Volume 18, Issue 1, 01 January 1950
Index of content:
Diffusional Boundary Value Problems Involving Moving Boundaries, Connected with the Growth of Colloidal Particles18(1950); http://dx.doi.org/10.1063/1.1747422View Description Hide Description
A method is suggested for treating problems of diffusion which involve moving boundaries. This method is applicable when the flux of material through any surface in the diffusion field is considerably greater than the rate of change of concentration on that surface. The method is applied to two problems dealing with the growth of monodispersed aerosols and hydrosols.
The solution of the first of these problems indicates that, in a naphthalene‐like aerosol system growing by means of the diffusion of vapor toward sinks (nuclei) which cannot support supersaturation, spontaneous nucleation will not occur if the number density of nuclei exceeds 100/cc.
The solution of the second problem permits the reproduction from theory of several curves due to Zaiser and La Mer which depict the rate of growth of sulfur hydrosols, therefore lending support to the idea that the particles grow by means of a simple diffusion mechanism rather than by a surface catalyzed deposition. The critical supersaturation concentration for sulfur in aqueous solution isand the diffusion coefficient of S8 isThese values are in reasonable agreement with those estimated by independent means, although the diffusion coefficient seems to have about one‐half the expected value. This indicates that a unit larger than S8 may be diffusing, e.g., a polythionate.
An Electron Diffraction Investigation of the Structures of Neopentyl Chloride and Silico‐Neopentyl Chloride: The Determination of Intensities through the Use of a Rotating Sector18(1950); http://dx.doi.org/10.1063/1.1747431View Description Hide Description
Constructional details and operational data on an electron diffraction apparatus, in which a rotating sector has been incorporated, are presented. Its range of application and limitations are listed, and methods for the reduction of microphotometer records are discussed.
Electron diffraction photographs of neopentyl chloride and silico‐neopentyl chloride were taken with and without sectors. Their structures were deduced by a combination of the visual and photometric procedures. Attempts were made to estimate quantitatively the equivalent temperature factors for libration about the C–C and Si–C bonds. Best values for the interatomic distances and their possible interpretations are presented in the concluding section.
18(1950); http://dx.doi.org/10.1063/1.1747453View Description Hide Description
The structure of uranium hexafluoride has been redetermined by electron diffraction. Special precautions were taken to eliminate sample contamination; both sector and non‐sector photographs were analyzed. Even casual inspection of the photographs and microphotometer traces shows that insofar as this type of measurement is concerned, the structure of UF6 is not a regular octahedron. The model which is in best agreement with the data is a distorted octahedron with three short (1.87A) and three long bonds (2.17A). However, a model with a center of inversion, possessing two short (1.87A), two medium (2.12A), and two long bonds (2.22A) cannot be eliminated.
The disagreement between the structures deduced from various technics is discussed, as are also possible experiments which might be done to resolve these differences.
The Structure of Hexamethylcyclotrisiloxane as Determined by the Diffraction of Electrons on the Vapor18(1950); http://dx.doi.org/10.1063/1.1747454View Description Hide Description
Hexamethylcyclotrisiloxane vapor has been shown to have a structure incorporating a planar ring with larger oxygen valence angles (125±5°) than silicon valence angles (115±5°); the methyl groups extend above and below the plane of the ring, their equilibrium bond positions making a probable angle of 112±6° with silicon, the temperature motion of the methyl groups allowing an average change in the interatomic distances involved of about 0.09A, as compared with the normal temperature motion change of about 0.03A. The Si–O distances are 1.66±0.04A and the Si–C distances are 1.88±0.04A.
The shortness of the Si–O distance suggests a larger ionic character of the bond than that indicated by the electronegativity table.
Spectroscopic Studies of Rotational Isomerism. V. The Infra‐Red Absorption Spectra of Six Solid Hydrocarbons in the Region 1600–650 cm−118(1950); http://dx.doi.org/10.1063/1.1747455View Description Hide Description
The infra‐red absorption spectra of six hydrocarbons have been measured at low temperatures. As with the Raman spectra, a considerable degree of simplification occurs on freezing, due to the existence of only one rotational isomer in the solid state. It has not proved possible to obtain accurate values of the energy differences between the isomers from this data. The possible ways of obtaining energy difference from spectroscopic data are discussed.
18(1950); http://dx.doi.org/10.1063/1.1747456View Description Hide Description
A general theory of Rayleigh scattering due to composition fluctuations in multi‐component systems is developed with the aid of the grand canonical ensemble of Gibbs. It reduces to the usual expression for systems of two components, but contains previously neglected terms arising from thermodynamic interactions between solutes in systems of more than two components. The theory is used to interpret the turbidity measurements of polystyrene in benzene‐methanol mixtures of Ewart, Roe, Debye, and McCartney.
