Showing papers in "Journal of Chemical Physics in 1948"

On the Structure of a Catalyst Surface

Abstract: A method is described which makes it possible to calculate rigorously the distribution of the adsorption energies of the sites of a catalyst surface when the adsorption isotherms are known, if the adsorption is localized and there are no interactions. This method is applied to a Freundlich isotherm, and also to a new theoretical isotherm which reduces to the Freundlich type for small pressures, but exhibits saturation for large pressures. It is shown that this isotherm corresponds to a distribution function which differs very little from a Gaussian one. The case of atomic adsorption of gases is also considered.

The Scattering of Light and the Radial Distribution Function of High Polymer Solutions

Abstract: A radial distribution function of polymer segments in a solution of a high polymer may be defined as a quantity proportional to the density of segments at a given distance from some given segment. An approximate expression is derived for this function for dilute solutions of chain molecules of moderate degrees of polymerization. By Fourier inversion a simple expression for the intensity of light scattering, as a function of angle and concentration, may be obtained.

Physical Adsorption on Non‐Uniform Surfaces

Abstract: Analysis of adsorption on a uniform surface using the quasi‐chemical theory of interaction shows that the hypotheses of the BET theory lead to substantially no adsorption beyond the first layer if E2 = EL, and stepwise isotherms if E1>E2>E3>···>EL. For the monolayer adsorption of gases on silver, platinum, and steel, the heterogeneous nature of the adsorbing surface is clearly indicated. Cooperative adsorption on the non‐uniform surface is treated, and the cooperative analog of the Freundlich equation derived. The typical multi‐layer isotherm is shown to be composed of three regions: non‐cooperative adsorption on a strongly heterogeneous surface; cooperative adsorption on a still heterogeneous surface; and cooperative multi‐layer adsorption induced by small van der Waals perturbations some distance from the surface.The isotherm p/p0=exp{—a/θr} is derived and shown to be a good representation of adsorption data that conform to the BET Type I, II, or III shapes.

Apparatus and Methods for Measurement and Interpretation of the Angular Variation of Light Scattering; Preliminary Results on Polystyrene Solutions

Abstract: A photoelectric apparatus for the measurement of the angular dependence of light scattering from solutions is described in detail and its performance is discussed. Methods of calculation for the determination of the average extension of the scattering molecules from the data are described. Data are presented for two fractions of polystyrene in various solvents, showing the effect of changing solvent power and temperature, and also confirming a theoretically derived formula for the concentration dependence of the scattering.

Nuclear Resonance Absorption in Hydrated Crystals: Fine Structure of the Proton Line

Abstract: Fine structure has been observed in the nuclear paramagnetic resonance absorption line for protons in crystalline hydrates. The magnetic field of 6820 gauss was provided by a permanent magnet, the inherent stability of which facilitated detailed study of line shape. Measurements on a single crystal of CaSO4·2H2O show a splitting into four component lines with maximum separation varying from zero to 22 gauss, depending upon the direction of the externally applied magnetic field in the crystal. Both the number of component lines and the dependence of their spacing on field direction are calculated by treating the magnetic dipole‐dipole interaction as a perturbation of the proton two‐spin system within the water molecule; the effect of the more distant protons, neglected in this calculation, gives a finite width to the component lines. Variation of the splitting with field direction determines the orientation of the line joining protons in the water molecule, which is found to be consistent with positions ascribed to hydrogen nuclei in the lattice through simple considerations of chemical bonding. The distance between protons in the water molecule is measured by the splitting to be 1.58A for CaSO4·2H2O; if one assumes an H–O–H bond angle of 108°, the O–H distance is 0.98A. Powdered hydrates show a characteristic fine structure arising from isotropic distribution in solid angle of single crystal granules. This type of fine structure determines the proton‐proton distance somewhat less accurately than does the single crystal experiment.

