Volume 49, Issue 7, 01 October 1968

Electron Paramagnetic Resonance of X‐Ray‐Irradiated Single Crystals of Potassium Cobalticyanide, K_{3}Co(CN)_{6}
View Description Hide DescriptionX‐ray irradiation of single crystals of undoped diamagneticpotassium cobalticyanide K_{3}Co(CN) has been shown to produce paramagnetic species. The electron paramagnetic spectra indicate that the eight‐line hyperfine interactions observed collapse into one set when the magnetic field is parallel to any one of the three crystallographic axes labeled , or . The widths of the hyperfine lines vary and the linewidths increase as the values of the nuclear magnetic spin quantum number decreases. The experimental results have been interpreted in terms of an appropriate spin Hamiltonian to yield the principal values of the axially symmetric g and hyperfine interaction tensor A. The results obtained are , and . A theoretical estimate of the values obtained by using the method described by Pryce leads to the conclusion that the paramagnetic center is most likely due to a species with configuration formed by the odd electron going into a orbital followed by a weak tetragonal distortion to symmetry of the ensuing structure as the result of the Jahn–Teller effect. An alternative possibility is that the original anion loses a CN group to form a paramagnetic species with symmetry .

Effects of Excluded Volume on Light Scattered from Flexible Macromolecules
View Description Hide DescriptionThe effect of the non‐Gaussian behavior of the chain‐segment distribution in flexible polymer coils on the angular distribution of scattered light is discussed. The explicit form of a general spherical‐segment distribution function, with different values of , is used to evaluate the general scattering equation for the particle scattering factor . In addition, the effects of excluded volume on the mean end‐to‐end chain separation is taken to be of the form , where is the number of chain steps and is a parameter which measures the excluded volume effect on the . In this paper, an expansion of the function to the first few terms is carried out and numerically evaluated for the dependence of on the variable , where is the wavenumber of the incident light, is related to the scattering angle, and is the radius of gyration determined from experimental data of the scattering cross section. The computations were carried out for the polymer in good solvent, for which data for and were adopted, based on the lattice model of nonself‐intersecting chain, and for polymer in theta solvent, for which Gaussian chain model was adopted. The computations were carried out for various degrees of polydispersity. A comparison was made between the theoretical and the experimental results on a polystyrene sample of molecular weight of 4 × 10^{6} in cyclohexane at 35°, 45°, 55°C and in benzene at 40°C.

Asymptotic Behavior of the Light‐Scattering Function of Coiled Molecules
View Description Hide DescriptionThis paper discusses the asymptotic solution of the scattering function for large , where is proportional to the scattering angle, radius of gyration, and the wavenumber. The theoretical model employed for the calculation of the curves was presented in the preceding paper. The results are discussed with respect to the experimental data, after the results for are corrected for various values of polydispersity. A general analysis of the theoretical curves is presented, and the effect of the shape of the chain‐end distribution function on the asymptotic behavior of the light‐scattering function is discussed.

Dipole Shielding Factor in Hartree–Fock Theory
View Description Hide DescriptionIn the coupled Hartree–Fock approximation, the dipole shielding factor is proved to be identically for any atomic state. This suggests that variational‐perturbation methods which yield poor values of the shielding factor may give unreliable Hartree–Fock values for other atomic properties such as the polarizability.

Concentration Dependency of the Fluorescence from Solutions of 2‐Phenyl Indole and Derivatives of 2‐Phenyl Indole. I. Fast‐Electron Excitation
View Description Hide DescriptionThe relative scintillation yield for excitation with fast electrons was measured as a function of the concentration of the solute. The property of self‐quenching of a series of 2‐phenyl indole and 2‐phenyl indole derivatives was correlated with the structure of the compound. It was shown that destroying the ability of the chromophore of the molecule to obtain a coplanar configuration would eliminate self‐quenching in most cases. The exceptions were those derivatives which had an H atom on the N atom of the indole ring. It is believed that in these cases self‐quenching may proceed through a hydrogen‐bonding mechanism. The substitution on long‐chain alkyl groups on the N atom of the indole did not eliminate self‐quenching even for a 12‐carbon‐atom chain. There was a gradual decrease in self‐quenching upon increasing the substituent from methyl to n‐hexyl.

Concentration Dependency of the Fluorescence from Solutions of 2‐Phenyl Indole and Derivatives of 2‐Phenyl Indole. II. uv Radiation Excitation
View Description Hide DescriptionThe fluorescence spectra and fluorescence yields were measured as a function of solute concentrations for uv excitation of 2‐phenyl indole and some derivatives of 2‐phenyl indole. Correlations between structure and self‐quenching were similar to the correlations obtained with fast‐electron excitation. The formation of excimers was demonstrated as the concentration of certain derivatives of 2‐phenyl indole was increased. A common pathway of excimer formation and self‐quenching was indicated from the results.

