Volume 58, Issue 10, 15 May 1973

Pressure dependence of proton spin‐lattice relaxation in liquid hydrocarbons
View Description Hide DescriptionThe pressure dependence of the proton spin‐lattice relaxation timeT _{1} in ten liquid hydrocarbons at room temperature (28°C) is reported. The ten compounds were (a) bicyclohexyl, (b) dicyclohexyl methane, (c) 1,3‐dicyclohexyl propane, (d) 1,4‐dicyclohexyl butane, (e) 1,9‐dicyclohexyl nonane, (f) 1,1‐dicyclohexyl ethane, (g) 1,2‐dicyclohexyl propane, (h) 1,3‐dicyclohexyl butane, (i) 1,3‐dicyclohexyl‐2‐methyl propane, and (j) phenyl cyclohexyl. The maximum pressure attained was 3000 kg cm^{−2}. Three compounds (a), (b), and (d) froze before this limit was reached. Three others (c), (e), and (h) gave evidence of higher order phase transitions. Three of the compounds (f), (g), and (i) showed T _{1} minima, all around 0.017 sec. The resonant frequency was 20.00 MHz. The volume of activation for the molecular correlation time is estimated for each compound. is nearly the same for (b), (c), (d), and (e). It is slightly lower for (a) and (j) and slightly higher for the rest. The significance of this and the value of at one atmosphere is discussed. It is felt that the reorientation of the cyclohexyl rings dominates the relaxation procsss.

Uranium‐fluorine lattice vibrations of β_{1}‐dipotassium uranium fluoride
View Description Hide DescriptionThe infrared spectrum of β_{1}‐dipotassium uranium fluoride, β_{1}‐K_{2}UF_{6}, has been measured in the frequency region from 4000 cm^{−1} down to 30 cm^{−1}. A normal coordinate analysis of the optically active U–F lattice vibrations has been made on the basis of a chain model of infinite neglecting the potassium atoms. Some of the observed bands have been assigned to the U–F lattice vibrations on the basis of the results of this analysis. The stretching and repulsion force constants have been obtained and discussed with respect to the uranium‐fluorine bond distances. Furthermore, to explain the lower vibration frequencies below 100 cm^{−1}, the interactions between the potassium ions and the infinite chains have also been investigated.

Infrared reflection from longitudinal modes in anisotropic crystals
View Description Hide DescriptionIn anisotropic crystals belonging to the tetragonal, hexagonal, trigonal, and orthorhombic systems it is often found that naturally occurring faces are normal to the transition dipole direction for vibrational modes which are reasonably well separated in the spectrum. Strong reflectivity from such faces of waves with transverse magnetic polarization at finite incidence angles is found at frequencies above that of the longitudinal mode. Experimental data for this configuration are presented for the ν_{2} and ν_{3} carbonate vibrations in calcite. Theoretical curves are calculated as a function of incidence angle and damping constant, and the special utility of this type of experiment is discussed.

Rates of CO + OH and H_{2} + OH over an extended temperature range
View Description Hide DescriptionUsing a fast flow reactor with a fixed ESR detector and movable NO_{2} source (for generation of OH by the H + NO_{2}reaction) it was possible to measure the rate constants for and under pseudo‐first‐order conditions with negligible OH loss by . Small losses of OH on the reactor wall were accurately taken into account, and data over an extended temperature range were obtainable. Both reactions show definite curvature in their Arrhenius plots over the range of direct measurement (298–915°K for k _{1} and 298–745°K for k _{4}). Good agreement is found in comparisons with other well‐defined results. In the case of Reaction (4), a definitive experiment was performed to show that by far the dominant reaction path involves breaking the H_{2}bond, rather than the OH bond as in Reaction (1).

Rate of the reaction
View Description Hide DescriptionNew measurements are reported on the rate constant for at room temperature. The study was made with a fast flow reactor using a fixed ESR detector and a movable NO_{2} injector for generating OH by the H + NO_{2}reaction. Careful attention was paid to accounting for the effect of OH loss on the walls and of the overall stoichiometry at varying H/NO_{2} ratios. A large number of runs with both H excess and stoichiometric H/NO_{2} ratios gave .

