bluuebunny/crossref_metadata_2025 huggingface dataset:
Simple Force Multipoles in the Theory of Deformable Surfaces
Authors: Balaban M. M. , Green A. E. , Naghdi P. M.
Published: January 2005

This paper is concerned with a nonlinear theory of simple force multipoles for a deformable surface, embedded in a Euclidean 3-space; the surface is not necessarily elastic. The theory is developed with the use of basic thermodynamical principles, together with invariance conditions under superposed rigid body motions. For simplicity, the basic kinematical ingredients are restricted to be the (ordinary) monopolar velocity of the surface and suitable first- and second-order gradients of the velocity. The theory of an elastic surface and other special cases of the general theory which bear on the foundations of the classical theory of shells are also discussed.
Spinor Fields as Distortions of Space-Time
Authors: Hestenes David
Published: January 2005

Spinor fields are introduced into Riemannian space-time in a new way. This approach admits a simple geometrical interpretation of spinor fields. A linear connection for space-time is derived which describes both gravitational and nongravitational forces. It is consistent with a straightforward generalization of the Dirac equation. This theory also entails a physical interpretation of inertial coordinates. The spin and current vectors of a spinor field are not in general orthogonal. This lack of orthogonality provides an absolute measure of one component of the gravitational field as seen in an inertial system.
Absence of Ordering in Certain Classical Systems
Authors: Mermin N. D.
Published: January 2005

A classical inequality giving lower bounds for fluctuations about ordered states is derived. The inequality, analogous to a quantum result due to Bogoliubov, is established by a purely classical argument which makes explicit the nature of the surface boundary conditions required, a point which is rather obscure in the quantum derivations. As in the quantum case the inequality is useful in excluding certain kinds of phase transitions in one- and two-dimensional systems. This is illustrated for several kinds of classical spin systems.
Recursive Evaluation of Some Atomic Integrals
Authors: Sack R. A. , Roothaan C. C. J. , Kołos W.
Published: January 2005

A simple recursion scheme is set up for the higher derivatives of functions of the form f(α,β)(α+β)−1 and f(α,β,γ)(α+β+γ)−1 and applied to the rapid calculation of the Calais-Löwdin two-particle atomic integrals.
Exact Distributions of the Reduced-Width Amplitude
Authors: Ullah Nazakat
Published: January 2005

The invariance hypothesis is used to derive the various multivariate distributions of the reduced-width amplitude. Simple expressions are given for the multi-level and multi-channel distributions valid for all dimensions of the random orthogonal matrix.
Wigner Method in Quantum Statistical Mechanics
Authors: İmre Kaya , Özizmir Ercüment , Rosenbaum Marcos , Zweifel P. F.
Published: January 2005

The Wigner method of transforming quantum-mechanical operators into their phase-space analogs is reviewed with applications to scattering theory, as well as to descriptions of the equilibrium and dynamical states of many-particle systems. Inclusion of exchange effects is discussed.
Derivation of the Principle of Compensation of Dangerous Diagrams
Authors: Kobe Donald H.
Published: January 2005

The principle of compensation of dangerous diagrams (PCDD) postulated by Bogoliubov to determine the coefficients in the canonical transformation to quasi-particles in superconducting systems is derived from four different criteria (1) the expected number of quasi-particles in the true ground state is a minimum, (2) the one-particle density matrix and the two-particle amplitude determined from the BCS ground state are equated to the true ones, (3) the expectation value of an arbitrary operator is simplified by diagonalizing its quadratic part, and (4) the starting point for the dressing of the quasi-particle is chosen in the most convenient way. The condition obtained for the PCDD is then expressed in terms of quasi-particle Green's functions. The ladder diagrams are eliminated by examining an integral equation for the Green's function describing the creation of two quasi-particles from the vacuum. Finally, the condition obtained here for the PCDD is compared with the condition obtained previously.
Asymptotic Theory of Electromagnetic and Acoustic Diffraction by Smooth Convex Surfaces of Variable Curvature
Authors: Hong Soonsung
Published: January 2005

