Volume 32, Issue 5, 01 May 1960
Index of content:
32(1960); http://dx.doi.org/10.1063/1.1730910View Description Hide Description
The intermolecular potential energy between two inert gas molecules is considerably altered when these molecules are next to a solid surface as in physical adsorption. The change in the interaction is evidenced by the additional long‐range repulsion that is often observed between the molecules of a monolayer and also by the additional attractions that must play a role in multilayer formation.
In this article, the two‐molecule‐surface potential is derived from quantum mechanical third‐order perturbation theory. It is shown that this potential consists of two parts just as the energy giving the van der Waals attraction of a single molecule to a surface does. The first part exists only when the surface has a net electrostatic field and this is equivalent to the classical polarization effect. The second part arises from the fluctuations of the surface fields and is of the same origin as the dispersion forces. The third‐order energy, i.e., the new intermolecular interaction caused by the surface, is directly related to the zero‐coverage heat of adsorption and except for this experimental quantity, the results do not require specific assumptions about the surface. Thus, the theory is applicable to either metal or insulator surfaces. When both the two‐molecule‐surface and the one‐molecule‐surface interactions are available experimentally (for example, from the application of virial coefficients treatment in physical adsorption) the electrostatic field of the surface can be estimated.
The fluctuation or dispersion part of the third‐order energy is shown to yield a repulsion between two molecules in a monolayer that amounts to 20–40% of the gas phase Lennard‐Jones potential minimum ε0. The same energy yields an additional attraction of about 10–20% of ε0 when the two molecules are on top of one another as in multilayer formation. The theory is applicable also when more than two molecules at a time need be considered on the surface.
Transferability of Urey‐Bradley Force Constants. I. Calculation of Force Constants on a Digital Computer32(1960); http://dx.doi.org/10.1063/1.1730911View Description Hide Description
An algorithm for the systematic calculation of Urey‐Bradley force constants has been programed for a digital computer (the Datatron 204). The secular equation is set up and solved in internal coordinates, the potential energy being transformed from Urey‐Bradley space to internal‐coordinate space by a matrix Z. This same matrix is also used to transform the Jacobian of λ with respect to the force constants from internal‐coordinate to Urey‐Bradley space, thereby allowing the direct determination of Urey‐Bradley force constants. A method is described whereby the Z matrix and Wilson's G matrix may be set up by the computer from the geometrical parameters of the molecule.
32(1960); http://dx.doi.org/10.1063/1.1730912View Description Hide Description
Urey‐Bradley force constants have been fitted to the observed vibrational frequencies of COF2, COCl2, and COBr2 by the method described in the previous paper. These force constants have been used to calculate the frequencies of COClF, COBrF, and COBrCl. Normal coordinates and the potential energy distribution among the various Urey‐Bradley coordinates have also been calculated. It is found that, despite the fact that the carbonyl stretching frequencies fall over a range of 100 cm—1, the carbonyl stretching force constant is essentially the same for all molecules in the carbonyl halide series.
32(1960); http://dx.doi.org/10.1063/1.1730913View Description Hide Description
The multicomponent chemical equilibrium composition problem is discussed generally and a formulation of it is presented in a form suitable for digital computer calculations. A geometric interpretation of the equations used to specify the chemical system is also given.
32(1960); http://dx.doi.org/10.1063/1.1730914View Description Hide Description
The statistical mechanical theory of the diffusion coefficients in binary liquid solutions is developed from the viewpoint of the pair space linear relations. Equations for the composition dependence of the ratios of the friction and diffusion coefficients are developed. For solutions which are regular it is found that the ratio of the two self‐diffusion coefficients is in the inverse ratio of the corresponding molar volumes. The assumptions of the theory are discussed critically.
Measurements of Multicomponent Diffusion Coefficients for the CO2–He–N2 System Using the Point Source Technique32(1960); http://dx.doi.org/10.1063/1.1730915View Description Hide Description
Measurements of the diffusion coefficient for a trace of carbon dioxide in a mixture of helium and nitrogen of varying composition have been made at room temperature and atmospheric pressure using the point source technique. The results are shown to be in agreement with the results of Fairbanks and Wilke in that an equation of the form can be used to relate the diffusion coefficient of a trace of species i in a mixture of composition given by the mole fraction xk to the binary diffusion coefficients Dik . Some data are presented on the separation of the mixture in the diffusion zone.
