bluuebunny/crossref_metadata_2025 huggingface dataset:
Spin—Echo NMR Studies of Chemical Exchange. I. Some General Aspects
Authors: Allerhand Adam , Gutowsky H. S.
Published: January 2005

The applicability to chemical-exchange studies of the Carr—Purcell nuclear magnetic resonance spin-echo method has been investigated for the case of two exchanging sites with equal T20, the transverse relaxation time ``in the absence of exchange.'' Theoretical calculations indicate that the decay of the echo amplitudes should be exponential, or very nearly exponential in all cases, the apparent decay constant T2 being a function of T20, of δω the chemical shift between the sites, of τ the lifetime between exchanges, and also of tcp the rf pulse separation. Values of the apparent T2 for different values of these parameters were obtained by numerical methods with a high-speed computer. These values agree with an approximate equation derived by Meiboom, except at slow exchange and large pulse separation.

A method is described for calculating the exchange rate from the observed dependence upon tcp of the apparent T2. This method has several advantages over the high-resolution NMR methods. A knowledge of δω and T20 is not required; these quantities are also determined from the spin-echo data. Larger values of exchange rate (shorter lifetimes) can be determined accurately. The spin-echo method does have the serious drawback that it lacks ``resolution.'' The method was applied to the hindered internal rotation of N,N-dimethyltrichloroacetamide (DMTCA) and dimethylcarbamyl chloride (DMCC) as a function of temperature. The resultant activation energies of 14.6 and 14.0 kcal/mole and frequency factors of 3.5×1012 and 7.1×1010, respectively, are appreciably higher than previously reported values. Comparative determinations were carried out using the high-resolution NMR methods. The relatively large differences in the results from the various methods and from different laboratories indicate that systematic errors are present, several possibilities for which are discussed.

A simple arrangement is described for generating the Carr—Purcell pulse sequence with three waveform generators and two pulse generators.
Quantum Cell Model Equation of State
Authors: Hillier Ian H. , Walkley John
Published: January 2005

A quantum-mechanical cell model equation of state is developed using the Wentzel—Kramers—Brillouin approximation to solve the Schrödinger wave equation. Compressibility data for hydrogen, deuterium, and helium is obtained for a Lennard-Jones 12–6 potential, over a wide range of temperature and density. A comparison with experiment shows the expected good agreement in the solid state, the agreement becoming progressively worse for the liquid and gas phases.
Luminescence in Mixed Solvent Systems : Factors Responsible for a Luminescence Minimum
Authors: Burton Milton , Dillon Michael A. , Mullin Charles R. , Rein Robert
Published: January 2005

Certain solutions containing a mixture of two solvents one of which is benzene, a scintillator (at fixed concentration) and air (also at fixed concentration) when irradiated with 60Co γ rays are known to yield luminescence, the intensity of which is a minimum at benzene concentration near 1 vol. %. A light-yield expression, analytically developed by Nosworthy, Magee, and Burton to explain this minimum, is examined and interpreted. It is shown theoretically and experimentally that the minimum can be made to disappear at sufficiently high concentration of scintillator solute, that the presence of air or other quencher is not in principle essential to the existence of a minimum, that the properties of benzene (the ``better'' solvent) pertinent to the effect are not affected by the presence of other solvent, that such necessary properties are establishable and selection of the ``better'' solvent can be deliberately made to conform to those properties, and that other solvent pairs of the required characteristics can be found. The results are interpreted in terms of structure of the liquid.
Mass Spectrometric Studies at High Temperatures. II. The Sublimation Pressures of Magnesium, Strontium, and Barium Fluorides
Authors: Green John W. , Blue Gary D. , Ehlert Thomas C. , Margrave John L.
Published: January 2005

A mass spectrometer has been employed to measure the sublimation pressures and heats of sublimation for MgF2 over the range 1241° to 1492°K; for SrF2 over the range 1207° to 1563°K; and for BaF2 from 1232° to 1505°K. For MgF2 the results are represented by logPatm=−[(88.3±0.9)/45.76]104T−1+8.53±0.2;for SrF2 by logPatm=−[(99.3±0.7)/45.76]104T−1+8.716±0.01;and for BaF2 the equation is logPatm=−[(85.1±0.9)/45.76]104T−1+7.659±0.01.The errors quoted are the standard deviations from the least-squares fitted lines. The heat of sublimation of MgF2 at 1366°K is 88.3±2.5 kcal mole—1 while the heats of sublimation at 298°K are 103.7±2.5 kcal mole—1 for SrF2 and 92.3±2.0 kcal mole—1 for BaF2.
Theory of Magnetic Multiple Resonance Spectra
Authors: Shimizu Mitsuko , Shimizu Hiroshi
Published: January 2005

A general theory of magnetic multiple resonance spectra is presented. It is shown that the spectra are conveniently calculated by transforming to an interaction frame. The pattern of the spectrum observed in this frame is equivalent to that observed in the laboratory frame. The theory is applied to the calculation of the resonance spectrum of a three-spin AMX system. It is theoretically shown that the multiple resonance technique is extremely powerful for the analyses of complex NMR spectra as well as for accurate determination of the magnitudes of chemical shifts and spin—spin coupling constants, even if the signals of the corresponding nuclei are hidden by other features of the spectrum. The relative signs of hidden spin—spin coupling constants can be determined from the intermediate patterns of multiple resonance spectra.
Self-Diffusion of Ions into Ion-Exchange Resins
Authors: Špan J. , Ribarič M.
Published: January 2005