A general method is presented for obtaining successive terms in short wavelength asymptotic expansions of the diffracted field produced by plane acoustic and electromagnetic waves incident on an arbitrary smooth convex surface. By introducing the geodesic coordinate system on arbitrary surfaces of non-constant curvature, both scalar and vector integral equations governing the surface fields are solved directly. The expressions for leading and second-order terms in the asymptotic expansion of the diffracted fields are obtained explicitly and the differences between acoustic and electromagnetic creeping waves are shown.
Logarithmic Density Behavior of a Nonequilibrium Boltzmann Gas
Authors: Goldman Robert , Frieman Edward A.
Published: January 2005

We consider the temporal evolution of the BBGKY hierarchy in the Boltzmann approximation for spatially homogeneous nonequilibrium situations, in the absence of initial correlations. For times of the order of the mean free time or greater, the single particle function f1 is found to be of the form f1=f10+εf11+ε2|lnε|f̃11+O(ε2)with ε=nr03 (n is the density, r0 the range of binary interaction) and f10, f11, and f̃11 of order unity. For times less than the mean free time, with t in units of the duration of a binary interaction, f1 is of the form f1=f10+εf11+ε2(lnt)f̃11+O(ε2). In both cases the same formally higher-order binary correlation functions are neglected.
Scattering of Electromagnetic Waves in Molecular Crystals
Authors: Mavroyannis C.
Published: January 2005

The scattering of electromagnetic waves in molecular crystals has been investigated by considering the polarization operator of the system that results from the Dyson equation in the first approximation. The Green's function for the photon field is then calculated and an expression for the frequency- and wavevector-dependent index of refraction of optical waves is developed including nonlinear effects. The excitation spectrum has been studied by evaluating the spectral intensity for the photon field. Expressions are derived for the electronic contribution to the spectral width and energy shift for physical processes: (i) resonance Raman scattering and (ii) resonances occurring when either two excitons are created or one exciton is created and the other is absorbed by a single incident photon. A theory for the dielectric permeability of the crystal is developed and a relation between the dielectric permeability, the polarization operator, and the photon Green's function is established. Contributions to the binding energy of the crystal resulting from the dispersion and scattering of the polarization waves at finite temperatures have been calculated and expressed in terms of the excitation energies and the index of refraction of the medium.
Empty Space-Times Algebraically Special on a Given World Line or Hypersurface
Authors: Collinson C. D.
Published: January 2005

The null tetrad formalism of Newman and Penrose is used to investigate empty space-times which are algebraically special on a given world line. It is found that, when the world line is timelike, the space-time admits a congruence which is geodesic and shear-free on the world line. A similar result is obtained for those empty space-times which are algebraically special on a given space like hypersurface.
Klein-Gordon Equation for Spinors
Authors: Marx Egon
Published: January 2005

Spinors obeying the Dirac equation also obey the Klein-Gordon equation, but the converse is not true. In this paper we make a systematic study of four-component spinors obeying the Klein-Gordon equation, with special regard for the additional solutions. The starting point is the Lagrangian density L=ψ̄,μγμγνψ,ν−m2ψ̄ψ, and we first develop from it the theory of a classical spinor field. We then proceed to the canonical quantization of this field and are confronted by some anticommutators of creation and annihilation operators equal to −1, and the subsequent need for an indefinite metric in Hilbert space. Quantum electrodynamics can be reformulated, and in spite of a modified fermion propagator, gradient coupling, and vertices with two photon lines, the amplitude for Compton scattering to order e2 is the usual one. Special problems arising for massless fermions are indicated, and we note that the four-fermion point interaction is now renormalizable. Some interesting variations of strong interactions also become possible.
Matrix Elements for Irreducible Representations of the U(6, 6) Algebra in Harmonic Function Space
Authors: Maduemezia Awele
Published: January 2005