Kinetics of Emulsion Polymerization

Abstract: As a basis for understanding emulsion polymerization, the kinetics of free radical reactions in isolated loci is discussed subject to the condition that the free radicals are supplied to the loci from an external source. Three cases of interest are considered: that in which the average number of free radicals per locus is small compared with unity, that in which this number approximates one‐half, and that in which the number is large. Of these three possibilities, the second, in which the free radicals per locus approximate one‐half, is by far the most interesting as it explains in a satisfactory manner the characteristic features of styrene emulsion polymerization. For this case the average rate of reaction per locus is independent of the size of the locus, since this rate is simply one‐half the rate of polymerization of a single free radical. Thus the rate of emulsion polymerization, the concentration of monomer in the loci, and the number of loci present provide the information needed for calculating t...

Errata: The Intrinsic Viscosities and Diffusion Constants of Flexible Macromolecules in Solution

Abstract: A theory of the intrinsic viscosities and translational diffusion constants of flexible macromolecules is developed on the basis of the random coil model with hindered internal rotation. Proper account is taken of the hydrodynamic interaction of the monomer units of the molecule and of inhibited flow through the chain. The theory leads to results qualitatively similar to those obtained by Debye on the basis of a molecular model consisting of a sphere containing a uniform distribution of resisting points. However, significant quantitative differences between the two theories are found.

Dielectric Properties of Aqueous Ionic Solutions. Parts I and II

Abstract: The dielectric constants and loss angles of a series of concentrated aqueous ionic solutions have been measured at wave‐lengths of 10 cm, 3 cm, and 1.25 cm. From these results the values of the static dielectric constant and relaxation time for these solutions have been calculated on the basis of the Debye formula, which appears to hold accurately. All salts show a lowering of the dielectric constant and a shift in the relaxation time of water. It is found that the dielectric constant e can be represented by a formula e=eω+2δc, where eω is the dielectric constant of water, c is the concentration in moles per liter, and δ has values between −7 and −15 for various salts in concentrations of up to 2 M.In Part I the measurements are described and the results discussed in relation to the structure of ionic solutions. In Part II the validity of the Debye‐Sack saturation theory of the dielectric constant and the effects of the fall of dielectric constant on the electrolytic properties of concentrated solutions ...

Intrinsic Viscosity, Diffusion, and Sedimentation Rate of Polymers in Solution

Abstract: Intrinsic viscosity, diffusion and sedimentation rate of polymers in solution is calculated by a generalization of Einstein's theory for impermeable spheres. For the coiled polymer molecule a sphere is substituted which hinders the liquid flow through its interior only to a degree depending on the average density in space of the polymer molecule in solution. The amount of shielding of the liquid flow which is introduced in this way determines the exponent in the customary exponential relation between intrinsic viscosity, diffusion, or sedimentation rate and molecular weight. This relation is shown to have only the merits of an interpolation formula. It is shown how the dimensions of the molecular coil can be derived from the experimental data on viscosity, and these dimensions are compared with those derived from interference measurements. The point is stressed that the relation between intrinsic viscosity and molecular weight is rather indirect and depends essentially on the type of polymer molecule unde...

The Stark Effect for a Rigid Asymmetric Rotor

Abstract: The Stark effect, arising from the interaction of a uniform electric field with a permanent electric dipole that is arbitrarily oriented within a rigid asymmetric rotor, and with a dipole induced in the rotor by the field, has been evaluated by perturbation methods. Tables are given for the perturbation of the energy levels so that, for J≤2, the rotational energies of an asymmetric molecule in an electric field may be readily approximated to terms quadratic in the electric field.The effect of accidental degeneracy upon the Stark effect and line intensities has been considered. A qualitative discussion of certain features of Stark patterns is given that may be useful in the identification of rotational spectral lines.

Consideration of the Gibbs Theory of Surface Tension

Abstract: The Gibbs theory of surface tension is discussed. Detailed consideration is given to the structure of transition layers between phases. This provides theoretical information, as to the magnitude of surface tension and as to the location of the surface of tension, which can be used in making applications of the Gibbs theory.