A theoretical model for the self-diffusion of ions into an ion exchange resin is proposed, using the concept of an effective diffusion boundary layer with nonlinear concentration profile. The derived equation is of a general character and fit for wide concentration of the flowing solution. From it one can derive specialized equations already known for self-diffusion of ions in ion exchangers. To test the adequacy of the proposed model, series of experiments were performed on the self-diffusion of cesium ions into polystyrene sulfonic acid resin Dowex 50×8 from solutions of cesium and potassium chloride. The concentration of solutions was varied over a rather wide range. Several runs were made with different rates of the flow of the solution. Good fitting of experimental results with theoretically calculated curves over the whole experimental range indicates that the proposed model is adequate.
Radio-Frequency and Microwave Spectra of LiBr by the Molecular-Beam Electric-Resonance Method
Authors: Hebert A. J. , Breivogel F. W. , Street K.
Published: January 2005

The molecular-beam electric-resonance technique has been used to obtain dipole moments μv, quadrupole interaction constants of bromine (eqQ)v, spin—rotation interaction constants cBr, and rotational constants for 6Li79Br and 6Li81Br in several of the lower vibrational levels. The observation of J=1 radio-frequency spectra for three or more vibrational states led to the following values:                     6Li79Brμv=7.22624+0.08318(v+12)+0.00057(v+12)2±0.001  D,(eqQ)v=37.015+2.918(v+12)−0.039(v+12)2±0.005 Mc/sec,cBr=9.2±0.2 kc/sec.                    6Li81Brμv=7.22611+0.08312(v+12)+0.00060(v+12)2±0.001  D,(eqQ)v=30.912+2.442(v+12)−0.034(v+12)2±0.005 Mc/sec,cBr=9.9±0.2 kc/sec.The observation of J=1→J=0 microwave transitions yielded the following rotational constants: Li796Br (Mc/sec)Li816Br (Mc/sec)B0=19 090.296±0.006,B0=19 057.005±0.006,B1=18 882.800±0.009,B1=18 850.050±0.020,B2=18 677.242±0.055.B2=18 645.035±0.217.
Reactions of the Triplet States of Some Aromatic Compounds
Authors: Kusuhara S. , Hardwick R.
Published: January 2005

By means of flash photolysis, studies were made on the triplet states of anthracene, naphthacene, coronene, and rubrene dissolved in hexane at temperatures ranging from 20° to —30°C. When the concentration of triplet substances is small, the decay appears to follow first order; under these circumstances, the temperature dependence is small for anthracene and naphthacene (activation energy: 0.2–0.8 kcal/mole). The quenching of the triplet states by added reactants (CCl4, CHCl3, and NO) was studied, and bimolecular rate constants were calculated. Activation energies of the reaction between anthracene and carbon tetrachloride and of other triplet deactivation processes are ∼2.5 kcal/mole; the rate constants themselves are of the order of 104 moles liter—1 sec—1.
Liquid—Vapor Equilibrium in the System Equilibrium Hydrogen—Helium
Authors: Sonntag R. E. , Van Wylen G. J. , Crain R. W.
Published: January 2005

Liquid—vapor equilibrium-phase compositions for the binary system 20.40° equilibrium hydrogen—helium have been determined for six isotherms in the range 20.40°—31.50°K and at pressures up to 500 psia. The vapor recirculation method of obtaining equilibrium was used in conjunction with a liquid-hydrogen vapor-pressure-controlled cryostat. Analyses were made on a mass spectrograph. The results are presented in both tabular and graphical form, and comparisons with those reported previously for the system normal hydrogen—helium have also been made.
Boundary Conditions and the Anharmonic Contributions to the Free Energy of a Lattice
Authors: Lloyd P. , O'Dwyer J. J.
Published: January 2005

In the evaluation of the free energy of a lattice in the harmonic approximation it is well known that the results are, to thermodynamic accuracy, independent of the boundary conditions used. It is shown here, by way of a simple example, that this is not so in the evaluation of the anharmonic contributions to the free energy. Physically the difference corresponds to whether or not the lattice is free to expand, or is constrained to a fixed volume, for the differing temperatures at which the partition function is evaluated.
Computer Simulation of a Molecular Stopping-Power Problem
Authors: Blackman S. S. , Hirt C. W.
Published: January 2005

A high-speed computer is used to calculate the trajectory of a fast ``test'' particle injected into a two-dimensional system of interacting point particles. All particles interact along lines of centers according to a repulsive inverse-power force law. The evolution of the test-particle velocity and energy averaged over many machine calculated trajectories is compared with a statistical theory based on binary collisions. In the case of an inverse-cube force law explicit theoretical results are obtained and show excellent agreement with the machine calculations. A combined relaxation-time—Fokker—Planck kinetic equation for the test-particle distribution function is discussed; this equation includes the effects of both strong and weak collisions. For the inverse-cube force law this equation is approximately solved for the energy distribution function and exhibits the principal features of the machine calculated energy distribution.
Evaluation of Lattice Sums for Metals and Metalloids Using Morse Potentials
Authors: Anderson J. R. , Barraclough C. G.
Published: January 2005

A method is presented for the rapid computation of the sum of the pairwise interactions between the atoms of a crystal and a like atom on a surface of the crystal, where it is assumed that each pairwise interaction is represented by a Morse function.
Reinterpretation of the Electron Spin Resonance Spectrum of the o-Xylene Negative Ion
Authors: Bolton J. R.
Published: January 2005

The electron spin resonance spectrum of the o-xylene negative ion has been re-examined in view of a discrepancy between one of the previously reported splitting constants and the predictions of molecular orbital theory. This splitting constant has been found to be 1.81 G instead of ∼0.2 G.