In this paper we realize the algebra of the group U(6, 6) as an algebra of differential operators acting in the Hilbert space of functions defined on a 23-dimensional pseudosphere. We then calculate the matrix elements of the generators of this algebra between certain harmonic function states.
Finiteness of the Number of Positive-α Landau Surfaces in Bounded Portions of the Physical Region
Authors: Stapp Henry P.
Published: January 2005

It is shown that if the spectrum of physical particle rest masses contains neither accumulation points nor the zero point, then the number of different positive-α Landau surfaces that enter any bounded portion of the physical region of any multiple-particle scattering process is finite. This implies that if the physical-region singularities of scattering functions are confined to the closure of the set of points lying on positive-α Landau surfaces, then the scattering functions are analytic at almost all points of the physical region. The proof is made by proving an equivalent property of systems of classical point particles scattering via point interactions.
Solutions to the Neutron Transport Equation for a Critical Slab by Perturbation Theory
Authors: Hendry W. L.
Published: January 2005

A perturbation-theoretic method is developed by which solutions to the monoenergetic neutron transport equation for an unreflected critical slab can be obtained in the case of anisotropic scattering and/or nonconstant cross sections. The method rests upon the use of a generalized Green's function to solve the perturbation equations. The Green's function is derived by an eigenfunction expansion technique and as the solution to two coupled singular integral equations, and the results are compared numerically.
Gauge Field of a Point Charge
Authors: Loos Hendricus G.
Published: January 2005

The problem and treatment of integration ambiguities in the conventionally defined Yang-Mills charges is demonstrated explicitly, using a non-Abelian solution of the Yang-Mills equations for a point charge. The internal holonomy group H for this solution is noncompact and nonsemisimple, and the solution is not expected to have a direct physical meaning. However, it provides a convenient example showing important and quite unexpected features of gauge theories of the Yang-Mills type, before quantization. It is found that the number of unambiguously definable and comparable charges is less than the dimension of H and less than the rank of H as well. If a gauge group G is present in the conventional manner, i.e., H⊆G, this number of charges is less than the rank of the gauge group. Other interesting features of the solution found are: discreteness of certain components of the gauge field, as a result of regularity conditions together with the condition that the Yang-Mills charge density vanishes outside a sphere of finite radius, and a harmonic oscillation of the other gauge components, while the observable charges are steady. Higher-order charges are all found to be zero. No action principle is used and no a priori particle fields are introduced. Use is made of the differential-geometric properties of gauge fields.
On the Validity of the Reduced Potential Curve (RPC) Method
Authors: Jenč F.
Published: January 2005

Reduced Rydberg—Klein—Rees—Vanderslice potential curves were approximated by the reduced Hulburt—Hirschfelder function for a series of diatomic molecules to obtain a qualitative test on the behavior of the ground-state reduced potential curves. The results seem to confirm unequivocally that the regularities previously observed in studying reduced potential curves are of general validity. Possible applications of the reduced-potential-curve method are briefly outlined.
Further Study of the Reaction of Hot Hydrogen with Methane
Authors: Seewald David , Wolfgang Richard
Published: January 2005

The reaction of hot hydrogen atoms with methane (hot hydrogen in the form of recoil tritium produced by nuclear reaction) has been studied in further detail. Earlier work had been incomplete because in the presence of moderator, small amounts of HT, the abstraction product, were produced by what were recognized as spurious processes. An exhaustive investigation of possible limitations of the recoil method indicated that if helium is used as a moderator, not all the recoil tritium reaches chemical energies as neutral ground-state atoms. This finding is in accordance with the adiabatic principle. The use of neon or argon as moderators eliminated this difficulty and permitted estimation of the true yield of HT and the total reactivity integral for the reaction. The consequent complete analysis of the system results in several new significant findings: (1) Values of the reactivity integral IHT measured using a helium moderator are probably too high and require downward revision (other products are apparently not subject to this effect); (2) The most stringent test of the kinetic theory of hot reactions to date discloses no deviation despite the approximate nature of the assumptions underlying this theory; (3) The relative energy loss on collision of hot T with Ne, Ar, and He seems to accord with the soft-sphere predictions of Estrup; (4) Contrary to earlier belief, the abstraction product HT is formed at higher average energies than the displacement product CH3T; (5) The pressure dependence of the double displacement product CH2T·, suggests a generalization regarding the mechanisms by which such products are formed.
Kinetics of Hydrogen Halides in Shock Waves. II. A New Measurement of the Hydrogen Dissociation Rate
Authors: Jacobs T. A. , Giedt R. R. , Cohen Norman
Published: January 2005

