Showing papers in "Journal of Chemical Physics in 1954"

High‐Temperature Equation of State by a Perturbation Method. I. Nonpolar Gases

Abstract: A theoretical study is made of the equations of state of argon and nitrogen, at high temperatures and densities. The intermolecular potential used is of the Lennard‐Jones form, with an adjustable rigid sphere cutoff. A perturbation theory is developed, by which the thermodynamic properties of one system may be related to those of a slightly different system and to the difference in the intermolecular potentials of the two systems. In this article, the unperturbed system is a rigid sphere fluid, and the Lennard‐Jones potential is the perturbation. The results are in fair agreement with experiment, and also lead to an experimental test of the theoretical rigid sphere equation of state.

Theory of Concentration Quenching in Inorganic Phosphors

Abstract: A theory is presented for concentration quenching in solid systems, based on the migration of excitation energy from one activator center to another and eventually to an imperfection which may act as an energy sink. Calculations are made on the dependence of the fluorescence yield on concentration, and to indicate typical activator concentrations at which appreciable quenching may be expected to occur. If the transition in the activator is of the electric dipole or electric quadrupole type, appreciable quenching may arise when the activator concentration is 10‐3 to 10‐2; if it is a magnetic dipole transition, transfer will occur by exchange, rather than by overlapping of magnetic dipole fields, and the critical concentration will be of the order of a few percent. The implications of transfer phenomena upon the observed absence of luminescence in most ``pure'' inorganic crystals are discussed, and it is concluded that transfer rates are so high in strongly absorbing crystals that the energy can easily migrate to a very few sinks dispersed throughout the lattice.

Markoff Random Processes and the Statistical Mechanics of Time‐Dependent Phenomena. II. Irreversible Processes in Fluids

Abstract: The procedures developed in a previous paper of the same main title are applied to the specific case of irreversible processes in fluids. The gross variables are chosen to be a finite number of the plane‐wave expansion coefficients of the local particle, momentum and energy densities. As an example, the gross variables describing the local particle density are ∑ i=1Nexpik·xi, where pi and xi are the momentum and position of the ith molecule and N the total number. k runs over a finite number of values which are all small compared to the reciprocal mean distance between molecules. The phenomenonological equations are derived and expressions are given for the viscosity, diffusion, and heat conductivity in terms the autocorrelation coefficients of certain phase functions. These expressions are supposed to be valid for both liquids and gases. They are shown to coincide with the Chapman‐Enskog expressions for dilute gases.

Molecular Orbital Theory of Orientation in Aromatic, Heteroaromatic, and Other Conjugated Molecules

Abstract: As to the LCAO MO treatment of the orientation problem in chemical reactions of π‐electron systems, the frontier electron concept which has been previously introduced by the authors for explaining the reactivities in aromatic hydrocarbons is subjected to an extension in the sense that the frontier orbitals are specified according to the type of reaction. Thus, fundamental postulates relating to the reactivities of π‐electron systems are set up, which are believed to include general principles involved in the mechanism of both substitution and addition of electrophilic, nucleophilic, or radical type. On the basis of these postulates it is possible to predict the position of attack in conjugated molecules in all the three types of substitution as well as addition in a consistent manner. There is a nearly perfect agreement between the theoretical conclusions and experimental results hitherto reported.

Statistical Mechanical Theory of Transport Processes. VII. The Coefficient of Thermal Conductivity of Monatomic Liquids

Abstract: A molecular theory of the coefficient of thermal conductivity is developed from the general theory of transport processes presented in the first article of this series. The thermal conductivity of liquid argon at its normal boiling point is evaluated using the Lennard‐Jones intermolecular potential and a theoretically determined radial distribution function. The theory leads to an explicit expression for the product of the thermal conductivity and the friction constant of the theory of Brownian motion. With a reasonable estimate of the friction constant, the results of the theory agree satisfactorily with experiment.

A Note on the Fluorine Resonance Shifts

Abstract: A theoretical analysis is given of the fluorine magnetic resonance shifts in molecules. It is shown that the large range of shifts among different fluorine compounds arises from the effects of binding on the magnetic fields at the nucleus produced by the orbital motion of the electrons in the unfilled valence shell. The simple dependence on ionic character of the bond is also explained. The chemical shift between F2 and HF is calculated to be 14×10—4 compared to the experimentally observed value 6.3×10—4.

