Volume 48, Issue 9, 01 May 1968

Elastic Scattering of Light by Binary Mixtures above and below the Critical Solution Temperature. I. Methanol Cyclohexane
View Description Hide DescriptionAn investigation was made of the light‐scattering properties of the methanol–cyclohexane binary system in the one‐phase region above the critical solution temperature and in the two‐phase region below . Measurements were made down the critical isochore for and along the methanol‐rich side of the coexistence curve for . A modification of the Ornstein–Zernike–Debye theory of light scattering was found to be in reasonable agreement with the results for . The Debye parameter “” was 14.5 ± 0.5 Å above and 14.0 ± 1.3 Å below . The ratio of the extrapolated zero‐angle inverse intensity at any below to that quantity at the same above was 3.6. The persistence length for fluctuations below as determined by the Debye theory was of the same order of magnitude as the thickness of the binary interface.

Asymptotic Solution of the Excluded‐Volume Problem in a Linear Polymer Chain
View Description Hide DescriptionAn asymptotic form of the expansion factor for the end‐to‐end distance of a linear polymer chain is derived, based on the self‐consistent‐field approach developed recently by Reiss. Reiss' integral equation for the distribution function is corrected, since some factor in the transition probability is dropped. The self‐consistent potential is evaluated in the perturbed state by introducing the uniform‐expansion approximation. In addition, the present potential is appropriate for use near the peak of the distribution function, whereas his potential is valid at extremely large distances. The corrected integral equation is equivalent to that of James except that the present potential is evaluated in the perturbed state. The present theory predicts that at large , where is the excluded‐volume parameter. An approximation that leads to an equation for of the fifth‐power type, as suggested first by Flory, is discussed in detail.

Dynamic Viscoelastic Properties of Dilute Polyisobutylene Solutions
View Description Hide DescriptionIn order to examine the Rouse and the Zimm theories, measurements have been made on complex rigidity of very dilute solutions of polyisobutylene by means of the torsional crystal method at high frequencies. The complex intrinsic rigidity, , and the limiting relaxation time,, have been obtained by extrapolation to zero concentration, where is the th relaxation time factor determined on the basis of the above theories. In benzene at the theta temperature, curves based upon the Zimm theory excellently represent the experimental plots of vs , in which (nondraining). In cyclohexane at 15.0° and 30.0°C, the results are intermediate between the Rouse and the Zimm theories (partial draining). The draining effect seems to correlate with the excluded volume effect.

Ion‐Pair Theory of Concentrated Electrolytes. I. Basic Concepts
View Description Hide DescriptionThe statistical thermodynamics of symmetrical “primitive‐model” electrolytes is formulated in such a way that all ions are uniquely paired. The behavior of the resulting fluid of “polar molecules” may conveniently be described by a wavelength‐dependent dielectric constant. A rigorous formula of the Kirkwood type for is derived. Since ion‐atmosphere mean charge densities may be obtained from , this dielectric function is utilized in construction of an electrolyte free‐energy expression [Eq. (50)], as well as to establish an exact second‐moment condition on the ion atmospheres [Eq. (73)]. From the latter it is demonstrated that for rigid spherical ions of diameter , the ion atmospheres necessarily each have nonuniform charge sign when .

Ion‐Pair Theory of Concentrated Electrolytes. II. Approximate Dielectric Response Calculation
View Description Hide DescriptionThe theoretical program initiated in the preceding paper is continued. The wavelength‐dependent dielectric response function for the “primitive‐model” electrolyte,, is evaluated by means of a self‐consistent torque calculation for ion pairs in an external field. The result is used to obtain the longestranged component of the ion‐atmosphere charge density. The rigorous second‐moment condition on the ion atmosphere then is used to compute crudely the short‐ranged components. Besides the usual lowconcentration terms, the implied free energy [Eq. (76)] and activity coefficient [Eq. (77)] contain negative terms varying with the four‐thirds power of concentration.

Electron‐Impact Ionization Cross Sections. V. Classical Calculations and Comparison
View Description Hide DescriptionAbsolute ionization cross sections for single ionization by electron impact on gaseous atoms have been calculated for elements 41–98 using the equations derived by Gryzinski based on classical theory. The results are compared with those given by Mann and with available experimental data. The discrepancies are discussed and analyzed.