Decomposition rates for H2, diluted in Ar, were studied behind incident shock waves over the temperature range 2900° to 4700°K. HCl and the infrared emission from this molecule were used in a manner to trace the course of decomposition of the H2. In terms of recombination rate constants, we found (cc, moles, sec units) k−3=1018T−1, k−4=2.5k−3, and k−5=20k−3, where the subscripts 3, 4, and 5 refer respectively to Ar, H2, and H as third bodies.
On the Accurate Wavefunction of H2+
Authors: Patel Jashbhai
Published: January 2005

For hydrogen molecular ion, it is shown that the James function is an approximation to the more general Guillemin and Zener wavefunction. From 1sσ and 2pσ, Guillemin and Zener orbitals, a correlated wavefunction of H2 is constructed. It contains all the terms which occur in the James and Coolidge wavefunction for H2 molecule. The proposed function for H2 is dealt with in parts so as to study the contributions from configuration interaction and the correlation factor to the total binding energy of the H2 molecule.
Vibrational Spectra and Rotational Isomerism in Acrylyl (Propenoyl) Chloride and Related α,β-Unsaturated Acyl Halides
Authors: Katon J. E. , Feairheller W. R.
Published: January 2005

The complete vibrational spectra of acrylyl (propenoyl) chloride have been recorded and analyzed. This compound exists as a mixture of two discrete rotational isomers in the vapor and liquid states, their energy differing by about 0.6 kcal/mole in the vapor state. The spectra of the two isomers have been tentatively assigned and it has been found that all of the skeletal stretching modes are conformation dependent. Three other α,β-unsaturated acyl chlorides have been studied and the results are compared with those of acrylyl chloride.
Microwave Spectrum of trans-2,3-Epoxybutane
Authors: Emptage Michael R.
Published: January 2005

The microwave spectrum of[Complex chemical formula]was studied from 8 to 40 Gc/sec. The rotational constants and the dipole moment of the main isotopic species in the ground torsional state were found to be A = 12 237.38 Mc/sec, B = 3 423.02 Mc/sec, C = 3 072.52 Mc/sec (κ=−0.9235122) and μ=2.03±0.04 D, respectively. An approximate structure was obtained by varying the two least-well-known structural parameters to fit the observed moments of inertia, and a barrier to internal rotation of 2444±150 cal/mole was obtained from the splittings of the lines in the ground torsional state. These results are discussed in terms of steric effects in this molecule and in the cis isomer studied by Sage.
Vibrational Study of the Chain Conformation of the Liquid n-Paraffins and Molten Polyethylene
Authors: Snyder R. G.
Published: January 2005