Symmetric Gaseous Diffusion Coefficients
View Description Hide DescriptionThe kinetic theory development of expressions for the diffusion velocities in multicomponent gaseous mixtures is reconsidered. A set of equations for multicomponent diffusion coefficients which are symmetric in the indices is developed. The special cases of two‐and three‐component systems are considered explicitly.

Temperature Dependence of F‐Center Absorption in KBr and NaBr
View Description Hide DescriptionThe absorption due to centers in x‐irradiated KBr and NaBr has been measured over a wide range of temperatures from 4 to 370°K. In NaBr (which is exceedingly difficult to color) there is also formed a well‐isolated band without the usual difficulty of overlapping bands and so the temperature dependence of the shape of this band could also be determined accurately. The difficulty of the overlapping band has been dealt with in two ways: by Gaussian plots of the untreated data (after background subtraction) and by a computer resolution of the and bands. The latter calculations confirm the asymmetry of the band. The half‐widths of the and bands obey the usual formula and from the temperature dependence of the half‐widths, values of the effective ground‐state frequency were obtained. To what extent this represents a genuine local mode remains unresolved. There is some evidence for structure in the band at low temperatures.

Two‐Temperature van der Waals Potentials
View Description Hide DescriptionThe Linder formulation of the van der Waals potential, expressed in terms of susceptibilities, between two weakly interacting molecular systems at different temperatures is applied to a simple model. The model molecules are assumed to have the low‐frequency characteristics of rigid rotors and the high‐frequency characteristics of harmonic oscillators. It is shown that the induction potential is always attractive; the orientation potential becomes repulsive when the temperature difference is large. The dispersion potential becomes repulsive when the temperature difference is large provided the hotter system has the higher natural frequency.

Environmental Effects on Phosphorescence. III. Oxygen Quenching of Naphthalene Triplets in Compressed Polymethylmethacrylate
View Description Hide DescriptionBimolecular, diffusion‐controlled oxygen quenching shortens triplet lifetimes and reduces phosphorescence intensities of organic solutes embedded in polymethylmethacrylate at room temperature. Matrix compression reduces the quenching of naphthalene and naphthalene‐d _{8} triplets until at pressures of about 12 kbar the presence of oxygen is no longer felt and the pressure dependence of the lifetime in the 12–30‐kbar range is indistinguishable from measurements on thoroughly deaerated samples. The activation volume for oxygen diffusion in this polymer is approximately +12 cm^{3}/mole, as measured from the phosphorescence lifetimes of naphthalene‐d _{8}. The high‐pressure results confirm that diffusional quenching is not responsible for the effects of pressure on phosphorescence lifetimes in deaerated polymer matrices.

Environmental Effects on Phosphorescence. IV. Triplet Decay of Halonaphthalenes in Compressed PMMA
View Description Hide DescriptionThe effects of high pressure (0–32 kbar) on the phosphorescence lifetime of seven monohalogen‐substituted naphthalenes, dispersed in polymethylmethacrylate (PMMA), have been measured at room temperature. It is observed that the pressure‐induced shortening of the lifetimes becomes less significant in those halonaphthalenes which possess the heavier atoms, i.e., the greater the intramolecular heavy‐atom effect the less influential are environmental perturbations. “Activation volumes,” ranging in magnitude between , were computed from linear plots. Qualitative arguments are given to support the observed magnitudes and trends in the pressure‐induced volume effects on triplet decay.

Studies of the Evaporation Mechanism of Sodium Chloride Single Crystals
View Description Hide DescriptionThe vacuum evaporation rate of the (100) face of pure sodium chloride single crystals has been measured with a vacuum microbalance in the temperature range 450°–650°C. The steady‐state vaporization rates of pure crystals with dislocation densities of ∼1 × 10^{6}/cm^{2} were lower by about a factor of two than the maximum thermodynamic rate . When the dislocation density was increased an order of magnitude (to ∼ 10^{7}/cm^{2}) by straining the crystals, the steady‐state evaporation rate increased to approximately the thermodynamic rate . The relative vaporization rates of monomer and dimer were measured using a quadrupolemass spectrometer.Vaporizationactivation energies and were found for the monomer and dimer, respectively, in the temperature range of the experiments for low dislocation crystals. No dependence of the monomer to dimer ratio on the dislocation density was detected. The presence of the divalent cation impurity, Ca^{2+}, in the NaCl crystals markedly reduced the vaporization rate and increased the activation energy of vaporization. Crystals doped with 300 ppm Ca^{2+} exhibited vaporization rates approximately an order of magnitude lower than the maximum thermodynamic rate . The average activation energy of vaporization for these crystals was as computed from the total rate of vaporization. The monovalent impurities, Br^{−}, OH^{−}, O_{2} ^{−}, had no detectable effect on the vaporization rate. An evaporation mechanism was postulated which could account for the experimental observation.