Vibrational Spectra and Structures of Ionic Liquids. II. The Pure Alkali Metal Nitrates
View Description Hide DescriptionAttenuated total reflectioninfrared spectroscopy has been used together with thin‐film transmission measurements to obtain detailed spectra for the molten nitrates of lithium,sodium, and potassium in the 250–4000‐cm^{−1} range. The techniques, which yield spectra approaching the ultimate in resolution and precision possible for salt melts, permit the detection of several features which, when combined with Raman data, definitely rule out a melt structure dominated by either ion pairs or simple 1:1 complexes. Rather, systems wherein important factors include both cation distortion of the nitrate symmetry (site effect) and vibrational coupling of neighboring anions (correlation field effect) are definitely suggested. Thus, an assignment based on a perturbed orthorhombic lattice structure is presented which accounts very satisfactorily for all observed features. Order in the melts seems to be slightly greater in LiNO_{3} than for the other salts.

Interpretation of Mesophase Transitions
View Description Hide DescriptionNew data have provided a means for quantitatively testing the statistical theory of Frenkel for explaining the pretransitional effects adjacent to first‐order transitions in mesophase systems. This theory has been frequently suggested as a qualitative explanation for pretransitional changes in physical properties that occur within 10°C of mesophase–isotropic transitions. The one previous quantitative test used compressibility and volume expansion data on p‐azoxyanisole, which forms a single mesophase of the nematic type. It was concluded that the Frankel theory was of limited applicability; that (a) the equations did not apply closely, within about l°C of the transition, and (b) did not apply to pretransition effects below the transition. Calculations made here using new data on p‐azoxyanisole show, in contrast, that the Frenkel theory (a) applies well near the nematic–isotropic transition, (b) the theory may be applied equally well on both sides of the transition, (c) that asymmetrical pretransitional effects are accurately treated, and (d) in contrast to an earlier result, specific‐heat anomalies near the transition are accurately predicted and differ by a factor of 2 from previous estimates.

Radiolysis of Methylcyclopentane. I. Nonhomogeneous Kinetics of Charge Scavenging in the Liquid Phase
View Description Hide DescriptionMethylcyclopentane (MCP) was irradiated in the presence of a number of solutes. The hydrogen yield from pure MCP, was decreased to 2.2 by the addition of N_{2}O or SF_{6}, whereas the addition of ND_{3} increased the total hydrogen yield above the value in pure MCP. In the ND_{3} solutions the yield of HD was twice the decrease in H_{2} yield, so not all positive ions formed in the absence of ND_{3} lead to H_{2} formation. In pure MCP, PH^{+} leads to hydrogen formation and QH^{+} does not. Both types of positive ions react with ammonia by proton transfer: and By using a nonhomogeneous kinetics model of charge scavenging, it was determined that electrons are an order of magnitude more readily scavengable than are positive ions in the radiolysis of methylcyclopentane. Determination of the value of the kinetics parameter in various radiolysis scavenging systems will help to determine the nature of the scavenging reactions that occur in them.

Magnetothermodynamics of Single‐Crystal CuSO_{4}·5H_{2}O. III. Properties over the Range of 0.4°–4.2°K with Fields to 90 kG ‖ to the Magnetic Axis
View Description Hide DescriptionThe heat capacity and magnetic moment of CuSO_{4}·5H_{2}O have been measured over the range 0.4°–4.2°K in stabilized magnetic fields of 0, 1, 3, 5, 10, 20, 30, 50, 70, and 90 kG. The field was directed along the magnetic axis of a 3.70‐cm‐diam spherical single crystal. A sensitive carbon thermometer was used to measure the change of temperature during demagnetizations at essentially constant entropy to connect the several isoerstedic heat‐capacity series. Magnetic saturation, corrected for diamagnetism and an almost trivial temperature‐independent paramagnetism, was used to evaluate the gyromagnetic ratio as and as a zero entropy reference. Within the limit of accuracy of the estimated “tail” above 4°K the electronic entropy was found to be ln2. All observations were uncorrected for the demagnetizing effect of the spherical sample. At 90 kG the heat‐capacity observations show that the nuclear spin polarization is in thermal equilibrium down to 0.7°K.

