Volume 58, Issue 7, 01 April 1973

Sound velocity in colloidal SiO_{2} suspensions
View Description Hide DescriptionThe velocity of sound in three colloidalsuspensions of silica was measured in the temperature range between 10 and 75°C. The measurements show that the temperature dependence of the velocity is affected by the presence of the silica, but agreement between the observed values and classical theory, which considers the colloidalsuspension made up of elastic particles, is poor. This suggests that the temperature and concentration dependence of the total hydrated SiO_{2} particles is important.

Deactivation of laser excited CH_{3}F in mixtures
View Description Hide DescriptionThe vibrational relaxation of CH_{3}F in mixtures of rare gases, O_{2}, N_{2}, H_{2}, and D_{2} has been studied by means of laser induced fluorescence. The data can be interpreted qualitatively in terms of a combination of energy transfer processes from both the ν_{3} and states of CH_{3}F. processes seem to be dominant for heavy collision partners while processes appear to dominate for light collision partners. The quantitative agreement between theory and experiment is also considered.

Laser fluorescence study of vibrational energy transfer in CH_{3}Cl
View Description Hide DescriptionA laser induced infrared fluorescence technique has been used to measure both vibration to vibration and vibration to translation/rotation energy transfer rates in CH_{3}Cl. The rates were measured using H_{2}, D_{2}, CH_{4}, and rare gases as collision partners. Qualitative comparison of these data with and theories indicates that the mechanism dominates for collisions with small reduced masses while the mechanism dominates for collisions with large reduced masses. The V–V rate equilibrating the ν_{6} and ν_{3} modes was measured as a function of CH_{3}Cl pressure and was found to be . A lower limit was also obtained for the rate of V–Venergy transfer from states near 1000 cm^{−1} to high lying states near 3000 cm^{−1}.

Fluorescence quenching by the stable free radical di‐t‐butylnitroxide
View Description Hide DescriptionBimolecular rate constants (k_{Q} ) were measured for the fluorescence quenching of a series of aromatic hydrocarbons by di‐t‐butylnitroxide (DTBN). In methylcyclohexane, measured values of k_{Q} were close to the diffusion limit with only a 6.5‐fold variation through the hydrocarbon series. A study of the viscosity dependence of the quenching reaction, in the Smoluchowski manner, suggests an interaction distance of 4–6 Å. A comparison is made of the efficiency of the DTBN and O_{2}fluorescence quenching reactions. Possible mechanisms are discussed.

Depolarized light scattering from monatomic fluids
View Description Hide DescriptionComputer experiments on dense argon are used to evaluate the depolarized spectrum of scattered light. Certain features of the spectrum can be associated with the dynamics of atomic motions in the fluid. The calculations show that the uncorrelated binary collision picture is inadquate since the major time dependence in the variation of the polarizability of the system comes from the correlated reorientation of pairs.

Equations‐of‐motion method: Potential energy curves for N_{2}, CO, and C_{2}H_{4}
View Description Hide DescriptionWe have applied the equations‐of‐motion method to various states of N_{2}, CO, and ethylene at nuclear configurations slightly distorted from the ground equilibrium geometry. This approach attempts to calculate energy differences instead of absolute energies and is thus relatively insensitive to the accuracy of the assumed ground statewavefunction. By using the experimental behavior of the ground state on distortion, we can generate accurate potential energy curves for the excited states in the region of spectroscopic interest. These curves confirm the spectroscopic behavior of the states of N_{2} and the ^{1}Σ^{+} states of CO where valence and Rydberg states of the same symmetry interact. The results for the T and V states of ethylene agree with experiment and show that the V state is predominantly a highly correlated valence state. Oscillator strengths across an absorption band are also accurately determined in this method. We report the dependence of the transition moment on bond length for the transition in CO, which is in excellent agreement with experiment.

