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Volume 38, Issue 3, 01 February 1963

Thermal Conductivity of Dissociating Phosphorous Pentachloride
View Description Hide DescriptionThe thermal conductivity of the dissociating system PCl_{5}⇌PCl_{3}+Cl_{2} has been measured between 145° and 175°C at a pressure below 1 atm. The thick‐wire variant of the hot‐wire method and an all glass apparatus has been employed. The experimental thermal conductivity values are in good agreement with the values calculated on the assumption of local chemical equilibrium.

Simple Model for the Helix—Random Coil Transition in Polypeptides
View Description Hide DescriptionA simple model for the helix—random coil transition in polypeptides is constructed. Only the limiting case of a sharp transition is considered; however, the model could easily be extended to treat the actual case of a diffuse transition. The formulation of the problem given by Lifson and Roig is used; the main innovation is the introduction of a model interaction with a small number of parameters. For transitions occurring near room temperature, the transition temperature and thermodynamic functions are given in terms of only two parameters, each of which has a simple physical interpretation. The parameters are treated as temperature independent. The model describes in a natural way systems in which both normal and inverted transitions occur. In a normal transition, the helix is the phase stable below the transition temperature; in an inverted transition, it is the phase stable above the transition temperature. In the latter case, the model also describes a reversion of the helix to coil form at elevated temperatures. On the basis of experimental data, the parameters of the theory and the thermodynamic functions are calculated for two systems, one having a normal, and one an inverted transition. The interpretation of the theory in terms of the nature of the polymer—solvent interaction is discussed. The relationship of our work to that of Gibbs and DiMarzio is discussed.

One‐Center Wavefunction for the Hydrogen Molecule Ion
View Description Hide DescriptionAn examination of the one‐center, noninteger principal quantum number, Slater‐type orbital representation applied to the hydrogen molecule ion is presented. The results give rapid convergence to the experimental value for the total electronic energy. A value of —1.09770 a.u. is obtained using only five terms in the expansion. This is 0.00207 a.u. closer to the experimental value than the fifteen term Howell and Shull calculation. The limiting energy which can be obtained using only s‐type terms agrees with the Howell and Shull estimate.

Ultrasonic Investigation of the Rate of Hydrolysis of Potassium Cyanide
View Description Hide DescriptionThe kinetics of the hydrolysis of the cyanide ion have been studied by ultrasonic absorption measurements over the frequency range 30 kc to 25 Mc. A single relaxation frequency has been observed which depends on concentration in the manner expected theoretically for the hydrolysis reaction. The relaxation frequency at 25°C is 450 kc for a 0.01Msolution and 950 kc for 0.05M. The corresponding forward and reverse rate constants calculated for the reaction CN^{—}+H_{2}O⇌HCN+OH^{—} are k _{1}=5.2×10^{4} sec^{—1} and k _{—1}=3.7×10^{9} M ^{—1} sec^{—1} at 25°C. From the magnitude of the maximum excess acoustic absorption per wavelength (90×10^{—6} at 25°C for the 0.05Msolution), the partial molal volume change ΔV° for the process is calculated to be — 12.4 cm^{3}/mole. The temperature dependence of the relaxation frequency indicates an energy of activation for the process HCN+OH^{—}→CN^{—}+H_{2}O of 6±2 kcal/mole.

Electron Spin Resonance in an Irradiated Single Crystal of Tetramethyl Ammonium Chloride
View Description Hide DescriptionAn analysis of the electron spin resonance spectrum of γ‐irradiated crystals of N(CH_{3})_{4}Cl shows that the paramagnetic species stable at room temperature is (CH_{3})_{3}N^{+}. The isotropic coupling constants are found to be 18.0 G for the nitrogen and 26.7 G for the methyl protons. All methyl protons are found to be equivalent. The radical is probably planar and is found to execute restricted rotation at room temperature.

Information Regarding both Molecular‐Weight Distribution and Density Distribution in a Polymer Subjected to Density‐Gradient Centrifugation
View Description Hide DescriptionA polymer sample that is subjected to density‐gradient centrifugation distributes itself over a band in the centrifuge cell. From results obtained in previous work, equations are derived which relate the magnitude of the fluctuations in molecular weight and apparent partial specific volume to certain integrals over the polymer band. To obtain explicit results, the assumption is made that both the distribution over molecular weight and that over effective density are narrow. It is found that the distribution of the polymer over the band can, in principle, give quantitative information concerning the magnitude of the fluctuations.

Melting Curve of Ice VII to 200 kbar
View Description Hide DescriptionThe melting curve of ice VII has been determined to 200 kbar, where ice VII melts at 442°C. The curve can be given as where P is the freezing pressure in kilobars at T°K. The results agree within experimental error with the Simon equation in the formbut the power series fit is better. The main uncertainty in the results is the actual pressure values at the highest pressures.

