Polarizability Ratio Research Articles

Gas Chromatography/Mass Spectrometry of Polyethylene Glycol Oligomers

Polyethylene glycol (PEG) oligomers, H(OC2H4O) nH, were analyzed by gas chromatography/mass spectrometry (GC/MS) for oligomers, n = 2–11, without indications of pyrolysis of the higher oligomers at oven temperatures of 330°C. The electron ionization (EI) mass spectra (70 eV and 12–14 eV) of these PEG oligomers contain only low molecular weight fragment ions and, essentially, no M+ ions. The low-voltage EI spectra contain more abundant high mass ions and allow easier identification of the PEG oligomers. The major fragment ions in all EI spectra are (C2H4O) xH+ at m/z 45, 89, 133 and 177. The base peak in the low-voltage spectra varies with molecular weight and suggests preferential cleavage at the second and third ether linkages. The relative molar sensitivities (70 eV EI) of PEG oligomers ( n = 1–6) are linear functions of molecular weight or polarizability ratios. The CH4 chemical ionization mass spectra of the PEG oligomers contain, predominantly, (C2H4O) xH+ ions at m/z 45, 89, 133 and 177. The relative abundances of MH+ ions vary markedly across the chromatographic peaks because these ions are formed predominantly by sample ion / sample molecule reactions. Proton transfer reactions from CH5+ and C2H5+ to the PEG oligomers are almost entirely dissociative. The i-C4H10 CI mass spectra of PEG oligomers contain MH+ as the base peaks. The relative abundances of MH+ ions do not vary significantly across the chromatographic peaks but do increase with increasing pressure of i-C4H10. The extent of decomposition of MH+ ions in i-C4H10 CI mass spectra increases with increasing molecular weight of the PEG oligomers. Relative molar sensitivities (CH4 CI and i-C4H10 CI) of PEG oligomers ( n = 1–6) are essentially the same linear functions of molecular weight ratio.

Anisotropic Molecular Polarizabilities of HCHO, CH3CHO, and CH3COCH3. Rayleigh Depolarization Ratios of HCHO and CH3CHO and First and Second Kerr Virial Coefficients of CH3COCH3

Available information in relation to the anisotropic electric dipole polarizabilities of HCHO, CH3CHO, and CH3COCH3 is complemented by measurements of the vapor-phase Rayleigh depolarization ratios of HCHO and CH3CHO and the temperature dependence of the vapor-phase electrooptical Kerr effect of CH3COCH3 at 632.8 nm. In the cases of HCHO and CH3CHO the polarizabilities remain incompletely defined by the experimental data; but in the case of CH3COCH3 the three principal polarizabilities are determinable from an analysis of the Kerr effect together with the previously reported mean polarizability and Rayleigh depolarization ratio of this species. The experimental polarizabilities of CH3COCH3, in conjunction with Rice and Handy's computed polarizabilities of HCHO and a simple group additivity model, allow the reliable prediction of the four components of the polarizability of CH3CHO. As well, the temperature dependence of the first Kerr virial coefficient of CH3COCH3 provides uncertain estimates of the first and second Kerr hyperpolarizabilities, which have not previously been reported. The temperature dependence of the second Kerr virial coefficient, which measures contributions from pairwise molecular interactions, is found to be explicable in terms of a recent statistical-mechanical theory of the effect.

Crossed Waveguide Directional Couplers for High Power Applications

The small aperture coupling theory of the broad wall to broad wall (Moreno) coupler is reviewed and extended. It is shown that a lower limit on the directivity is given by the ratio of magnetic polarizability to electric polarizability for the coupling apertures. Hence directivity may be improved by using very narrow crossed slots for coupling The results of coupling measurements on a Moreno coupler are presented to demonstrate the accuracy of the small aperture theory. A small aperture design procedure has also been developed for the narrow wall to broad wall coupler, which takes into account the effect of wall proximity on slot coupling The measured results for the manufactured coupler are in excellent agreement with this theory.

Correlation of the Flux Tube Constant with the Nucleon Electric Polarizability

A three-quark shell model of the nucleon is used to calculate analytically thepolarizability using a scalar linear flux tube potential with no one-gluon exchangepotential included. A value of 12.02 × 10−4 f 3 is obtained for the proton, ingood agreement with experiment, with the flux tube constant adjusted to reproducethe proton Δ average rest energy. The magnetic polarizability of the proton isthen calculated as 1.51 × 10−4 f 3, which is in agreement with the experimentalvalue. The neutron/proton electric polarizability ratio is calculated as 2/3, andthe neutron electric polarizability is predicted to be 8.01 × 10−4 f 3.

Polarization properties of light multiply scattered by non-spherical Rayleigh particles

Multiple scattering of incoherent polarized light propagating through a random medium comprised of spheroidal Rayleigh particles is studied using Monte Carlo simulations. Two approaches are taken for the implementation of the simulation: the first uses individual realizations of particle orientation and the second, an accelerated method, averages over the particle orientation. These different methods produce results that are indistinguishable within statistical errors. The depolarization of light is examined in both transmission and backscatter for media comprised of spheroids of different polarizability ratios. In media containing spheroidal particles the depolarization is greater than that for spherical particles. Media containing prolate spheroids are more depolarizing than media comprising oblate particles of the same polarizability ratio. The extra depolarization due to asphericity is much less pronounced in the multiple scattering regime than for single scattering.