A vibrational and attendant conformational analysis of the liquid n-paraffins and molten polyethylene is presented. For the purposes of the analysis a valence force field was derived which is applicable to both planar and nonplanar chains. The force field was evaluated from observed frequencies of trans (T) and gauche (G) n-C4H10; TT and GT n-C5H12; TTT, GTT, and TGT n-C6H14; and (T)∞ polyethylene, all of whose infrared spectra were assigned in detail. Infrared spectra of the liquid-n-paraffins n-C4H10 through n-C17H36 were measured at room temperature and n-C4H10 through n-C12H26 also at a temperature just above their melting point. Frequencies and normal coordinates were calculated for the extended forms and for forms having one gauche bond of n-C4H10 through n-C8H18. These quantities were also calculated for the conformations of n-C5H12 through n-C7H16 having two gauche bonds and for the nonplanar but regular conformations (TG)∞ and (G)∞ of polyethylene. Some bands attributable to forms of n-C5H12 and n-C6H14 having two gauche bonds were found. In the case of n-C5H12 the energy difference between the GT and TT states was found to be nearly the same as that between the GG and GT states. Bands in the region 1400–1300 cm−1 were found to be characteristic of specific conformations involving sequences of five or fewer methylenes, such as —GTTG— (1338 cm−1), —GTG (1368 and 1308 cm−1), —GG— (1352 cm−1), and terminal —TG groups (1344 cm−1). All these bands together with two broader ones centered near 1270 and 1080 cm−1 owe their intensity to the wagging of methylenes adjoining gauche bonds. An interpretation of the general features of the C–C-stretching, methylene-rocking, and methylene-scissoring regions is given. Bands associated with molecules or chains having trans sequences involving at least four methylene groups are found. In the region 1300–1150 cm−1 there are chain-length-dependent band progressions resembling those observed for the crystalline n-paraffins. These indicate the presence of molecules with gauche bonds, but these gauche bonds are few in number and are located near the ends of the chains. It is shown that for certain kinds of vibrations, particularly totally symmetric C–C stretching and ∠CCC bending, there is very little change in frequency in going from a fully extended chain to one having one or even two or more gauche bonds. Hence, it is very difficult in the case of the longer n-paraffins to distinguish spectroscopically between fully extended and almost fully extended conformations.
Far-Ultraviolet Spectrum of Ethylene and Ethylene-d4
Authors: McDiarmid Ruth , Charney Elliot
Published: January 2005

The ultraviolet absorptions of the V←N transitions of C2H4 and C2D4 have been reinvestigated. The strongest observed bands are found to fit the empirical expressions: C2H4, ν̄ (cm−1)=46 697+807ν; C2D4, ν̄ (cm−1)=46 948+547ν. From the ratio 807/547 of the corresponding term differences of the two isotopic species, geometric considerations and group theoretical arguments, the frequencies 807 (C2H4) and 547 (C2D4) cm−1 are concluded to be the torsional frequencies in the V state. In the V state the two CH2 groups are consequently deduced to be skewed. Another frequency, 150 cm−1 in C2D4 has been observed but not interpreted.

An analysis of the torsional progression shows the torsional potential of the V state to be parabolic. If a parabolic potential is also assumed for the ground state, the experimental and theoretical energy-level diagrams are shown to be in reasonable agreement.
Vibrational Relaxation of Diatomic Molecules in Gases and Liquids
Authors: Berne Bruce J. , Jortner Joshua , Gordon Roy
Published: January 2005

When a diatomic molecule in a vibrationally excited state is placed in a host fluid it can lose a vibrational quantum by either radiative or nonradiative processes. In this article the rate of nonradiative vibrational transitions is expressed in terms of the rotational-kinetic-energy autocorrelation function. An interpolative approximation is made for the autocorrelation function and the vibrational relaxation time is computed. Good agreement with measurements of gaseous systems is obtained.
Photolysis of Ethylene at 1048–1067 Å. Reactions of C2H4+ and Fragmentation of the Superexcited Ethylene Molecule
Authors: Gorden R. , Ausloos P.
Published: January 2005