Moment Equations for Vibrational Relaxation Coupled with Dissociation
View Description Hide DescriptionSets of equations for the moments of the vibrational energy distribution for a diatomic species in a gas are derived, considering simultaneous dissociation and vibrational relaxation. In first approximation a set of two coupled equations are obtained, one for the number of diatomic molecules and the other for the vibrational energy per molecule. The latter contains two correction terms to the Bethe—Teller equation, due to the coupling. The next higher approximation gives three coupled equations, in which the second moment (dispersion) of the distribution function is taken into account. In these equations the dissociation rate ``constant'' is a function of both the average vibrational energy and the second moment. The recombination process is described by three constants which define the over‐all rate, the average vibrational energy, and the dispersion about the average energy of just recombined molecules. The starting point in the development is a gain—loss equation for occupation numbers of vibrational levels. The assumption of harmonic vibrations is used. In order to close the set of equations in any order of approximation, those terms involving higher moments are determined by application of a general method due to Jaynes which gives the least biased estimate in view of the information contained in the moments considered. Consideration of the steady state in first approximation leads to Onsager reciprocal relations and, in second approximation, to more complicated relations.

Field‐Electron and Field‐Ion Emission from Single Vapor‐Grown Whiskers
View Description Hide DescriptionA technique is described for mounting a single vapor‐grown whisker on the point of an otherwise ordinary field‐emission tip assembly with sufficient bond strength to permit both field‐electron and field‐ion microscopy. Field‐electron emission patterns are shown for clean Au and Pt whiskersurfaces. Hydrogen field‐ion images of thermally cleaned Pt whiskersurfaces and helium field‐ion images of field‐evaporated Pt whiskersurfaces are shown. Imperfections in central {011} planes are sometimes found, but there is no strong evidence that these are axial screw dislocations.

On the Robinson and Price (Kramers—Kronig) Method of Interpreting Reflection Data Taken through a Transparent Window
View Description Hide DescriptionIt is shown that the usual integral formula used to obtain the phase shift from the reflectivity (at all frequencies) must be modified when the reflectivity is measured off a surface covered by a transparent window. The discussion is first restricted to reflection at normal incidence but is later generalized to include all possible angles of incidence. There are found to be three distinct cases defined by the conditions , where ε_{0} is the static dielectric constant of the sample, ε_{ w } is the dielectric constant of the window, and α is the angle of incidence. Case (1) involves the addition of an extra factor to the usual expression for the phase shift. This extra factor involves either zero, one, or two unknown parameters depending upon the particular values of α, ε_{ w } and ε_{0}. In case (2) the expression for the phase shift is quite complicated and of doubtful practical value. In case (3), it was found possible to write a simple expression for the phase shift in terms of a different integral than the one ordinarily used.

Melting of Graphite at Very High Pressure
View Description Hide DescriptionA method of flash‐heating small rods of graphite inside a superpressure cell has been developed. The heating energy was inserted in less than 7 msec from a bank of electrolyticcapacitors. This quick heating and cooling allowed fusion and freezing of the graphite to occur without serious melting or reaction of the surrounding wall material. Electrical data were recorded with oscillographs and cameras. The start of melting was found to be indicated by an abrupt downward trend of resistance. Polished cross sections of the samples showed clearly the part which melted. Melting temperatures increased from about 4100°K at 9 kbar to a maximum of about 4600°K in the region of 70 kbar, then decreased to about 4100°K at 125 kbar. A value of 25 kcal/mole for the heat of fusion at 48 kbar was determined. The graphite/diamond/liquid triple point is shown to be at about 4000 to 4200°K and 125 to 130 kbar.

Direct Conversion of Graphite to Diamond in Static Pressure Apparatus
View Description Hide DescriptionStatic pressure apparatus has been developed which is capable of pressures up to 200 kbar and transient temperatures up to about 5000°K, using an electric flash‐heating technique. At pressures above about 125 kbar and temperatures in the 3000°K range it is found that graphite spontaneously collapses completely to polycrystallinediamond which may be retrieved quantitatively. The threshold temperature of the transformation is several hundred degrees lower than the melting temperature of graphite. The diamond/graphite/liquid triple point is found to be located at about 125 (+10, —0) kbar and 4100 (±200)°K. The shock compression results of DeCarli and Jamieson, and of Alder and Christian, are linked with the present results to construct a phase diagram of carbon extending to 5000°K and 800 kbar.

Chemical and Magnetic Enhancement of Perturbed Lines in the Violet Spectrum of CN
View Description Hide DescriptionA chemical kinetictheory based on the quantum‐mechanical properties of perturbed molecular states is developed to explain the rotational intensity anomalies observed in the CN‐band spectrum emitted by an active nitrogen flame. Relative intensities of perturbed lines are calculated in terms of parameters which specify the rates of chemical formation, collisional relaxation, and radiative decay of CN molecules in the excited electronic states where the perturbed lines originate. Numerical values of these parameters are found which, inserted in the intensity expressions, predict correctly the observed pressure‐dependent enhancement of each perturbed line. From this analysis the approximate value 6×10^{—7} sec is found for the radiative lifetime of the A ^{2}II_{ i }, v′=10 state of CN. It is also found that nearly every gas kinetic collision changes the rotational state of an excited CN molecule, but that only about 1 collision in 100 can cause the exchange of vibrational energy for electronic energy represented by the transition A ^{2}II_{ i }, v′=10→B ^{2}Σ^{+}, v′=0. The theory also predicts, in agreement with recent observations, an additional selective enhancement of certain perturbed lines by a strong magnetic field.