^{14}N nuclear quadrupole resonance in compounds containing N–N bonds. IV. Nitrosamines
View Description Hide DescriptionThe complete nitrogen‐14 nuclear quadrupole resonance spectra of six nitrosamines at 77°K have been determined with cw and pulsed techniques. Absorption lines belonging to the amino nitrogen atom lie at rather low frequencies and are virtually undetectable with cw techniques. The low frequencies of the amino lines indicates a considerable loss of π charge to the oxygen atom. As a result of this charge transfer, the polarity of the N=O bond is smaller than the polarity of a N–OH bond. The N–N bond was found to be slightly polarized toward the amino nitrogen atom, the charge unbalance of this bond amounts to about 0.08 electrons.

Stress tensor for arbitrary flows of dilute solutions of rodlike macromolecules
View Description Hide DescriptionAn equation for the stress tensor in terms of the rate of strain tensor is obtained for a dilute suspension of rigid macromolecules with Brownian motion. The result is given as a series of memory integrals up through terms of third order; the kernel functions contain two constants: the number density and time constant for the macromolecules. In obtaining this series, the distribution function for arbitrary unsteady homogeneous flows is developed up through terms of second order. It is shown that one need consider only irrotational flow in determining the kernel functions for the memory integral expansion. Relations between the kernel functions and the coefficients in the retarded motion expansion are also given. In addition it is shown how the Eulerian components of the rate‐of‐deformation tensor are related to the fixed components by using the theory of matrizants.

Variational formalism and intermolecular forces in OCS lattice dynamics
View Description Hide DescriptionA variational formalism for lattice dynamics in molecular crystals (consisting of ionic or neutral molecular units) is developed. We take account of the fact that in the presence of large‐amplitude motions, the librational and translational degrees of freedom in the crystal are in general not separable, even at the zone center in crystals with centrosymmetric sites. This formalism has been brought to practical realization and applied to the OCS crystal as a test case using an intermolecular potential function for determined from gas‐phase and crystal‐phase experimental data. The determination of the potential function yields information on the intermolecular forces in the crystal, and a discussion of these forces is given. Theoretical results for the zero‐point energy of the crystal and for the spectroscopic frequency of the ``librational'' transition at zero wave vector are compared with available experimental data. The comparison indicates the essential validity of the intermolecular potential function and the variational formalism employed. It is found that, as expected, a strong coupling exists between the librational and translational degrees of freedom in the crystal. The results obtained show that the methods used are powerful tools for circumventing the harmonic approximation in the lattice dynamics of molecular crystals.

Lattice sum transformations and potential function expansions in lattice dynamics
View Description Hide DescriptionMathematical techniques are presented for the treatment of both harmonic and anharmonic lattice dynamics in molecular crystals. We first give Ewald‐type transformation formulas for the accurate and rapid evaluation of the slowly convergent lattice sums associated with long‐range isotropic and anisotropicintermolecular force laws. The nature of these lattice sums is discussed in light of the properties of the transformed sums. We then give a systematic procedure for obtaining the Taylor series expansion of the intermolecular potential functions, in terms of the translational displacements of molecular centers of mass from their equilibrium positions. This expansion is valid for arbitrarily large orientational displacements. The need for such an expansion arises since the intermolecular potential functions are naturally expressed in molecular‐pair coordinates but for many applications these potential functions must then be written in terms of lattice‐fixed or space‐fixed coordinates. Although the procedure involved is discussed from the viewpoint of lattice dynamics, further applications in the investigation of intermolecular dynamics of weakly bound molecular complexes and adsorption of molecules on solid surfaces are anticipated.

Theory of chemically induced dynamic electron polarization. I
View Description Hide DescriptionA general and detailed analysis is given of the phenomenon of chemically‐induced dynamic electron polarization (CIDEP) by means of the stochastic‐Liouville method in accordance with the earlier preliminary report. The finite‐difference technique employed permits rapid and convergent solutions without requiring any untoward assumptions on the nature of the models. The dependence of the polarization on the exchange interactionJ(r), the Larmor frequency differences between the interacting pair of radicals, diffusion rates, and rates of spin‐selective chemical reactions are given in detail. It is shown that models in which J(r) is taken to decay exponentially with r, the radical‐separation distance of the radical pair, yield results which are distinctly different from those for a contact exchange model, when J _{0} [the value of J(r) when r is at the distance of closest approach] is appreciable. The former, more realistic model yields substantial polarizations asymptotically independent of J _{0}, but larger the slower the decrease of J(r) with r; the contact exchange model, however, rapidly goes to zero with increasing J _{0}. These asymptotic values of polarization are predicted to be as high as 10–40 times the equilibrium polarizations (P _{eq}) for sensible values of the relevant parameters, while for values of J _{0} yielding maximum polarizations (generated at the formative reaction), they can be greater than 100 P _{eq}. These results are of the correct order for agreement with recent experiments. The polarizations have been related to the CIDEP intensities that one may observe for typical schemes of radical production, reaction, and relaxation in order to allow a comparison of the theoretical predictions with experiment.