The new values of the hyperfine splittings reported here are in excellent agreement with the predictions of both molecular orbital and valence bond theory.

A technique is described by which molecules such as o-xylene can be reduced.
Stochastic Model for Bimolecular Reaction
Authors: Ishida Kenji
Published: January 2005

The kinetics of two bimolecular reactions A+B→C and 2A→C are investigated by the theory of stochastic process, in which the number of molecules of reactive substances is a discrete random variable. The set of fundamental differential-difference equations satisfying the probability distribution for the number of reactive molecules is solved by the method of Laplace transformation. The mathematical expectation and variance are derived from the generating functions, which can be expressed by Jacobi's polynomial for A+B→C and by Legendre's polynomial for 2A→C. The stochastic models are discussed in comparison with the deterministic models, and it is proved that the stochastic rate equations are not consistent with the deterministic rate equations in the mean.
Vibrational Spectrum and Force Constants of Au(CN)4—
Authors: Jones Llewellyn H. , Smith J. Michael
Published: January 2005

Raman and infrared spectra of aqueous and solid KAu(CN)4 have been studied. Ten of the 16 fundamental vibrations of the Au(CN)4— ions have been assigned. The stretching force constants and some of the bending force constants have been calculated. The high CN force constant (17.4 mdyn/Å) and high MC force constant (3.0 mdyn/Å) indicate strong metal—ligand sigma bonding and weak metal—ligand pi bonding, as expected because of the high effective nuclear kernel charge on the gold.
Vibrational Relaxation in Propane, Propylene, and Ethane
Authors: Holmes R. , Jones G. R. , Pusat N.
Published: January 2005

Sound-propagation measurements have been made in propane, propylene, and ethane at 30°C in the frequency/pressure range 0.16 to 1000 Mc/sec·atm. Vibrational relaxation was observed in all three gases. For propane and propylene single relaxation times, and for ethane two relaxation times, were observed experimentally. The relaxation time for propane is (1.56±0.08) 10—8 sec and for propylene (1.48±0.08) 10—8 sec at 1 atm. For ethane the observed relaxation times are (1.12±0.03) 10—8 sec and (0.71±0.06) 10—9 sec at 1 atm, the shorter being associated with the de-excitation of the hindered rotational mode and the longer with the de-excitation of the higher vibrational modes. Possible mechanisms for the de-excitation of vibrationally excited propane, propylene, and ethane molecules are discussed in the light of these results.
Photoconductivity of Anthracene
Authors: Raman R. , Azarraga L. , McGlynn S. P.
Published: January 2005

The transport properties of current carriers in anthracene have been studied by a crystal counter technique. It has been shown that the charge pulses may be analyzed as the sum of two contributions, a primary component which varies linearly with time and which breaks at a time equal to the transit time, and a secondary component which is caused by slow release of holes from traps in the surface region. Analysis of both components leads to carrier mobilities, thermal dependence of carrier mobilities and of carrier populations, surface trap depths, etc. The interpretation of pulse height vs voltage behavior which is superlinear invokes recombination and/or detrapping processes which are field-dependent. Experiments are presented which show that recombination at the surface is kinetically more important than recombination in the bulk. It is indicated that the photogeneration of charge carriers at the irradiated surface may be biphotonic.
Raman Spectrum of Anthracene
Authors: Abasbegović N. , Vukotić N. , Colombo L.
Published: January 2005

Raman spectra of the anthracene solution are recorded using a Raman source of high luminosity. Twelve new frequencies are found and an assignment is proposed using earlier measurements on a single crystal.
Proton and Fluorine NMR Spectra of HBF2
Authors: Farrar T. C. , Coyle T. D.
Published: January 2005

Proton and fluorine NMR spectra of HBF2 were recorded in the temperature range 140°K to 230°K. The values for the spin-coupling constants JHF, J11B—H and J11B—F are 108±1 Hz, 211±2 Hz, and 84±1 Hz, respectively. JHF is temperature independent. The apparent values of J11B—H and J11B—F decrease below 165°K due to the interaction of rapidly fluctuating electric field gradients with the electric quadrupole moment of boron. The center of the proton multiplet is about 0.12 ppm downfield from the center of the terminal proton multiplet in diborane. The fluorine multiplet is about 60 ppm downfield from the fluorine resonance in BF3, which in this case was a single structureless line. The dependence of 11B–H coupling constants on the orbital hybridization of boron is discussed.
Cell Model for Quantum Fluids. II. Thermodynamic Properties of Liquid H2
Authors: Reed Robert D. , Henderson Douglas
Published: January 2005

The thermodynamic properties of liquid hydrogen are computed on the basis of the cell model of Lennard-Jones and Devonshire for those temperatures and volumes which are characteristic of its liquid state. The lowest energy levels are calculated exactly and the higher energy levels are calculated by the WKB method. The effects of the first three shells of neighbors are taken into account. The thermodynamic properties are in moderate agreement with experiment with the quantum corrections given accurately.
Ion Dissociation in the Drift Tube of a Time-of-Flight Mass Spectrometer: Spurious Fragments Arising from Charge-Transfer and Dissociation Reactions of Retarded Ions
Authors: Hunt W. W. , McGee K. E.
Published: January 2005

