Volume 26, Issue 1, 01 January 1957

Configuration of a Polyelectrolyte Chain in Solution
View Description Hide DescriptionStarting with the Gibbs‐Boltzmann relation between the probability of a configuration and its energy, an expression is derived for the probability of the configuration of a random chain having central interactions among its groups. By an approximate integration method suggested by Debye, a distribution function is derived for the vector between the chain ends. The result is applied to find the distribution and the mean square end‐to‐end distance of a polyelectrolyte ion.

Comment on the Significance of Diffusion Potentials in Ion Exchange Kinetics
View Description Hide DescriptionThe effect of the electric potential produced by diffusion in ion exchange kinetics is examined for the film‐controlled exchange of monovalent ions. It is shown that, rather than resulting in a minor correction, the electric field as a rule makes an essential contribution to the process.

Simple Molecular Orbital Treatment of Conjugation in Chlorobenzene
View Description Hide DescriptionSimple molecular orbital theory, with inclusion of overlap, has been used to calculate the electron distribution and energy levels in chlorobenzene. Spectroscopic parameters were used, supplemented by the value of β_{CCl} previously obtained from quadrupole coupling data for vinyl chloride. Resonance dipole moments were also calculated for chlorobenzene and vinyl chloride. The results are in reasonable agreement with the observed dipole moment decreases and ionization potential shifts, assuming these to be chiefly brought about by conjugation.

Theoretical Investigation of Vibrational Frequency Distributions for Molecular Crystals Having the Cyanogen Iodide Structure
View Description Hide DescriptionFrequency distributions are determined for a molecular stretching vibration band in a cyanogen iodide lattice. The eigenfrequencies of the vibrational problem are calculated with first order perturbation theory. Distributions for possible reasonable sets of coupling constants are determined. The behavior of the distributions near extremal values are computed by the method of van Hove. The behavior of the distributions between extremal values is obtained by interpolation based on a qualitative examination of the eigen‐frequencies as a function of wave‐number vector.

Electron Impact Studies on C_{2}H_{5}Cl, C_{2}H_{5}Br, and C_{2}H_{5}I
View Description Hide DescriptionThe appearance potentials and process of formation of the C_{2}H_{5}X^{+}, C_{2}H_{5} ^{+}, CH_{2}X^{+}, and HI^{+} ions have been studied. From the appearance potential data evidence is obtained for the following processes of production of these ionsorThese processes and their corresponding appearance potentials permit certain ionization potentials and bond energies to be derived. The ionization potentials obtained for the ethyl halides are I(C_{2}H_{5}Cl) ≤11.2±0.2 ev, I(C_{2}H_{5}Br) ≤10.7±0.1 ev, and I(C_{2}H_{5}I) ≤9.6±0.2 ev. The carbon‐halogen bond energies of these ethyl halides as determined from process (b) are (C–Cl) ≤3.6±0.3 ev, (C–Br) ≤2.8±0.2 ev, and (C–I) ≤2.4±0.4 ev. Values of the carbon‐carbon bond energy of C_{2}H_{5}Br and the ionization potential of CH_{2}Br are estimated to be 3.6 ev and 9.1 ev respectively. The ionization efficiency curves of the negative halogen atoms from the ethyl halides are presented and some of their features discussed.

Curved Fluid Interfaces. II. The Generalized Neumann Formula
View Description Hide DescriptionFollowing an analysis of the phenomenological concept of surface stress, the confluence properties of three fluid phases are examined from the molecular point of view. The detailed theory leads to a generalization of the Neumann surface tension triangle, which provides a boundary condition for the Laplace equations describing the surfaces of a fluid lens. It is found that the classical equation must be supplemented by a thermodynamic length parameter which, however, does not contribute to the Archimedean equilibrium of the lens. As in the preceding investigation, the first‐order correction terms of the theory again provide criteria for the breakdown of thermodynamic concepts.