32(1960); http://dx.doi.org/10.1063/1.1730916View Description Hide Description
The theory of preferential etching at dislocations has been presented by Cabrera. In the present report the theory is reviewed and compared to empirical observations on the dissolution of lithium fluoride. The observed dissolution behavior is consistent with Cabrera's theory as modified by the effect of dissolution poisons.
Calculation of the Coupling Terms Neglected in Performing the Born‐Oppenheimer Separation for the Hydrogen Molecule Ion32(1960); http://dx.doi.org/10.1063/1.1730917View Description Hide Description
A method is given for calculating the coupling between the nuclear and electronic motion in the hydrogen molecule ion using the exact wave functions. Calculations are carried out for the transition 1sσ—2sσ and compared with values obtained from simple approximate methods. Estimates are made of the cross sections for excitation and capture into the 2s state during a proton‐hydrogen atom collision, using approximate H2 +wave functions to describe the state during collision. Finally, it is shown that a Born‐Oppenheimer separation carried out in relative coordinates should be slightly more accurate than the usual treatment using fixed space coordinates. Two different types of relative coordinates suggest themselves for use at different ranges of internuclear separation.
32(1960); http://dx.doi.org/10.1063/1.1730918View Description Hide Description
The author's earlier theory of sputtering has been simplified to a form from which direct computations are possible without extended numerical analysis. A considerable analytic simplification is obtained by a new choice of boundary conditions, and certain mathematical expressions have been modified by physical considerations where a detailed analysis is not justified by the present state of experimental information. The special cases of very high and very low energy sputtering are examined in some detail. The (lnE 0)/E 0 high‐energy results of Goldman and Simon are shown to be fortuitous but still significant. Low energy results are of the form reported by Wehner.
32(1960); http://dx.doi.org/10.1063/1.1730919View Description Hide Description
The connection between intermolecular potential energies and the unit cell vibrational frequencies in molecular crystals is summarized in Sec. I. Details of the treatment of potentials which can be written as functions of intermolecular atom‐atom distances are developed. The frequencies of vibration of methyl chloride in the crystal are treated by the methods discussed in Sec. II. Dipole‐dipole interactions are insufficient to explain the observed splittings. For vibrations which are primarily hydrogen motions, an intermolecular hydrogen‐hydrogen repulsion potential accounts satisfactorily for the observed effects.
32(1960); http://dx.doi.org/10.1063/1.1730920View Description Hide Description
The problem of calculating the probability of electron capture by neutral molecules is analyzed. It is shown that capture is possible only through the breakdown of the separation of nuclear and electronic motion in the Schrödinger equation, and that this is equivalent to the use of the nuclear kinetic energy as a perturbation operator. For diatomic molecules, it is found that capture is improbable except for those states of the negative ion whose major configuration contains at least as many MSO's of a given spin‐symmetry type as the neutral molecule. Experimental verification of this result is found in the case of hydrogen.
32(1960); http://dx.doi.org/10.1063/1.1730921View Description Hide Description
A system of excess functions is developed for electrolytesolutions and other solutions with an essentially unsymmetrical solvent‐solute relation. These new functions vanish for a solution whose practical (molal scale) osmotic coefficient is unity at all compositions, temperatures and pressures. The use of these excess functions offers some advantages over other methods of comparing Mayer's ionic solution theory with experiment, of representing the properties of solutions of single or mixed electrolytes, and of making qualitative interpretations of the molecular basis of thermodynamic properties.
Graphs showing the ionic‐strength dependence of the excess free energy, excess enthalpy, excess entropy, and excess volume are given for several aqueous solutions of single electrolytes up to 6 molal. Experimental values of the cluster integral sum, the characteristic function of the Mayer theory, have also been calculated. The concentration dependence of this function is very similar to that of the excess free energy.
32(1960); http://dx.doi.org/10.1063/1.1730922View Description Hide Description
A mass spectrometric investigation of the vapor in thermodynamic equilibrium with powdered molybdenum dioxide has shown the vapor phase to consist, in decreasing order of importance, of the species MoO3, (MoO3)2, MoO2, and (MoO3)3. The heats, entropies, and free energies of reaction have been determined for the reactions (T=1600°K):For the case x=1, 2, 3 the ΔHT 's are 121.8±3, 133.4±7, and 142.6±13 kcal/mole, respectively. Entropies of the gaseous molecules MoO3, (MoO3)2, (MoO3)3, and MoO2 at T=1600°K are 96.6, 151.0, 201.2, and 85.5 eu, respectively. In addition, the atomization energies (ΔH 0 o) for the reactionwere calculated to be 277.4±7 and 419.7±10 kcal/mole for x=2 and 3, respectively.