Numerical Experiments on Scattering of Noble Gases from Single‐Crystal Silver
View Description Hide DescriptionThree‐dimensional numerical experiments on the scattering of noble‐gas atoms from single‐crystal surfaces of silver are described. This numerical method can be very useful in determining the relative importance of different variables in the interactions although it cannot be expected to give quantitative agreement with individual cases until a better knowledge of the interatomic binding energies and the surface state is available. Most of the cases are for neon on the fcc (111) surface, but isolated cases of helium and argon on (111) and neon on (100) are included. The energies include those of effusive molecular beams from 300° to 45 000°K equivalent source temperatures (0.06 to 7.8 eV). Several interaction parameters describing mean energy and momentum exchanges and traces of the spatially resolved flux in the incident plane are given for most of the cases. Sample out‐of‐plane flux data and some typical data on spatially resolved energy are also given, and general trends for the rest of the data are described. The results give trapping probabilities that are much greater than those inferred from laboratory experience, and flux patterns that are significantly broader than those encountered in the experiments for the few cases that can be compared directly. The neon trends with increasing energy are quite similar to those of the Saltsburg and Smith experiments for xenon, with new effects appearing in the present results for energies higher than those of the laboratory experiments. These new effects include multiple peaks, one above and one below specular, and a broadening of the patterns with increasing incident energy. They are attributed to increased resolution of the surface atomic configuration due to deeper penetration of the potential field above the surface. The trends of the Logan, Keck, and Stickney hard‐cube theory are shown in the present results at low incident energy, and the expected hard‐sphere limit behavior is observed at very high incident energy, in agreement with the recent calculations of Goodman.

Error Bounds for the Long‐Range Forces between Atoms
View Description Hide DescriptionA calculation of the long‐range (van der Waals‐London) forces between atoms is presented. Error bounds on the interaction constant are given when the following properties of the atom are known: (1) the energy of the first excited state, (2) the electron density at the atomic nucleus, (3) the number of electrons in the atom, and (4) the refractive index(polarizability) in the optical region. The error bounds are shown to be the most precise possible, given only the above information. In practice, the accuracy is limited mainly by that of the refractive‐index data. The results for rare‐gas atoms are in agreement with recent molecular‐beam and gas‐kinetic measurements.

Shock‐Tube Study of the Radiative Combination of Oxygen Atoms by Inverse Predissociation
View Description Hide DescriptionAbsolute emission‐intensity measurements of the radiative combination of oxygen atoms in the temperature range between 2500° and 3800°K are presented. The emission intensity was recorded simultaneously in six spectral intervals in the wavelength range between 2300 and 4511 Å. The absolute emission intensity was found to be proportional to the square of the oxygen atom concentration and to be characterized by an activation energy of 28.9 ± 2.2 kcal mole^{− 1}. These results are interpreted in terms of an inverse predissociation mechanism in which the oxygen atoms combine along a repulsive potential energy surface with a transition to the state of molecular oxygen and a subsequent radiative transition to the ground electronic state of oxygen. The rate constant for the over‐all radiative combination of oxygen atoms was found to be for the wavelength range 2300–5000 Å.

Glory Scattering of Lithium by a Series of Molecules. I. Diatomics
View Description Hide DescriptionThe velocity dependence of the total cross section has been measured for the scattering of lithium‐7 by D_{2}, N_{2}, O_{2}, CO, NO, HF, HCl, DCl, HBr, HI, ICl, Cl_{2}, and Br_{2}. Glory undulations are observed for all systems except Cl_{2} and Br_{2} although in some cases these undulations are considerably smaller than might be expected for comparable atom–atom scattering. Potential parameters are derived for these systems. Chemical reaction, time‐dependent anisotropic potentials, and inelastic processes are discussed as possible mechanisms for the observed quenching.

