Volume 41, Issue 8, 15 October 1964
Index of content:
41(1964); http://dx.doi.org/10.1063/1.1726250View Description Hide Description
The valence bond method has been used to calculate the spin densities in the positive and negative ions of azulene. Though there is some question as to what value of Q CH H should be used in the expression , the experimental hyperfine constants for the azulene negative ion are converted to spin densities through the use of 13C–1H spin‐coupling data. The results of the valence bond calculations, when the parameters are chosen to minimize the error in the three largest spin densities, are in as good agreement with experiment as are the results of several molecular orbital calculations. A previously determined parameter was used to compute the effect of methyl substitution. Though the spin densities themselves are in no better agreement with experiment than in the case of the unsubstituted ion, the change in spin density at the unsubstituted positions is correctly predicted in both direction and magnitude. Since the spin densities in the azulene positive ion should be quite different from those in the azulene negative ion, these quantities are calculated as well. The results for the azulene positive ion do not agree with the results of available molecular orbital calculations, and thus some experimental values are needed to evaluate the relative merits of the methods.
Luminescence Phenomena in Gamma‐Irradiated Pure 3‐Methylpentane Glass: Implications for Radiation Chemistry41(1964); http://dx.doi.org/10.1063/1.1726251View Description Hide Description
Gamma irradiation of 3‐methylpentane glass at 77°K causes prolonged luminescence at that temperature with a decay law resolvable into three first‐order decays with specific rates of the order of 10—3 sec—1. Activation energies for the release of this ``isothermal'' luminescence are tightly grouped around a value near 0.1 eV. Additional luminescence produced in a ``warmup'' region corresponds to activation energies broadly grouped near 0.25 eV. Absorption of infrared light causes rapid release of ``isothermal'' luminescence but has no observable effect on ``warmup'' luminescence. Added quenchers affect both parts. The spectrum of the luminescence seems to be unaffected by the temperature or other treatment of the sample. Results are interpreted in terms of release of weakly trapped electrons and their interaction with positive holes to yield emitting states. The results suggest that in the radiation chemistry of condensed systems at room temperature some of the electron‐neutralization processes require >10—11 sec for their completion. During this time the positive holes involved can react chemically with their environs.
41(1964); http://dx.doi.org/10.1063/1.1726252View Description Hide Description
Certain solutions containing a mixture of two solvents one of which is benzene, a scintillator (at fixed concentration) and air (also at fixed concentration) when irradiated with 60Co γ rays are known to yield luminescence, the intensity of which is a minimum at benzene concentration near 1 vol. %. A light‐yield expression, analytically developed by Nosworthy, Magee, and Burton to explain this minimum, is examined and interpreted. It is shown theoretically and experimentally that the minimum can be made to disappear at sufficiently high concentration of scintillator solute, that the presence of air or other quencher is not in principle essential to the existence of a minimum, that the properties of benzene (the ``better'' solvent) pertinent to the effect are not affected by the presence of other solvent, that such necessary properties are establishable and selection of the ``better'' solvent can be deliberately made to conform to those properties, and that other solvent pairs of the required characteristics can be found. The results are interpreted in terms of structure of the liquid.
41(1964); http://dx.doi.org/10.1063/1.1726253View Description Hide Description
The crystal structure of the yellow compound (NH4)2CuCl4 has been determined by x‐ray diffraction studies. The compound crystallizes in the orthorhombic space group Cmca with a=15.46 Å, b=7.20 Å, and c=7.20 Å. The structure contains discrete, planar CuCl4 = ions with Cu–Cl distances of 2.30 and 2.33 Å. These ions are then bonded together by longer Cu–Cl bonds of 2.79 Å to form infinite two‐dimensional sheets. The yellow compounds (CH3NH3)2CuCl4 and (C2H5NH3)2CuCl4 probably have closely related structures.
Mass Spectrometric Studies at High Temperatures. II. The Sublimation Pressures of Magnesium, Strontium, and Barium Fluorides41(1964); http://dx.doi.org/10.1063/1.1726254View Description Hide Description
A mass spectrometer has been employed to measure the sublimation pressures and heats of sublimation for MgF2 over the range 1241° to 1492°K; for SrF2 over the range 1207° to 1563°K; and for BaF2 from 1232° to 1505°K. For MgF2 the results are represented byfor SrF2 byand for BaF2 the equation isThe errors quoted are the standard deviations from the least‐squares fitted lines. The heat of sublimation of MgF2 at 1366°K is 88.3±2.5 kcal mole—1 while the heats of sublimation at 298°K are 103.7±2.5 kcal mole—1 for SrF2 and 92.3±2.0 kcal mole—1 for BaF2.
