were measured by methods similar to those of P. W. Bridgman.
Pressure‐volume isotherms can be described adequately by the Tait equation, v _{0}—v=C log(1+P/B), or for pressures above a certain minimum, whose value depends on the compound, by the Hudleston equationFor the Tait equation the parameter C can be predicted for hydrocarbon liquids from the relation C=0.2058 v _{0}.
Compressibility for a given hydrocarbon decreases with increasing pressure at constant temperature and increases with increasing temperature at constant pressure. The compression, and the compressibility, of liquid hydrocarbons are strongly dependent on molecular structure. Cyclization introduces a rigidity of molecular shape which decreases the compressibility markedly. Furthermore, fused ring cyclization as exemplified by naphthyl and decalyl structures has a considerably greater effect in decreasing compressibility than cyclization to nonfused rings such as cyclopentyl, cyclohexyl, or phenyl, even at equivalent carbon atom in ring percentages.
Isobars and isochores were drawn and studied over the full range of temperature and pressure. The coefficient of thermal expansion, (1/v _{0}) (δv/δT) _{ P }, for a given hydrocarbon, decreases with increasing pressure at constant temperature. (δ^{2} v/δT ^{2}) _{ P } undergoes a sign change at a certain pressure, whose value depends on the compound; (δv/δT) _{ P } increases with increasing temperature below this pressure and decreases with increasing temperature above this pressure. The pressure coefficient, (δP/δT) _{ v }, is not a function of volume alone but is also dependent on the temperature and pressure. (δE/δv) _{ T } and (δE/δP) _{ T } go to zero and then reverse sign for compounds that can be studied to sufficiently high pressures.

Fluorescence Spectrum of PrCl_{3} and the Levels of the Pr^{+++} Ion
View Description Hide DescriptionPrCl_{3} shows strong fluorescence from the ^{3}P_{0}, ^{3}P_{1}, and ^{1}D levels to all low‐lying levels of the Pr^{+++} ion (^{3}H, ^{3}F, ^{1}G). This makes it possible to obtain all multiplet components of ^{3}H and ^{3}F. Previously unreported lines in the absorptionspectrum are interpreted as transitions to the hitherto unknown ^{1}I_{6}. Zeeman effect data corroborate this. All levels to be expected from a 4f ^{2} configuration are now known for PrCl_{3} except ^{1}S_{0} which should give a line in a different part of the spectrum.

Microwave Absorption and Molecular Structure in Liquids. XXIV. The Dielectric Relaxation of Liquid Ammonia
View Description Hide DescriptionDielectric constant and loss measurements at wavelengths of 3.22 and 1.24 cm have been carried out upon liquid ammonia at temperatures from —55° to —35°C. The results have been used to calculate the approximate dielectric relaxation time values, 1.5×10^{—12} sec at —50° and 1.3×10^{—12} at —40°. The relaxation times and the liquidviscosities are much smaller than those of water, but extrapolation to the boiling points of the two liquids gives values of comparable magnitudes.

Thermodynamics for Nonisothermal Systems. The Classical Formulation
View Description Hide DescriptionThe classical theory of Thomson, Eastman, and Wagner of the thermodynamics of nonisothermal systems is studied in the light of the Gibbs formulation of heterogeneous equilibrium. It is found that an extension of Gibbs' derivation will include the classical theory of nonisothermal equilibrium as a special case. The Onsager reciprocal relations can be obtained from macroscopic considerations which also give a relation between the second‐order phenomenological coefficients. The concept of second‐order independence is introduced, which provides a way of finding the actual processes.

Paramagnetic Resonance in Rare Earth Trichlorides
View Description Hide DescriptionParamagnetic resonance absorption of all the naturally occurring rare earth trivalent ions in the LaCl_{3}structure have been investigated. The results are summarized in the form of a tabulation of the parameters g _{∥}, g _{⊥}, A, B, P, Δ in the spin‐Hamiltonian. Theoretical calculations of crystal field states and eigenvalues as well as of g _{∥} and g _{⊥}, based on optical measurements, are discussed.

Internal Barrier of Propylene Oxide from the Microwave Spectrum. II
View Description Hide DescriptionSeveral long progressions of perpendicular transitions have been measured in the microwave spectrum of propylene oxide. These have provided an opportunity to test the theory of internal rotation over a very large range of rotational quantum numbers, J=1 to 48 and K=1 to 25, in the ground torsional state. For low K, the K doubling which arises from the asymmetry of the molecule is much larger than the splittings due to tunneling through the potential barrier. The spectrum resembles that of an ordinary asymmetric rotor except that each line is split into a close doublet by the tunneling. At high K, the K doubling becomes negligible. A triplet fine structure is observed in which the spacings show a periodic dependence on K, essentially the same as that calculated for the case of two coaxial symmetric tops. (For a true symmetric rotor, the selection rules would prevent the observation of this pattern.) At intermediate K, the K doubling and the tunneling perturbations become comparable. The mixing of the rotational wave‐functions which results permits ``forbidden'' lines to appear. Very good agreement with theory is obtained over the whole range of K, with the barrier height V _{3}=895 cm^{—1} (2560 cal/M).
Rotational transitions have also been assigned for molecules in the first and second excited torsional states, in which the tunnel effect splittings are greatly magnified. For both the excited states, the barrier height is found to be identical with the ground state result. This supports the usual assumption that perturbations from vibrational interactions with internal rotation and from the sixfold V _{6} term in the potential barrier are small enough to be safely neglected.