Infrared Absorption Spectra of LiF and Li_{2}F_{2} in Solid Argon, Krypton, and Xenon Matrices
View Description Hide DescriptionThe infrared absorption spectra of LiF and Li_{2}F_{2} isolated in solid argon, krypton, and xenon have been investigated from 2 to 35 μ. Infrared frequencies of both molecules have been obtained, and the assignment of the B _{2u } and B _{3u } modes of Li_{2}F_{2} has been made assuming a planar rhomboid structure, (V_{h} ). An interesting case of a so‐called ``matrix effect'' is also presented.

Thermoelectric Effects in Fused Ionic Materials
View Description Hide DescriptionMeasured values of the thermoelectric power of fused PbCl_{2}, PbBr_{2}, AgNO_{3}, NaCl, and KCl are reported for temperatures in the range 200°—1000°C. Theoretical correlations of the thermoelectric power derived by Holtan from the principles of irreversible thermodynamics do not check closely with the empirical results if it is assumed that the entropies of transport for the materials investigated are negligible. Such an assumption, in general therefore, seems unjustified.

Mechanism of the Conversion of CdF_{2} from an Insulator to a Semiconductor
View Description Hide DescriptionIn a previous publication, the authors proposed a mechanism for the conversion of CdF_{2} containing small amounts of trivalent ion impurities from an insulator to an n‐type semiconductor when heated in Cd vapor at 500°C. Additional experimental evidence is presented in support of this mechanism in which the interstitial F^{—} ions, which normally compensate the extra positive charge of the trivalent ion impurity, diffuse to the surface of the crystal and combine with Cd atoms from the gas phase to form a surface layer of CdF_{2}. Simultaneously electrons from the Cd atoms diffuse into the crystal and give rise to observed conductivity and optical absorption. It is demonstrated using Cd^{109} that no appreciable diffusion of Cd into the crystals takes place during heating in Cd vapor. The dependence of the amount of added Cd upon the Cd pressure is in good agreement with the proposed mechanism. Finally the observed changes in the fluorescencespectrum of Sm^{3+} after heating in Cd vapor are used to show that the symmetry of the crystal field at the Sm site is changed from noncubic symmetry to a higher symmetry, most probably cubic.

Reactions of Nitrogen—Hydrogen Radicals. I. NH_{2} Recombination in the Decomposition of Ammonia
View Description Hide DescriptionPhotoelectric measurements of NH_{2} absorption as a function of time following an rf discharge pulse through ammonia are described. The extinction coefficient of the strong vibration—rotation line at 16725.40 cm^{—1} is found to be 1.02±0.10×10^{3} liter mole^{—1} cm^{—1} as an upper limit. Under the proper conditions the kinetics of NH_{2} disappearance is second order with respect to NH_{2}. Arguments attribute the initial stages of the observed reaction to NH_{2} recombination to form hydrazine. The recombination rate constant is 2.33±0.20×10^{9} liter mole^{—1} sec^{—1} and is independent of the total pressure in the range 425 to 850 μ.

Study of the H_{6} Ring in the Molecular Orbital and Alternant Molecular Orbital Approximation
View Description Hide DescriptionA configuration interaction calculation in a molecular orbital basis has been carried out on a system of six hydrogen atoms arranged in a regular hexagon. The alternant molecular orbital and second‐order perturbation theory approximations have been investigated. All multicentered integrals have been accurately computed.

Kinetics of Reactant Isolation. I. One‐Dimensional Problems
View Description Hide DescriptionThis paper treats the time‐dependent statistics of bond formation (both irreversible and reversible) between fixed sites. This model corresponds to a number of real physical processes. Among these are reaction of adjacent functional groups on a linear polymer, matrix isolation of free radicals, and chemisorption. Because the sites are fixed, certain of them become isolated from others, not yet reacted, and must survive to infinite time. A certain amount of survival occurs even when bonds can be undone.
Exact descriptions of the kinetics of these processes are given for one‐dimensional systems. The mean probability of site survival as a function of time is calculated for linear arrays and for rings. The probability of site survival as a function of position on the chain (end effects) is treated in Sec. IV. A generating function is introduced in order to calculate higher moments of the survival probability distribution function and to treat the effect of a random diluent. An approximate method of solution is developed for the time dependence of the number of reacted particles in the reversible case.

On the Isomerization of Isobutyl Radicals
View Description Hide DescriptionAn experimental assessment has been made of the competition between isomerization of a deuterium‐labeled isobutyl radical,and the straight decomposition,It was found that the first reaction was never more than 1% as rapid as the second, up to 540°C. Therefore, the only measurable unimolecular reaction of isobutyl up to 540° is the straight decomposition reaction.