Mass Spectrometric Studies at High Temperatures. III. Dissociation Energies of the Alkaline Earth Monofluorides41(1964); http://dx.doi.org/10.1063/1.1726255View Description Hide Description
By heating the difluorides of magnesium,strontium, and barium under reducing conditions, one obtains significant amounts of the respective monofluorides. Mass spectrometric studies of equilibria involving these monofluorides have yielded the dissociation energies (D°298) 4.62±0.1 eV, 5.43±0.1 eV, and 5.83±0.1 eV for gaseous MgF, SrF, and BaF, respectively. These results support an ionic model for these molecules and are considerably higher than those previously accepted.
Application of the Theory of Absorbing Markov Chains to the Statistical Thermodynamics of Polymer Chains in a Lattice41(1964); http://dx.doi.org/10.1063/1.1726256View Description Hide Description
A concept of absorbing Markov processes is employed in order to study the statistical thermodynamics of infinitely long polymer chains, simulated by a random flight on a lattice. These polymer chains interact in the sense that certain chain conformations are associated with intramolecular interactions, defined by short‐range, steplike potentials. Various thermodynamic functions are derived from the polymer partition function, which, in turn, is obtained from the largest eigenvalue of the matrix of transition probabilities. The thermodynamic functions of this simplified polymer model are evaluated for some lattice models and for different forms of the interaction potentials. The results thus obtained are then compared with more accurate, but much more lengthy, Monte Carlo or direct‐counting computations.
41(1964); http://dx.doi.org/10.1063/1.1726257View Description Hide Description
A theory for the collision cross section due to first‐order London dispersion forces has been developed on the basis of the Anderson—Tsao—Curnutte's theory of pressure broadening. The widths of OCS J = 1→2 line broadened by helium and argon are explained.
41(1964); http://dx.doi.org/10.1063/1.1726258View Description Hide Description
Radiolysis of solutions of 1% cyclohexene‐1‐14C in cyclohexane with 60Co γ rays yields radioactive cyclohexane, bicyclohexyl, cyclohexylcyclohexene, and bicyclohexenyl. Measurements were made of the total yield of these products, their specific activity, the total yield of hydrogen, and also the yield of hydrogen from pure cyclohexane. It is shown by material and radioactive balance considerations based on a simplified free radical mechanism, together with some known kinetic data, that a major fraction of the decrease in the H2 yield relative to that in pure liquid cyclohexane can be accounted for in terms of the reactions of H atoms with cyclohexene and the resulting formation of the radioactive C6H11 and C6H9 radicals. Detailed analysis shows that the specific rate of addition of H atoms to cyclohexene is 41 times greater than the specific rate of abstraction by H atoms from cyclohexane, and that the molecular (unscavengeable) and free radical yields in the irradiation of pure cyclohexane are, respectively, 1.7 and 3.7 molecules/100 eV. The latter conclusion is in fair agreement with results obtained by a number of other workers, but is in sharp contrast with recent results of Dyne. A plausible explanation is suggested to reconcile the discrepancy between the two sets of results.
41(1964); http://dx.doi.org/10.1063/1.1726259View Description Hide Description
Numerical integration of the zero‐temperature Thomas—Fermi—Dirac equation has been carried out on the IBM 701 for atomic numbers Z = 1 to 100. Compressed, expanded, and isolated atoms were treated, the latter using the boundary condition suggested by Jensen. Physical properties of interest for compressed and expanded atoms are presented graphically and, in the case of isolated atoms, tabularly as well.
41(1964); http://dx.doi.org/10.1063/1.1726260View Description Hide Description
We consider a model dimer composed of units with one allowed excited state and one symmetric vibration. The vibrational mode has the same force constant in the ground and excited states, but the excited state is assumed to have its equilibrium position shifted by an amount measured by λ. The dimer possesses a symmetry operation that exchanges the units and has an exciton coupling ε. Spectra for various λ and ε values are derived by computer. It is shown that the absorption intensity of the two polarizations rigorously satisfies two theorems: the center of gravity is at ±ε for all λ; the bandwidth is | λ | for all ε.