Spurious fragment peaks that simulate fragment-ion dissociation products formed in the drift-tube reaction region have been observed in a time-of-flight mass spectrometer adapted for kinetic studies of ion dissociation processes. These peaks arise from processes occurring after the reactant ion has passed through the reaction region and entered the potential barrier that is normally used to separate reactants and products by selectively shifting their flight times. The flight-time shifts characteristic of such spurious peaks depend on the distance from the ion source to the potential barrier, whereas the shifts characteristic of normal fragment peaks are independent of this distance. Comparisons of experimentally measured flight-time shifts with analytically calculated values identify a fragment peak observed in association with the N2+ mass-28 peak in N2O as a spurious fragment peak, which represents not dissociation products of N2+ formed in the reaction zone, but neutrals formed inside the potential barrier. The absence of other fragment peaks then establishes that the neutrals are formed by the charge-transfer process N2+ lim fast+N2O lim thermal→N20 lim fast+(N2O)+· lim thermalSince such spurious fragment peaks can, as in this case, be much larger than any real fragment peaks present, a cautious approach to peak identification is essential when using the TOF—potential barrier technique for ion dissociation studies. The recognition of such spurious fragment peaks is greatly facilitated by making flight-time shift measurements at more than one value of the distance from the ion source to the potential barrier.
Photoluminescence of Lanthanide Complexes. III. Synergic Agent Complexes Involving Extended Chromophores
Authors: Halverson F. , Brinen J. S. , Leto J. R.
Published: January 2005

The partial development of an insulating sheath via formation of synergic agent complexes is shown to enhance the photoluminescence of a series of europium β-diketone chelates. Equilibria which may occur in solution are discussed and provide a satisfactory explanation for certain variations in behavior.
Range of Validity of Born Approximation for Molecular Fragmentation Following High-Energy Proton and Electron Impact
Authors: Wexler S.
Published: January 2005

Arguments based on the Born approximation lead to the expectation that the ionic fragmentation pattern of a polyatomic molecule is independent of the nature of the ionizing and exciting charged projectile provided the velocity is the same and is sufficiently high. An experimental assessment of this expectation has been made. The patterns of positively charged fragments of methane, acetylene, ethylene, ethane, propane, and n-butane from bombardment of these molecules with 2.25-MeV protons have been compared with the mass spectra resulting from impact of 1225-eV electrons. At these energies the velocities of the two particles are 2×109 cm/sec, 9.5 times the Bohr velocity. The relative abundances of the more prominent ionic species were observed to be generally in good agreement, but large differences were found for ions of low yield. Almost invariably, the fragments were produced in higher abundances relative to the parent ion in electron impact than in proton bombardment.

The apparent failure of the Born approximation for describing molecular dissociation in high-energy-transfer collisions was expressed for each fragment quantitatively as the deviation from unity of the ratio of relative abundances from the electron and proton bombardments. Correlations of these deviations with several other characteristics of inelastic collision processes have been made. At the velocity employed the Born approximation is found to be valid for a large fraction of the ionizing and exciting collisions of almost all the target molecules. The apparent failure of the approximation appears to be related to the amount of energy transferred to the struck molecule by the projectile and to the kinetic energy of the fragment.
Vapor Pressures of the Rare-Earth Metals
Authors: Habermann C. E. , Daane A. H.
Published: January 2005

Vapor-pressure measurements on the rare-earth metals were made by the Knudsen effusion technique using a quartz-fiber microbalance over a pressure range of 10—1 to 10—4 mm of Hg. The material used was specially prepared in order to minimize impurity effects. Ytterbium is the most volatile of the rare-earth metals, while lanthanum and cerium are the least volatile.

The data were fitted to a straight line by the least-squares method and the heats of vaporization or sublimation were calculated from the slope of the line. The heats of sublimation at 298°K were then calculated using the best available data for the enthalpies of the condensed and vapor states. For nine of the elements, measured heat content and entropy data for the condensed state as well as calculated free energy functions for the gaseous state were available, permitting a third law calculation of ΔH298°. The second- and third-law methods were generally in good agreement, but a comparison of the present work and previous investigations revealed several differences, amounting to as much as 15 kcal/mole in the case of gadolinium.

A possible explanation for the variations in the room temperature heats of sublimation of the different rare-earth metals, based on the differences in the electronic structures of the gaseous atoms and the number of d electrons present in the condensed phase is presented.
Longitudinal Optical Phonons in CaF2, SrF2, and BaF2
Authors: Richman Isaac
Published: January 2005

Off-normal reflection spectra of thin films of CaF2, SrF2, and BaF2 deposited on a silver substrate have been obtained. They exhibit decreased reflectivity at the long wave limit of the longitudinal optical branch. The values so obtained are in agreement with the predictions by the Lyddane—Sachs—Teller relation. They are also in agreement with vibrational levels obtained from vibronic data for SrF2:Sm2+ and BaF2:Sm2+. The observed longitudinal optical phonons are at 466 cm—1 in CaF2, 366 cm—1 in SrF2, and 319 cm—1 in BaF2. The close agreement between vibronic data and direct observation of these vibrations is considered further evidence that a good model for these vibronic transitions must consider vibrations of a relatively large segment of crystal and not merely nearest neighbors.
Infrared Studies of the Photolysis of HN3 in Inert and Reactive Matrices. The Infrared Spectrum of NH
Authors: Milligan Dolphus E. , Jacox Marilyn E.
Published: January 2005