C2H4–NO, C2H4–O2 and C2H4–(CH3)2NH–O2 mixtures have been irradiated with an argon resonance lamp emitting only the 1048- and 1067-Å lines. The ionization efficiency ratios: ηC2D4/ηNO, ηC2H4/ηNO, ηC2D4/ηC2H4 were determined to be 0.30±0.003, 0.27±0.003 and 1.12, respectively. trans-2-Butene and cis-2-butene are major products when NO (I.P.=9.25 eV) or (CH3)2NH (I.P.=8.24 eV) are added to C2H4. Radiation of pure C2H4 or of C2H4–O2 mixtures yielded only minor traces of 2-C4H8. In accord with earlier radiolysis studies we ascribe the formation of 2-C4H8 to the charge-transfer process C4H8++NO (or (CH3)2NH)→C4H8+NO+ (or (CH3)2NH+),where C4H8+ may possess some excess internal energy carried over from the exothermic condensation reaction (C2H4*)++C2H4→(C4H8*)+. For a constant C2H4–NO mixture M(C4H8)/N increases drastically with an increase of the pressure of C2H4 from 0.1 to 6 torr. Also, in pure C2H4, M(CH3)/N which is close to unity at 0.5 torr is seen to diminish to 0.2 when the pressure is raised to 29.8 torr. These effects are largely ascribed to a competition between decomposition and stabilization of the [C4H8*]+ product ion. A rate constant of 107 sec−1 is derived for the unimolecular decomposition of (C4H8*)+ assuming that stabilization occurs at every collision with C2H4. It is shown that Ne is about 100 times less efficient than C2H4 in stabilizing (C4H8*)+. The superexcited C2H4* dissociates as follows, C2H4*→C2H2+H2 and C2H4*→C2H2+2H. Isotopic analysis of the hydrogen formed in the photoionization of CH2CD2 shows that the relative probabilities for the elimination of H2, HD, and D2 from CH2CD2* are the same for the superexcited molecule as for the excited molecule formed by absorption of 8.4- to 10-eV photons.
Molecular Theory of Counterion Conductivity and Self-Diffusion in Polyelectrolyte Solutions
Authors: Manning Gerald S.
Published: January 2005

A previous theory of counterion self-diffusion in a polyelectrolyte solution is extended to describe the counterion flow in the presence of an applied electric field. A term proportional to the velocity of the polyion is obtained in a natural way, with no assumptions concerning ``bound'' counterions. The previous expression for the counterion self-diffusion coefficient is regained as a special case. The significance of the formal agreement with the ion binding model is discussed at some length.
Mössbauer Resonance Studies of Ferrous Ions in Ice
Authors: Nozik Arthur J. , Kaplan Morton
Published: January 2005

Mössbauer resonance experiments have been carried out over a wide temperature range on frozen aqueous solutions of ferrous chloride and ferrous sulfate. Well-resolved spectra were obtained which show the two-line absorption pattern characteristic of a nuclear quadrupole hyperfine interaction in 57Fe. Measurements of quadrupole splitting, resonance linewidths, and anisotropic intensities were made as a function of temperature and for samples with different temperature histories. Upon quenching from the liquid state to −196°C, hexaquo ferrous ions are trapped in the ice lattice and induce the formation of cubic ice, rather than the stable hexagonal form. Warming of the quenched sample to −80°C causes a nonreversible transformation to hexagonal ice and associated pronounced changes in the Mössbauer spectrum. Analysis of the experimental data, and comparison with results obtained for the crystal FeSiF6·6H2O which contains hexaquo ferrous ions, has permitted a detailed description of the symmetry properties of ferrous ion in ice. In hexagonal ice, the ferrous ion is located at the center of an axially ``squashed'' octahedron of water molecules, the ground state wavefunction being the orbital singlet | xy 〉. The temperature dependence of the quadrupole splitting in hexagonal ice is consistent with a crystal-field axial splitting δ∼700 cm−1. In cubic ice, the symmetry contains a rhombohedral field component which can be fitted with splitting parameters Δ1∼450 cm−1 and Δ2∼950 cm−1. A model is suggested for the structure of ferrous ion in cubic and hexagonal ice. The model satisfies the necessary symmetry requirements and is consistent with the observed anisotropic Mössbauer intensities in hexagonal ice and isotropic intensities in cubic ice.