Self‐diffusion in liquid ammonia and deuteroammonia
View Description Hide DescriptionCoefficients of self‐diffusion have been measured by the spin‐echo technique for neat NH_{3} and ND_{3} from 200 to 298°K. The data are well represented by for NH_{3} and by for ND_{3}. The difference in activation energy for self‐diffusion between NH_{3} and ND_{3} is shown to be consistent with the viscosity measurements of Hutchison and O'Reilly. These results are interpreted by means of a quasilattice model for self‐diffusion in the liquid state. Values of the work required to create a molecular vacancy are evaluated from liquid density, isothermal compressibility and the scaled particle theory. The quasilattice model yields pre‐exponential factors for self‐diffusion that are in reasonable agreement with experiment.

Study of the reactions and using crossed beam techniques
View Description Hide DescriptionThe proton transferreactions and have been studied in the laboratory energy range 1–25 eV. The first process, which is endothermic for ground state reactants, has been studied over the indicated energy range with different degrees of vibrational excitation present in the particles. Below 9 eV, the reaction is found to depend strongly on vibrational energy while above this energy the reaction cross sections appear to depend mainly on the kinetic energy of the reactants. The exothermic reverse reaction exhibits a 1 / ν dependence in the low‐energy region indicating an ion‐dipole mechanism. Methods of measuring the degree of dissociation obtained in forming the hydrogen atom beam are discussed.

Measurement of the thermal conductivity of helium up to 2100°K by the column method
View Description Hide DescriptionThe thermal conductivity of helium was measured at atmospheric pressure in the range 800–2100°K by the column method. The data could be correlated by the polynomial, where λ is in watts per meters degrees Kelvin and T is in degrees Kelvin. The results obtained were compared with previous thermal conductivitymeasurements. The data of Desmond and Saxena and Saxena agree closely with the present results; the data of Timrot and Umanskii appear to be too low and those of Blais and Mann too high. Values for , computed using measuredthermal conductivities and available viscosity data, were found to agree well with classical results from kinetic theory.

Magnetic field dependence of thermal correlations in molecular gases
View Description Hide DescriptionThe effect of a magnetic field on the time‐dependent correlation functions appropriate to the thermal conductivity and self‐diffusion in a dilute molecular gas is investigated. For the thermal conductivity and the energy current correlations, calculations are made for the rough sphere interaction as well as for nitrogen gas. For the calculation of the velocity correlation function, the rough sphere model is used to study the effects due to correlations arising from terms odd in angular momentum. The qualitative similarity that is found in various diagonal correlation functions and in the oscillating structure that is found in many transverse correlation functions is discussed.

Exponential or scaled SCF orbitals in correlated wavefunctions for two‐electron atoms
View Description Hide DescriptionWavefunctions for the ground state of H^{−}, He, Li^{+}, and Be^{2+} are approximated by the product of orbitals with a correlation function. Use of optimally scaled SCF orbitals in place of fully optimized orbitals causes an additional energy error of at least 0.001 hartree. Exponential orbitals are superior to scaled SCF orbitals in open‐shell cases or if the correlation function increases with (r _{1} − r _{2})^{2}; otherwise SCF orbitals are superior. Application of correlation functions to open‐shell wavefunctions causes the outer orbital to contract more than the inner orbital, which actually expands slightly except at low atomic numbers. If the correlation factor depends on (r _{1} − r _{2})^{2} as well as r _{12}, the inner and outer exponential orbitals can become identical when Z is greater than 2. Several three‐parameter wavefunctions have errors of 0.0010–0.0018 hartree. Good approximations to completely flexible correlation functions of r _{12} alone are 1 − A exp(− B r _{12}) and (1 + A r _{12})^{ C }. In the latter function and the optimum C can be predicted accurately by extrapolation.

Studies in molecular Compton scattering. II. The Compton profile of C_{4}H_{8}O_{2}‐dioxane, isobutyric, and n‐butyric acids
View Description Hide DescriptionThe Compton profiles of MoK_{a} x rays inelastically scattered from three liquids of molecular formula C_{4}H_{8}O_{2} (dioxane, n‐butyric and isobutyric acids) are compared with one another and with theoretical profiles computed from localized molecular orbital wavefunctions. The three experimental profiles are found to be not significantly different from one another, in agreement with the theoretical model, but they differ slightly from the theoretical profiles.

