Volume 28, Issue 3, 01 March 1958

Nuclear Resonance Spectrum of Al^{27} in Chrysoberyl
View Description Hide DescriptionThe nuclear magnetic resonance spectrum of Al^{27} in a single crystal of chrysoberyl (BeAl_{2}O_{4})_{4} has been investigated at room temperature in a field of 7800 gauss. The spectra obtained as the crystal was rotated about the three crystal axes have been interpreted on the basis of eight Al^{27} sites of two distinct types, the four sites of each type differing only in the orientation of the principal field gradients. Quadrupole coupling constants and electric field asymmetry parameters at the two types of sites were determined to beIn addition, the orientation of the principal field gradients has been determined at each of the eight sites.

Nature of the Glass Transition and the Glassy State
View Description Hide DescriptionThe thermodynamic properties of amorphous phases of linear molecular chains are obtained from statistical mechanics by means of a form of the quasi‐lattice theory which allows for chain stiffness and the variation of volume with temperature. A second‐order transition is predicted for these systems.
This second‐order transition has all the qualitative features of the glass transition observed experimentally. It occurs at a temperature which is an increasing function of both chain stiffness and chain length and a decreasing function of free volume.
The molecular ``relaxation times'' are shown to increase rapidly as the second‐order transition temperature is approached from above.
To permit quantitative application of the theory and determine the relationship between the second‐order transition and the glass transition observed in ``slow'' experiments these two transitions are tentatively identified. By this means quantitative predictions are made concerning the variations of (1) glass temperature with molecular weight, (2) volume with temperature, (3) volume with molecular weight, (4) volume at the glass temperature with the glass temperature for various molecular weights of the same polymer, (5) specific heatvs temperature, and (6) glass temperature with mole fraction of low‐molecular weight solvent, since extensive experimental results are available for these properties. These and other theoretical predictions are found to be in excellent agreement with the experimental results.

Infrared Spectrum of Methyl Chloride near 6000 cm^{—1}
View Description Hide DescriptionThe rotational fine structure of the parallel component of 2v _{4} of methyl chloride has been resolved. The Q branches of the sub‐bands, and the P and R branch lines of the K = 3 sub‐band have been identified and analyzed. The molecular constants obtained are (in cm^{—1}): v _{0} = 6015.56, B′ = 0.4439, B″ = 0.4436, B′ — B″ = 0.00044, and (A′ — B′) — (A″ — B″) = —0.0481.

Proton Magnetic Resonance of the CH_{3} Group. IV. Calculation of the Tunneling Frequency and of T _{1} in Solids
View Description Hide DescriptionThe thirty lowest eigenvalues of the Mathieu equation have been calculated numerically to nine places for a hindered rotor with threefold symmetry attached to a rigid framework. The results are tabulated for eight values of IV_{0}/2ℏ ^{2} ranging from 56.25 to 115.3125. The splittings of the torsional states of the CH_{3} group have been used to calculate the average tunneling frequency, ν_{ t }, as a function of temperature for barrier heights of 825 cm^{—1} to 2770 cm^{—1}. Some useful relations are developed between the eigenvalues and torsional splittings for the 2‐ and 3‐nodal potential functions.
The BPP theory is used to calculate the proton spin‐lattice relaxation time,T _{1}, for CH_{3} groups undergoing hindered reorientations in solids and also over‐all molecular tumblings, assuming Debye spectral density functions for both motions. The manner in which the tunneling affects T _{1} is considered at some length and two ways of introducing it are described. The coupling among the three protons within a given CH_{3} group is discussed briefly in relation to T _{1}.

On Time Smoothing. A Model for Momentum Transport
View Description Hide DescriptionAn investigation has been made of the time smoothing properties of the transportequations previously derived by the author [J. Chem. Phys. 26, 1421 (1957)]. A model is introduced, wherein momentum is transferred from one portion of a fluid medium to another via acoustical waves. This model is applied to the problem of viscous flow of a rare gas, and it is found that it is permissible and desirable to allow the time smoothing interval τ to become infinitely large. In practice this means that τ≫β^{—1}, where β is a friction constant. The model incidentally yields a value for the viscosity coefficient in fair agreement with the Chapman‐Enskog hard sphere value.

Anisotropic Color Centers in α‐Quartz. II. Germanium‐Doped Synthetic Quartz
View Description Hide DescriptionThe color center at 275 mμ produced by x‐irradiation in three specimens, two of Bell and one of Clevite synthetic quartz, depends on the presence of germanium impurity. It is absent in specimens free of germanium. The center is anisotropic with maximum absorption in the σ direction (electric vector perpendicular to the c axis). In the π direction (electric vector parallel to the c axis) the absorption is poorly resolved into two bands. The color center absorption is caused by an electric dipole transition. This center bleaches more rapidly than other color centers present in the specimens. This color center system is accompanied by the aluminum system which is in the 460 mμ region and by two other bands at 1900 and 2050 A. No relationships have been observed among these bands other than that they are found together in the three instances studied and the intensity increases with the energy of the given band. A question of a model for this center is discussed.