Photoionization and Total Absorption Cross Section of Gases. I. Ionization Potentials of Several Molecules. Cross Sections of NH3 and NO

Abstract: Ionization potentials determined by examining the long wavelength limit of the ionization continuum for H2S, CS2, C6H6, toluene, p‐xylene, C2H4, butadiene, and CH3I agreed with spectroscopic values obtained by Price and co‐workers. Values are reported also for NH3, NO, acetone, methyl‐ethyl‐ketone, CH3OH, and C2H5OH.Improved energy measurements showed that photoionization cross sections of NO in the region 1070—1340A obtained earlier were about 40 percent too low. At 1215.6A the photoionization and the total cross sections are 2.0×10—18 and 2.4×10—18 cm2, respectively, the difference being ascribed to an absorption band. The photoionization cross section of NH3 was found to rise rather gradually with decreasing wavelength in the region 1220—1060A and to reach a value of 9×10—18 cm2 at 1060A.

The Intermolecular Potentials for Some Simple Nonpolar Molecules

Abstract: Experimental data on the crystal properties, second virial coefficients, and viscosity coefficients of Ne, A, Kr, Xe, CH4, N2, CO, O2, and CO2 were analyzed for the purpose of obtaining values of the parameters in the exp‐six intermolecular potential, [open phi](r)=e1−6/α[6αeα(1−r/rm)−(rmr)6]. For gases whose molecules are spherical, it was possible to reproduce, with a single set of potential parameters, not only the crystal, second virial, and viscosity data, but also data on other transport properties with fair accuracy. For gases whose molecules deviate appreciably from spherical symmetry it was necessary to choose at least two different sets of potential parameters in order to reproduce different types of properties. Such behavior was taken to indicate the inadequacy of the assumptions, made in the fundamental gas theories, that intermolecular forces are central and that intermolecular collisions are elastic.

The Viscoelastic Properties of Plastics

Abstract: A general method has been devised to predict the viscoelastic behavior of plastics. A simplified model of the molecule is assumed and its general motion is treated by the method of normal coordinates. General equations have been developed such that when the manner of application of external forces to the molecule is known, the molecule's general behavior may be found in a convenient and straightforward fashion.This method has been used to obtain theoretical curves for the viscoelastic behavior of cross‐linked polymers subjected to sinusoidal forces. Also, the similar problem for linear material has been solved together with the creep and stress relaxation problems. It is shown that the temperature‐time superposition procedure of Ferry and Tobolsky has a firm theoretical basis. In general, the theoretical curves appear to agree with the limited experimental data available. The method is also applied to the case of dilute solutions and comparison is made with the result obtained by Rouse using a different a...

Vibrational Relaxation Times in Gases (Three‐Dimensional Treatment)

Abstract: The calculations previously made by Schwartz, Slawsky, and Herzfeld are extended to three dimensions. As before, an exponential repulsion is fitted to the Lennard‐Jones potential, with constants found from viscosity data. While the transition probability is determined directly by the short range repulsion forces, the attractive forces and the effect of the centrifugal quasi‐potential modify the effective velocity of the colliding molecules. The agreement with experiment is fairly good, although high up on the repulsion curve (O2,N2) the Lennard‐Jones 6—12 curve seems to be not quite steep enough.

The Origin of the Fluorescence in Self‐Activated ZnS, CdS, and ZnO

Abstract: It is proposed that the luminescent center in ``self‐activated'' ZnS consists of a cation vacancy whose nearest surroundings have lost one electron. Such a center is consistent with the fact that at low firing temperatures, the appearance of the blue fluorescence of self‐activated ZnS depends upon the presence of ``promoter ions'' (monovalent anions or trivalent cations) whereas, if the firing temperature be sufficiently high, some blue fluorescence is obtained without the presence of such promoter ions. The luminescence of reduced ZnS, CdS, and ZnO is also discussed, and is attributed to anion vacancies that have trapped one electron.

Analysis of the Near Ultraviolet Absorption Spectrum of Acetylene

Abstract: The absorption spectrum of acetylene in the region 1970—2470A has been photographed in the fourth and fifth orders of a twenty‐one‐foot grating spectrograph with absorbing paths of 0.007 to 70 m‐atmos.It has been possible to extend the arguments which led King and Ingold to conclude that in the upper electronic state the molecule is bent and has C2h symmetry. The upper electronic state is Au or, possibly Ag.The effective moment of inertia Ia of the excited state is small, causing sub‐band separations of 50 to 150 cm—1. These sub‐bands all have P, Q, and R branches, are well resolved, and have the appearance of bands of diatomic molecules. The following rotational constants of the upper state are derived: A0=12.94, B0=1.1247, C0=1.0297 cm−1. If the C–H distance is assumed to be between 1.070 and 1.090A, one finds rcc=1.388A, [open phi]CCH=120∘. Ground‐state combination differences are in agreement with precise values derived from infrared data. Some new lower state B values are obtained.The O–O vibratio...