Hindered Rotation in Molecules with Relatively High Potential Barriers
View Description Hide DescriptionThe theory of hindered rotation has been applied to the type of asymmetric molecule in which the hindering barrier is high enough so that the hindered rotation splittings of the energy levels are small compared with the rotational energies but yet large enough to be observable in the microwave spectrum. The specific type of molecule considered consists of a rigid asymmetric component which may undergo a hindered rotation about the symmetry axis of a rigid symmetric component where the symmetric component is in addition assumed to have threefold symmetry and the asymmetric component at least a plane of symmetry containing the symmetry axis of the symmetric component. An example might be the acetaldehyde molecule, CH_{3}CHO.
In principle, the theory developed by Burkhard and Dennison can be used directly but in practice the method is difficult to apply to such a molecule since the matrix elements of the Hamiltonian used previously do not degenerate naturally or easily to those for the rigid asymmetric rotator in the infinite barrier limit. In the present treatment a transformation is made on the Hamiltonian whereby this complication is avoided and the resulting calculations are greatly simplified.
It is found that the spectrum is essentially that of the rigid rotator with the important exception that all the strong lines are split into two components. For the low J transitions specific formulas have been derived for these splittings which are relatively simple functions of the barrier height, the principal moments of inertia, and two additional parameters involving the molecular dimensions and the masses. The barrier height can thus be deduced from the observed splittings without the use of the somewhat cumbersome machinery needed in the general case.

Vibration‐Hindered Rotation Interactions in Methyl Alcohol. The J=0→1 Transition
View Description Hide DescriptionThe hindered rotation fine structure of the J=0→1, K=0→0 transition which has been observed by Venkateswarlu, Edwards, and Gordy in normal methanol as well as in five additional isotopic species can be understood only qualitatively on the basis of earlier investigations of the theory of hindered rotation in methanol. It has been shown that the frequency separations between the various torsional transitions and the splitting of each of these can be explained quantitatively by including in the theory the effects of the vibration‐hindered rotation interactions during the rotation of the whole molecular framework in space. The effects of the asymmetry of the rigid hindered rotator, the Coriolis interactions, and the centrifugal distortion of the molecule are discussed separately. A frequency formula for the transition is derived which contains essentially only four new rotational constants. Three of these depend solely upon the known structure of the molecule and the elastic force constants and can therefore be calculated from a knowledge of the vibrational spectrum. Since this latter has never been analyzed in more than a rough way some small adjustments have been made in the indicated values of the elastic constants which are within the limits of uncertainty. This adjustment is made for the normal molecule after which the three rotational constants are calculated for the remaining isotopic species without further adjustment. The fourth constant in the frequency formula describes the dependence of the barrier height upon the normal coordinates and is the only constant which must be determined empirically for each isotopic species. It has thus been possible to predict the 30 observed separations and splittings with the aid of essentially only six empirical constants. The agreement with experiment is remarkably good with one possible exception where the theory predicts for the fully deuterated methanol a very large splitting of the normal state line whereas the line in question is observed to be single. It is not improbable, however, that the large splitting actually exists and that the second component lay too far away to be recognized.

Correlation Energies in Atoms and Electron Affinities
View Description Hide DescriptionThe well‐known orbital approach is applied to the 2, 3, and 4 electron systems of atoms and ions, and the extent to which it can be applied and the apparent nature of the correlation energies are surveyed. It is then discussed how the apparent correlation energies can be extrapolated to estimate the correct energy values of negative ions for which observation has not yet succeeded. According to such estimations, the electron affinities of H and Li are obtained as 0.75±0.01 ev and 0.66±0.03 ev, respectively. Finally it is attempted to extend the discussion to more complicated systems.

Displacement of the Maximum in the Concentration‐Time Diagram of Uni‐bi‐, Bi‐uni‐, and Bi‐bimolecular Consecutive Reactions
View Description Hide DescriptionAs an extension of the results previously reported for two first‐order consecutive reactions, the expressions k _{1}·t _{max} and [B]_{max}/[A]_{0} are studied as functions of temperature and initial parent concentration for uni‐bi‐, bi‐uni‐, and bi‐bimolecular consecutive reactions.

Vibrational Spectra and Structure of Solid Sulfamic Acid and the Sulfamate Ion
View Description Hide DescriptionThe infrared spectra of finely powdered samples in pressed disks of KBr have been obtained for sulfamic acid,sodium and potassium sulfamates, and the corresponding deutero‐compounds in the region from 4000 to 500 cm^{—1} at several temperatures. Satisfactory vibrational assignments could be made for the zwitterion model of the acid, H_{3}N^{+}–SO_{3} ^{—}, with site symmetry in the crystal of C _{1} in agreement with x‐ray data. The sulfamate ion spectra can satisfactorily be interpreted on the basis of the C_{8} model, H_{2}NSO_{3} ^{—}. The N–S stretching modes were found at somewhat lower frequencies than previously postulated, 682 and 790 cm^{—1}, respectively, for the acid and salt.

