Volume 20, Issue 2, 01 February 1952

Dipole Moments Derived from Force Constants and Ionic Refractions
View Description Hide DescriptionFor simple hydrogen compounds an approximate formula is derived which correlates the dipole moments of the H‐bonds with the corresponding stretching force constant, bond length, and ionic refraction—and which contains only a single adjustable parameter.

The Reaction of Ethyl Radicals with Deuterium
View Description Hide DescriptionThe reaction of ethyl radicals with deuterium has been studied. The ethyl radicals were produced by photodecomposition of diethyl ketone. As activation energy was found E=13.3±0.5 kcal. From this value it may be concluded that the activation energy is about 11.5±1 kcal for the reaction of ethyl radicals with hydrogen.

On the Early Stages of Condensation of Rare‐Gas Type Molecules
View Description Hide DescriptionThe early stages of condensation are treated from the standpoint of the associative equilibrium of single molecules and stable molecular aggregates. Formulas are presented for partition functions from which one can calculate standard chemical potentials and concentrations of specified configurations of up to 8 molecules having a Lennard‐Jones (6–12) interaction. Numerical results are given for nitrogen. It appears that nitrogen aggregate concentrations fall steeply with decreasing temperature. Results of this procedure, using a restricted region of phase space, are compared with those obtained with no restrictions for 2 and 3 molecule aggregates.

The Frictional Coefficient for Flexible Chain Molecules in Dilute Solution
View Description Hide DescriptionThe frictional coefficient, f _{0}, of a polymer molecule in dilute solution is assumed to vary directly as an average linear dimension of the chain. From this assumption equations are developed, as follows, which are analogous to those used successfully in the interpretation of intrinsic viscosity measurements;f _{0}/η_{0} =K_{f}M ^{½}α and K_{f} =P(〈r _{0} ^{2}〉/M)^{½} where α represents the factor by which the actual root‐mean‐square end‐to‐end distance exceeds the unperturbed distance (〈r _{0} ^{2}〉)^{½}, M is the molecular weight, η_{0} the viscosity of the medium, and P should be a universal constant.
Data in the literature on the dependence on molecular weight of sedimentation constants and diffusion coefficients, extrapolated to infinite dilution confirm the conclusions drawn from these equations.

Random Flight with Multiple Partial Correlations
View Description Hide DescriptionThe fundamental statistical properties of a linear polymer can be best studied by a more general model of random flight with multiple partial correlations. Results show that the problems of free rotation and symmetrically restricted rotation in polymers correspond to one and two partial correlations, respectively. The present study of the correlation function by means of difference equations enables one to carry out the generalization to higher orders of partial correlations. The mean square value of the distance r between the ends of the chain is studied for both finite and infinite number of links, and for multiple partial correlations. It is shown that the case of one partial correlation corresponds to a Markoff chain, and the distribution of r is found to be normal.

The Effects of Hydrostatic Pressure on the Ionic Conductivity of AgBr
View Description Hide DescriptionComparison of the conductivities of pure AgBr and AgBr doped with varying concentrations of CdBr_{2} in the intrinsic temperature range determines the concentration of defects and the mobilities of silvervacancies and interstitial ions. These quantities have been measured as a function of pressure up to 8000 kg/cm^{2} at three temperatures below 300°C. From the pressure variation of the defect concentration, the molar volume ΔV ^{*} of the imperfections is found to be 16 cc/mole below 300°C. An analysis of the pressure variation of the mobilitiesu _{0} and u _{□} of the Ag^{+}interstitial ions and of the silvervacancies, respectively, indicates that the free volumes associated with their motions are 2.7 cc/mole and 7.4 cc/mole. The value of ΔV ^{*}=16 cc/mole is consistent with the Frenkel disorder type. At temperatures above 300°C, however, the observed value of ∂ lnσ/∂p is larger than expected from a simple Frenkel disorder type. An effort is made to interpret this behavior in terms of mixed Frenkel and Schottky defects.

Dielectric Constant Measurements of Chlorine Trifluoride at 9400 mc/sec
View Description Hide DescriptionThe dielectric constant of chlorine trifluoride was determined at 9400 mc/sec by measuring the change in the resonant frequency of a cavity when it is filled with the vapor. Corrections were made for the amount of dimer formed. The monomer molar polarization was best represented by P=15.944+1882.0/T°K cc and the dipole moment was 0.554 Debye unit. The average dimer molar polarization was found to be 49.8 cc assuming no dipole moment.

