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Volume 38, Issue 7, 01 April 1963
38(1963); http://dx.doi.org/10.1063/1.1776902View Description Hide Description
Rate constants for the dissociation of bromine molecules in argon have been measured behind reflected shock waves. The disagreement between these values and those measured behind incident shock waves at the same temperature indicates that between 1500° and 1900°K the temperatures in the reflected shock waves are 35°±5° lower than those calculated from ideal theory. Possible uncertainties in the temperature, even if ideal theory is obeyed, are also discussed.
38(1963); http://dx.doi.org/10.1063/1.1776903View Description Hide Description
A new Monte Carlo method for the statistical study of the polymer chain excluded volume problem is presented. Random chains which are not allowed to have closed loops of fewer than R links are generated. Results of calculations for diamond lattice chains of up to 5000 links with R up to 1000 are given and discussed. These chain lengths are rather longer than those which have been studied previously. This is possible because (a) volume exclusion applies not to the entire chain, but only to the ``sliding segment'' of R links, and (b) a chain is not rejected when it comes back on itself, but forced not to cross and weighted appropriately. Results closely approximating the correct ones for the completely restricted random walk chain are obtained for R∼100. Results on number of configurations for long chain lengths and ring formation and trapping probabilities are given.
Jahn‐Teller Effect in the Eg Vibrational Mode of Hexafluoride Molecules. The Infrared Spectra of RuF6 and RhF638(1963); http://dx.doi.org/10.1063/1.1776904View Description Hide Description
The infrared spectra of RuF6 and RhF6 are reported and are interpreted in terms of a regular octahedral structure, point group Oh . The spectrum for RuF6 shows fewer bands than any of the known hexafluoride molecules, presumably owing to a Jahn‐Teller effect. The fundamental vibrational frequencies (cm−1) for RuF6 are v 1=675, v 3=735, v 4=275, v 5=262; for RhF6, v 1=634, v 2=595, v 3=724, v 4=283, v 5=269, and v 6=192; for RuF6 v 2 is estimated to be 573. A broad band arising from an electronic transition in RuF6 is also observed with maxima at 1950 and 1400 cm−1. The symmetry requirements for a Jahn‐Teller effect in a regular octahedral hexafluoride molecule are summarized. The evidence for a Jahn‐Teller effect in the Eg mode for hexafluoride molecules is reviewed. An analogous effect is not observed for the F 2g mode although it is symmetry allowed. Comparison of band widths for (v 1+v 3) and (v 2+v 3) permits the following estimates of the Jahn‐Teller splittings (cm−1) for the Eg mode: TcF6=80, ReF6=25, and OsF6=54. RhF6, like IrF6, does not show a Jahn‐Teller effect of comparable magnitude, presumably because of the ``spin character'' of its Γ8 electronic ground state. The corresponding effect for RuF6 is relatively larger and cannot be evaluated in this way because the band (v 2+v 3) is so broadened as to make it extremely difficult to characterize.
38(1963); http://dx.doi.org/10.1063/1.1776905View Description Hide Description
The crystal field split levels of the 4 I 9/2 and 4 I 11/2 states of CaF2:Nd3+ were determined from the fluorescence and absorption spectra. The data are compared to an energy‐level calculation for the case of a weak cubic field containing fourth‐ and sixth‐order terms. Both the absorption and fluorescence spectra were found to be strongly concentration dependent at relatively low concentrations (0.01 mole %).
Influence of Room‐Temperature Atmospheric Reaction Products on the Ductility of Sodium Chloride Single Crystals38(1963); http://dx.doi.org/10.1063/1.1776906View Description Hide Description
Bend tests were made using sodium chloride single crystals which had previously been exposed to one of several atmospheres at room temperature. Crystals exposed to moist carbon dioxide showed the most consistent brittle behavior while those aged in moist air containing hydrogen chloride showed more ductile behavior. Evidence is given which indicates that hydroxide ion is needed for carbon dioxide to cause embrittlement. Furthermore, room‐temperature hydrolysis is shown by experiments in which the increase of alkalinity of finely divided sodium chloride is measured upon long exposure to moist air. These results lead to the proposal of a new mechanism to explain age embrittlement of sodium chloride crystals: sodium chloride crystals containing hydroxide ion react with carbon dioxide to become embrittled. Crystal surfaces initially free from hydroxide can become contaminated with it by reaction with water vapor of the air. Changes in ductility due to physical adsorption of carbon dioxide or hydrogen chloride were not observed.