Near Ultraviolet Spectrum of Crystalline Hexamethyl Benzene and the Structure of the Hexamethyl Benzene Molecule
View Description Hide DescriptionThe absorption and fluorescence spectra of single oriented crystals of hexamethyl benzene were photographed at high resolution with polarized light at 20°K in the 2800 A region. The analysis shows that the 0–0 transition is observed with much greater intensity in light polarized perpendicular to the plane of the benzene ring than in light polarized in this plane. In the perpendicular component the vibrational structure of a weak allowed transition appears together with the 0–0 band. The in‐plane spectrum is a forbidden transition, similar to the benzene 2600 A absorption. A detailed calculation shows that the perturbation by the crystal lattice cannot be the cause of the observed behavior of the 0–0 band in polarized light. It is concluded, therefore, that this behavior must be caused by the lowering of the molecular symmetry by the methyl groups. The probable symmetry of the molecule is S _{6}. This symmetry approximately fixes the positions of the hydrogen atoms and determines the shape of the methyl rolling potential.

Concerning the Electron‐Withdrawing Power and the Electronegativity of Groups
View Description Hide DescriptionThe polar substituent constants, σ^{*}, obtained recently by Taft from reactivity considerations are discussed. Several qualitative relationships of σ^{*} values to substituent constitution are established. These relationships relate quantitative correlations of the effect of structure on reactivity to concepts of bonding and electronegativity. The Mulliken concept of electronegativity is supported.
The relatively large electron‐withdrawing powers of Cl, Br, and I in bonds to carbon suggest the participation of the d orbitals of the valence shell. A discrepancy is noted between σ^{*} values (and Mulliken's electronegativities) and the group electronegativities proposed by Dailey and Shoolery on the basis of protonnuclear magnetic resonance shifts in ethyl and methyl derivatives.

Dislocations as ``Active Sites'' in Heterogeneous Catalysis
View Description Hide DescriptionExperiments on the dependence of catalytic activity of nickel foils as a function of deformation and annealing are interpreted as evidence that dislocations are active sites in heterogeneous catalysis.

Rate of Dissociation of Bromine in Shock Waves
View Description Hide DescriptionThe rate of dissociation of bromine, pure and diluted with argon, was measured from 1200°K to 2225°K in shock waves, in order to study the mechanism of elementary reaction processes. The absorption coefficient of Br_{2} was measured over the same temperature range. In the case of dissociation produced by Br_{2}–A collisions the reaction rate constant is reproduced over a range of 10^{27} by a collision theory equation. The activation energy is approximately equal to the dissociation energy of Br_{2}, the frequency factor is about 6% of that deduced from the collision frequency, and it appears that both the vibration and rotation of the Br_{2} contribute energy to the dissociation. Br_{2} is roughly twice as efficient as A in producing dissociation at high temperatures. For dissociation produced by Br_{2}–Br_{2} collisions the measurements are in agreement with a rate constant in which the activation energy equals the dissociation energy, the steric factor is from 1% to 10% and five to seven square terms (e.g., the two vibrations and one to three rotations) contribute to the energy of dissociation.

Self‐Diffusion of Silver in Silver—Palladium Alloys
View Description Hide DescriptionThe self‐diffusion of silver has been studied in alloys containing 0.00, 1.49, 3.69, 9.87, and 21.84 atom percent palladium at four temperatures: 715.4, 799.4, 861.8, and 942.0°C. The rate decreases with increasing palladium atom fraction according to the relation: D _{Ag}=0.270e ^{—8.20X } e ^{—43, 700/RT }. An alternative expression is D _{Ag}=0.270e ^{—17.75T m/T }. Within experimental error, the activation energy is independent of palladium content. The rate of self‐diffusion of silver is related to the solidus line of the silver‐palladium phase diagram, and a simple corresponding states explanation is given.