An Investigation of Certain Solvent Effect in Absorption Spectra
View Description Hide DescriptionA study of the solvent effects in the spectra of non‐ionic compounds to whose structure a zwitter ion form makes appreciable contribution (particularly in the excited state) has revealed three distinct effects:
1. A shift of absorption bands to greater wavelength with increasing refractive index, as predicted by Kundt's rule. This is ascribed to the effect of electronic polarizability on the zwitter ion structure, and is seen unmixed with the other effects only when the solvents are hydrocarbons or aryl halides.
2. A further shift which appears with most solvents other than hydrocarbons and aryl halides, and is ascribed to orientation of molecules of nonuniform polarizability.
3. The Kuhn‐Brockmann effect—a large shift which appears whenever hydrogen bonds between the solvent and solute occur. This is believed to be due to the stabilization of the zwitter ion by the electrostatic nature of the hydrogen bond.
No correlations of the spectra of phenolphthalein, p‐rosaniline hydrochloride, or iodine with the properties of the solvent were found.

Long‐Lifetime Phosphorescence and the Diffusion Process
View Description Hide DescriptionThe long‐lifetime phosphorescence of certain, easily oxidizable organic compounds in rigid media at the temperature of liquid nitrogen has been found to decay by an inverse power function of the time. Decay kinetics of this type have been observed previously in inorganic phosphors. Employing the diffusion equation and the observed rate law, a distribution function for electrons in the solid media is derived. Data from the experiments are discussed in relation to this theoretical treatment.

The Configurational Distribution Function in Quantum‐Statistical Mechanics
View Description Hide DescriptionThe function F{N} which gives the relative probability of a configuration {N} is studied for the case of a quantum‐mechanical system to which classical statistics can be applied. By means of a device originally used in quantum electrodynamicsF{N} is obtained in a new form which is very closely related to the form of the analogous classical distribution F_{CL} {N}. The new form of F{N} shows clearly how the difference between F{N} and F_{CL} {N} is related to the uncertainty principle. As an illustration of the utility of the methods presented here several applications are presented. The first application is a high temperature development of F{N} as a power series in ℏ/kT which is carried through to the fourth order. The second application is the development of F{N} as a series of configuration space integrals. A previously published low temperature development of F{N} is obtained in a simple manner, and it is shown that all higher terms in the development can be written down explicitly by starting from the new form of F{N}. Finally, several integral equations for F{N} are presented which give physical insight into its structure, by establishing mathematical analogies with such physical processes as neutron diffusion.

The Scattering of Atoms from Diatomic Molecules
View Description Hide DescriptionThe quantum mechanics of the collision of an atom with a diatomic molecule is discussed. This is an example of the scattering of particles by a nonspherical potential field. In the region in which the atom and molecule are not interacting, the wave function for the system can be written as the product of a wave function for the free atom and that of the free molecule. By an analysis of this function one can write the asymptotic form of the true wave function in the terms of the scattering coefficients, representing the angular dependence of the transition probabilities. In a previous paper, group theoretical arguments were used to separate the rotational coordinates from the n‐particle Schroedinger equation. A set of coupled differential equations for the internal wave functions was derived. In the present paper, the scattering coefficients are obtained by an analysis of the solutions of the internal waveequations involving the three coordinates specifying the internal configuration. This set of equations is transformed into a set of coupled ordinary differential equations in which the coupling is the result of the transitions in the state of the molecule. The equations are solved by a perturbation method which is valid in the case of low energy collisions in which transitions occur relatively seldom. The angular transition probabilities are obtained explicitly in terms of integrals of the interaction potential and a set of phase shifts.

Photochemical Oxidation‐Reduction and Photocatalysis. The Photochemical Activity of FeCl_{4} ^{−} in Alcohol as Oxidizing Agent and as Catalyst
View Description Hide DescriptionA true photocatalytic reaction in which the concentration of the sensitizer remains constant is described in this paper. It is shown that FeCl_{4} ^{−} acts as a photocatalyst for the oxidation of alcohol by thionine. In the absence of thionine FeCl_{4} ^{−} is the oxidizing agent. A mechanism is put forward which includes (1) photoexcitation, primary dark back reaction and separation of the primary product, (2) oxidation of the CH_{3}CHOH radical by FeCl_{4} ^{−}, (3) reaction between two CH_{3}CHOH radicals, (4) oxidation of FeCl_{4} ^{=} by thionine. The latter occurs because of a considerable shift in the oxidation‐reduction potential by the complexing of both ferric and ferrous iron. Various constants and constant ratios are evaluated from the experimental results.