Infrared and ultraviolet observations have been made on the products of the photolysis of HN3 and DN3 suspended in Ar, N2, and CO matrices at 4°, 14°, and 20°K. Appreciable concentrations of NH (ND) in the ground (3Σ—) state are produced. The vibrational fundamental of NH has been observed directly at 3133±2 cm—1 in Ar and N2 matrices. The observation that H atoms are produced when HN3 is photolyzed in a CO matrix suggests that some of the HN3 molecules undergo photolytic rupture at the H–N bond. Consideration is given to the secondary reactions which occur between NH and itself or HN3. It appears likely that HN=NH and/or HN=N–N=NH may contribute to the observed products of these secondary reactions.
Kinetic Studies of Hydroxyl Radicals in Shock Waves. IV. Recombination Rates in Rich Hydrogen—Oxygen Mixtures
Authors: Schott Garry L. , Bird Paul F.
Published: January 2005

The rate of disappearance of OH following [OH]max in shocked H2–O2–Ar mixtures has been measured by a refined ultraviolet line absorption technique. Thirty-one experiments have been done with mixtures of 4% H2, 1% O2, 95% Ar; 2% H2, 0.5% O2, 97.5% Ar; and 8% H2, 1% O2, 91% Ar at initial pressures between 50 and 200 mm Hg. The approximate rate equation found to describe the OH disappearance is −d[OH]/dt=kapparent[OH]2[M], where [M] is total gas concentration. Assuming that the equilibrium relationship α=[OH]/[H]=K[H2O]/[H2] is maintained, and that the recombination reactions are: H+H+M→ lim k1H2+M,and H+OH+M→ lim k2H2O+M,kapparent may be interpreted as (A/α) (k1+αk2) where A is a factor near unity which incorporates the definitions of the k's as volumetric rate coefficients, the small variation of α and density during the reaction, and the participation of O and O2. (k1+αk2) increased linearly with α between α=0.01 and α=0.1, yielding k1=6±1×108 liter2 mole—2·sec—1 and k2/k1≈10±5. No dependence on temperature was evident. Estimation of the contributions of H2, H, and H2O as third bodies indicates that k1Ar=4±2×108 liter2 mole—2·sec—1 near 1700°K.
Unperturbed Dimension and Translational Friction Constant of Branched Polymers
Authors: Kurata Michio , Fukatsu Masaaki
Published: January 2005

A theory of the conformational properties of random-flight branched molecules is developed for estimating the branching effect on the translational friction constant Ξb as well as on the mean-square statistical radius 〈S2〉b½. Calculations are made for three types of branching—star, normal (or linear), and random types, and for two types of distribution of the branch units—uniform and random types. It is found that the contraction of molecular dimensions produced by branching occurs to the highest degree in the star types of branching and to the lowest degree in the normal type of branching, and that the heterogeneity in the distance between the nearest pair of branch units generally diminishes the degree of the molecular contraction. The applicability of the Flory-type equation, Ξb=η0Pb〈S2〉b½, to the branched molecules is discussed with the intention of searching the experimental method for determination of the number of branch units involved in the various types of branched molecules. Here η0 is the viscosity of solvent and Pb is the proportional factor corresponding to Flory's universal constant in the linear polymers.
ESR Study of X-Irradiated Sodium Thiosulfate Single Crystals
Authors: DeLisle Janice M. , Golding R. M.
Published: January 2005

Three paramagnetic species have been observed in x-ray-irradiated single crystals of sodium thiosulfate. Two of the radicals have been identified as SO2− and SO2+ with principal g values of 2.0070, 2.0047, 2.0095 and 2.0070, 2.0105, 2.0305, respectively. The orientation of the SO2+ radical in the crystal lattice is discussed.
On the Use of the Langevin Equation of Brownian Motion for the Analyses of Cold and Slow Neutron Scattering by Liquid Methane
Authors: Griffing George W.
Published: January 2005

The Langevin equation of Brownian motion is used to analyze the experimental data on the scattering of cold and slow neutrons by liquid methane. Scattering of neutrons by a molecule in the liquid is treated analytically as for a gas except the translational mode of the molecule is assumed to obey the Langevin equation. To obtain agreement with the experimental data using this model, it is necessary to adjust the viscous damping coefficient η appearing in the Langevin equation as the magnitude of the momentum transfer κ in the collision between the neutron and the molecule changes. Plotting the value of η needed to best fit the observed quasielastic peak against the momentum transfer κ resulted in a straight line on a semilogarithm plot. An extrapolation of the straight line to zero momentum transfer gave a value of 1.7×1013 sec−1 for the viscous damping coefficient. This value is in agreement with the experimental value of the diffusion coefficient which is related to the viscous damping coefficient by the Einstein relation. It is pointed out that the analysis is, at least qualitatively, in accord with results on the scattering of neutrons by other liquids. There is evidence, although not conclusive, that the rotational motion is partially hindered.
Decomposition and Oxidation of C2F4 Behind Shock Waves
Authors: Modica Anthony P. , LaGraff John E.
Published: January 2005

Ultraviolet absorption and mass-spectrometric observations of shocked C2F4–Ar gas mixtures have indicated that the C2F4 monomer exists in thermal equilibrium with CF2 radicals and that the initial C2F4 oxidation mechanism involves two steps C2F4→ lim Ar2CF2CF2+O2→CO+2F+O.Dissociation and oxidation rates were determined from uv absorption measurements of CF2 at 2536 Å behind incident shock waves.

The C2F4 dissociation reaction appeared to be second order, 12d[CF2]/dt=kAr[C2F4][Ar], with kAr=7.82×1015T12 exp(−55 690/RT) cc/mole·secover the temperature interval from 1200° to 1800°K at total concentrations between 0.9×10−5 and 1.7×10−5. A least-squares fit to the experimental equilibrium constants for the reaction C2F4=2CF2, using the integrated form of the van't Hoff equation, yielded logKc=−69 432/2.303RT+4.62 (Kc in mole/cc).From the measured heat of reaction, the heat of formation of CF2 at 298°K was calculated to be −39.7±3.0 kcal/mole.

