Volume 20, Issue 6, 01 June 1952
Index of content:
Radial Distribution Functions and the Equation of State of Fluids Composed of Molecules Interacting According to the Lennard‐Jones Potential20(1952); http://dx.doi.org/10.1063/1.1700653View Description Hide Description
The integral equation for the radial distribution function of a fluid composed of spherical molecules interacting according to a modified Lennard‐Jones potential has been integrated in the Kirkwood approximation and in the Born‐Green approximation over a wide range of temperature and density. The distribution functions so obtained have been used to calculate the equation of state and the thermodynamic functions of the fluid. The calculated thermodynamic functions are compared with the experimental values for liquid argon.
20(1952); http://dx.doi.org/10.1063/1.1700654View Description Hide Description
A study of the effects of ultrasonics on the inversion of sucrose was made and negative results were obtained. In the light of these results one can make the following conclusions.
Chemical reactions attributed to ultrasonics can be classified according to three mechanisms. (1) Reactions due to cavitation never occur without the formation of bubbles. All of these reactions take place in the gas phase, are primarily thermal and are due to the heat developed during adiabatic compression. Thus, only reactants with an appreciable vapor pressure are affected. (2) Many reactions in the liquid phase are of secondary origin due to reactions with dissolved products of the primary reaction in the gas phase. Luminescense is also a secondary effect. (3) Some reactions are due to the uniform temperature elevation caused by absorption of acoustic energy of very high intensity in a short path length.
20(1952); http://dx.doi.org/10.1063/1.1700655View Description Hide Description
A review of published experimental data and theoretical discussions of spinning detonation reveals that there does not exist a consistent explanation of all the characteristics of such a phenomenon, particularly the dependence of spinning frequency upon tube diameter. In view of this, it is proposed to treat the problem principally from a hydrodynamic viewpoint by considering a possible periodic fluid motion with a characteristic frequency.
It is found that the calculated natural frequencies of vibration of the gaseous products behind a detonation wave agree closely with the measured frequencies of spinning detonation previously published in the literature. An analysis of such vibrations in the light of experimental evidence indicates that the vibratory motion is principally transverse. Of the various possible modes of vibration, the one which is observed depends upon the mixture composition and the tube size.
The observed existence of pressure waves in the wake of a spinning detonation wave is probably due to nonuniform combustion at the detonation front. It is shown how the initiation or cessation of combustion in a plane wave gives rise to compression or expansion waves respectively, and how a nonplanar disturbance excites a transverse vibration of characteristic frequency.
It is proposed that the uneven combustion of the spinning detonation wave is sustained by the heating and cooling effects of the vibratory pressure waves, which are themselves generated by such irregular combustion; i.e., spinning detonation is a self‐excited vibratory phenomenon. Its appearance may thus be‐attributed to the susceptibility of the reaction rate to the heating or cooling effects of pressure waves.
20(1952); http://dx.doi.org/10.1063/1.1700656View Description Hide Description
An attempt has been made to calculate the coefficients in LCAO molecular orbital functions of SF6, and ionization and excitation energies of this molecule, using a self‐consistent field method. The lowest ionization potential computed is 20.1 ev. Excitation energies to some forbidden and allowed levels are obtained, but are too large to be considered trustworthy. The present treatment was restricted in detail to twelve electrons, six from the sp 3 d 2 valence configuration of sulfur, and six 2pσ of fluorine. The other electrons were treated in smoothed‐out core potentials of the sulfur and fluorine atoms. It is believed that unexpectedly large errors may have been introduced by the neglect of detailed interactions of these electrons, and that the molecular orbitals in which they might be put are of importance.
The present calculation is purely theoretical and only the empirical value of the S–F bond distance has been used. All necessary integrals have been evaluated, most of them for the first time, and are collected in tables.
20(1952); http://dx.doi.org/10.1063/1.1700657View Description Hide Description
The isotopic composition of oxygen liberated in the catalytic decomposition of hydrogen peroxide using MnO2, Fe2O3, colloidalgold, metallic platinum, and soluble catalase as catalysts has been measured. All the catalysts except catalase produced a measurable fractionation of the oxygen isotopes in the case of complete decomposition. A few rate experiments were also carried out, and the kinetics studied from the standpoint of isotope separation as a function of fraction of hydrogen peroxide decomposed. It is demonstrated that none of the liberated oxygen comes from the substrate water or from the potassium permanganate when hydrogen peroxide is oxidized. Observed fractionation factors are somewhat smaller than the maximum values calculated on the basis of Bigeleisen's equations. A minimum in the O18 percentage of the evolved oxygen in the case of the catalase experiments suggests that two mechanisms are operative for this type of catalysis.