Symmetries of Electric Fields About Ions in Solutions. Absorption and Fluorescence Spectra of Europic Chloride in Water, Methanol, and Ethanol
View Description Hide DescriptionThe theoretical and experimental correlations between the symmetries of the microfields about ions, the degree of splitting of energy levels, and the selection rules for radiation have been so successful for ions in crystals that the extension of this approach to discover the precise point symmetries about ions in solutions appears limited only by instances where the spectra of the solutions are sufficiently discrete. The spectra of crystals containing a rare earth ion in known local symmetry furnish the quantum characters of the energy levels and then the numbers of lines in the respective transitions of the ions in solutions lead to the symmetries of the fields about the dissolved ions.
Salts of europium which are regarded as strong electrolytes exhibit sufficiently sharp absorption spectra in solutions at room temperature while their fluorescence spectra become adequately discrete at the temperature of dry ice. The absorptionspectrum of europic chloride in water proved to be the same as in a mixture of water and alcohol. The latter solutions furnished the fluorescence spectra at the temperature of dry ice.Fluorescence spectra of the alcoholic solutions in the form of glasses were obtained at 77°K and 4°K.
The symmetry of the microfields about the europiumions in the anhydrous alcohols was C _{2v } while that about the ions in aqueous solutions was D _{2h }.

Numerical Solution to the Poisson‐Boltzmann Equation for Spherical Polyelectrolyte Molecules
View Description Hide DescriptionThe Poisson‐Boltzmann equation for a penetrable spherical polyelectrolyte ion in the presence of smaller ions has been solved precisely by numerical integration methods using a high‐speed computer. The polyelectrolyte ion was assumed in one case to be immersed in a sea of simple electrolyte and in another case to be surrounded by an appropriate volume of solution containing only the polyelectrolyte's counter ions. Since the absolute value of the electrostatic potential energy of a small ion in the center of a polyelectrolyte ion is found to be several times kT, the nonlinear differential equation cannot justifiably be rendered linear by the Debye‐Hückel type of approximation. The fraction of the counter ions held within the sphere of the polyelectrolyte ion is calculated from the solution to the differential equation. The extent of such ion association is found, for reasonable values of the molecular parameters, to range between 50 and 75% in substantial agreement with experimental observations based on transference studies. The results of the numerical computations are for the most part presented graphically.

Raman Spectrum and Vibrational Assignments of Gaseous Dimethyl Ether
View Description Hide DescriptionThe Raman spectrum of gaseous dimethyl ether has been obtained and that of the liquid reinvestigated. In the low‐frequency region of the gas spectrum, two bands have been observed which are attributed to overtones of the torsional motions of the methyl groups. The assignment of vibrational frequencies is discussed on the basis of a C _{2v } symmetry in the molecule.

Photochemical Separation of Mercury Isotopes. I. A Study of the Emission and Absorption Hyperfine Lines of Mercury at 2537 A
View Description Hide DescriptionAn experimental and theoretical investigation has been made of the emission and absorption parameters in the excitation of Hg^{202} atoms in natural mercury to the 6(^{3} P _{1}) state by irradiation with the resonance line from an electrodeless discharge containing Hg^{202}. The absorption has been studied as a function of (a) absorption path length, (b) the concentration of mercury in the absorption cell, (c) the pressure of certain foreign gases in the absorption cell, (d) the operating temperature of the lamp, and (e) the type of excitor used with the lamp.
The results of the study show that for the unique formation of Hg^{202}6(^{3} P _{1}) atoms in natural mercury it is necessary to use a well‐cooled source operating at the minimum power level consistent with steady radiation output. Furthermore, the pressure of foreign gas in the absorption cell must be kept low to eliminate Lorentz broadening effects on the absorption hyperfine line.
It has been found that the emission line from an electrodeless discharge operated at 26°C, and excited by a 2450 Mc oscillator, can be satisfactorily represented as a Doppler line modified by self‐absorption. For the calculation of the frequency distribution of the emission line, the Doppler temperature of the emitting gas and the equilibrium temperature of the mercury in the lamp were taken as identical with the lamp wall temperature (26°C). The optical thickness of the path of self‐absorption was evaluated from the dimensions of the lamp. It was found that the observed absorptions could be calculated directly from the ratio of the areas of the Doppler absorption line of the Hg^{202} atoms in the absorption cell to that of the self‐absorbed emission line. The agreement between theory and experiment is taken as evidence that only Hg^{202} atoms are undergoing excitation under the defined conditions.
During the investigation the cross sections for Lorentz broadening of hydrogen, methyl chloride and isopropyl chloride were determined with respect to the Hg^{202} absorption line. The values found were respectively 53.1, 192, and 297×10^{—16} cm^{2}.
This study was undertaken as a precursor to a systematic investigation of the reactions of various substrates with photo‐excited mercuryisotopes.