Several interesting phase changes in the ice—salt systems have been observed. In ferrous chloride frozen solutions, the sharp disappearance of the Mössbauer effect above −40°C is associated with eutectic formation. Also, by careful temperature treatment, the hydrate FeCl2·6H2O has been produced (it is unstable above −10°C) and its Mössbauer spectrum in ice was obtained. In the ferrous sulfate experiments, complex precipitation phenomena were observed and are not well understood.
Excluded-Volume Effect of Polystyrene Solutions
Authors: Kuwahara N. , Okazawa T. , Kaneko M.
Published: January 2005

Osmotic pressures of moderately concentrated solutions of polystyrene in toluene are examined with the object of evaluating the free energy parameter B which describes the long-range interactions between segments. The B value evaluated through an analysis of the data is used to estimate the excluded-volume parameter, z=0.330B(6〈s2〉0/M)−3/2M1/2, for polystyrene solutions in which solvent is toluene. The behavior of αη3=[η]/[η]0 over a wide range of z(0<z<6) is compared to the theoretical predictions. It is found that αη3 is not a linear function of z. The dependence of αη3 on z seems to be described better by the recent Fixman relation than the Stockmayer—Fixman relation.
Rotation—Translation-Coupling Effect in Noble-Gas Crystals Containing Molecular Impurities
Authors: Friedmann H. , Kimel S.
Published: January 2005

A generalized perturbation theory has been developed, valid in the case where the perturbation can no longer be considered as small relative to the separation between successive unperturbed energy levels. This is applied to the problem of coupling between the rotational and translational motions of a molecule trapped in a spherically symmetric cell. A representation which is diagonal with respect to the total angular momentum and parity operators has been used, taking advantage of the rotation—inversion symmetry presented by the cell model. It has been found possible to obtain closed expressions for the perturbed energy levels valid in the case of near resonance between rotational and translational frequencies. General expressions for the intensity of rotation—translation transitions have also been derived. A quantitative discussion is given of the effect of finite linewidth on the position of maxima of ``hot'' lines. The theory is applied to the interpretation of the spectra of hydrogen halides trapped in noble-gas crystals. The anisotropy of the crystal field is included and leads to an estimate of 0.5×10−42 esu for the hexadecapole moment of HCl. The limitations of the cell-model treatment due to coupling between molecular rotation and lattice vibrations are discussed.
The Mechanism of Processes Initiated by Excited Atoms II. Photosensitization by Excited Mercury and Cadmium
Authors: Laidler Keith J.
Published: January 2005

The treatment of the preceding paper is extended to the reactions of excited mercury and cadmium in their triplet and singlet states. It is shown that with the hydrogen molecule quenching of a physical nature is prohibited for the triplet atoms by the necessity for conservation of spin angular momentum, and that dissociation must take place with the initial formation of the metal hydrides. In the reactions of Hg 3P0, Cd 3P1, and Cd 3P0 these are also final products, but with Hg 3P1 and the singlet excited atoms, dissociation of the hydride into the metal and a hydrogen atom takes place at once. Quenching to the metastable state is found to be usually inefficient. The atoms react with saturated hydrocarbons by splitting off a hydrogen atom, but the unsaturated ones usually interact with the initial formation of an excited molecule which when activated by singlet atoms have vibrational energy only, but which with triplet atoms are excited to triplet electronic states. The subsequent reactions of the excited olefines are discussed with reference to the experimental material.
Statistical Mechanics of Nearest Neighbor Systems II. General Theory and Application to Two-Dimensional Ferromagnets
Authors: Montroll Elliott W.
Published: January 2005

This is a continuation of an effort to reduce to the solution of a characteristic value problem the rigorous calculation of thermodynamic properties of systems in which the intermolecular forces are sufficiently short ranged so that practically the entire potential energy of the system results from interactions between nearest neighbors. The partition function of such a system can be expressed in terms of the largest characteristic value of a linear operator equation and finally as the ratio of partition functions of systems with relatively few particles whose potential energy functions differ somewhat from those in the original system. A method of evaluating grand partition functions and one of introducing interactions between more distant neighbors are discussed. The general theory is applied to the calculation of magnetization, internal energy, and specific heat of two-dimensional ferromagnets on the basis of the Ising model. There seems to exist a λ-point phase transition in the change from ferromagnetic to nonferromagnetic states.
The Long Wave-Length Spectra of Saturated Carboxylic Acids, Esters, and Salts
Authors: McMurry Henry L.
Published: January 2005