Diffusion of Hydrogen in Palladium
View Description Hide DescriptionThe rate of flow of hydrogen through palladium has been measured in a range of temperatures 200°C to 600°C over the pressure range 10 to 70 cm Hg. The flow rate is found insensitive to palladium wall thickness. The data do not seem to be explainable in terms of existing theory.

Reaction of Methyl Radicals with Ethylene
View Description Hide DescriptionThe gas phase reaction between methyl radicals and ethylene has been studied between 124° and 159° by the thermal decomposition of di‐t‐butyl peroxide in presence of ethylene. The value of k _{4a }/k _{3} ^{1/2} for the reactions,is and the steric factor for the addition of methyl radicals to ethylene is about 7.6×10^{—3}. At low ethylene concentrations no evidence could be found for polymerization beyond the initial methyl radical addition.

On the T _{1}/T _{2} Ratio for Protons in Aqueous Mn^{++} Solutions
View Description Hide DescriptionThe T _{1}≠T _{2} anomaly for water protons in solutions containing Mn^{++} has been investigated. At 40 Mc (proton frequency), T _{1}/T _{2}=9.5(±0.5) for Mn^{++} solutions. When the Mn^{++} is complexed by the hexadentate ligand, ethylenediaminetetraacetate (MnY^{—2}), or by the tetradentate ligand, nitrilotriacetate (MnX^{—1}), T _{1} is increased slightly and T _{2} is increased markedly, so that T _{1}=T _{2} and the anomaly disappears. For MnX^{—1}, there are probably still 2 H_{2}O molecules complexed to Mn^{++}. EPR studies show that the paramagneticrelaxation time is reduced by complexing (from 3×10^{—9} sec for Mn^{++} to 3×10^{—10} sec for MnX^{—1}). The results therefore support the suggestion by Bloembergen that the anomalous T _{2} broadening is caused by an A I·S coupling between the electron spin, S, of Mn^{++} and the proton spins, I, in the coordination sphere plus a long paramagneticrelaxation time. All features of the variation of T _{1} and T _{2} with frequency are explained rather well by consideration of the combined effects of the I·S interaction and the dipole interaction.
The experimental results are

Mobile Electron Model in a Magnetic Field
View Description Hide DescriptionThe motion of an electron in a circular loop containing equally spaced Dirac delta‐function potential spikes is considered. This problem is solved exactly for the case when a static magnetic field is present, and is of physical interest for the π‐electron motions in benzene.

Molecular Composition of Alkali Fluoride Vapors
View Description Hide DescriptionThe abundances of polymeric species of the alkali fluorides in the vapor phase and their dissociation energies have been determined by use of the method of Miller and Kusch. For LiF, NaF, KF, RbF, and CsF, the dissociation energies of the dimer are 58.9, 54.3, 47.6, 42.0, and 37.8 kcal/M, respectively. For LiF the trimer was also observed, with a dissociation energy of 38.3 kcal/M. When the salt is in equilibrium with its vapor at a temperature where the vapor pressure is 10^{—2} mm of Hg, the abundance of the dimer decreases in the sequence from LiF to CsF. The heats of sublimation for the various species were also found.

Spin Exchange and Spin‐Lattice Relaxation Induced by Mechanical Rotation of Solids
View Description Hide DescriptionMeasurements with spin‐echo apparatus have shown that mechanical rotation of a sample in the static magnetic field decreases the protonT _{1} in solid chlorobenzenes for particular protonmagnetic resonance frequencies within the range 23.2–41 Mc/sec. The results are explained by the following model: magnetic coupling between protons and lattice is weak while the quadrupolar coupling of chlorine nuclei with the lattice is strong. Upon rotation of the sample, the angular dependence of the Zeeman splitting of the chlorine quadrupole levels enables the chlorine resonance frequencies to be brought into coincidence with that of the protons. The resulting spin exchange and energy transfer between protons and chlorine nuclei provides an indirect but nonetheless effective thermal contact of protons with the lattice, thereby reducing the protonT _{1}. The general question of anomalies in the dependence of T _{1} upon resonance frequency is discussed briefly.