The Vibrational Spectra of Molecules and Complex Ions in Crystals. I. General Theory

Abstract: It is shown that if a crystal is approximated as a harmonic oscillator, only a very small number of vibrational modes may be active in the infra‐red or Raman spectra. These modes are all totally symmetric with respect to translation. They must also have proper symmetry with respect to the factor group of the space group which we have called the unit cell group. The active frequencies may be calculated from a single unit cell. It is shown further that the number and symmetry type of vibrational modes may be correctly calculated from the local symmetry (site group) of the center of gravity of each kind of molecule. In the harmonic approximation the spectrum should consist of very sharp lines. The wide bands obtained experimentally are probably due to combination lines with lattice vibrations and indicate anharmonic coupling between molecular and lattice modes. Such combinations may cause apparent violations of selection rules for internal vibrations. The symmetry basis for obtaining selection rules in this case is given. The importance of obtaining spectra over a wide temperature range and particularly at very low temperatures is emphasized. In cases where all internal modes have a frequency great compared to the frequency of lattice modes the problem is examined from the point of view of the Born‐Oppenheimer approximation. It is shown that for some symmetries perturbations linear in the lattice displacement may occur. In these cases considerable splitting of degenerate molecular vibration modes is possible. Groups for which first‐order splitting is not expected are listed. Symmetry species of other groups are classified into those which may and which may not be split in this approximation, and the lattice modes responsible for splitting are classified as rotations or translations and by symmetry type.

The Transport Properties for Non‐Polar Gases

Abstract: Chapman and Cowling have related the coefficients of viscosity, diffusion, thermal diffusion, and heat conductivity to a set of integrals, Ωn(l)(T) involving the law of force between pairs of molecules. We have evaluated these integrals for l=1, n=1, 2, 3; l=2, n=2, 3, 4, 5, 6; l=4, n=4, assuming that the energy of attraction is inversely proportional to the sixth power of the separation and the energy of repulsion is inversely proportional to the twelfth power. This assumption is excellent for spherical non‐polar molecules and a big improvement on the Sutherland assumption. The mathematical analysis was very difficult but the results are simple. The transport integrals are evaluated for all temperatures in terms of the maximum energy of interaction and the collision diameters. This gives a ``corresponding states'' relationship which should apply to extremely hot and extremely cold temperatures where good experimental data are not available. The molecular constants can be obtained very accurately from exp...

Ionization Potentials of Some Hydrocarbon Series

Abstract: A new method is described which permits ionization and appearance potentials to be determined reproducibly, within ±0.02 volt, by electron impact in a conventional 180° mass spectrometer. The energy spread of the ionizing electrons, while not eliminated, is accounted for in an analytical expression that describes the ionization efficiency curve of argon near the initial upward break. It is shown that an ionization or appearance potential can be determined graphically by drawing a tangent of critical slope to the efficiency curve which has been plotted on a semilog scale. Absolute values are obtained by referring the unknown to the ionization potential of a calibrating gas (usually krypton). For the monatomic gases studied, electron impact and spectroscopic values agree within the experimental uncertainty. For some known polyatomic molecules, the ``vertical'' impact values exceed the ``adiabatic'' spectroscopic potentials by 0.02 to 0.2 volt, depending on molecular complexity. Paraffins, 1‐olefins, and 2‐olefins show a systematic reduction in potential with chain length. A similar decrease is observed when the mono‐olefins are arranged according to the number and size of substitutions on the basic ethylene structure.

The C–H Bond Energy in Toluene and Xylenes

Abstract: The pyrolysis of toluene and the xylenes was investigated by a new technique, which made it possible to study these reactions for degree of decomposition ranging from 0.01 percent up to a few percent. It was shown that these reactions are homogeneous, unimolecular reactions. It was found that the weakest bond in these molecules is the C–H bond in the methyl group. The bond energy of that C–H bond was found to be 77.5 kcal. for toluene and meta‐xylene, 75 kcal. for para‐xylene and 74 kcal. for ortho‐xylene. These data indicate that the resonance energy of the benzyl radical is 24.5 kcal. and that the hyper‐conjugation in para‐xylene decreases the C–H bond energy in the methyl group of this molecule by 2.5–3 kcal.

A Tabulation of General Formulas for Inverse Kinetic Energy Matrix Elements in Acyclic Molecules

Abstract: In terms of internal coordinates of the bond stretching and bending type, together with a torsional type of coordinate, general formulas for inverse kinetic energy matrix elements have been computed for all 33 possible acyclic configurations involving the given types of coordinates. Tabulations are given both for the general case and for three special cases in which all valence angles of the configuration are assumed to be 90°, 109°28′, and 120°, respectively.