Permeation of Hydrogen through Tungsten and Molybdenum
View Description Hide DescriptionUsing ultrahigh‐vacuum and mass‐spectroscopic techniques, permeation of hydrogen through wrought‐and vapor‐deposited W tubes and through a drawn Mo tube has been measured for pressures between 10^{−6} and 200 torr and temperatures between 1050° and 2400°K. Permeation rates varied with pressure and temperature in a complex manner. Expressions for the permeation rate are derived on the assumptions that (a) the rate determining step of permeation is diffusion of hydrogen in the bulk of the sample, and (b) the rate of desorption of hydrogen atoms the rate of recombinative desorption of hydrogen molecules and the concentration of dissolved hydrogen atoms are each determined by the concentration of hydrogen atoms adsorbed on the metallic surface. For the hydrogen–tungsten system, this analysis agrees with measured rates over the entire range of temperature and pressure, and the experimental data is consistent with Hickmott's values for: the rates and the sticking probability for hydrogen atoms; and the probability that an incident hydrogen molecule adsorbs as two atoms. For the hydrogen–molybdenum system, permeation is controlled by phase‐boundary processes at low driving pressures.Measured permeation constants follow the equation above 1 torr. The results and are found for W. For Mo, the corresponding numbers are (7.1 ± 2) × 10^{−4} and (21.5 ± 1).

Permeation, Diffusion, and Solution of Nitrogen in Tungsten and Molybdenum
View Description Hide DescriptionUsing ultrahigh‐vacuum and mass‐spectroscopic techniques, permeation, diffusion, and solution of nitrogen in W and Mo have been measured for pressures between 5 × 10^{−5} and 500 torr and for temperatures between 1100° and 2500°K. The following values for the permeation constants, (torr·liter/cm·sec·torr^{1/2}), diffusion constants, (cm^{2}/sec), and solubility constants, (torr·liter/cm^{3}·torr^{1/2}), are obtained: ; ; ; ; ; . For nitrogen in Mo, the diffusion constant is in agreement with Zener's theory of interstitial atomic diffusion. For nitrogen in W, the frequency factor of the diffusion constant and the diffusionactivation energy are abnormally high and not in agreement with Zener's theory.

Electronic Raman Effect. II. Asymmetry of the Scattering Tensor for Electronic Raman Transitions
View Description Hide DescriptionThe theory of electronic Raman scattering for trivalent rare‐earth ions in crystals is formulated in a general way. It is shown that vibronic coupling is unimportant. The antisymmetric part of the scatteringtensor, which vanishes for vibrational Raman scattering, turns out to be dominant for several electronic Raman transitions. The implications of this with respect to selection rules and depolarization ratios are pointed out.

Selection and Focusing of Polar Diatomics in States of Positive Induced Electric Dipole Moment Using a Ten‐Pole Field
View Description Hide DescriptionUsing a ten‐pole electric field (with two‐pole symmetry) it has been possible to select and focus the rotational states for velocity‐selected thermal molecular beams of CsF and RbCl. However, because of the nonideality of this focusing field, the enhancement in intensity of the separated states (focusing effect) over the thermal population is only about a factor of 2.

NMR and EPR Line‐Broadening Effects of Vanadyl Ion in N,N‐Dimethylformamide
View Description Hide DescriptionThe temperature dependence of the NMRlinewidths of the formyl proton in solutions of VO^{2+} in N,N‐dimethylformamide (DMF) indicates that proton relaxation is controlled by outer‐sphere dipole–dipole interactions, chemical exchange, and inner‐sphere dipole–dipole interactions, in the temperature ranges −55°–+6°, +7°–107°, and 108°–150°, respectively. At 25°C the rate constant for chemical exchange is , , and eu, where is the number of exchanging DMF molecules. The linewidths of the EPR spectrum of VO^{2+} in DMF solutions have been interpreted in terms of the theory developed by Kivelson. The rotational correlation time,, calculated from this theory is shown to be consistent with the observed EPRlinewidths and adequately explains the dipole–dipole line broadening observed in the NMR spectra.

Low‐Temperature Viscosities of Argon, Krypton, and Xenon
View Description Hide DescriptionThe viscosities of nitrogen, argon, krypton, and xenon have been measured by a capillary flow technique in the temperature range 114°–374°K relative to that of nitrogen at 273.15°K. The results for nitrogen and argon below 170°K are lower than those reported by previous workers, but at higher temperatures the results are consistent with other recent determinations.