The Physical Properties of Molecules in Relation to Their Structure. I. Relations between Additive Molecular Properties in Several Homologous Series
View Description Hide DescriptionRelations between the additive physical properties of the substituted methanes, ethanes, ethylenes, benzenes, and the acyclic saturated hydrocarbons have been derived assuming strict additivity for the contributions from nonbonded atoms as well as for the contributions from bonded atoms.

The Infrared Spectra of Naphthalene Crystals, Vapor, and Solutions
View Description Hide DescriptionThe infrared spectra of naphthalene in the gas phase, in solutions of carbon tetrachloride, carbon disulfide, and methyl cyclopentane, and as single crystals have been obtained in the region 3300–450 cm^{−1}. The dichroism of three different single crystal planes, including the cleavage plane, has been studied using polarized infrared radiation. The frequencies were segregated into their respective symmetry classes on the basis of an assumed oriented gas model. Band contour data, together with a statistical comparison of the spectrum of the gas phase with the spectra of the condensed phases, establish the usefulness of this model.

The Velocity of Sound in Electrolytic Solutions
View Description Hide DescriptionA relationship between the velocity of sound in electrolytes and concentration has been derived for extremely dilute solutions from the Debye‐Hückel limiting law. The equation fits the observed data at higher concentrations when the theoretical coefficients are replaced by empirical constants.

Correlation of Hammett's σ‐Values with Electron Densities Calculated by Molecular Orbital Theory
View Description Hide DescriptionIt is shown that Hammett's σ‐values can be correlated with electron densities calculated by the MO LCAO method. Since Coulomb and exchange integrals for atoms other than carbon are not accurately known, an absolute calculation of σ's is not possible. Nevertheless, σ‐values permit derivation of a self‐consistent and reasonable set of parameters which can be used to calculate reasonable values for absorption frequencies, mesomeric moments, and orienting power of the substituents.

On the Calculation of Electronic Levels in Pyridine and the Isomeric Picolines
View Description Hide DescriptionThe molecular orbital method was used for calculating electronic levels in pyridine and the picolines. The change of the benzene Coulomb integrals caused by the nitrogen atom in the ring and the CH_{3} substitution is treated by introducing into the secular determinant perturbation parameters δ_{ k } at the appropriate positions. Bonding and antibonding single‐electron molecular orbitals are calculated neglecting the overlap integral and electronic repulsion. The average heights are determined for the four one‐electron transitions corresponding to the fourfold degenerate level in benzene. By using the assumption that the centers of gravity of the actual singlets are proportional to these average heights, these centers of gravity are predicted for pyridine and the three picolines using two different perturbation parameters δ_{N}. The values for pyridine show satisfactory agreement with the experimental mean value 6.14 ev.

The Origin of the Ultrasonic Absorption in Liquids. II
View Description Hide DescriptionExcess absorption in nonassociated liquids has been explained by the same mechanism as is responsible for molecular absorption in gases, namely, slow exchange of energy between internal and external degrees of freedom.
In this paper the rate of energy exchange is calculated for benzene and found to be three times too rapid. The Lennard‐Jones interaction potential and model of the liquid are used; the fourth‐order terms in the interaction provide the coupling between internal vibrations and Debye waves.

The Prediction of Thermodynamic Properties of Nonideal Solutions from Turbidity Measurements
View Description Hide DescriptionTurbidity measurements have been made on the systemsnear the critical solutiontemperature at seven atmospheres pressure and at a considerably higher pressure. The effect of pressure is to elevate the critical solutiontemperature and to decrease the minimum transmission. The wavelength dependence is consistent with the theory of Ornstein and Zernike. The change of fugacity with concentration is calculated as a function of temperature,pressure, and composition.

Effect of Various Gases on Potassium Ion Emission from Hot Platinum
View Description Hide DescriptionThe effect of several gases on the emission of potassium ions from a hot platinum surface has been studied. It has been found that oxygen, carbon tetrachloride, bromine, and helium cause a marked decrease in the potassium emission; nitrogen has a smaller effect; and hydrogen causes an increase in the emission.