Volume 18, Issue 5, 01 May 1950

The Surface Tension of Liquid Metals and the Excess Binding Energy of Surface Atoms
View Description Hide DescriptionBy assuming that the cohesive energy of a liquid metal can be expressed as the sum of the pairwise interaction energies of nearest neighbors, and by obtaining the number of effective nearest neighbors for atoms on the surface and in the interior from simple considerations, it is shown that the pairwise bonding energy of surface atoms is greater than that for atoms in the interior of liquid metals. With mercury as the sole exception, this excess bonding energy is a nearly constant 2 percent of the cohesive energy when the liquids are taken as close‐packed, but greater variation of this proportion is obtained when the liquids are taken as solid‐like in structure.

Reactions of Recoil Atoms in Liquids
View Description Hide DescriptionThe reactions in liquid phase of the recoil atoms formed in the (n, γ) process are discussed in terms of a model involving energy loss by elastic collisions,dissociation of solvent molecules by impact, and eventual reaction in a liquid cage. Expressions are derived which relate the fraction of the recoil atoms ultimately found in a given molecular species to the composition and properties of the liquid. Previously published data are interpreted in terms of this model.

Isotope Effect in the Vibrational Frequency Spectra and Specific Heats of Sodium Hydride and Deuteride
View Description Hide DescriptionThe prediction by the Born and von Karman lattice dynamicstheory of the effect of isotopic substitution on crystal vibration frequencies has been determined by calculation of frequency spectra of sodium hydride and sodium deuteride. In each case 6690 of the lattice frequencies have been calculated with the aid of I.B.M. punched card computers. They have been chosen and weighted in such a way that the whole frequency spectra of the crystals are uniformly sampled. Both spectra exhibit acoustical branches which are nearly identical and optical branches, the frequencies of which are essentially in the ratio of the square root of two. In both cases, the optical branches extend somewhat uniformly over very broad ranges of frequencies, in marked contrast to the estimation of optical frequencies as a few monochromatic lines.
The molar heat capacities of these two compounds have been determined experimentally between 60 and 90°K with an adiabatic calorimeter and compared to corresponding curves calculated from the frequency spectra. The theoretical and experimental sets of curves possess the same general form. In both cases the deuteride values are higher than the hydride values, with the curves of the two substances diverging with increasing temperature. The theoretical curves, however, are nearly uniformly displaced from the experimental curves by about ten percent, an effect which could have arisen from an error in the repulsive force constants.

I. The Infra‐Red Spectrum of Tetramethyl Lead and the Force Constants of M(CH_{3})_{4} Type Molecules
View Description Hide DescriptionThe infra‐red absorption of tetramethyl lead has been measured in the region 2–23μ. A frequency assignment has been proposed. A partial normal coordinate analysis has been made using the fundamental frequencies of this investigation and the data of previous investigators of tetramethyl compounds. Thereby M — C valence‐type force constants of all the Group IV tetramethyl derivatives and the analogous tetramethyl ammonium ion have been determined. These force constants are compared with those predicted by the rules of Badger and Gordy and the relationship between bond force constants and atomic parameters is briefly considered.

II. The Effective Methyl Mass and Its Use in Determining the Force Constants and Character of Metallo‐Organic Bonds
View Description Hide DescriptionThe ``effective methyl masses'' of the Group IV tetramethyl derivatives and the analogous tetramethyl ammonium ion are shown to give a linear relationship when plotted against their respective stretching and bending frequencies. The linear relationships are used to determine ``effective methyl masses'' from Group V trimethyl stretching and bending frequencies and from some Group VI dimethyl stretching frequencies. Then the ``effective methyl masses'' so determined are used in simplified calculations to predict stretching and bending force constants for Groups V and VI methyl derivatives. This procedure is shown to give stretching force constants for dimethyl mercury and dimethyl zinc which are in good agreement with those obtained by Gutowsky on the basis of a less approximate normal coordinate treatment, the average deviation being 1 percent. Finally this large number of new metallo‐organic force constants is summarized with existing metallo‐organic force constants and the nature of the metallo‐organic bond is discussed.

