Volume 44, Issue 7, 01 April 1966

Anisotropy of Polarizability of Polymeric Chains
View Description Hide DescriptionA general formula is given for γ^{2}, the square anisotropy of the polarizability of a molecule, in terms of bond polarizabilities and angles between bonds. Expressions are derived for 〈γ^{2}〉, the average over configurations, for a chain of N axially symmetric units. This is done for the freely jointed model and for the diamond‐lattice model. The formulas are valid for small N as well as for large N. For both models 〈γ^{2}〉 increases linearly with N for large N.

Calculation of the Surface Tension of a Simple‐Cubic Crystal According to Two Different Methods
View Description Hide DescriptionA comparison is made of the surface tension of a simple‐cubic crystal calculated according to two different methods: (i) from the variation of the surfacefree energy with surface area and (ii) from the surface‐stress tensor.
A Lennard‐Jones 12–6 potential is employed for the interaction between pairs of atoms and the effects of surface relaxation are investigated extensively. The numerical results show that the two surface tensions approach one another as the relaxation of the surface region of the crystal is extended further into the crystal.

Reduction of the Fourth‐Order Asymmetric‐Rotor Hamiltonian
View Description Hide DescriptionBy use of the angular‐momentum commutation relations, the fourth‐order asymmetric‐rotor Hamiltonian for molecules of orthorhombic symmetry has been considerably simplified. The number of rotational coefficients has been reduced to 19: three coefficients of second power, six coefficients of the fourth power, and 10 coefficients of sixth power in the angular momentum.

Infrared Spectrum and Normal‐Coordinate Analysis of SF_{4}
View Description Hide DescriptionThe vibrational spectrum of sulfur tetrafluoride has been examined in the gas phase to 33 cm^{−1}. A previous assignment of the fundamental vibrations has been revised. A normal‐coordinate calculation, employing mean amplitudes of vibration as additional constraints to the vibrational problem, has been used to support the proposed assignment.

Force Fields for Group IV Tetrafluorides and Group V Trifluorides
View Description Hide DescriptionThe Coriolis zeta constants of the degenerate modes of SiF_{4}, GeF_{4}, NF_{3}, PF_{3}, and AsF_{3} were obtained from infrared‐band contour measurements. These Coriolis coupling data provided the necessary constraints for determining unique force fields for the F _{2} and E symmetry species of the XF_{4} and XF_{3} molecules, respectively. In an attempt to limit the force field for the A _{1} species of the XF_{3} molecules, the rotational distortion constants, which are functions of both the A _{1} and E species force constants, were calculated for a range of values of the F _{12} interaction force constant. For the purpose of this calculation, the E species force constants that were determined from Coriolis coupling data were held fixed. For NF_{3}, a satisfactory value of F _{12} was obtained using the rotational distortion data. However, the rotational distortion data were not useful in fixing the A _{1} species force fields for PF_{3} and AsF_{3}.

Rodlike Behavior of Poly(n‐butyl)isocyanate from Dielectric Measurements
View Description Hide DescriptionDielectricmeasurements have been made on dilute benzene solutions of poly(n‐butyl)isocyanatewhere R = n‐C_{4}H_{9}, at 22.5°C over a frequency range 10^{−1} to 2×10^{6} Hz. Measurements of relaxation time τ on six samples which have molecular weights in the range 1.4×10^{5} to 2.3×10^{6} showed that τ depends on molecular weight to the 2.7 power. In addition, only one dispersion region was observed for each sample and the corresponding dielectric increments were very large. We conclude from these observations that (1) the poly(n‐butyl)isocyanate molecule is a rigid rod whose relaxation time in dilute solution is associated with the end‐over‐end rotation of the entire rodlike molecule around its minor axis, and (2) the net dipole moments of the molecule have a direction parallel to the major axis of the molecule. Calculation of the length of the molecule from relaxation data indicates that the conformation of the polymeric chain appears to be nonplanar and possibly helical. The dipole moments calculated from the static dielectric constant were not directly proportional to the molecular weight as expected. To explain this a model of the polymerization growth step, in which dipole reversal takes place, was proposed. In this model chain element dipolar senses are not uniform throughout the chain but undergo reversal after a finite sequence length which is independent of the over‐all length.