Mixtures of C2F4 and O2 in varying mole ratios were allowed to react at temperatures between 1500° to 2500°K with molar concentrations of reactants ranging from 4×10−8 to 6×10−7 mole/cc. The oxidation reaction was observed to be first order in both CF2 and O2, d[CF2]/dt=−kox[CF2][O2], with kox=2.92×1010T12 exp(−13 280/RT) cc/mole·sec.
Analysis of Carr—Purcell Spin-Echo NMR Experiments on Multiple-Spin Systems. I. The Effect of Homonuclear Coupling
Authors: Allerhand Adam
Published: January 2005

The effect of homonuclear coupling in a molecule on Carr—Purcell spin-echo (CPSE) nuclear magnetic resonance experiments is investigated. A density-matrix approach is used to derive a general equation for the CPSE train of multiple-spin molecules in the liquid state. This general equation predicts a CPSE train modulated with one or more frequencies, whose relative amplitudes are, in general, not equal. Unmodulated contributions may also arise. It is shown that the modulation frequencies and their relative amplitudes are functions not only of the relative chemical shifts and coupling constants, but are strongly dependent on the separation between the 180° pulses, tcp. In addition, the modulation can always be eliminated by making the pulse repetition rate, 1/tcp, large with respect to all the relative chemical shifts and coupling constants. It is also shown that, for weak coupling, it is possible to derive simplified equations by neglecting the nonsecular part of the coupling Hamiltonian, but this approximation is valid only when 1/tcp is of the order of, or smaller than the relative chemical shifts.

Procedures for solving the general equation to obtain closed formulas for the CPSE train of a specific system are discussed. Solutions for spin-½ nuclei are treated in detail. Closed equations are derived for the AB, A2B, and A3B systems, and they are used in some numerical calculations. Simplified weak-coupling formulas are also derived for these systems, and their range of validity is discussed.

A very brief discussion of heteronuclear coupling is presented.
Hyperfine Coupling Constants of 2,2-Bis-p-nitrophenyl−1-picrylhydrazyl
Authors: Chalmers J. S. , Kim Y. W.
Published: January 2005

Polycrystalline samples of 2,2-bis-p-nitrophenyl−1-picrylhydrazine, which are doped with 2,2-bis-p-nitrophenyl−1-picrylhydrazyl (free radical), have been prepared. The EPR absorption of the samples has exhibited seven partially resolved hyperfine lines. The observed hyperfine spectrum has been computer fitted by adjusting the nuclear hyperfine coupling constants of the free radical. The results have indicated that the difference between densities of the unpaired electron at the two nitrogen nuclei of the free-radical molecule is larger in the case of the polycrystalline samples than in the case of liquid-solution samples.
ESR Absorption of Cesium and Rubidium Solutions in Ethylamine
Authors: Bar-Eli Kedma , Tuttle T. R.
Published: January 2005

Electron spin resonance absorption spectra of cesium and rubidium solutions in ethylamine have been observed at temperatures between −29° and +23°C. These spectra are characterized by a sharp single-line resonance near the center of a hyperfine pattern. The lines of a hyperfine pattern vary in amplitude and breadth. The larger amplitude, narrower lines lie near the center of the spectrum. The hyperfine patterns are attributed to 85Rb and 133Cs nuclei interacting with an unpaired electron. The spin density at the 85Rb nucleus varies from 1.05±0.1×1024 cm3 at −25°C to 1.90±0.05×1024 cm3 at 23°C and at the 133Cs nucleus from 2.29±0.03×1024 cm3 at −29°C to 2.80±0.03×1024 cm3 at −10°C. The variations in line breadths are interpreted in terms of the structure of the metal monomer. The difference in g values between the single-line resonance and the hyperfine pattern is attributed to spin—orbit coupling in the monomer and structural implications are discussed. The single-line resonance is assigned to the solvent anion, i.e., the solvated electron.
Electronic Spectrum of (2, 2)Paracyclophane. II
Authors: Ron Arza , Schnepp O.
Published: January 2005

The studies of the absorption and fluorescence spectra of single crystals of (2, 2)paracyclophane in the region 3300–3100 Å reported in a previous paper have been extended. Well-characterized samples with the (hk0) developed crystal plane were used. In absorption two distinct spectra were obtained in the two polarization components. The fluorescence was strongly polarized in one direction (parallel to the fourfold c axis) and represents the mirror image of the equally polarized absorption component. It was concluded that the observations prove conclusively that the differently polarized spectral components represent transitions to two different electronic states, with an energy difference of 369 cm−1. The lowest-energy transition certainly contains the 0–0 line and all available evidence supports the conclusion that also the second transition has allowed character. The only interpretation consistent with all observed features of the spectra is as follows. The two observed states are the gerade dimer states (B2g and B3g in D2h) being the out-of-phase combinations of the B2u and B1u benzene moiety states. The transitions have allowed character due to a torsional distortion of the molecule in the excited state. The interpretation is fully consistent with theoretical energy calculations.
Simple Classical Model for the Scattering of Gas Atoms from a Solid Surface
Authors: Logan R. M. , Stickney R. E.
Published: January 2005

A simple classical model for the scattering of gas atoms from a solid surface is proposed and its characteristics are determined. The principal assumptions are (1) the interaction of a gas atom with a surface atom is represented by an impulsive force of repulsion, (2) the gas—surface intermolecular potential is uniform in the plane of the surface (hence the interaction does not change the tangential velocity of the gas particle), (3) the surface atoms are represented by independent particles confined by square-well potentials, (4) the surface atoms have a Maxwellian velocity distribution. The model incorporates many of the same features as that proposed by Goodman. As a result of these assumptions, the model is simplified to the extent that it contains no adjustable constants.