van der Waals‐Lifshitz forces between anisotropic ellipsoidal particles
View Description Hide Descriptionvan der Walls‐Lifshitz forces between an ellipsoidal particle and a dielectric wall as well as between two ellipsoidal particles suspended in a liquid are calculated on the basis of the theory of McLachlan. The materials constituting the ellipsoids may be anisotropic. It is assumed, however, that in each ellipsoid the principal axes of the tensor of dielectric permeability coincide with those of the ellipsoid. The obtained formulas include those for spheroids by Kihara and Honda as well as those for spheres by Dzyaloshinskii, Lifshitz and Pitaevskii as particular cases. The variations of the free energies of interaction with respect to the mutual orientations of the interacting bodies are discussed. The three‐body forces among three ellipsoids as well as among two ellipsoids and a wall are also calculated.

Temperature effects on radiative and radiationless transitions of Gd^{3+} in solution
View Description Hide DescriptionTemperature effects on the fluorescence of Gd^{3+} in H_{2}O solution are presented and discussed. The quantum yield does not approach unity near the freezing point. In the case of Gd^{3+}, high energy vibrations of single solvent molecules do not quench the fluorescence. The results are interpreted by use of the ``junction'' mechanism involving the ion and solvation shell [Y. Haas and G. Stein, J. Phys. Chem. 76, 1093 (1972)] and by clarifying the role of the levels giving rise to a broad band in both absorption and emission in solution.

Partial vibration energy transfer map for methyl fluoride: A laser fluorescence study
View Description Hide DescriptionInfrared fluorescence has been observed from the 2ν_{3} overtone, the combination band and the ν_{1}, ν_{2}, ν_{4}, ν_{5}, and ν_{6} fundamentals of CH_{3}F after pumping of the ν_{3}, transition by the P (20), 9.6 μ line of a Q‐switched CO_{2} laser. All observed states exhibit a single exponential decay curve with a rate of . The fluorescence risetimes of the ν_{6}, ν_{2} and ν_{5}, ν_{1} and ν_{4}, and 2ν_{3} states were also observed. The rate of rise of the ν_{1} and ν_{4}fluorescence and the 2ν_{3}fluorescence is faster than 7 μsec at 1 torr. The ν_{6}fluorescence risetime is pressure dependent with a rate constant of . The pressure dependent rate of rise of the ν_{2} and ν_{5}fluorescence is . Measurements of the steady state dependence of the ν_{2} and ν_{5}fluorescence intensity versus laser intensity were made. The temperature dependence of the Q‐switch excited fluorescence intensity from the 2ν_{3} and ν_{1} and ν_{4} states was also studied. No evidence of excited state absorption was observed and both sets of measurements indicate collisional processes rather than excited state absorption play the major role in establishing an equilibrium among the excited vibrational states of CH_{3}F. The ramifications of these results for energy transfer mechanisms, laser action, and laser induced chemical reactions in polyatomic molecules are discussed.