Theoretical Derivation of Traube's Rule
View Description Hide DescriptionA theoretical derivation of Traube's rule for the surface tension of dilute aqueous solutions of homologous series of long chain compounds is given. It is demonstrated that a quantitative interpretation of the rule requires that the molecules of the chain extend randomly upward out of the surface and permit hindered rotations of the CH_{2} groups about each carbon‐carbon bond. It is shown that the old arguments for supposing that the molecules of the chain lie parallel to the surface for dilute solutions are unconvincing.

Surface Ionization Phenomena on Polycrystalline Tungsten
View Description Hide DescriptionBy assuming the existence of patches of different work functions on the surface of tungsten filaments, the ratio of ions to atoms emitted from the total surface has been computed by applying the Langmuir‐Saha equation to each patch. From a suitable choice of the fraction of the surface covered by patches of work function [open phi]_{ n }, a good fit to published data is obtained. The significance of these patches in the interpretation of surface ionization data is discussed.

Infrared Spectra of the Isotopic Nitrous Oxides
View Description Hide DescriptionThe infrared spectra of N^{14}N^{15}O^{16}, N^{15}N^{14}O^{16}, and N^{15}N^{15}O^{16} have been observed from 2.5 μ to 20 μ using a model 112 Perkin‐Elmer spectrometer. The frequencies of the three fundamental vibrational bands and fifteen overtone and combination bands have been tabulated and compared with the frequencies of N^{14}N^{14}O^{16}. Using known anharmonic constants and isotopic relations, approximate zero‐order frequencies have been calculated for the isotopic molecules. A set of force constants for infinitesimal displacements have been computed for the set of molecules, and the partition function ratios for the various species calculated from the data.

Ion Exchange Kinetics. A Nonlinear Diffusion Problem
View Description Hide DescriptionIdeal limiting laws are calculated for the kinetics of particle diffusioncontrolled ion exchange processes involving ions of different mobilities between spherical ion exchanger beads of uniform size and a well‐stirred solution. The calculations are based on the nonlinear Nernst‐Planck equations of ionic motion, which take into account the effect of the electric forces (diffusion potential) within the system. Numerical results for counter ions of equal valence and six different mobility ratios are presented. They were obtained by use of a digital computer. This approach contains the well‐known solution to the corresponding linear problem as a limiting case. An explicit empirical formula approximating the numerical results is given.

Compression and Densities of Four Solidified Hydrocarbons and Carbon Tetrafluoride at 77°K
View Description Hide DescriptionThe piston displacement method of Bridgman has been used to measure the volume changes and compressibilities of solid ethane, ethylene, propane, propylene, and carbon tetrafluoride from 0 to 20 000 kg/cm^{2} at 77°K. The only polymorphic phase change observed is a first‐order transition at P = 180±80 kg/cm^{2} at 77° in CF_{4}. The densities of these solidified gases at 77° have been measured at atmospheric pressure by direct condensation into a volumetric flask. The accompanying pressure drop in a storage tank of known volume is observed.

Stark Effect from 1.1 to 2.6 Millimeters Wavelength : PH_{3}, PD_{3}, DI, and CO
View Description Hide DescriptionThe Stark effect has been observed in the microwave rotational spectra of PH_{3} and PD_{3} at 1.1 and 2.1 mm wavelength, respectively, in DI^{127} at 1.5 mm, and in C^{12}O^{16} at 2.6 mm. The J = 1→2 transition of PD_{3} has been observed at 1.08 mm. Analysis of the data yields values of the electric dipole moment, μ, as follows: PH_{3}, 0.578±0.010 debye; DI, 0.316±0.010 debye; and CO, 0.112±0.005 debye. The centrifugal stretching constants, D_{J} and D_{JK}, for PD_{3} are found to be 0.80_{0} Mc and 1.3_{1} Mc, respectively.

Reaction Rates by Nuclear Magnetic Resonance
View Description Hide DescriptionThe Bloch equations for nuclear magnetic resonance are modified to describe the magnetic resonance of a single nuclear species X which is transferred back and forth between two (or more) magnetic environments (A,B) by kinetic molecular processes. The modified Bloch equations involve the usual assumptions of the Bloch theory and, in addition, require (a) that the X nuclear relaxation times be independent of the molecular exchange rates, and (b) that the X nuclear magnetization in A relax independently of the X magnetization in B, and vice versa. The modified Bloch equations are easily solved in the slow passage case, with arbitrary rf saturation. Earlier relations between reaction rates, and resonance line shapes, which were developed by Gutowsky, McCall, and Slichter, and extended by a number of other investigators, are easily derived using the modified Bloch equations. In the present work the modified equations are used to show how rapid exchange rates can sometimes be measured in solutions where the Xrelaxation times are relatively long in one system, A, and short in the second, B.