Results are obtained for the angular distribution of the scattered particles. Significant quantitative results are not expected from such a simple model, but the qualitative behavior of the model does agree surprisingly well with the experimental results. The model correctly predicts the general appearance of the scattering pattern and its dependence on the angle of incidence of the beam and on the temperatures and masses of the gas and surface atoms. We conclude that, contrary to the assumption often made in theoretical studies of gas—surface interactions, the temperature of the surface is a significant parameter when considering the existing experimental data.
On the Quantum-Mechanical Pair-Correlation Function of 4He Gas at Low Temperatures
Authors: Larsen Sigurd Yves , Witte Kathleen , Kilpatrick John E.
Published: January 2005

The density-independent part of the direct- and exchange-correlation functions for 4He, using the de Boer and Michels Lennard-Jones potential, have been calculated at 2°, 1°, 0.5°, and 0.1°K. The necessary wavefunctions were obtained by numerical integration of the Schrödinger equation. The peak of the direct-correlation function is much less than its classical value and occurs at a slightly larger radius. The tail (large r) agrees very well with the form given by the Wigner—Kirkwood expansion. The exchange-correlation function which represents the entire effect of the spin and statistics of the system vanishes very rapidly with increasing temperatures.
Pressure and Entropy for Hard Particles at High Density
Authors: Hoover William G.
Published: January 2005

A hard-particle model is introduced. For this model it is possible to calculate the thermodynamic limit of both the pressure and the entropy at high (solid-phase) densities. The model embodies both the simplicity associated with a nearest-neighbor lattice-gas interaction, and the realism of a continuous configuration space.

The volume of the system is divided into V cells, with particles in nearest-neighbor cells interacting as hard parallel squares (cubes, in the three-dimensional case). When written in terms of the cell occupation numbers the configurational integral for this system bears a superficial resemblance to a lattice-gas partition function. It is possible to calculate the maximum term in the lattice-gas partition function explicitly. This makes it possible to establish tight bounds on the continuum configurational integral; these bounds show that the free-volume form of the pressure and the entropy is exact at high density.

At close packing, where the upper and lower bounds coincide, the absolute entropy is determined. It is shown that the communal entropy vanishes at close packing, and cannot be fully excited for densities greater than half the close-packed density.
Kinetic Theory of Nuclear Spin Relaxation in Gases
Authors: Gordon R. G.
Published: January 2005

A theory of nuclear spin relaxation in linear molecules is developed for dilute gases and mixtures. The main assumptions used are those often employed in the kinetic theory of dilute gases: (1) binary collisions, (2) no correlation between the effects of successive binary collisions, and (3) classical mechanics for the molecular translational and rotational motion. The calculations result in expressions relating the spin relaxation times to the rotational angular momentum transfered by collisions. Using the results, it is possible to calculate the spin relaxation times for any given intermolecular potential which includes angle-dependent terms.
Functional Representation of the Wave Operator
Authors: Hirschfelder Joseph O.
Published: January 2005

Considerable simplification in the algebraic formalism of quantum-mechanical perturbation theory is achieved by representing the wave operator by a function Ψ / (Nψ0). The differential equation for the wave operator is derived and used to generate Rayleigh—Schrödinger perturbation theory. The Löwdin bracketing theorem is derived without the use of formal algebra and discussed in the context of perturbation theory. It is shown that nonlocal potential terms can be introduced into the zeroth-order Hamiltonian H0 so that the wavefunction, accurate through the first order of perturbation, is equal to the exact wavefunction, or the wave operator times the reference function.
Viscosity, Sedimentation, et Cetera, of Ring- and Straight-Chain Polymers in Dilute Solution
Authors: Bloomfield Victor , Zimm B. H.
Published: January 2005

The hydrodynamic properties of straight-chain and ring-chain polymers whose dimensions are expanded over those of similar Gaussian coils have been calculated by a perturbation method based on the normal-coordinate treatment with hydrodynamic interaction. Expansion is characterized by a parameter ε, such that the mean-square length is proportional to N1+ε, N being the number of chain segments. For straight chains the intrinsic viscosity, expressed in terms of the Flory Φ (×10−23), decreases from 2.81 at ε=0 to 0.686 at ε=0.5, while for rings Φ varies from 1.85 to 0.422; the ratio straight:ring increases slowly from 1.5 to 2.0. The sedimentation coefficient of the straight chain increases by a factor of 2.4 over this range of ε, while that of the ring goes up 2.2-fold. The ratio straight: ring rises slowly from 0.85 to 0.91. The results on straight chains agree with those of previous workers, and the straight:ring ratio agrees with several experiments on the sedimentation of straight and ring forms of various DNA's. It is apparent that viscosity should be a much more sensitive measure of ring formation than sedimentation, and that the effect of ring formation is roughly the same regardless of chain expansion (i.e., the same both in Gaussian coils and in a stiff chain such as DNA).
First Differential Ionization Efficiency Curves for Fragment Ions by Electron Impact
Authors: Dorman F. H.
Published: January 2005

Electron-impact dissociations which yield an ion pair have been studied, by examination of first-differential ionization efficiency curves. No evidence has been found for the occurrence of recently postulated reactions RH→R++H− in hydrocarbons.
Microwave Spectrum of Silver Chloride
Authors: Krisher Lawrence C. , Norris Wilfred G.
Published: January 2005