Thermodynamic properties of oxalyl fluoride from 13°K to its boiling point
View Description Hide DescriptionThe saturated molar heat capacity has been measured from 13°K to its normal boiling point, 270.13°K, for a sample of 99.94 mole% purity. The molar heat of fusion was found to be 3204 cal/mole at the triple‐point temperature of 260.73°K. The molar heat of vaporization at the normal boiling point was found to be 6753 cal/mole. The vapor pressure of the solid in the range from 234°K to the triple point of 260.73°K is represented by the equation lnP(torr)=115.38986 − 8720.5964/T − 13.623524 lnT. The vapor pressure of the liquid from the triple point to the boiling point of 270.13°K is represented by the equation lnP(torr)=185.93601 − 10 317.218/T − 25.202996 lnT. The standard entropy of oxalyl fluoride gas at the normal boiling point was found to be . Neither of the two fundamental frequency assignments reported in the literature when used in the statistical entropy calculation gives satisfactory agreement with the calorimetric entropy. It is believed that the discrepancy results from the uncertainty in the assignment of one or more of the low frequency Raman‐active modes of the molecule.

Reaction : Investigation into the effects of pressure, stoichiometry, and the nature of the third body species
View Description Hide DescriptionThe detection of H atom concentrations by Lyman α photometry has been employed in a time resolved experiment to obtain the pressure dependence of the apparent bimolecular rate constant for the reaction of H atoms with C_{2}H_{4} at room temperature. A computer simulation analysis has been applied to adjust the observed rate constants for H atom depletion in reactions subsequent to the initial reaction. The pressure falloff behavior at low pressures of various heat bath species He, H_{2}, N_{2}, Ar, Ne, Kr, and SF_{6} were also obtained. Experiments at high pressures of He have permitted an extrapolation to the high pressure limit of the rate constant of .

Application of RRKM theory to the chemical and thermal activation of ethyl radicals
View Description Hide DescriptionThe quantum statistical RRKM theory of unimolecular reactions has been applied to the decomposition of excited ethyl radicals. These radicals can be formed either by collisional activation in a thermal system or chemically by the addition of hydrogen atoms to ethylene molecules. The assessment of pertinent parameters has been based on an appraisal of theory and experiment. The pressure dependence of the rate constant for the chemical activation reaction was used to assist in the assignment of activated complex parameters. These parameters were varied until good agreement was obtained between the calculated pressure falloff and data from this laboratory for the reaction. The final parametric assignments were then used in calculations at higher temperatures for comparison with the thermal decomposition data for ethyl radicals from other laboratories.

Eigenfunctions and eigenvalues of the Thomas‐Fermi density matrix. The simple harmonic oscillator
View Description Hide DescriptionThe eigenfunctions and eigenvalues of a Hermitian Thomas‐Fermi density matrix for the one‐dimensional harmonic oscillator are examined in detail. The major defect of Thomas‐Fermi theory is shown to be the departure of the density matrix from N representability. The imposition of indempotency leads to greatly improved particle densities, including very well developed density oscillations.

Resolution of the visible‐infrared absorption spectrum of I_{2} into three contributing transitions
View Description Hide DescriptionNew extinction coefficient measurements are reported for I_{2} in the region 4200–8000 Å. An argon discharge source is used to estimate the underlying continuum absorption in the banded region. Together with other work these results locate the maximum in the absorption at 4985 Å with a peak extinction of . From the shape of the spectrum the 1u (^{1}Π) potential curve behaves as r ^{−9} in the region of strong absorption. The absorption is found to be a factor of 2 stronger than previous estimates with a peak extinction of at 6730 Å. Earlier indications of a linear dependence of the dipole strength on r centroid for the system are supported in this study. Spectroscopic data for the transition are reviewed and new spectroscopic constants recommended for the B state.

Mechanism of shear induced structural changes in liquid crystals‐cholesteric‐nematic mixtures
View Description Hide DescriptionThe reflection spectrum of a mixed nematic‐cholesteric liquid crystal has been obtained as a function of mechanical shear. Data are explained in terms of a layered structure consisting of tilted and untilted helical Grandjean texture and a dynamic focal‐conic texture for shear rates less than 10^{3} sec^{−1}. The correlated helical structure is shown to tilt under applied shear with slight distortion. At shear rates greater than 10^{3} sec^{−1}, homeotropic texture is generated. The results of this study are consistent with a theoretical model prepared earlier and suggest that the molecular forces maintaining the integrity of the helical structure in cholesteric systems in the Grandjean texture are significantly weakened by incorporation of nematic liquid crystalline materials.