Ionization Potentials of Free Radicals Formed by Electron Impact. Methylstannyl Radicals
View Description Hide DescriptionThe vertical ionization potentials of the (CH_{3})_{3}Sn, (CH_{3})_{2}Sn, and CH_{3}Sn radicals have been measured using a double‐pulsed mass‐spectrometric method in which the radicals were formed by the impact of electrons on hexamethylditin. As a check on the internal consistency of the method and measurements, the vertical ionization potentials of several alkyl radicals, R, produced by electron impact on compounds of the type (CH_{3})_{3}Sn–R, were measured. The values found were generally somewhat higher than recent measurements using photoionization and pseudomonoenergetic electron‐impact methods, but were in excellent agreement with the vertical ionization potentials obtained by the impact of nonmonoenergetic electrons on thermally‐produced alkyl radicals.

Radial Integrals for the Atomic Many‐Body Problem
View Description Hide DescriptionA full analysis is presented of the radial integrations arising from certain two‐, three‐, and four‐electron integrals for correlated wavefunctions, assuming only pair correlations between the electrons in an atom.

Self‐Consistent Perturbation Theory. I. Finite Perturbation Methods
View Description Hide DescriptionA general method is proposed for quantum‐mechanical study of physical properties of molecules involving polarization or distortion of the electronic structure. This consists of the calculation of self‐consistent molecular orbital wavefunctions (single determinants) in the presence of small but finite perturbations. The general theory of such methods is presented together with a preliminary discussion of numerical error.

Self‐Consistent Perturbation Theory. II. Nuclear‐Spin Coupling Constants
View Description Hide DescriptionThe finite pertubation method developed in the first paper of this series is applied to isotropic nuclear‐spin coupling constants, assuming that only a Fermi contact mechanism couples the electron and nuclear spins. Results for some simple systems are calculated using self‐consistent molecular orbital methods involving the neglect of differential overlap, and on the basis of these results, certain points regarding the mechanisms of spin coupling are discussed. A detailed discussion of the sources and magnitudes of the errors is also presented.

Spin Hamiltonian of ^{51}V^{2+} in MgO, as Derived from Electron Nuclear Double Resonance
View Description Hide DescriptionThe electron nuclear double resonance spectrum of ^{51}V^{2+} diluted in a single crystal of MgO has been measured at 4.2° and 77°K. The spin‐Hamiltonian parameters have been determined, including an additional hyperfine contribution of the type . Perturbation theory up to the fourth order has been used to calculate the latter term as a result of interactions of the ground orbital singlet with higher orbital levels.

Indirect Spin Saturation. III. Solutions of Spin‐Density Matrix
View Description Hide DescriptionFor homonuclear spin one‐half systems, in which and are in chemical exchange, the effect of a strong irradiation at on the intensity of the group is studied. Alexander's treatment on spin‐density matrix is applied to the double‐resonance systems. The matrix equations are solved. The results are compared with experimental data for an system. A new quantity which is dependent upon , and , is introduced to characterize the spin exchange due to spin–spin interaction.

Temperature Dependence of Surface Tension for Liquid Metals
View Description Hide DescriptionThe surface‐tension temperature dependence is calculated for liquid metals. In this calculation the ion motion is taken as a harmonic oscillation and it is shown that the difference in oscillation frequencies for surface and inner ions is mainly responsible for the temperature dependence of the surface tension. There is, however, a second influence caused by the change of particle density due to thermal expansion. An expression for the surface tension is derived and comparison is made with experimental values. The change of oscillator frequency, the surface tension at zero temperature, and a characteristic temperature corresponding to the critical temperature are calculated.

Ionization of Strong Electrolytes. XI. The Molecular States of Nitric Acid and Perchloric Acid
View Description Hide DescriptionRecent proton magnetic measurements in the ternary systems HNO_{3}–DNO_{3}–water and HClO_{4}–DClO_{4}–water partly confirm older data and furnish new information on the molecular states of the acids, on hydration and solvation of the hydrogen ion, and on the distribution of H in deuterated acids between the ion and water. The dissociation constants of HNO_{3} and DNO_{3} between 0° and 65° are derived from the measurements.