Novel two‐photon radiative interaction operators from relativistic theory for Rayleigh scattering and for spin‐dependent Faraday rotation
View Description Hide DescriptionThe quantum field theoretic treatment of Akhiezer and Berestetskii is generalized to a Dirac electron in a time‐dependent electromagnetic field (versus static electric field). From the Hamiltonian a unique set of Hermitian, time‐dependent interaction operators applicable to two‐photon, as well as one‐photon, processes are obtained. Some of the two‐photon interaction operators have not been considered in literature. This is in contrast to more conventional treatments which obtained two sets (instead of one) of apparently equivalent interaction operators with each set containing a non‐Hermitian term for both time‐dependent and time‐independent fields. The two sets of interaction operators obtained from the conventional treatment differ in order and are only applicable to one‐photon processes. When applied to two‐photon processes, the said operators are non‐Hermitian due to the noncommutation of quantized electromagnetic fields (in Π and in E) which also makes the ordering of the operators important. We examine in detail two of the newly obtained Hermitian two‐photon interaction operators, one related to and one is spin dependent and proportional to . The first‐order matrix elements for the two‐photon processes of simultaneous absorption and emission are calculated. It is found that one matrix element corresponds to a new mechanism for first‐order Rayleigh scattering. This matric element is comparable in magnitude to the conventional first‐order matrix element in the x‐ray region. The other matrix element corresponds to a new mechanism for magnetic optical rotation(Faraday effect) due only to spin of the electron and is applicable to molecular radicals with nonsinglet spin multiplicity. In the microwave region, this new matrix element appears to be comparable in magnitude to the matrix element for conventional magnetic optical rotation. Both operators are of potential astrophysical interest because of the various radiation processes in space.

Interpretation of the far infrared spectra of the dimers of HCl and of DCl trapped in monoatomic solids
View Description Hide DescriptionA computation of the far infrared spectral properties due to the orientational motions of hydracid and deuterid dimers trapped in a noble gas solid matrix is proposed. The molecules of the dimers are located at fixed distances, which have been calculated by using a cell model for the representation of the solid containing the impurities. An asymptotic method is proposed that is particularly suitable when the orientational dependent part of the interaction potential between impurities is large compared with the rotational energy of the free molecules. The numerical study of the orientational quantum states of the and DCl–HCl dimers enables the building of the theoretical spectra. The comparison with the corresponding experimental data shows that the present calculations of orientational motions of dimeric impurities in solids give a fairly consistent description of the spectra. The nearly orthogonal equilibrium configuration of the molecular axes in these dimers obtained here, due essentially to the quadrupole‐quadrupole interaction, is consistent with the well‐known ``zig‐zag'' chain in the hydracid pure solids. Moreover, the dependence of the observed spectra on the nature of the monoatomic matrix is taken into account through the variation of the intermolecular distance in the dimer with the matrix under consideration.

On a semiclassical study of molecular collisions. I. General method
View Description Hide DescriptionA method has been developed for calculating rotationally inelastic cross sections of atom‐diatom collisions in a semiclassical approximation (classical path, quantum internal states). An analysis of the relations among the intermolecular potential, the cross sections, and the experimental quantities indicates that many experiments related to inelastic scattering give significant information about the intermolecular potential. A computer program embodying this method of calculation has been developed and tested. Quantities related to experimental measurements have been calculated to within experimental accuracy in a reasonable computing time, which suggests that the information about the intermolecular potential contained in various experimental results can be extracted by a semiclassical calculation.

On a semiclassical study of molecular collisions. II. Application to HCl‐argon
View Description Hide DescriptionExtensive calculations on the rotationally inelastic collisions between HCl and argon have been carried out using the semiclassical method described in the preceding paper. By a detailed study of a single system it is hoped to clarify the behavior of an atom‐diatomic system during a collision, and the nature of the semiclassical model. This study also elucidates the relations between the different parts of the intermolecular potential and various experiments. We obtain an angle‐dependent intermolecular potential by a least squares fit to the available experimental data, and suggest which other experiments will provide useful information about the potential.

Exact solution of the mean spherical model for charged hard spheres in a uniform neutralizing background
View Description Hide DescriptionThe exact solution of the mean spherical model integral equation is found for a system of charged hard spheres in a uniform neutralizing background. This may be considered as a simple example of a fluid with nonadditive hard sphere diameters. Analytic expressions are given for the direct correlation function and for the Laplace transform of the radial distribution function. These, and the thermodynamic properties of the system, are compared with previous solutions of the mean spherical model.