On the refractive indices, polarizabilities and order parameter of a nematic discogenic mixture

Abstract The phase diagram of a mixture of the discogens triphenylene hexa-n-heptanoate (HET7) and triphenylene hexa-(2-methyl-4-n-decyloxy)benzoate is presented. This mixture provides a more accessible nematic temperature range than was previously possible. The refractive indices of one mixture composition are measured and a rather small, negative birefringence found. The two-parameter Haller extrapolation method is used to calculate the molecular polarizability ratio Δα/α. This has a rather small magnitude compared with calamitic mesogens, although the individual polarizabilities are much larger, due to the greater molecular mass of these compounds. The calculated value of Δα/α is used to give the uniaxial orientational order parameter S, whose value is comparable to those of calamitic examples. Tabulated bond polarizability data are used to predict a value for Δα/α, which is found to be similar to the experimental result.

Empirical and semiempirical interaction potentials for rare gas–rare gas and rare gas–halide systems

The Tang–Toennies (TT) semiempirical model potentials for ion–atom systems is applied to the rare gas–halide negative ion exciplexes. The coefficients defining the repulsive Born–Mayer term in the TT semiempirical potentials are determined from the equilibrium bond length Re and dissociation energy De taken from ab initio calculations and from transport studies of these molecular ions. The damped dispersion and induction energy terms in the TT potentials are obtained from coupled Hartree–Fock calculations for the neutral rare gas atoms and F− and Cl− ions. The multipole polarizabilities for the heavier halogen atomic negative ions are estimated from a knowledge of polarizability ratios across isoelectronic sequences. The resultant semiempirical ionic potentials are compared to available ab initio calculations and the results of inversion of transport theory. To facilitate the comparison of the (sparse) ab initio data with the semiempirical potentials, a simple fitting procedure is presented for determining empirical potentials for diatomic molecules from a set of three constraint equations. The fitting procedure is applied to a total of 22 rare gas excimers and rare gas–halide exciplexes (both neutral and ionic) of interest to a variety of applications in gaseous discharges and excimer lasers. A three-term representation of the empirical potentials generated is accomplished with the use of a minimal data set which include the ‘‘geometric’’ parameters {R0,Re,De} and the additional parameters {αd, I.P., E.A.} needed for the dispersion and induction energy terms. A novel feature of the empirical procedure is the formulation of the constraint equations at two nuclear displacements (one constraint at R0, wherein the potential passes through zero, and two constraints at Re the equilibrium separation) which yields an accurate fit to available ab initio data and greatly extends the range of internuclear separations R for which an accurate piecewise analytical empirical potential can be generated. To test the relative importance of the different terms in the fitted three-term empirical representations, the classical orbiting cross section Qorbit(E) is computed using the full empirical potential and compared against the standard Langevin orbiting cross section Qpol(E) for a pure polarization interaction.

Calculated Raman overtone intensities for H2 and D2

Dynamic dipole polarizabilities pertinent to the Raman intensities of the fundamental and first two overtones of H2 and D2 have been calculated. To do this an energy-shifted sum-over-states formula has been used in conjunction with accurate electron-correlated wave functions. The results for the relevant polarizability ratios agree, in the static limit, with a previous calculation. The dynamic values are in fair agreement with the recent experimental ones for H2 but there is a strong disagreement with a previous experimental determination for D2.

Orientation effects on the electrophoretic mobility of rod-shaped molecules in free solution

The effect of molecular orientation on the electrophoretic mobility of rod-shaped polylons as measured by free solution capillary electrophoresis is studied by using the tobacco mosaic virus (TMV) as a model solute. This orientational dependence of molecular mobility is measured by observing the influence of electrical field strength (up to 400 V/cm) on the electrophoretic mobility of TMV. The electrophoretic mobility of TMV increases with increasing field strength. This increase can be quantitatively correlated with the decrease in the translational frictional coefficient (f) due to the increasing alignment of TMV with the electric field. A model is developed relating the decrease in f to the alignment of TMV with the electric field through its polarizability and aspect ratio. To confirm the observed orientational affects on mobility, control experiments were performed with 0.364 micron diameter Latex spheres. Due to their spherical symmetry, no orientational effects would be expected. Indeed, no increase in mobility was observed for these spherical particles. Calculations are presented to demonstrate that the increase in mobility is unlikely to be caused by either the Wien effect or any temperature variation resulting from Joule heating of the electrophoresis buffer.