Excited States of the Naphthalene Molecule. I. Symmetry Properties of the First Two Excited Singlet States

Abstract: The detailed polarization properties of the bands in absorption and fluorescence spectra of the naphthalene molecule have been determined by a method which makes use of a substitutional solid solution of naphthalene in durene. A single crystal of about 0.1 percent naphthalene in durene was cut so that the short axes of the naphthalenes lie strictly parallel to the surface and in one direction. The spectra were then determined in polarized light at 20°K under moderately high dispersion. The results clearly indicate that the first state is 1B3u (the transition from the ground state is long‐axis polarized) and the second 1B2u. Vibrational‐electronic interaction involving b1g vibrations apparently couples the first state with the second, and this results in a large short‐axis polarized transition moment. This fact has been at the root of most of the previous difficulties with analysis of the spectra.

The Electronic Spectra of Cata‐Condensed Hydrocarbons

Abstract: It is shown how the main features of the spectra of cata‐condensed hydrocarbons may be explained on the basis of a very simple model. This, so‐called perimeter model was used, in its free‐electron variant, by Platt in order to classify the spectra. In this note, a more quantitative version is formulated which enables calculations to be made; it may be considered as an approximation either to an antisymmetrized molecular orbital treatment or to the method of atoms in molecules.

The Valence Structure of the Boron Hydrides

Abstract: A set of extended valence postulates is presented including the concept of the localized three‐center bond. These postulates are applied systematically to the boron hydrides and account for their unusual geometry, their unexpected dipole moments, and the fact that they are not ``electron‐deficient.''

Theory of Electromagnetophoresis. I. Magnetohydrodynamic Forces Experienced by Spherical and Symmetrically Oriented Cylindrical Particles

Abstract: This paper is the first of a series dealing with the theory of the electromagnetokinetic effect This effect consists of the exertion of a force upon a body submerged in a fluid which is traversed by an electric current and a transverse magnetic field In this communication the conditions for equilibrium of an homogeneous fluid are established and forces upon particles suspended in the fluid are determined The computations are carried out for spherical bodies and long cylindrical bodies oriented parallel to the magnetic field, to the electric current, and to the exerted force It is shown that the effect could be observed with suspended particles which differ from the surrounding fluid in the value of their electrical conductivity or dielectric constant, and/or their magnetic permeability

Thermodynamics of Alcohol‐Hydrocarbon Mixtures

Abstract: The thermodynamic properties of alcohol‐hydrocarbon mixtures are explained on the basis of association of the alcohol to form polymers of all orders from two to infinity. Our treatment differs from that of Redlich and Kister in using the Flory‐Huggins expression for free energy, and an equilibrium constant in terms of concentrations rather than mole fractions. The equations derived are in satisfactory agreement with vapor‐pressure data for several systems. They also agree with the experimental energy of mixing and excess entropy for ethanol‐methylcyclohexane solutions. For mixtures of alcohols with aromatic hydrocarbons, it is necessary to assume that each alcohol monomer or polymer can combine with one molecule of hydrocarbon.

The Intermolecular Potentials of Helium and Hydrogen

Abstract: The parameters for helium and hydrogen of the ``exp‐six'' potential, [open phi](r)=e1−6/α[6αeα(1−r/rm)−(rmr)6], have been calculated by use of experimental values of the second virial coefficients and viscosity coefficients. Because of the uncertainty of the quantum corrections, no low temperature data were used in determining the parameters. The exp‐six potential is able to reproduce both the second virial and the viscosity coefficients within experimental error, and is thus an improvement over the simpler Lennard‐Jones (12‐6) potential. In addition, other transport properties are accurately predicted. A combination rule is suggested for calculation of the exp‐six potential between two unlike molecules from the potentials between two pairs of like molecules, and is used to calculate a number of properties of helium‐hydrogen mixtures with satisfactory results.

Structural Investigations by Means of Nuclear Magnetism. III. Ammonium Halides

Abstract: The proton magnetic resonance absorption has been measured in NH4Cl, NH4Br, and NH4I crystal powders from —195°C to room temperature, and for NH4Cl to 200°C. Line width transitions were found at —144, —171, and about —198°C in the chloride, bromide, and iodide, respectively. The N–H distance in the ammonium ion was determined to be 1.035±0.01A from the second moments of the broad, low‐temperature absorption lines observed in NH4Cl and NH4Br, with allowance for broadening by modulation effects and narrowing by zero‐point torsional oscillations. The relatively narrow room temperature line shapes are consistent with the broadening estimated for inter‐NH4+ interactions, the intra‐NH4+ interactions averaging to zero over the hindered rotational motions of the NH4+ ions. No appreciable line shape changes were found at the λ temperatures. An electrostatic calculation is made of the potential barriers to rotation of the NH4+ ion giving values comparing favorably with experimental inferences. The results clarify t...