Solvent effects on electronic spectral oscillator strengths
View Description Hide DescriptionThe effect of long‐range dispersion forces on the conversion from the total integrated absorption of an allowed solute transition in solution to the corresponding unperturbed oscillator strength in the isolated solute is investigated. As an illustration of this effect, calculations are performed on the transition of an H solute in a variety of inert and other gases. The commonly used Lorentz field correction factor is shown to be of minor importance compared to an additional ``IMF'' factor arising from the intermolecular forces between the solute and the solvent molecules and the translational fluctuations between the induced moments. While the former factor is always greater than one, the latter can be greater than as well as less than unity. Implications regarding more complex solutes are considered.

Irreversible statistical mechanics of polymer chains. III. A dynamic model of vinyl polymers
View Description Hide DescriptionComputational works are made of the dynamic rotational isomer model of vinyl polymers, of which theoretical foundation has been given in the first paper of this series. First, a concept of ``simple elementary mode'' is newly introduced, based on the assumption of short‐range order of vinyl polymers, and 2317 simple elementary modes for (where ν is the length of local chains) are found with the aid of a computer. Langevin equations for local chains rotating in a viscous medium are introduced to derive transition probabilities for these modes. They are given as functions of the monomer size (R_{m} ), the free volume (ν _{f} ) of the system, and a hydrodynamic parameter . Two kinds of systems, dilute polymer solutions and bulk polymers (including concentrated polymer solutions), are discussed separately. Two dimensionless quantities, [D_{a} ] (intrinsic diffusion coefficient) and [T_{a} ] (intrinsic relaxation time) for normal coordinates Q _{a} , are newly defined and they are computed numerically for various , and gauche state energy (E_{g} ). The following are found in the present work. (1) [D _{α}] strongly depends on ν _{f} both in the range and , but not on , where is almost independent of R_{m} and E_{g} in the whole range In dilute solutions all the (2317) elementary modes participate in the Brownian motion of the polymer chains, but with the increase in polymer concentration (i.e., with the decrease in ν _{f} the larger elementary modes begin to freeze up and, near the glass‐transition temperature, the only two smallest modes, (^{4},^{1})S and (^{6},^{2})S remain unfrozen. (4) Even in dilute solutions, the Brownian motion of the normal coordinate with a large is determined by several small elementary modes alone. (5) takes its minima in the range . (6) strongly depends on both ν _{f} and E_{g} , but depends only on E_{g} . The following subjects are also discussed: The superposition of time and temperature changes, behaviors of long elementary modes, and the glass‐transition phenomena.

Continuum theory of smectic liquid crystals
View Description Hide DescriptionThe anisotropic physical properties resembling those of fluids and solids of smectic liquid crystals are discussed. Based upon micropolar theory, a set of constitutive equations generalizing the Kelvin‐Voigt model has been derived. Material moduli are restricted by material symmetry and physical considerations. The concepts of reference state fundamental to smectic liquid crystals are discussed. Three types of problems, bending, torsion, and wave propagation, are presented. Future studies and experiments are suggested with the hope of creating further confidence in the theory.

Lifetimes and quenching cross sections of
View Description Hide DescriptionFluorescence lifetimes, self‐quenching cross sections, and foreign gas quenching cross sections have been measured for by direct observation of fluorescence decay for excitation in the region 640–499.5 nm, corresponding to excited electronic state levels between v′ ≈ 5 and v′ ≈ 70, close to the dissociation limit. The foreign gas experiments represent the first measurement of foreign gas quenching rates using lifetime methods. A pulsed tunable nitrogen‐laser‐pumped‐dye laser with a linewidth of 0.3 to 0.7 nm and a pulse time of less than 10^{−8} sec was used as the excitation source. Lifetimes were found to be strongly dependent on v′, varying from less than 0.4 μsec to greater than 7 μsec. Self‐quenching cross sections showed less v′ dependence, varying between 47 and . Foreign gas quenching cross sections were measured for Ar, Br_{2}, CO_{2}, H_{2}, He, Kr, N_{2}, NO, Ne, O_{2}, SF_{6}, and Xe, and showed a dependence on both v′ and the gas used. Values for light gases, such as H_{2} and He, were typically or less, while values for Xe were as high as .