Molecular Motion in Certain Solid Hydrocarbons
View Description Hide DescriptionAn investigation has been made of the variation of the nuclear resonance absorption line width with temperature for four long chain aliphatic compounds and eight aromatic hydrocarbons. The aliphatic compounds are dimorphous; in the lower temperature modification it is concluded that the molecules are rigid at the lowest temperatures, but that an increasing number of molecules rotate about their length as the temperature increases; in the upper temperature modification all the molecules rotate. The naphthalene crystal lattice is found to be rigid up to the melting point. Benzene and anthracene, however, show sharp line‐width transitions at about 110° and 190°K, respectively. It is suggested that in benzene this is due to tunnelling or rotation of the molecules about their hexagonal axes. The explanation for anthracene is less clear, but it is suggested that each molecule rotates about its long diad axis. The xylenes, mesitylene, and hexamethylbenzene show internal rotation of the CH_{3} groups at all temperatures above 95°K. In addition, hexamethylbenzene has a line‐width transition over the range 135–210°K, attributed to tunnelling or rotation of the molecules about their hexagonal axes.
A calculation is made of the reduction of the intramolecular contribution to the resonance line second moment caused by rotational oscillation of molecules in a crystal lattice. The effects of certain types of molecular motion on the intermolecular contribution are also calculated.

The Logical Position of the ``Average Bond Energy,'' the ``Dissociation Energy of a Bond,'' and the ``Force Constant''
View Description Hide DescriptionThe concepts of ``bonddissociation energy'' and ``average bondenergy'' are analyzed. A mathematical treatment is suggested which makes it possible in principle to distribute the energy of atomization among the various bonds of the molecule. The relationship between the ``bonddissociation energy,'' ``average bondenergy,'' and ``reorganization energy'' is examined in the light of various molecular force fields.

Expansion of the Montmorillonite Lattice on Hydration
View Description Hide DescriptionWhen exposed to water vapor, water, or some non‐aqueous solvents, montmorillonitic clays display expansion of their lattices. Assuming that the expansion on hydration is a uni‐dimensional swelling phenomenon, a thermodynamic analysis has been made which furnishes quantitative evaluation of interplanar forces. This analysis indicates that for lattice expansions of 3 or 4A from the dehydrated contracted state, the force between montmorillonite lattice layers is substantially constant; but for greater expansions the force diminishes in a complex manner. The analysis also indicates the possibility of determining quantitatively the forces exerted by molecules of solvents which expand the lattice, providing ion exchange does not occur. Problems in determining molecular forces and structure are discussed.

The Determination of Energy Levels from Thermodynamic Data. I. The Effect of Experimental Error
View Description Hide DescriptionThe problem of calculating energy levels from thermodynamic data can be reduced to that of inverting the Laplace transform, for which several procedures have been developed. Using the method of Widder, we show that the resultant calculated energy level density function consists of a series of broadened peaks, whereas in the true density the levels are represented by a series of Dirac delta‐functions.
Alternatively, if the distribution of the energy levels is specifically assumed to be composed of discrete energies, the calculation reduces to the moment problem.
In either case the calculation is shown to have an inherent ``resolving power,'' in that levels within a certain closeness cannot be distinguished as separate. By a generalization of this idea, it is shown that the computation can lead to a knowledge of the over‐all density of energy levels within a given region, but cannot reveal their exact locations.

The Determination of Energy Levels from Thermodynamic Data. II. The Heights of Potential Energy Barriers Restricting Intramolecular Rotation
View Description Hide DescriptionThe uncertainty in the distribution of the energy levels implies a corresponding uncertainty in the shape of the associated potential energy function. The estimation of barrier heights is known to depend upon the shape of the potential, therefore implicitly upon the energy level distribution. We apply these ideas to the restricted rotation problem by introducing a shape parameter into the assumed potential function, and show that the currently accepted barrier height ranges should be widened. On the basis of our modified function, we found the following barrier heights to be consistent with published thermodynamic data: ethane 1550 to 2700 calories per mole; 1,1,1‐trifluoroethane 2300 to 8300; methanol 800 to 3000.

On the Fluctuation of Energy of Gases in the Bose‐Fermi Quantum Statistics
View Description Hide DescriptionThe energy fluctuation of monatomic gases is calculated in the Bose‐Fermi quantum statistics computing the mean values by the Bose and Fermi distribution functions and on the base of the entropy equation. The obtained results are compared with Fürth's calculations.

The Contribution of the Surface of the Specific Heat of Disperse Systems
View Description Hide DescriptionA theory of Brager and Schuchowitzky concerning the contribution of the surface of the specific heat is extended to the interfaces of binary systems.