41(1964); http://dx.doi.org/10.1063/1.1726261View Description Hide Description
The hydrogen—oxygen reaction in reflected shock waves has been studied in the range of conditions 890°≤T≤1350°K, 4.5≤P≤5.6 atm, 1.3≤O2≤13×10—3 moles/liter, and 0.5≤[H2]/[O2]≤2. Measurements of both the induction period of OH absorption and that of pressure increase suggest that the reaction H+O2→OH+O is the rate‐determining step of OH formation in this temperature range and has an activation energy of 18.9±0.9 kcal/mole, but that the rate‐determining step of over‐all reaction is HO2+H2→H2O2+H below 1100°K, while H+O2→OH+O is rate determining above 1100°K. Also, the mechanism of the hydrogen—oxygen reaction below 1100°K is discussed in some detail.
41(1964); http://dx.doi.org/10.1063/1.1726262View Description Hide Description
Trivalent dysprosium,thulium, and holmium ions in calcium fluoride, strontium chloride, and barium bromide have been successfully reduced to the divalent state by solid‐state electrolysis. In contrast with similar samples reduced by gamma irradiation which are unstable with respect to light and heat, the electrolytically induced divalent rare‐earth ions are optically and thermally stable. Unlike the gamma‐reduced samples, recombination hole centers are believed to be absent in these samples. The majority of trivalent ions have been reduced, and the concentration of divalent rare‐earth ions obtainable by the electrolytic process far exceeds that by gamma irradiation in all the samples, with or without charge‐compensating monovalent cations. The completeness of the reduction, the stability of the reduced samples and, therefore, the apparent absence of recombination hole centers suggest that the reduction of the rare‐earth ions follows the migration of the corresponding halide ions (which, in the case of calcium fluoride, served as charge compensators for the trivalent ions) to the anode, where they are presumably oxidized to the neutral state and escape from the crystal lattice. This mechanism is not unlike that proposed for the electrolytic coloration of alkali halides.
41(1964); http://dx.doi.org/10.1063/1.1726263View Description Hide Description
41(1964); http://dx.doi.org/10.1063/1.1726264View Description Hide Description
Both the chemical shifts of nuclear magnetic resonances and molecular diamagneticsusceptibilities have their origin in the electronic currents induced by an external magnetic field. For the aromatic hydrocarbons detailed chemical‐shift measurements and extensive measurements of the magnetic anisotropies are available to aid in a study of the validity of various theories connecting magnetic properties with magnetic electron currents.
The available experimental data seem to present a definite paradox. The chemical shifts due to ring currents are theoretically directly proportional to the values of Δχ, the anisotropy in the diamagneticsusceptibility; yet the experimental values of Δχ are much larger than those calculated from theory, while the experimental chemical shifts are substantially smaller than the theoretical ones.
Hoarau has suggested that only a part, χ L , of the total anisotropy Δχ arises from the π electrons involved in the ring current and that one should add Δχσ , a contribution from the electrons in the σ bonds, and Δχ p , the contribution due to the localized p electrons. The SCF—MO calculations of χ L for benzene give a value of approximately —30×10—6, which is only about half the experimentally observed value of —59.7×10—6. Rough calculations are presented which indicate that the contributions of the σ and localized p electrons are large enough to account for the observed values of Δχ and χ z for the aromatic hydrocarbons.
An analysis of the chemical shifts of the aromatic hydrocarbons shows that they are in agreement with a Δχ value for benzene of approximately —31×10—6 in good agreement with the SCF—MO value of χ L . Calculations of the chemical shifts due to localized magnetic anisotropies show that they are quite small and can frequently be neglected. In calculating ring current contributions to the chemical shift in NMR spectroscopy it is recommended that the SCF—MO value of χ L , —30×10—6, be used in place of the classical value, —49.5×10—6.
41(1964); http://dx.doi.org/10.1063/1.1726265View Description Hide Description
The paramagnetic resonance of the cycloheptatrienyl radical (C7H7) has been observed in single crystals of thiourea and naphthalene and in polycrystalline thiourea, naphthalene, cycloheptatriene, and argon at temperatures ranging from 4.2° to 300°K. The spectra are of two types: (a) high‐temperature spectra—eight equally spaced lines with splittings in the range 3.5–4.1 G; (b) low‐temperature spectra—highly anisotropicspectra which are markedly different for each crystalline environment. The transitions from (a) to (b) occur within 5°K, and the transition temperatures are 40°, 20°, and around 13°K in thiourea, naphthalene, and cycloheptatriene, respectively.