Steric Effects. I. Van der Waals Potential Energy Curves

Abstract: Reliable van der Waals potential energy functions are available in only a limited number of cases. An approximate semi‐empirical method is presented for estimating these curves in other cases, based on an extrapolation from the nature of the curves that are known. The relation of the above method to calculations of the type discussed by Westheimer and Mayer on the activation energy for racemization of substituted symmetrical diphenyls is considered.

Structure and Conductivity in the VIb Group of the Periodic System

Abstract: In the sequence oxygen, sulfur, selenium, tellurium, and polonium a systematic alteration takes place from diatomic molecules, through ring and chain molecules, to a simple cubic lattice structure formed by atoms. This transition is paralleled by a modification in the electrical behavior from insulator (O,S), to semiconductor (Se,Te), to metal (Po). This paper is concerned with this progressive change in structure and conductivity and with the interrelation of the two phenomena. It discusses first the stability of ring and chain molecules and how the chain lattices of Se and Te may be derived by a simple distortion of the Po structure. Next, it considers schematically the electronic conductivity of selenium from the standpoint of the band picture, and finds that metallic Se is probably an intrinsic P‐type conductor. Finally an alternative approach is suggested which connects structure and conductivity by extending qualitatively the concept of quantum‐mechanical resonance from molecular structures to lattice structures and makes use of Pauling's resonating bond. The actual structure and conductivity of Se and Te thus appear as the outcome of a resonance between an insulating chain structure held by van der Waals cohesion and a metallic lattice of simple cubic structure, in which for Se the chain structure and for Te the Po lattice makes the stronger contribution.

Rotation‐Vibration Spectra of Diatomic and Simple Polyatomic Molecules with Long Absorbing Paths. I. The Spectrum of Fluoroform (CHF3) from 2.4μ to 0.7μ

Abstract: The spectrum of fluoroform has been investigated under high resolution (21‐ft. grating) in the photographic infra‐red with an absorbing path of up to 60 meters, obtained by multiple reflection according to the method of J. U. White. In addition, with the same path length the spectrum from 1.2 to 2.4μ was obtained under low resolution with a photoelectric infra‐red spectrometer. A large number of overtone and combination bands, 47 in all, were found. Two parallel bands in the photographic region were well resolved and analyzed, yielding, for the moment of inertia about an axis perpendicular to the symmetry axis, IB[0]=81.08×10−40 g cm2 From this value, assuming tetrahedral angles and a C–H distance as in methane, the C–F distance in fluoroform is found to be 1.329A, a value that is appreciably lower than that found in methyl fluoride, 1.380A. A provisional vibrational assignment of all the bands is given.

A ``Metallic'' Model for the Spectra of Conjugated Polyenes

Abstract: The π‐electrons belonging to the double bonds of trans‐conjugated polyenes are assumed to be a one‐dimensional electron gas in a field of uniform potential energy whose length is approximately that of the conjugated system. The energy levels, the selection rule (Δn odd) and the transition intensities are deduced. The model predicts that the oscillator strength of the main absorption band of a trans‐conjugated polyene is given by f = 0.134(2N+1), where N is the number of double bonds. The calculated values are in good agreement with experimental data. The wave number of the main band is related to the length of the conjugated system and the number of double bonds with moderately good agreement with experiment. The second, weaker absorption band of trans‐carotene is discussed briefly.