The initial enhancement of the O18 percentage of the evolved oxygen over that in the peroxide remains unexplained.
20(1952); http://dx.doi.org/10.1063/1.1700658View Description Hide Description
The dielectric constant,dielectric loss, and density of compressed fluoromethane have been measured at 50°C and 75°C in the pressure range 20 to 160 atmospheres. The ratio (ε−1)/d(ε+2) shows a large and regular decrease as the density increases. The theories of Debye, Onsager, and Kirkwood have been applied to the results. Evidence of the restriction of molecular rotation at high densities is adduced.
20(1952); http://dx.doi.org/10.1063/1.1700659View Description Hide Description
High precision measurements of the specific heat of germanium were carried out in the temperature region between 20°K and 200°K. Three samples of germanium were investigated: an extremely pure sample, one of intermediate purity (1018 impurity centers/cm3), and one with an addition of 0.006 atomic percent aluminum (2×1020 impurity centers/cm3). No anomaly such as reported by Cristescu and Simon was found in any of the samples. However, a small dependence of the specific heat on the concentration of impurity centers was observed.
20(1952); http://dx.doi.org/10.1063/1.1700660View Description Hide Description
Two rules are presented which relate the intensities of vibrational fundamentals of different isotopic species. They are thus analogous to the Teller‐Redlich product rule which relates frequencies. They apply to either infrared or Raman intensities. One rule permits the calculation of dipole‐moment derivatives without the determination of normal coordinates. The application of the rules is illustrated.
20(1952); http://dx.doi.org/10.1063/1.1700661View Description Hide Description
Diffusion coefficients are presented for the system C14O2–CO2 in the pressure range 100–1000 atmospheres, at temperatures 0°—25°—50°C. In the lower part of the range the results are consistent with those of Robb (see reference 2) and show little temperature coefficient for diffusion at constant density. At higher densities the temperature coefficient increases rapidly. The dense gas theory of Enskog is totally inapplicable, but the results are correlated in the formThe activation energy (E) at constant density and D 0 are given as a function of density in a form useful for extrapolation.
20(1952); http://dx.doi.org/10.1063/1.1700662View Description Hide Description
By a spectrophotometric method the acid‐base equilibrium between bromcresol green and triethanolamine was measured over the range of temperature from −6°C to +50°C in the three solvents—methanol, ethanol, and n‐butanol. In each solvent the equilibrium constant was found to vary rapidly with temperature; and in methanol the value of logK was found to change sign near 0°C. This behavior is very different from the well‐known results for weak acids in aqueous solution, and in the theoretical part of the paper a unified theory is presented to cover all types of proton transfer. The work required to transfer a proton consists of two parts, a part sensitive to the environment and a part insensitive to the environment; the behavior of the equilibrium constant depends on whether the two parts are of the same sign or of opposite sign. Families of curves are drawn to show the various possible types of behavior.
20(1952); http://dx.doi.org/10.1063/1.1700664View Description Hide Description
Large, single crystals of magnetite, 1 cm in diameter and up to 4.3 cm long, of high purity and perfection have been grown from the melt. The density at 20° is 5.185, i.e., 99.58 percent of the x‐ray density. The composition corresponds to stoichiometric Fe3O4 within analytical error. Phase diagram considerations, growing procedure, methods of chemical analysis, and composition data are discussed.
20(1952); http://dx.doi.org/10.1063/1.1700665View Description Hide Description
The velocity of steady detonation waves in 2.5 CO–O2 mixtures containing hydrogen agrees with the calculations of the Chapman‐Jouguet theory. When all sources of hydrogen atoms are eliminated from such mixtures, much hotter shock waves must be used to initiate detonation. The detonation waves in hydrogen‐free mixtures are stable but nonsteady. The velocities observed by piezoelectric pressure gauges undergo violent and not very regular fluctuations similar to, but not identical with, spinning detonations. Moving film slit photographs show that these fluctuations are caused by detonation fronts developing behind the forward shock, overtaking it at irregular intervals, and decaying in their stead. Similar detonation fronts are observed in delayed initiations of explosive mixtures capable of stationary detonation, but the waves upon initiation and after a few fluctuations settle into the stationary Chapman‐Jouguet regime. Photographic observations show that the detonations developing behind the shock front are initially localized near the opposite walls of the cylindrical tube, while the guage records demonstrate that the fronts of nonsteady waves are not normal to the tube axis but undergo irregular girations. The significance of these observations in terms of the rates of chemical reactions in shock fronts is discussed.