The high‐temperature spectra are readily accounted for in terms of seven equivalent protons and a uniform electron spin distribution about the ring. The high‐temperature spectra thus provide evidence that there is no significant static (Jahn—Teller) distortion of C7H7. The uniform spin distribution around the molecular ring is brought about by the combined effects of rapid molecular reorientation about the seven‐fold axis, plus the crystalline electric‐field splitting of the orbital degeneracy. That is, in a sense, the crystal field splitting ``locks'' the spin distribution to the lattice, and molecular reorientation moves the nuclei relative to a fixed spin distribution. The low‐temperature spectra correspond to the electronic ground state of (nonreorienting) C7H7, as determined by the crystalline electric field. The observed low‐temperature spectra of C7H7 in naphthalene are compared with spectra calculated using the Hückel, valence‐bond, approximate unrestricted Hartree—Fock LCAO—MO, and Pariser—Parr approximations to the molecular electronic structure of C7H7. The observed spectra appear to be in semiquantitative agreement with calculations based on the Hartree—Fock and Pariser—Parr approximations. However, detailed comparisons between these theoretical calculations and experiment are uncertain since both vibronic interactions as well as torsional molecular oscillations have an effect on the low‐temperature spin distribution.
41(1964); http://dx.doi.org/10.1063/1.1726266View Description Hide Description
An x‐ray back‐reflection, rotating‐camera technique has been used to obtain lattice constants and thermal expansivities of single‐crystal silicon and calcium fluoride. Absolute expansivity was obtained over a broad range with an error less than 3 ppm. For silicon, this absolute method discriminates between earlier experiments showing some disagreement, and establishes with improved precision the temperature variation of the Grüneisen parameter γ in the region of particular interest (γ<0). For calcium fluoride the present x‐ray measurements test a prediction of Ganesan and Srinivasan that γ should rise sharply below about 80°K. The prediction is not confirmed.
41(1964); http://dx.doi.org/10.1063/1.1726267View Description Hide Description
A general theory of magnetic multiple resonance spectra is presented. It is shown that the spectra are conveniently calculated by transforming to an interaction frame. The pattern of the spectrum observed in this frame is equivalent to that observed in the laboratory frame. The theory is applied to the calculation of the resonancespectrum of a three‐spin AMX system. It is theoretically shown that the multiple resonance technique is extremely powerful for the analyses of complex NMRspectra as well as for accurate determination of the magnitudes of chemical shifts and spin—spin coupling constants, even if the signals of the corresponding nuclei are hidden by other features of the spectrum. The relative signs of hidden spin—spin coupling constants can be determined from the intermediate patterns of multiple resonance spectra.
41(1964); http://dx.doi.org/10.1063/1.1726268View Description Hide Description
A tensortheory for crystalline field stress dependence has been developed and the components expressed as matrix elements of ground‐state electronic wavefunctions which contain the type of crystal bonding. The theory is applied to ruby and an approximate form of the theory is compared with an ionic model theory and with NMRexperiments on 27Al in ruby from which and were determined. From the approximate form of the theory it is concluded that not more than 15% covalency is present in ruby. A splitting of an 27Al satelliteNMR line under stress at 20° to the c axis was observed and is explained by the C 3 site symmetry of ruby.
41(1964); http://dx.doi.org/10.1063/1.1726269View Description Hide Description
A theoretical model for the self‐diffusion of ions into an ion exchange resin is proposed, using the concept of an effective diffusion boundary layer with nonlinear concentration profile. The derived equation is of a general character and fit for wide concentration of the flowing solution. From it one can derive specialized equations already known for self‐diffusion of ions in ion exchangers. To test the adequacy of the proposed model, series of experiments were performed on the self‐diffusion of cesium ions into polystyrene sulfonic acid resin Dowex 50×8 from solutions of cesium and potassium chloride. The concentration of solutions was varied over a rather wide range. Several runs were made with different rates of the flow of the solution. Good fitting of experimental results with theoretically calculated curves over the whole experimental range indicates that the proposed model is adequate.