38(1963); http://dx.doi.org/10.1063/1.1776907View Description Hide Description
By means of the general theory of the classical grand ensemble, the complete formal relations for pressure and number of molecules in an open system, as a function of activity, are derived without approximation within the scheme of the Frenkel‐Band equilibrium cluster theory of association. The physical clusters, defined geometrically by overlap of spheres drawn about each molecule, are not regarded as statistically independent, but their mutual exclusion property gives rise to free energies of formation work for cavities necessary to contain those clusters. A connection is established between these free energies and a suitable generalization of the Mayer irreducible cluster sum. The appropriate modification of the theory to include external forces (such as the gravitational field) is displayed. A rigorous expansion of molecular distribution functions in terms of physical (rather than Ursell‐Mayer) cluster integrals is also presented.
38(1963); http://dx.doi.org/10.1063/1.1776908View Description Hide Description
The recombination of oxygen atoms has been studied in an O2‐free system containing a known initial atom concentration. The value of the rate constant for the reactionwas found to be 2.8×10−33 cm6 molecule−2 sec−1. Failure to remove condensable products from the gas stream resulted in a 40% increase in the recombination rate. The efficiencies of other third bodies relative to N2 are: Ar, ≤0.3; He, 0.3; N2O, 1.4; CO2, 3.0; SF6, 3.0. The presence of vibrationally excited N2 did not affect the recombination rate. The wall recombination coefficient γ was found to be 1.65×10−5. Comparison of these results with high‐temperature shock‐tube results indicates that the temperature coefficient of the recombination is small.
Infrared Studies of Hydrogen Bonding in Isopropanol and in Mixtures of Isopropanol with Poly (n‐Butyl Methacrylate) and with Poly(Propylene Oxide)38(1963); http://dx.doi.org/10.1063/1.1776909View Description Hide Description
Infrared spectra have been measured in the 3‐μ region for isopropanol in carbon tetrachloride solutions from 0.005 to 1.0M and from 0° to 60°C. Equilibrium constants for cyclic dimer formation were calculated from the spectral data for this temperature range. The enthalpy for cyclic dimer formation is −5.7±0.9 kcal/mole. Infrared spectra have also been measured for three hydrogen‐bonding systems with isopropanol as the proton donor over the same temperature range. The proton acceptors were di‐isopropyl ether, liquid poly (propylene oxide), and poly (n‐butyl methacrylate). Equilibrium constants were determined. The enthalpies of formation for the three complexes are −2.1±0.4, −3.8±0.8, and −2.4±0.5 kcal/mole, respectively.
38(1963); http://dx.doi.org/10.1063/1.1776910View Description Hide Description
The rotational constants of (C12H3)3C12Cl35, (C12H3)3C12Cl37, (C12H3)3C13Cl35, (C12H3)3C13Cl37, and (C13H3) (C12H3)2C12Cl35 have been measured. The rs structure of the t‐butyl chloride skeleton calculated from these constants is: r(CCl) = 1.803±0.002 Å, r(CC) = 1.530±0.002 Å,∠CCC=110.9°±0.1°. The quadrupole coupling constant for Cl35 is −66.9±1.5 Mc. The structures of a number of t‐butyl compounds are compared. The t‐butyl group is practically unaffected by substitution, while the CX bond in (CH3)3CX is systematically longer than in CH3X molecules. Conventional concepts of valence theory do not provide a satisfying explanation for this behavior.
38(1963); http://dx.doi.org/10.1063/1.1776911View Description Hide Description
In this paper we have compared the application of the exciton and the molecular orbital methods to the calculation of n→π* transitions in N‐heteroaromatic molecules. A number of the features of the n→π* transitions were treated by these two methods, including energies of the (n, π*) states, the intensities of the allowed n→π* transitions, the ordering of the allowed and forbidden transitions and singlet‐triplet splittings. From a comparison of experiment and theory, it is concluded that the assumption, which is made in the exciton calculations, that n→π* transitions are essentially localized ``atomic‐like'' transitions, is a poor initial approximation and leads to a number of incorrect predictions. The assumption that the promoted lone‐pair electron is delocalized over the pi‐aromatic system appears to be a much better initial approximation, and when the effect of electron repulsion between lone‐pair electrons is included in the MO calculations, there is very good agreement between the theoretical predictions and experimental observations on n→π* transition in the mono‐ and polycyclic azines. The relation between MO theory in the one‐electron approximation and MO theory in which electron repulsion between the lone‐pair electrons has been included and is also discussed.