Direct Radiative Exciton—Exciton Annihilation
View Description Hide DescriptionSeveral experiments on organic crystals have demonstrated the existence of triplet—triplet exciton annihilation in terms of fluoresence from the resulting singlet‐exciton state. We point out the possibility of direct emission of a photon from a pair of excitons and estimate the corresponding lifetime and bimolecular rate constant. While this decay channel for triplet—triplet collisions is very weak compared with decay into a singlet exciton in a crystal such as anthracene, the process is observable in principle as a characteristic emission with a transition probability of ≲ 10^{5} sec^{−1} at an energy equal to that of two interactingexcitons. Its rate depends strongly on the relative energies of all the molecular states involved. Conditions for observation of this emission band are discussed.

ESR of Cu(NO_{3})_{2} and CuF_{2} Molecules Oriented in Neon and Argon Matrices at 4°K
View Description Hide DescriptionAn experimental apparatus is described which allows the trapping of preferentially oriented molecules in neon and argon matrices at 4°K and the measurement of their ESRspectra at various orientations relative to the magnetic field. Application to Cu(NO_{3})_{2}, vaporizing at 150°C, and CuF_{2}, vaporizing at 925°C, demonstrates that the degree of orientation is dependent upon the temperature of the vaporizing molecule and the matrix gas used. The ESRspectra of highly oriented Cu(NO_{3})_{2} in neon at 4°K (there was essentially no orientation in argon) indicate that the molecule is planar with the four nitrate oxygen atoms surrounding the Cu^{++} ion in a square array. The g and A values are very similar to those found in copper chelate molecules: g∥ = 2.2489±0.003, g⊥ = 2.0522±0.0005, A∥ (^{63}Cu) = 570±3 Mc/sec, and A⊥ (^{63}Cu) = 50±3 Mc/sec. Computer simulation of the spectra not only confirms this assignment but provides an estimate of the degree of orientation as a function of the inclination. CuF_{2} isolated in argon at 4°K has been found to be highly oriented also. Its ESR assignment supports the view that the molecule is linear with magnetic parameters g∥ = 1.913±0.001, g⊥ = 2.601±0.001, A∥ (^{63}Cu) = 1933±5 Mc/sec, A⊥ (^{63}Cu) = 2090±5 Mc/sec, A∥ (F) = 308±1 Mc/sec, and A⊥ (F) = 206±1 Mc/sec. The unusually large hyperfine interaction with the Cu nucleus indicates a substantial admixture of its 4s orbital. For both molecules the assignments were greatly facilitated by the partial orientation of the molecules in the matrices. The optical spectra of CuF_{2} in neon at 4°K yielded the asymmetric stretching frequency at 769 cm^{−1}. No absorption bands were found between 8900 and 3300 Å.

Franck—Condon Factors for the Ionization of H_{2} and D_{2}
View Description Hide DescriptionFranck—Condon factors for ionization of H_{2}(^{1}Σ_{ g } ^{+}) and D_{2}(^{1}Σ_{ g } ^{+}) are presented for 19 levels in H_{2} ^{+}(^{2}Σ_{ g } ^{+}) and for 27 levels in D_{2} ^{+}(^{2}Σ_{ g } ^{+}). Comparisons are made with calculations, using less accurate potential functions for the molecular ion. Vibrational eigenenergies are given for D_{2} ^{+}.

On Polymer Dynamics
View Description Hide DescriptionThe properties of a polymer solution in which the polymer dynamics contain both bending and spring forces are determined in the free‐draining limit. All properties may be determined in closed form in terms of a few fundamental parameters by use of a correlation‐function technique.