Delta‐Function Model for Short‐Range Intermolecular Forces. I. Rare Gases
View Description Hide DescriptionA delta‐function model is proposed for the calculation of short‐range intermolecular forces. The features which must be incorporated into such a model to make it yield quantitative results for repulsion energies are investigated by considering first the repulsion interaction of two hydrogen atoms with parallel electron spins. Extension to the rare gas atom interactions is then made by replacing their many electrons by an effective charge distribution. This procedure permits the simple treatment developed for hydrogen atoms to be taken over formally for rare gas atoms. Interactions between unlike atoms are also considered. As finally formulated, there are no disposable parameters and the interactionenergy is directly related to known properties of the isolated atoms. The properties needed are the atomic number, the first ionization potential, and the average radius of the largest electronic orbit. Agreement with experiment is good in all cases, and is almost always superior to that achieved by conventional valence bond or molecular orbital methods.

Absorption Spectra of Molten Salts
View Description Hide DescriptionThe ultraviolet absorption spectra of a variety of molten salts have been determined. Generalizations about the character of such spectra are made and certain implications about the structure of the liquids are examined.

Irreversible Electrochemical Processes in Membranes. II. Effects of Solvent Flow
View Description Hide DescriptionThe correlation of the osmotic flow of the electrolytesolution with the membrane potential and the ionic permeability is discussed from the standpoint of the irreversible thermodynamics of continuous systems. The entropy production in the membrane having a porous structure is evaluated by means of hydrodynamical calculation taking into account the pressure, concentration, and electric potential gradient under the assumption that the ionic concentration can be determined by the Debye‐Hückel approximation even in the membrane capillaries. From this entropy production a new equation for the volume flow is derived which enables us to give a reasonable explanation of the ``abnormal osmosis.'' The equations for the membrane potential and for the ionic permeability derived similarly from the entropy production contain the additional terms due to the solvent flow in comparison with the theoretical ones given in the previous paper. The new equation for the membrane potential is found to be more satisfactory than the previous one.

A One‐Center Wave Function for the Hydrogen Molecule
View Description Hide DescriptionSlater atomic orbitals, s, p, d, etc., centered at the molecular midpoint and having variable orbital exponents and variable principal quantum numbers, are used to construct a seven‐term wave function for the ground state of the hydrogen molecule of the formValues for the seven linear coefficients, the twelve orbital exponents and the twelve principal quantum numbers are determined by the variational method. The total molecular energy obtained is — 1.15883 a.u., or 31.53 ev (exptl. 31.96 ev), corresponding to a binding energy of 4.32 ev (exptl. 4.75 ev). A ten‐term function of similar form is constructed which gives a binding energy of 4.34 ev.

Gaseous Species in the Vaporization of Sodium Hydroxide
View Description Hide DescriptionMass spectrometric studies of the gaseous species in sodium hydroxide vapor have shown that in the temperature range 300°C to 450°C, NaOH (1) vaporizes mainly as gaseous dimers. A thermodynamic treatment of ion current data yields for the reactions:Comparison with existing data on the gaseous alkali halides shows the trend in dimerization energies:

Field Emission from Mercury Whiskers
View Description Hide DescriptionA method for growingmetal whiskers in a modified field emission tube has been developed and applied to Hg. Emission patterns from whiskers show these to be 110 oriented single crystals when grown on a tungsten substrate. Their strength, estimated from the electric field necessary for emission is ∼10^{10} d/cm^{2}. An electrical method of following length based on the relation between this quantity and the surface field, has been used to elucidate whiskergrowth kinetics. It is found that growth is positively exponential, indicating that it occurs by diffusion of impinging atoms to the growing end, where incorporation occurs. From the length where exponential growth ceases it is possible to find a limit for the diffusion coefficient of Hg on Hg and to estimate the activation energy of the surface diffusion as ∼1.1 kcal. Elastic twisting under tensile stress is sometimes found and ascribed to the presence of screw dislocations. Possible applications of the technique are pointed out.

Structure in Ionic Solutions. II
View Description Hide DescriptionThe diffraction patterns of concentrated KOH and LiCl solutions have been analyzed. The results indicate that the hydration number for the OH^{—} ion is 6. Previous work on less concentrated KOH solutions had indicated a hydration number of 4 for the K^{+} ion and a substitutional entry of the cation into the water lattice. The present work agrees with these findings. The dissolution process in LiCl appears to be of a different nature, in that there is a breakdown of the water structure, probably caused by the Li^{+} ion. The water molecules and the hydrated Li^{+} ions then pack around the large Cl^{—} ion to give an apparent hydration member for Cl^{—} of 8–9.