20(1952); http://dx.doi.org/10.1063/1.1700616View Description Hide Description
A logical computation method is suggested for approximating the thermodynamic properties of a simple molecular system. In this method the thermodynamic functions of a nonequilibrium system are computed exactly. The state of the system is then varied at fixed volume and temperature so as to give a minimum Helmholtz free energy, consistent with such conditions as are imposed to permit the exact computation. The condition under which this method leads to self‐consistent equations is discussed. The method is then applied in a way that is very close to the Lennard‐Jones and Devonshire cell method, but with cells of variable size. The distribution within a cell is assumed to be Gaussian. The method is numerically far easier than the cell method, and apparently somewhat better.
20(1952); http://dx.doi.org/10.1063/1.1700617View Description Hide Description
The thermal dimerization of chlorotrifluoroethylene leads to 1,2‐dichlorohexafluorocyclobutane consisting mainly of the high boiling isomer. On the other hand, the photochemical or catalytic chlorination of hexafluorocyclobutene yields a dichloride consisting mainly of the low boiling isomer. These isomers may be readily separated by fractional distillation. Dielectric constantmeasurements permit one to indicate that the high boiling one is cis and the low boiling is the trans. The infrared spectra in the sodium chloride region were measured and compared with the existing data on the Raman spectra.
20(1952); http://dx.doi.org/10.1063/1.1700618View Description Hide Description
The reaction between atomic sodium and ethyl chloride has been studied over the range 260° to 380°C by the diffusionflame method. From the temperature coefficient of the rate constant the activation energy was found to be 10.2 kcal per mole. The maximum uncertainty in this quantity from all causes, is estimated to be ±0.5 kcal per mole. The steric factor was 1.0±0.3, based on the customary value assigned to the collision diameter.
20(1952); http://dx.doi.org/10.1063/1.1700619View Description Hide Description
The ionization potentials of some 83 organic molecules have been measured with the mass spectrometer, using the critical slope method to interpret the ionization efficiency curves for the molecular ions. A self‐consistent group of values has been obtained in which the main relationships between ionization potential and molecular structure can be clearly distinguished. The results are compared with those obtained by spectroscopic and other methods, and some regularities in the discrepancies are pointed out.
20(1952); http://dx.doi.org/10.1063/1.1700620View Description Hide Description
The wave functions of molecules in their ground states can be expressed to a good approximation as single determinants made up of terms orthogonal to each other. The probability distribution for such systems can then also be expressed as a determinant. By integrating this quantity over all the spatial and spin coordinates except those of two electrons, a function is obtained which gives in effect the probability of finding a pair of electrons in assigned places with assigned spins. The properties of this function, called for short the correlation function, are examined in some particular cases. It is shown that the electrons of an inert gas atom, like neon, tend to dispose themselves so that those of the same spin subtend tetrahedral angles at the nucleus. The six outer electrons of the nitrogen molecule and acetylene tend to the same approximation to arrange themselves so that those of the same spin are in three planes through the nuclear axis inclined at 120° to each other. Similarly the eight outer electrons of the same spin in carbon dioxide tend to be correlated with each other in such a way that there are four between the carbon and the oxygen nuclei and four at the extremities of the molecule, there being two on each oxygen atom like ``lone electrons.'' In general the ``bonds'' of a molecule, when interpreted in terms of molecular orbitals, may be regarded as providing the appropriate correlation of electrons of the same spin.
20(1952); http://dx.doi.org/10.1063/1.1700621View Description Hide Description
It is shown that Onsager's formula for the dielectric constant of liquids, derived on the assumption of spherical molecules and a central mathematical dipole, still holds for extended dipoles of arbitrary position and direction as long as the molecules are spherical in shape.
20(1952); http://dx.doi.org/10.1063/1.1700622View Description Hide Description
The potentials, observed with a galvanic cell with two iodide‐iodine electrodes, at two different radii in a centrifugal field, have been studied with solutions of potassium and sodium iodides, to which were added varying concentrations of iodine. Using a short extrapolation the transference numbers of sodium iodide have been obtained. The earlier results using potassium iodide have been confirmed. These results, when interpreted with the aid of conductance measurements, indicated the presence of the ionic complex I3 −. A small deviation from the theory has been found with the results for sodium iodide‐iodine solutions. The emf centrifuge used in our earlier work has been simplified, and a galvanic cell has been utilized which avoids the collection of suspended particles on the electrodes.