Microwave Spectrum of Germylacetylene
View Description Hide DescriptionThe microwave spectrum of germylacetylene has been investigated in the region 7–36 Gc/sec. The rotational constants for the isotopic species ^{76}GeH_{3} ^{12}C≡^{12}CH, ^{74}GeH_{3} ^{12}C≡^{12}CH, ^{73}GeH_{3} ^{12}C≡^{12}CH, ^{72}GeH_{3} ^{12}C≡^{12}CH, ^{70}GeH_{3} ^{12}C≡^{12}CH, ^{74}GeH_{3} ^{13}C≡^{12}CH, ^{74}GeH_{3} ^{12}C≡^{13}CH, ^{72}GeH_{3} ^{13}C≡^{12}CH, ^{72}GeH_{3} ^{12}C≡^{13}CH have been determined to be 3553.78, 3572.40, 3582.04, 3591.97, 3612.55, 3531.69, 3423.48, 3551.60, 3442.89 Mc/sec, respectively. From these data the structural parameters r _{GeC}=1.896 Å and r _{CC}=1.208 Å are determined. If r _{CH} is assumed to be 1.056 Å, then r _{GeH}=1.521 Å and ∠HGeH=109.9°. Measurement of the Stark effect leads to a dipole moment of 0.136 D. Analysis of the hyperfine components of ^{73}Ge transitions leads to a nuclear quadrupole coupling constant eQq of +32.5 Mc/sec.

Low‐Temperature Transport Properties of Gaseous H_{2}, D_{2}, and HD
View Description Hide DescriptionA complete quantal phase‐shift calculation of the transport properties of gaseous H_{2}, D_{2}, HD, and some of their mixtures is presented from 10° to 300°K, based on the Lennard‐Jones (12–6) potential. It is found that H_{2} and D_{2} have slightly different intermolecular potentials, in agreement with evidence from other sources. Agreement between calculation and experiment is generally good, but there are some small but clear indications that the (12–6) potential model is oversimplified, such as the necessity to use slightly different potantial parameters for the transport properties than for the second virial coefficients.

Debye Relaxation in Symmetric‐Top—Foreign‐Gas Mixtures; Temperature Dependence of Collision Cross Sections
View Description Hide DescriptionThe Debye relaxation spectra of three symmetric‐top gases, CH_{3}Cl, CHF_{3}, and SO_{2}F_{2}, in the pure state and in dilute mixtures with the foreign gases, He, H_{2}, D_{2}, Ar, N_{2}, CH_{4}, CO_{2}, and C_{3}F_{8}, were obtained over the temperature range −20° to 145°C at a frequency of 1220 MHz. Relaxation‐rate parameters and the corresponding collision cross sections are derived. The cross sections vary with the absolute temperature as T ^{−m }, where the value of m ranges from 0.3 to 0.9 for the different systems. The cross sections are considered from a classical kinetic veiwpoint and an empirical relation is obtained which accurately relates the dielectric cross section to the effective viscosity cross section (or the corresponding Lennard‐Jones parameters), the internal‐to‐orbital‐angular‐momentum ratio, and one additional parameter related in some way to the shape (prolateness or oblateness) of the top. Deviations in the shape of these spectra from the simple Debye form, which are attributable to a distribution of relaxation rates, are examined in some detail and correlated with the effective collision number.

Microwave Spectrum, Internal Barrier, Molecular Structure, and Dipole Moment of Disilanyl Fluoride
View Description Hide DescriptionThe microwave spectra of five isotopic species of disilanyl fluoride (Si_{2}H_{5}F) have been studied in the region 12–38 Gc/sec. Several of the ground‐state transitions are split into doublets, some into triplets, due to the coupling of internal and over‐all rotation. Analysis of the splittings gives a barrier value V _{3} = 1048±40 cal/mole.
Rotational constants have been determined for molecules containing silicon−28, −29, and −30 isotopes in each position and have been used to calculate the following structure:
Stark‐effect measurements yield μ_{ A } = 0.934 D, μ_{ B } = 0.850 D, and a total dipole moment μ = 1.26±0.01 D inclined at an angle of 10° to the SiF bond.

Transport in Dense Square‐Well Fluid Mixtures
View Description Hide DescriptionA simple kinetic theory of transport in a dense fluid of square‐well molecules, due to Longuet‐Higgins and Valleau, is here extended to mixtures. A minor extension of the original set of postulates is required. The ratio, κ/η=5/3, of the bulk and shear viscosities is again obtained and the purely diffusive Onsager relations are obeyed. In the case of a two‐component ``isotopic'' mixture, it is possible to show that the Onsager relation linking the Soret and Dufour effects is also obeyed. In this and other respects the results differ from some others recently published on the same problem and some reasons for this are discussed.