Analysis of high-pressure adsorption data on activated carbon to obtain generalized characteristic and heats of adsorption curves

High-pressure adsorption data were obtained for methane, ethane, ethylene, propane, carbon dioxide, and nitrogen on activated carbon. Adsorption isotherms up to 60 atm and at a number of temperatures were measured and isosteric heats of adsorption determined from adsorption isosteres by the Clausius-Clapeyron equation. Affinity coefficients were used to reduce adsorption characteristic curves and variation of the isosteric heats of adsorption for the various gases to a generalized curve. It was found that affinity coefficients calculated by the ratio of polarizability of an adsorbate with that of a reference adsorbate did not yield a generalized heat of adsorption curve. When account was taken of the quadrupole moments of the adsorbate in defining affinity coefficients, characteristic curves for adsorption and heats of adsorption data for all the gases resulted.

Theory of optical ellipsometric measurements from muscle diffraction studies

A theory of optical ellipsometry describing the complete phase shift and ellipticity of light diffracted from a single muscle fiber is developed. We show that both the phase shift information, described commonly by the birefringence of the fiber, and the ellipticity information, described by the differential polarizability ratio, are necessary to provide a complete picture of the complex contributions to the total optical anisotropy spectra from a diffraction pattern derived from the striated muscle cell. Both form and intrinsic contributions play significant roles in either the birefringence measurement or the differential field ratio measurement. However, we show that their relative weights in these two measured quantities are different, and measuring both of these parameters is necessary to obtain a more complete assessment of the cross-bridge structure and dynamics. The theoretical results have been tested for three different situations: solvent index matching, passive stretch of a resting fiber, and cross-bridge changes under isometric conditions. Comparisons between experimental data and simple model calculations provide much information regarding cross-bridge orientation and structure.

Stark interference effects in a weak magnetic field on the 6S–7S forbidden transition of cesium

Hyperfine mixing in a weak magnetic field gives rise to new interference terms between the Stark-induced amplitudes of the 6S–7S forbidden transition of cesium. Compared with typical allowed transitions, effects of unusual size (circular dichroism of ∼10% in a 10 G field) and/or symmetry (3% upper state spin polarization induced by linearly polarized light in a direction normal to both the beam and the magnetic field) are observed. The circular dichroism yields a new method to determine the scalar to vector polarizability ratio; our result (α/β=-10.0±0.15) agrees with those of other techniques. The analysis of systematic effects in our recent measurement of parity violation required an understanding of these hyperfine mixing effects. One of them will be utilized to calibrate a new version of the parity experiment.

New measurement of the Cs 6S → 7S scalar to vector polarizability ratio

We have measured the ratio |α/β| of the scalar to vector polarizabilities of the forbidden 6S 1 2 → 7S 1 2 transition of cesium by a method free of background difficulties. Our result, | α/ β| = 9.90 ± 0.10, agrees with that of Hoffnagle et al. The slight disagreement with our earlier result is examined.

The local field acting on oxygen ions in SrTiO 3 and its structural phase transition

By using the Lorentz correction factor 14.456 for O x and O y in SrTiO 3 the strength of the dipole interaction can be estimated as a function of the ratio of electronic polarizability of the oxygen ions to the unit cell volume, which is found to exert a large influence upon the structural phase transition.

Intensities of rotation and vibration‐rotation Raman transitions in asymmetric top molecules

AbstractThe derivation of the intensities of rotation and rotation‐vibration Raman transitions for asymmetric top molecules is given, based on irreducible spherical tensor formalism. A computer program package written to calculate such intensities is described. Its use is demonstrated by reproducing the observed contours of the pure rotational band and the asymmetric stretching vibrational band in the Raman spectrum of the SO2 molecule. The polarizability tensor component ratio required to simulate the pure rotational contour is combined with literature values for mean polarizability and depolarization ratio to obtain the principal values of the SO2 polarizability tensor. A correlation of the polarizability tensor component ratio with band types is discussed for totally symmetric bands which have been reproduced using our program and those of others.

Raman spectra of asymmetric top molecules

A detailed analysis of the Raman-active v 1, v 3 (both A-type) and v 5 (Bc -type) vibration-rotation bands of ethylene is presented. In addition to structural data simulation of the spectra yields values for the polarizability ratios of the totally symmetric bands, giving information on the polarizability ellipsoid as the molecule vibrates. v 3 is shown to be perturbed by a c-type Coriolis interaction which complicates the interpretation of the negative value of the polarizability ratio required to match the observed spectrum. The effects of asymmetry are pronounced; one result being the formation of heads in the R,PR K p and R,P P K p branches of low K p in the v 5 band.

Ratio of Atomic Stopping Power of Graphite and Diamond for 1.1-Mev Protons

The theory describing energy loss of heavy charged particles in matter predicts that different physical or chemical forms of the same element will have slightly different stopping powers. Since two different forms of a pure element exhibit the same nuclear scattering cross section, it was possible to measure the relative atomic stopping power of graphic and diamond by observing the yields of backscattered protens from thick targets. The atomic stopping power of graphite was measured to be 1.0604 plus or minus 0.0090 times that of diamond (for 1.1- Mev protons). Using the theoretical density of graphite, a calculation based on this result and Brandt's version of stopping theory yields the result that the molecular polarizability of graphite is 4.9 times thnt of diamond. If this calculation is made using the measured density of graphite, this polarizability ratio is 1.5, in agreement with the theoretical value. (auth)