Transport Properties of Gases Obeying a Modified Buckingham (Exp‐Six) Potential

Abstract: A large number of the Chapman and Cowling collision integrals have been calculated for gases obeying a modified Buckingham potential, [open phi](r)=e1−6/α[6αeα(1−r/rm)−(rmr)6]. The results are tabulated over a large temperature range, kT / e from 0 to 200, and for four values of the parameter α, 12, 13, 14, and 15. The treatment was entirely classical, and no corrections for quantum effects were made. The results should be applicable to most simple, nonpolar gases, and may be used to obtain information about intermolecular forces from the observed temperature dependence of gaseous transport properties.The second approximation to the thermal diffusion ratio and the third approximation to the coefficient of ordinary diffusion have been derived according to the method of Chapman and Cowling.Evaluation of the potential parameters for specific substances and applications of the results will be published later.

Ionic Components of Charge in the Electrical Double Layer

Abstract: The rate of change with concentration of the capacity of the electrical double layer on mercury has been measured. From this there have been calculated Γ+, the excess of cations in the double layer, and Γ—, the excess of anions. The latter has been subdivided into η—d, the excess of anions in the diffuse double layer, and η—i, the excess of anions in the inner part of the double layer. From these data it has also been possible to evaluate ψ0, the potential of the outer Helmholtz plane.It is found that fluoride ion remains unadsorbed on mercury at all potentials investigated, including potentials anodic to the e.c.max. Other anions are strongly adsorbed (chemisorbed) when the mercury is positively charged, and sometimes even when it is negatively charged. The ``hump'' in the capacity curves of salts of such anions as chloride, bromide, acetate, and nitrate, are found to be present in curves of C—, the capacity attributable to anions alone. No chemisorption of monatomic cations could be detected.The kinetic...

A Treatment of Chemical Kinetics with Special Applicability to Diffusion Controlled Reactions

Abstract: If a molecule is produced in a medium containing molecules able to react with it, its instantaneous reactivity is a function of the time since its formation. At very short times the reactivity is determined by the conventional ``true'' rate constant k, which is the product of the rate constant for encounters and the probability of reaction during an encounter. At long times (10—9 sec or greater in many liquids), the reactivity falls to a value determined by the ``long‐time'' rate constant k′. The constants k and k′ differ by the factor 1 — β′, where β′ is the probability that a specific pair of molecules separating from a nonreactive encounter will ultimately react with each other. If β′ is small either because there is little chance of reaction per encounter (activation control), or because there is little chance the specific pair will undergo a subsequent encounter (as in gas phase), the two rate constants are virtually identical and conventional kinetics apply.Equations are developed for the time depen...

Polarization Effects in the Ionic Conductivity of Silver Bromide

Abstract: Alternating current impedance measurements on samples of silver bromide with silver and with gold electrodes show the presence of polarization effects. These effects appear as a capacitive component of the impedance and a slight dependence of the resistance on the frequency of the measurement, and their dependence on temperature, frequency, pressure, voltage, and impurity content has been investigated. A macroscopic theory is developed to describe the motion of the mobile charge carriers (ionic defects) which exist in AgBr at elevated temperatures. The general equations contain the effects of conduction and diffusion currents, space charge, and formation and recombination. Since these equations are nonlinear, an approximation procedure is developed, which is valid for small values of the applied voltage. The results of the theory with appropriate boundary conditions give semiquantitative agreement with the temperature and frequency dependence of the observed results and afford a good qualitative descripti...

Diameter Effect in Condensed Explosives. The Relation between Velocity and Radius of Curvature of the Detonation Wave

Abstract: The limiting slope of the detonation velocity‐wave front curvature locus for small velocity deficits is obtained under an assumption concerning the ``reaction zone length'' as related to the charge diameter and the radius of curvature of the wave front. The model is an extension to two dimensions of von Neumann's classical theory of the plane wave detonation.

Mass spectrometric study of the molecular sublimation of graphite

Abstract: The emission of neutral and charged carbon molecules from spectroscopically pure graphite has been studied by rate of vaporization experiments in a 180° mass spectrometer. Small filaments (diameter: 0.015 in.), heated by ac up to 2600°K, yielded neutral particles which were converted into positive ions by bombardment with low‐energy electrons. C3+, C2+, and C1+ ions were found. Although the effects of fragmentation and of differences in ionization cross sections may not be negligible, it is believed that carbon vapor consists largely of C3 molecules. Graphite was found to emit negative ions containing from one to eight carbon atoms. C2—, C4—, and C3— were the most abundant species, in that order. A search was made for carbon particles emitted as positive ions, but none were found.Heats of activation were obtained for the neutrals and the more abundant negative ions from the slopes of logp vs 1/T plots. Identical heats measured for C1 and C3 (178±10 kcal/mole at 2400°K) suggest that these two species may s...

Further Results on Monte Carlo Equations of State

Abstract: The equation of state of three‐dimensional hard spheres has been obtained by the Monte Carlo method Some qualitative results for a system of two‐dimensional molecules with Lennard‐Jones interaction are also given, as well as a general discussion of the usefulness and limitations of the Monte Carlo method