Nonstoichiometry in Uranium Dioxide
View Description Hide DescriptionAn extension of Anderson's formulation of the defect theory of nonstoichiometry is used with an oxygen—interstitial oxygen‐vacancy model to calculate the composition of the uranium dioxide phase at the lower phase boundary and the relative partial molar thermodynamic functions for oxygen at compositions ranging from the lower phase boundary to UO_{2.08}. The model is used as a basis on which to argue that differing experimental results near UO_{2.00} are more likely due to differing, nonequilibrium, concentrations of uraniumvacancies than to failure to reach oxygen equilibrium. The present form of the model, with an interstitial site density of one per uranium site fails sharply at about UO_{2.08} rather than gradually as the oxygen content is increased from UO_{2.00}. Discussion of the effects of alternate site densities is used to explain the observed values of the partial molar entropy of the oxygen in the range from UO_{2.02} to UO_{2.24}.

On a Derivation of a Quantum‐Mechanical Linearized Boltzmann Equation
View Description Hide DescriptionMethods recently developed to derive the classical Boltzmann equation are extended to quantum mechanics.

Absorption of Sound Near the Critical Point of the Nitrobenzene—Iso‐octane System
View Description Hide DescriptionMeasurements by the pulse technique were made of the absorption of sound in the nitrobenzene—iso‐octane system (T_{c} =30.2°C) over the full composition range, at temperatures of 30.5°C, 34.8°, and 44.8° for five frequencies between 4.5 and 16.5 Mc/sec. At the lowest frequency and at 0.3°C above the critical temperature, the absorption is anomalously large by a factor of 47; 14.6°C above T_{c} , the absorption is still in excess of classical predictions by a factor of 11. The data cannot be represented by a model involving only a single relaxation frequency. The Fixman theory is in reasonable, but not exact, agreement with the data with regard to functional conformity in temperature and frequency; in particular, the predicted frequency dependence, α/f ^{2}∝f ^{−5/4}, at the critical state is verified within experimental error. The Fixman theory and the data preclude anything but a simple pole at the critical temperature for the reciprocal square of κ, the exponential decay constant in the long‐range correlation function. However, if it is assumed thatthe theory and experiment are in agreement over the full range of temperature and frequency, with a value of a _{1}=0.0296.

Magnetic‐Rotation Spectra of the 2–0 Vibration—Rotation Band of NO
View Description Hide DescriptionMagnetic‐rotation spectra of the 2–0 bands of ^{14}N^{16}O and ^{15}N^{16}O in the 2.7‐μ region were obtained and analyzed. A qualitative explanation of the observed spectra is given. Beginning with the predicted Zeeman patterns, a classical approach is used which takes into account the circular dichroism in the region of strong absorption as well as the Faraday rotation and the effects of finite resolution. These qualitative arguments are used to explain the major intensity irregularities which appear in these spectra.

Low‐Lying Pi—Sigma Transition in the Spectrum of Norbornadiene
View Description Hide DescriptionA vibrational analysis of the first electronic band of norbornadiene (NBD), with origin at 45 120 cm^{−1}, shows that the band is electronically allowed, the accompanying vibrations being totally symmetric. This is contrary to earlier theoretical work which assigned the band as N→V _{1}, forbidden. A comparison with the spectra of cyclopentene and norbornene (NBE) suggests that the first band of norbornadiene is to be associated with the weak band of uncertain assignment found at approximately 45 000–50 000 cm^{−1} in all olefinic substances.
Gross changes in the vibrational spacing and shape of the vibronic envelope are observed on freezing the NBD and NBE molecules in low‐temperature matrices. The spectral changes appear to be due to modifications of the upper‐state potential surfaces as a consequence of the rigidity of the matrix.
There is some evidence in the NBD spectrum for weak vibronic coupling between the two halves of the diene molecule, and it is shown how the observed splitting pattern might be explained on such an assumption.