38(1963); http://dx.doi.org/10.1063/1.1776912View Description Hide Description
The three‐body recombination of O atoms by Ar catalysts was measured over a temperature range of 1340–2920°K in a shock‐tube experiment. The excess amount of O atoms was produced by shocking dilute O3–Ar mixtures. Under the experimental conditions, the O atoms in excess of equilibrium produced by the reaction O3+M→O+O2+M had to recombine via the reaction O+O+M→O2+M. The reaction O3+O→2O2 was ineffective due to the high temperature and high concentration of Ar. The O2 formed by the recombination of the O atoms was monitored behind the shock wave by absorption of 1270‐Å radiation. The data scatter by about a factor of 2, but a slight negative temperature dependence is apparent. At 2000°K the recombination coefficient is about 0.7×10−34 cm6/particle2‐sec. The experimental results are compared with calculated curves based on various authors' dissociation‐rate constants divided by the equilibrium constant. A dissociation‐rate constant given by kd = 2.5×1016 T −½ exp (−D/RT) cc/mole‐sec, which is shown to fit dissociation data obtained in previous work and covering a temperature range of 5000–18 000°K, was found to fit best the present recombination data.
38(1963); http://dx.doi.org/10.1063/1.1776913View Description Hide Description
The effect of anharmonicity in linear triatomic molecules in II electronic states has been considered. Expressions for the anharmonic corrections to the vibrational energy are presented for molecules exhibiting a very small Renner effect and a small spin—orbit interaction.
Photochemistry in the Photo‐Ionization Region. II. Photochemistry of Methane, Ethane, and Ethylene at Wavelengths below 900 Å38(1963); http://dx.doi.org/10.1063/1.1776914View Description Hide Description
The photolysis of methane has been investigated, using light from a microwavedischarge through helium which is thought to have consisted mostly of the strongly self‐reversed 584‐Å resonance line. A windowless fast‐flow separation system was used to separate the light source from the photolysis vessel. Methane pressure was varied from 0.001 to 0.3 mm, with helium as a carrier gas making up a total pressure of 1.85 mm.
Products were correlated with saturation ion‐currents, ranging up to 25 μA, which were measured in the photolysis vessel. The main products were hydrogen, ethane, ethylene, and acetylene, with estimated yields of 4.0, 0.37, 0.31, and 0.11 molecules per ion‐pair, respectively. Smaller amounts of propane and propylene, and traces of C4 hydrocarbons, were also observed. Formation of unsaturated polymer was inferred from the carbon deficit of the volatile products. The effects of adding ethylene and neon to the system were studied, and in some experiments an electric field was applied.
The photolyses of ethane and ethylene were also briefly investigated. Hydrogen was the only product measured, with yields ranging from 1.0 to 1.9 and from 0.8 to 1.2 molecules per ion pair from ethane and ethylene, respectively.
Mechanisms are presented to account for the observed results. It was concluded that both direct photolysis and helium sensitization were important primary processes in all three hydrocarbons.
Influence of Electric and Magnetic Fields on the Dielectric Constant and Loss of the Liquid Crystal Anisaldazine38(1963); http://dx.doi.org/10.1063/1.1776915View Description Hide Description
The real and imaginary parts of the complex dielectric constant of the normal liquid phase of anisaldazine were measured at a temperature of 185°C for a frequency range from 900 Mc to 24 kMc. A plot of the complex dielectric constant in the complex plane satisfies the requirements for the Cole—Cole representation reasonably well. The temperature dependence of the dielectric loss at frequencies 6, 15, and 24 kMc indicates that any changes in the dielectric loss for a random orientation are very small as anisaldazine passes from its anisotropic to normal liquid phase. This implies that a plot of the complex dielectric constant in the complex plane for the anisotropic phase would probably satisfy the requirements for a Cole—Cole plot. Measurements of the dielectric loss in the presence of an external electrostatic field show that an ordering exists with the long axes of the molecules parallel to the external electric field.