18(1950); http://dx.doi.org/10.1063/1.1747457View Description Hide Description
A general equation is developed for the fluctuation of refractive index in multi‐component systems, thus permitting the interpretation of turbidities for such systems in the absence of angular dissymmetry. Applications to several special cases of interest are presented.
18(1950); http://dx.doi.org/10.1063/1.1747458View Description Hide Description
The variation of the solubility of a solute due to the presence of a second solute in a solid ionic compound as solvent is investigated theoretically with the aid of the ideal law of mass action. Ions of the solvent in interstitial positions, cation and anion vacancies, quasi‐free electrons, and electron holes are to be taken into account in the same manner as the constituents of conventional chemical systems. The theoretical conclusions are illustrated by experimental data, however, qualitatively rather than quantitatively.
The solubility of lead chloride in solidsilver chloride is decreased by presence of cadmium chloride. The solubility of iodine (or cupric iodide) in cuprous iodide is likewise decreased by presence of cadmium iodide. The behavior of the corresponding bromide system is analogous. Conversely, gallium oxide increases the solubility of zinc in zinc oxide. The phenomena to be expected in lead sulfide as solvent are more complicated, since this substance can dissolve both excessive lead and excessive sulfur.
The oxidation rate of nickel is increased by presence of chromium and manganese, whereas the chlorination rate of silver is decreased by presence of lead and cadmium chloride.
18(1950); http://dx.doi.org/10.1063/1.1747459View Description Hide Description
For the decomposition of nitrous oxide on metals and oxides, a tentative mechanism is indicated which involves quasi‐free electrons as reactants and adsorbed oxygen ions as intermediate product. This mechanism is in accordance with experimental facts such as retardation by oxygen, a fractional order of the reaction with respect to nitrous oxide in the case of indium oxide as catalyst, and the decrease of the electrical conductivity of zinc oxide due to the presence of nitrous oxide. A mixture of zinc oxide and gallium oxide, however, has about the same catalytic activity as pure zinc oxide, although the electrical conductivity of the mixed catalyst is about fifty times greater than that of pure zinc oxide. This finding can be accounted for by the assumption that the reaction between nitrous oxide and electrons of the catalyst takes place in the vicinity of an adsorbed zinc ion or an anion vacancy.
18(1950); http://dx.doi.org/10.1063/1.1747460View Description Hide Description
The mobility of cation vacancies and the equilibrium concentration of cation and anion vacancies in solidpotassium chloride are calculated from measurements of the electrical conductivity of pure potassium chloride and solid solutions of strontium chloride in potassium chloride.
Transference Numbers of Solid Potassium Chloride with Strontium Chloride, Potassium Oxide, and Sodium Sulfide as Additives18(1950); http://dx.doi.org/10.1063/1.1747461View Description Hide Description
The transference number of cations in solid potassium chloride at 600°C has been found to be 0.88 in accordance with previous experiments of Tubandt, Reinhold, and Liebold. Addition of strontium chloride causes increase of the transference number approaching unity. Addition of potassium oxide and sodium sulfide, respectively, lowers somewhat the transference number of cations and accordingly increases the transference number of anions. These results are in accordance with the Schottky disorder model, but the presence of interstitial cations apart from cation and anion vacancies cannot be ruled out.
18(1950); http://dx.doi.org/10.1063/1.1747462View Description Hide Description
The entropies,free energies,heat capacities and heat contents of methyl mercaptan and dimethyl sulfide have been calculated from 298.16°K to 1500°K at 100°K intervals. The free energies of formation of these compounds have also been calculated for this temperature range based both on sulfur gas and rhombic sulfur as the standard states of sulfur.
Quantitative Studies of Radiation‐Induced Reactions in Aqueous Solution. I. Oxidation of Ferrous Sulfate by X‐ and γ‐Radiation18(1950); http://dx.doi.org/10.1063/1.1747463View Description Hide Description
A study has been made of the oxidation of ferrous ions in 0.8N sulfuric acid solution by x‐ and γ‐radiation in different types of system and using different energies of incident radiation. The conclusion is reached that simple modes of dosimetry, such as have been used in previous determinations of the ionic yields for a number of reactions induced by radiation in aqueous systems, are adequate if accuracy within 20 percent is all that is required. For greater precision, more rigorous methods have to be adopted, and using such a method, the ferrous sulfate system has been calibrated with a view to its possible use as a mode of integral dosimetry for aqueous media. Some speculations as to the mechanism of this particular reaction are included.