32(1960); http://dx.doi.org/10.1063/1.1730923View Description Hide Description
The evaporation of alumina under nearly neutral conditions in tungsten and molybdenum Knudsen cells has been investigated by mass spectrometric methods. The atomization energies of the gaseous molecules are D 0 o(AlO) = 115±5 kcal/mole; D 0 o(Al2O) = 245±7 kcal/mole; D 0 o(Al2O2) = 365±7 kcal/mole.
32(1960); http://dx.doi.org/10.1063/1.1730924View Description Hide Description
Partial pressures of the gaseous oxides MoO, MoO2, MoO3, WO, WO2, WO3, UO, UO2, and UO3 in the systems Mo–Al2O3 and U–Al2O3 have been measured by mass spectrometric methods. The vapor pressure of uranium has also been determined. The reactionenthalpies derived from these measurements are:
32(1960); http://dx.doi.org/10.1063/1.1730925View Description Hide Description
High resolution NMR spectra of four epoxides have been observed at 40 Mcps and analyzed. These epoxides are of the type[Complex chemical formula]where R is a phenyl group (styrene oxide), a cyanide group (glycidonitrile), an acetyl group (1,2‐epoxy‐3‐butanone), and a carboxyl group (glycidic acid). For each molecule the spin‐spin coupling constants and nuclear magnetic screening parameters for the A, B, and Cprotons were derived from the experimentally determined energy levels. The method for obtaining numerical values for the energy levels from the spectra is described fully. ABK and AA′K approximations as well as an iterative ABC method of solution are described and illustrated.
Corresponding coupling constants are found to be about the same in all four molecules with JAB =5.8±0.5 cps, JAC =2.2±0.5 cps and JBC =4.6±0.5 cps. However, the variations from molecule to molecule are considerably greater than the estimated precision of ±0.05 cps. The ABX approximation is shown to be inadequate either for the precise determination of the constants or for the calculation of relative intensities. As compared with the iterated ABC solution, the ABK or AA′K approximation leads to good values for the constants and adequately describes the relative intensities.
32(1960); http://dx.doi.org/10.1063/1.1730926View Description Hide Description
The refractive indices of the benzene‐carbon tetrachloride system have been measured at seven different wavelengths in the visible region. These indices show only slight departure from linearity in the mole fraction. The molar refractions, calculated according to the Lorentz‐Lorenz equation, are not additive in the mole fraction. Moreover, no simple relation between the molar refractions and the frequency of the light source is obtained.
32(1960); http://dx.doi.org/10.1063/1.1730927View Description Hide Description
The refractive indices of the benzene—methanol system have been measured at 25° at seven wavelengths in the visible region. The electronic polarizability of benzene, methanol, and carbon tetrachloride have been calculated from the refractive indices of this system and those of the benzene‐carbon tetrachloride system by use of the Böttcher equation. The data are then used to calculate the molar electronic polarizations of the carbon tetrachloride‐methanol system which are found to be in good agreement with experimentally determined values. These results show that, within the experimental error, the electronic polarizabilities of the three components are independent of the composition and hence of the environment. The electronic polarizabilities of the three substances are found to follow a dispersion equation with only one term.
32(1960); http://dx.doi.org/10.1063/1.1730928View Description Hide Description
A discussion is given of the relations which exist among vibrational matrix elements for diatomic molecules represented as Morse oscillators. This is done according to the wave function approximation of Trischka and Salwen. It is shown how the matrix element of the dipole moment is related to the matrix elements where v′—v≤i≤v′+v with v′>v. This relation is examined for the case of the 1–2 band of HCl. It is also shown how the matrix element for DCl can be related to the matrix elements of HCl. Finally, the influence of the vibration‐rotation interaction is incorporated in the wave function approximation. In an example, it is shown that the matrix element can be expressed in terms of the set of matrix elements .
Application of Least‐Squares Method to Density‐Intensity Calibration in Electron Diffraction Studies32(1960); http://dx.doi.org/10.1063/1.1730929View Description Hide Description
A new method based on the principle of least squares is proposed for the calibration of the characteristics of photographic emulsion employed in electron diffraction studies. The calibration procedure consists of two steps. First, a function having three parameters was found which represents the relation between the optical density and exposure. Secondly, the most probable values of the parameters and their standard errors were determined in a straightforward way by the method of least squares. An application of this method to the diffraction patterns of benzene is described. The standard errors of final relative intensities were evaluated over the entire observed range of optical densities.