38(1963); http://dx.doi.org/10.1063/1.1776916View Description Hide Description
The absorptionspectrum of gaseous fluoride ion has been observed in shock‐heated vapors of CsF, RbF, and KF. The spectrum is a continuum with two sharp thresholds at 3595 and 3542 Å, similar to those of the other halide ions. The electron affinity determined from the low‐energy threshold is 3.448±0.005 eV. The cross‐section for photodetachment at 3565 Å is about 2.5±2×10−18 cm2 and at 3525, about 3.3±2×10−18 cm2. The electron affinities of chlorine, bromine and iodine are revised, respectively, to 3.613, 3.363, and 3.063 eV, all with uncertainties of 0.003 eV.
38(1963); http://dx.doi.org/10.1063/1.1776917View Description Hide Description
The role of the point symmetry of the Cr3+ ion in the spectral analysis of Cr3+ in Al2O3 is reviewed. Previous energy‐level calculations were made on the basis of C 3v symmetry with a reflection plane perpendicular to the unique axis. Little change in the gross spectral features is expected if C 3 (noninversion center) operators are used. However, as noted by McClure, it is necessary to go to C 3(NIC) when calculating electric dipole radiation matrices. For consideration of the axial optical and microwave electric effects it is sufficient to consider C 3v (NIC). For the full microwave electric effect tensor,C 3(NIC) must be used. The interelations between the electric effects and the optical radiation dipole operators are explored. A substantial contribution to the ruby4 A 2 ground‐state splitting 2D is expected from the ``odd NIC fields.'' The magnitude of this effect for Cr2O3 is considered.
38(1963); http://dx.doi.org/10.1063/1.1776918View Description Hide Description
A method is described for a direct calculation of the barrier to internal rotation in ethane and ethanelike molecules. The approach suggested should identify the physical origin of the barrier, provided a satisfactory account would be forthcoming from exact Hartree—Fock calculations of the energies of the staggered and eclipsed forms in the Born—Oppenheimer approximation.
A simple model is considered in which the electronic distribution is taken to be cylindrically symmetric about the central bond. It is demonstrated that this model predicts energy differences between staggered and eclipsed forms, composed solely of nuclear—nuclear repulsion energy, that are consistently about 5/3 of the experimental energy barriers. A slight expansion of the wavefunction in the eclipsed configuration is shown to be required by the virial theorem, but this does not appreciably change the predicted magnitude of the barrier.
It is proposed that the model can be refined by a calculation of the electronic energies of the actual staggered and eclipsed forms of ethane relative to that for the cylindrical distribution. By means of second‐order Hartree—Fock perturbation theory, it is shown that the energy differences are a simple sum of contributions from the nine occupied molecular orbitals. The individual contributions can be calculated by the solution of certain differential equations or their variational equivalent. To simplify the treatment further, an approximate set of uncoupled differential equations is suggested for finding the perturbed functions from estimates for the charge densities of the cylindrical‐model molecular orbitals.
38(1963); http://dx.doi.org/10.1063/1.1776919View Description Hide Description
The potential‐energy curves of the excited states of NaH and KH have been obtained by the Rydberg‐Klein‐Rees method as described by Singh and Jain. The simple‐harmonic curves and ionic curves for LiH, NaH, KH, and RbH have also been calculated. It has been found that the potential‐energy curves mostly agree with Mulliken's findings as to the anomalous behavior of the excited states of alkali hydrides.
38(1963); http://dx.doi.org/10.1063/1.1776920View Description Hide Description
Spin—orbit splitting of the first excited state of the F center is estimated in the simple effective‐mass approximation. The splitting due to the outermost s orbitals of the atoms neighboring the vacancy in the crystal is related to the splitting of the p state in the free atom. As an example, spin—orbit splitting of the F center in cesium halides is estimated. It is found to 4‐to‐6 orders of magnitude too small to account for the structure observed in the F‐center absorption band in cesium halides.
38(1963); http://dx.doi.org/10.1063/1.1776921View Description Hide Description
The fluorine resonance of CF4, SiF4, SF6, and CHF3, and in a variety of gas mixtures have been measured at pressures up to 50 atm at room temperature. The pressure dependence of the chemical shift is much more pronounced than for protons [W. T. Raynes, A. D. Buckingham, and H. J. Bernstein, J. Chem. Phys. 36, 3481 (1962)]. The results are interpreted in the same manner as for the proton work (see reference above) in terms of a field and field square contribution to the medium shift. The field square contribution is primarily due to dispersive forces and is 15 to 44 times as large as for hydrogen in CH bonds. The polar contribution (first power of the field) for CF bonds is also larger than for CH bonds but of opposite sign, being responsible for high‐field medium shifts for CF bonds.