18(1950); http://dx.doi.org/10.1063/1.1747464View Description Hide Description
The absorptionspectrum of hydrogen peroxide vapor was examined under low dispersion in the range 2–15μ. Four bands were observed at 3590, 2630, 1255, and 877 cm−1. The spectrum of the liquid also was measured between 2 and 21μ; it showed five bands at about 3400, 2780, 1350, 880, and 550 cm−1. The last one, which seems very diffuse, is presumably the torsional oscillation of the OH groups; as such it corresponds to a potential energy barrier of the order of 4 kcal./mole. New assignments are proposed in agreement with the model of Penney and Sutherland. Under high dispersion the second harmonic O–H frequency was found to consist of two identical hybrid bands at 7036.6 and 7041.8 cm−1, of which the rotational constant for the ground state is in perfect agreement with that already found for the third harmonic band. The explanation given previously for the doublet character of the vibrational levels of hydrogen peroxide is further substantiated by the present results. From both vibrational and rotational data the O–H distance in hydrogen peroxide appears to be slightly greater than that in water.
18(1950); http://dx.doi.org/10.1063/1.1747465View Description Hide Description
Sets of valence force displacement coordinates are given which are applicable to practically any system. The coordinates for ideal bonding‐angles arise as special cases. The derived symmetry coordinates for a few typical systems are obtained, and it is shown how the force constants can be corrected for small deviations of the angles from their ideal hybrid‐bond values.
18(1950); http://dx.doi.org/10.1063/1.1747466View Description Hide Description
An investigation has been made of the chemical forms assumed by Cr51 when it is produced by positron decay of Mn51 under a variety of conditions. The data have shown that the oxidation state of the parent Mn51 plays an important role in determining the oxidation state of daughter Cr51. By variation of experimental conditions some information has been obtained regarding the types of chemical reactions undergone by the Cr51. These reactions have also been shown to play important roles in determining the ultimate chemical form of daughter Cr51.
The complexity of the factors determining the chemical forms of Cr51 after Mn51 decay has been pointed out, and possible explanations of some of the observed phenomena have been suggested. We believe the results are consistent with the hypothesis that appreciable ionization in the valence shell accompanies the beta‐decay process.
Incidentally it has been demonstrated that the manganeseisotope of 44‐min. half‐life (Mn51) decays to the chromiumisotope of 26‐day half‐life (Cr51).
18(1950); http://dx.doi.org/10.1063/1.1747423View Description Hide Description
A method of preparation of potassium ferrate of 97 percent purity is described. Although the product contained an inseparable ferromagnetic impurity, the susceptibility of the ferrate was determined by extrapolation to infinite field strength of data obtained by the Gouy method. The observed effective magnetic moment of the ferrate ion agrees approximately with that expected for hexavalent iron.
18(1950); http://dx.doi.org/10.1063/1.1747424View Description Hide Description
Inaccuracies in previously published theories dealing with the swelling of networkpolymers in solvents are pointed out. The treatment of Flory and Rehner, based on the tetrahedral model, is overly restrictive and leads to an entropy of swelling which is too small. A more recent treatment of Kuhn, Pasternak, and Kuhn introduces an error in the opposite direction. In the present paper the entropy of swelling a network of any degree of connectivity, or functionality f, is derived in a manner which avoids these inaccuracies. Corrected relationships are given for the partial molal‐free energy of dilution, swelling equilibrium and the influence of deformation on swelling equilibrium. These differ appreciably from those previously given when the degree of interlinking (i.e., concentration of cross linkages if f=4) is large and the equilibrium degree of swelling therefore is small. Previous expressions for elastic deformation at constant volume are unaffected.
18(1950); http://dx.doi.org/10.1063/1.1747425View Description Hide Description
The development of the preceding paper is applied to the calculation of the internal pressure contribution arising from the nature of the polymer structure. A network structure imposes a positive (compressive) internal pressure which increases with the degree of interlinking. In polymers composed of finite molecules the internal pressure should, of course, decrease in proportion to the reciprocal of the molecular weight. A general formula for the dependence of the internal pressure on polymer structure is given which embraces both of these extreme cases and includes also imperfect network structures possessing unattached terminal groups. Magnitudes of the calculated internal pressure contributions are sufficient to alter the specific volumes perceptibly.
18(1950); http://dx.doi.org/10.1063/1.1747426View Description Hide Description
Using the ultrasonic pulse method, the velocity of longitudinal waves in metallic beryllium has been measured from 300°K to 23°K, and transverse waves from 300°K to 3°K. The adiabatic moduli and compressibility have been computed from the velocities. A new technique for affixing the quartztransducer to the solid for ultrasonicmeasurements, in suitable solids, below 100°K, has been successfully employed for the measurements in beryllium.