Pure rotational measurements have been made at about 800°C on the four naturally occurring AgCl species. The internuclear distance is re=2.28079±0.00004 Å. Stark-effect measurements give a dipole moment μ=5.70±0.15 D. Quadrupole hyperfine interactions for the 35Cl isotope give a coupling constant eqQ=−37.32±0.20 Mc/sec. An analysis is made of the pure rotational spectra in higher vibrational states. Values of the molecular constants for 107Ag35Cl are: Be=3687.04±0.09 Mc/sec, αe=17.855±0.011 Mc/sec, γe=0.019±0.004 Mc/sec, De=0.003±0.003 Mc/sec. Molecular constants are given for the remaining isotopic combinations of AgCl. The bond type of the gaseous AgCl molecule is discussed.
Far-Infrared Spectra of HCl Trapped in the β-Quinol Clathrate
Authors: Allen S. James
Published: January 2005

To investigate the rotational and translational states of HCl trapped in the β-quinol clathrate, the clathrate dielectric response has been measured in the spectral region between 10 and 100 cm−1, at liquid-helium temperatures. The attenuation coefficient of dilute mixtures of 40μ clathrate powder in paraffin was measured with a slowly modulated lamellar grating interferometer. By making suitable assumptions about the particle geometry, it is possible to extract, by an analysis based on the Hilbert transform, both real and imaginary parts of an effective dielectric constant for the suspended powder. Inherent in the technique are corrections for dielectric mismatch between the powder and paraffin. To help interpret the spectra, clathrates of SO2, HBr, N2, and a mixture of HCl, DCl have also been measured.

At 1.2°K, the HCl clathrate has three salient features: an absorption due to the β-quinol lattice at 66 cm−1, a translational vibration of the HCl dipole near 52 cm−1, and in the vicinity of 20 cm−1 a resonance absorption due to the rotational motion of the trapped dipole. The translational vibration is consistent with cage-wall interactions described by van der Waals forces. Both the intensity of this absorption and the shift of the rotational resonance 3 cm−1 below the gas-phase value of 21 cm−1, at the lowest concentration of HCl can be consistently explained by a coupling between the rotation and translational vibration. At high concentrations of HCl, the rotational resonance increases by nearly 50% and is commensurate with shifts predicted by dipole—dipole interactions between solute molecules.
Heat and Entropy of Hydration of α-NiSO4·6H2O to NiSO4·7H2O. Their Low-Temperature Heat Capacities
Authors: Stout J. W. , Archibald R. C. , Brodale G. E. , Giauque W. F.
Published: January 2005

The heat capacities of α-NiSO4·6H2O and NiSO4·7H2O have been determined over a range 13° to 300°K. These measurements have been combined with available heat-capacity data on these hydrates extending to 1°K. Heats of solution of the two hydrates give α-NiSO4·6H2O+H2O(l)=NiSO4·7H2O , ΔH298.15°K=−1836±25 cal/mole. For the reaction NiSO4·7H2O=α-NiSO4·6H2O+H2O(g) , at 25°C P(equil.)=21.0 torr, ΔF°=2126 cal/mole, ΔH°=12 356 cal/mole and ΔS°=34.31 gibbs/mole. From the heat-capacity data, the known entropy of H2O(g) and the third law of thermodynamics, ΔS°=34.47 gibbs/mole at 25°C, in good agreement. Tables of CP°, S°, (H°–H0°)/T, and (F°–H0°)/T of α-NiSO4·6H2O and NiSO4·7H2O are included.
Sign of JHF in CHFCl2
Authors: Mackor E. L. , MacLean C.
Published: January 2005

If a nuclear spin is relaxed by two relaxation mechanisms with the same correlation time, the NMR lines may have differing relaxation rates. The fluorine nuclear spin in CHFCl2 at low temperature is relaxed by dipole—dipole interaction and by an anisotropy in the chemical shift. The sign of the coupling constant between fluorine and hydrogen (JHF) has been determined from the relaxation pattern. JHF turns out to be positive.
Magnetic Properties of Lattice Imperfections in Alkali Halide Single Crystals
Authors: Adair T. W. , Sharp E. J. , Squire C. F.
Published: January 2005

Using a torque magnetometer, experimental results are reported on some new magnetic properties in high-purity, optical-quality single crystals of lithium fluoride, potassium chloride, and sodium chloride. Since the torque observations are not produced by the gross diamagnetism of these salts, the magnetic centers may be along dislocations because the magnetic susceptibility is observed to possess uniaxial anisotropy. Soft x irradiation increased the observed magnetization. In addition, there is a cooperative interaction among the magnetic centers which gives a remanent magnetization. The temperature dependence of the remanent magnetization is similar to the Bloch spin-wave concept of ferromagnetism. These new magnetic properties are an order of magnitude smaller when measured in crystals of magnesium fluoride and of calcium fluoride.
Partial Wave Theory of H2: Calculations of Σg+ States
Authors: Bhatia A. K. , Temkin A.
Published: January 2005

Calculations of the first four 1Σg+ and first three 3Σg+ states of H2 are carried out in lowest order of the partial wave theory of H2. Solutions are obtained using Hylleraas-type variational functions for the two electrons containing up to 50 terms. Comparison of the singlet potential-energy curves with precision curves, where available, reveals a comparable accuracy to what was obtained in the case of H2+ for the lowest state but not for higher states. The particular relevance of these wavefunctions as target wavefunctions in calculations of electron—molecule scattering is discussed.