Compressibility of Gases at High Temperatures. III. The Second Virial Coefficient of Helium in the Temperature Range 600°C to 1200°C
View Description Hide DescriptionAn apparatus is described for measuring the second virial coefficient of gases up to 1200°C. The method of measurement is based on a modification of an expansion method described previously. Results of measurements of the second virial coefficient of helium at 600°, 800°, 1000°, and 1200° are given.

On the Intermolecular Potential of Helium
View Description Hide DescriptionExperimental values of the second virial coefficient from 0°C to 1200°C (see preceding paper) were used to test various intermolecular potential functions for helium. A Lennard Jones potential,with m=6 and with n either 9 or 12 could not be made to fit the experimental data over the entire temperature range. The coefficients λ and μ derived from the data showed a marked temperature dependence. The theoretically calculated potentials of Slater and Kirkwood and of Margenau were found to give values of the second virial which were approximately 8.5 percent and 27 percent lower, respectively, than the experimental values. A potential function with exponential repulsion, which gives a more satisfactory fit with the experimental data, was derived empirically. A semi‐empirical expression given by Keyes (reference 17) for B as a function of temperature was also compared.

Light Scattering in the Critical Region. I. Ethylene
View Description Hide Description1. In the neighborhood of the critical point,light scattering reveals the presence of four regions: a. A region where the light scattering depends on the inverse fourth power of the wave‐length. b. A region of increasing scattering and decreasing dependence on wave‐length, beginning about a degree above the critical temperature, and extending about a degree. The maximum scattering in this region is of the order of 100 times the initial value. c. An abrupt decrease in scattering, accompanied by absorption which sets in at a higher temperature for the shorter wave‐length. d. A large and erratic increase in scattering, apparently resulting from condensation.
2. The scattering observed upon cooling and heating are identical, provided the temperature does not drop below the temperature for zero scattering or condensation.
3. The wave‐length dependence of light scattering is not completely described by any existing theory.
4. Applying the Ornstein‐Zernike equation where it is possible, one calculates clusters of about 20 molecular diameters more than a degree above the critical temperature. These clusters increase rapidly with decreasing temperature.

Light Scattering in the Critical Region. II. Ethane
View Description Hide DescriptionLight scattering experiments have been performed on ethane in the critical region, using apparatus and procedure previously applied to ethylene. The results are qualitatively quite similar to those obtained for ethylene, indicating that no theory so far developed completely describes the phenomenon.

The Approximate Rate of Exchange between Iodine Atoms and Molecules
View Description Hide DescriptionThe rate constant for the exchange reaction of iodine atoms with iodine molecules in hexane at 25° has been estimated by an indirect method. The rate constant is approximately 1.3×10^{−13} (atom/ml)^{−1} sec.^{−1} or 8×10^{10} (mole/ml)^{−1} sec.^{−1}. The energy of activation for the exchange is probably between 2 and 3 kilocalories.

The Primary Quantum Yield of Dissociation of Iodine in Hexane Solution
View Description Hide DescriptionThe primary quantum yield for the photo‐dissociation of iodine in degassed hexane at 25° has been calculated from measurements of the mean lifetime of the chains involved in the exchange of iodine atoms with trans‐diiodoethylene. The primary quantum yield to an accuracy of ±15 percent is 0.59 at 436 mμ and 0.37 at 578 mμ. The deviation of this quantity from unity is affected both by the ``primary recombination'' of atoms which fail to escape from the original ``cage'' of solvent molecules, and by the ``secondary recombination'' of the original atoms by diffusion during a time which is very short compared to that in which either is apt to encounter an atom from another molecule.
The specific rate constant for the recombination of iodine atoms in hexane solutions has been determined and has been shown to be about one fifth of the rate constant for collision in the gas phase.
The presence of air decreases the rate constant for the photochemical exchange of iodine with diodoethylene by a factor of four and increases the apparent mean lifetime of iodine atoms by a factor of one hundred.

Absorption by H_{2}S Vapor in the Region 3.6μ to 4.5μ
View Description Hide DescriptionThe region near the absorption band of hydrogen sulfide vapor at 3.7μ has been measured with high resolution. The data obtained corroborate some of the previously published work on this molecule. Results were obtained, however, which are difficult to reconcile with a predicted band based on a model of the probable size and shape of H_{2}S.