The Surface Tension of Liquid Metals

Abstract: The author is opposed to the generally established opinion that the surface tension of liquid metals is abnormally high (as compared with that of non‐metallic liquids) and that the metallic character (the presence of free electrons) is the main cause of the ``high'' surface tension of metals. He shows that this opinion is due to the fact that specific surface tensions (ergs per cm2) are compared and that the influence of temperature is not accounted for. Total surface energies σ M —T(dσ M /dT)—where σ M =σspec×A is the surface tension referred to the surfaceA occupied (in monomolecular layer) by N‐Avogadro's molecules—are of the same order of magnitude. The author expresses the opinion that the main cause of the surface tension of all liquids, whether metallic or not, is the same, viz., the total surface energy is determined by the amount of energy required to bring the molecules or atoms (and electrons) from the bulk of the liquid to its free surface while enlarging the surface area. He shows that in organic liquids showing no dipoles this energy can be calculated directly from the heat of vaporization at absolute zero and from the configuration of nearest neighbors. In the case of metals, the change of kinetic energy of electrons must be considered in addition. The author shows that the latter must contribute a negative term to the total surface energy. In fact, liquid metals show lowersurface energies than might be expected from their heats of vaporization and from the configuration of their nearest neighbors (Fig. 1). A short review of the recent electron theories of the surface tension of liquid metals is given.

Spectroscopic Studies of Rotational Isomerism. I. Liquid n‐Butane and the Assignment of the Normal Modes of Vibration

Abstract: The Raman spectrum of n‐butane has been investigated over the temperature range 147°K to 305°K. The results clearly show the presence of two rotational isomers in the liquid. These are the planar, trans‐form (symmetry C2h) and probably the gauche form obtained by a rotation of 120° about the central C–C bond (symmetry C2). The photoelectric spectrograph was used for quantitative intensity measurements on the line pair at 432 cm−1 and 325 cm−1 over the temperature range studied. These lines belong to the two rotational isomers and the results were used to give a value of 770±90 cal. mole−1 for the energy difference, —ΔH, between the two forms of n‐butane in the liquid phase. This result is shown to be in good agreement with a value assumed by Pitzer in his treatment of long chain paraffins. A detailed assignment has been made of the vibrational spectrum of the trans‐rotational isomer.

Low Frequency Dispersion in Ionic Crystals

Abstract: A new region of anomalous electrical response has been observed at low frequencies in ionic crystals that have been treated to introduce relatively large number of lattice defects. The crystals thus far studied include various alkali halides and silver chloride. The effect is attributed to a jumping of the positive ions to vacant lattice sites under the influence of the applied field. This jumping is observed as a relaxation process, producing a change in the dielectric constant which is small and frequently within the limits of error of measurement, and an associated peak in the dielectric loss tangent which is readily measurable. This maximum of tan δ has been studied both as a function of frequency at a fixed temperature and as a function of temperature at fixed frequency. From the magnitude of the peak and position on the frequency or temperature scales it is possible to calculate the number of lattice defects present in the sample and the activation energy for diffusion U of the positive ion in the crystal. A knowledge of U allows a separation of the activation energy for conduction, (W/2)+U, into its components, thus determining W, the activation energy for hole formation.

The Solubility of Water in Hydrocarbons

Abstract: The method in which tritium oxide acts as a tracer in the determination of water solubility in hydrocarbons has been used for the measurement of the solubility of water in a number of paraffinic, olefinic, and diolefinic hydrocarbons. The effect of temperature, pressure, size of hydrocarbon molecule, and the constitutive factors have been studied. Solubilities were determined in the temperature range from 5° to 30°C at pressures from 1 to 6 atmospheres.

The Vibrational Spectrum and Thermodynamic Functions of Acrylonitrile

Abstract: The infra‐red spectra of gaseous and liquid acrylonitrile have been studied from 2.5 μ to 25 μ with a spectrometer using LiF, CaF2, NaCl, and KBr prisms. The Raman spectrum of the liquid has been obtained, including intensity and polarization data. A normal coordinate calculation of the non‐planar frequencies has been made, using force constants from related molecules. This information permits a complete assignment of the fifteen fundamental frequencies and a calculation of the thermodynamic quantities for the molecule.

The Absorption Spectrum of Diborane

Abstract: The absorption spectrum of diborane has been investigated in the infra‐red from 1–25μ and in the vacuum ultraviolet down to 1000A. The rotational structure obtained for certain of the infra‐red bands rules out the ethane‐type structure but agrees very well with the interpretation of the electron diffraction results in terms of a bridge model. The ultraviolet spectrum indicates a simple electronic structure and a first ionization potential about 11–12 volts.