Electron configurations for the low excited states of the COOR radical (R = alkyl group or H atom) and the COO− ion are given. Their longest wave-length absorptions are interpreted in terms of transitions to their lowest excited states. In the COOR radical this absorption comes at λ2100 and is weak. It is interpreted as due to a transition like that producing the weak region at λ2900 in the spectrum of the >C = O group in aldehydes and ketones. The COO− ion appears to show an analogous weak absorption but this is largely covered by a much stronger region. The latter is interpreted as possibly due to a transition in which a non-bonding oxygen electron is excited to an antibonding molecular orbital of the unsaturation or x type. This transition should be strong in the ion, probably is weak in the acids and esters, and is entirely absent in the aldehydes and ketones. Possible interpretations of the λ1700 absorption in acids and esters are briefly discussed.
The Near Infra-Red Absorption Spectrum of Methyl Iodide
Authors: Lagemann R. T. , Nielsen H. H.
Published: January 2005

The infra-red absorption spectrum of methyl iodide vapor has been reexamined under improved conditions at 3.3, 6.9, 8, and 11.3 microns with the result that each region reveals new detail. Near 3.36 microns some regular structure of mean separation 4.8 cm−1 overlaps the parallel band. The Q branches of the 6.9 mu band show a definite fine structure. The Q branch of the 8 mu band converges toward lower frequencies. In the 11.3 mu band the lines composing the Q branches converge toward higher frequencies.
Remarks on the Absorption Spectra of Phenylalanine and Tyrosine in Connection with the Absorption in Toluene and Paracresol
Authors: Sponer H.
Published: January 2005

The absorption spectra of phenylalanine and tyrosine in the near ultraviolet are compared with those of toluene and paracresol and an interpretation of the individual bands is proposed.
Premelting Anomalies of Some Long Chain Normal Paraffin Hydrocarbons
Authors: Van Hook Andrew , Silver L.
Published: January 2005

The coefficients of thermal expansion of tetradecane, hexadecane, octadecane, and tetracosane have been measured continuously for considerable temperature ranges on both sides of the melting points. The increase of these coefficients in the neighborhood of the melting points is suggestive of an order-disorder mechanism for the transitions. Although the effect is observed to be larger on the solid side of the transition than on the liquid, the latter is interpreted as more significant, since the presence of impurities and the open, mosaic structure of the solid contribute largely to the increase. Likely impurities are not of the Raoult type, and do not cause appreciable variations.
The Photolysis of Azomethane in the Presence of Hydrogen
Authors: Taylor H. Austin , Flowers Ralph G.
Published: January 2005

The photolysis of azomethane in presence of hydrogen in the temperature range 20–200°C has been shown to yield ethane at a rate which is independent of the hydrogen. At low temperatures methane production is decreased by the presence of hydrogen but the rate increases with temperature faster than from azomethane alone. A mechanism involving CH5 has been suggested which accounts qualitatively for the observations. Essentially the same mechanism is shown to account for the decomposition of mercury dimethyl, roughly quantitatively. Strong evidence is offered that the reaction producing methane from methyl radicals and hydrogen is not CH3+H2→CH4+H. This is supported by the absence of hydrogen atoms during the azomethane photolysis studied.
Systematics in the Vibrational Spectra of the Halogen Derivatives of Methane
Authors: Wu Ta-You
Published: January 2005

On considerations of the symmetry and the approximate nature of the vibrations, the observed infra-red and Raman frequencies of the halogen derivatives of methane are classified and their transitions in passing from one molecule to another in the series CH4–CH3X–CH2XY–CH2X2–CHX2Y–CHX3–CX4 are given. A potential function of the valence force type containing six constants is suggested for CH2X2 and the frequency equations given.
Dispersion and Absorption in Dielectrics II. Direct Current Characteristics
Authors: Cole Kenneth S. , Cole Robert H.
Published: January 2005

In the first paper of this series [J. Chem. Phys. 9, 341 (1941)], it was shown that the complex dielectric constant, ε*, of many liquid and solid dielectrics is given by a single very general formula ε*=ε∞+(ε0−ε∞)/[1+(iωτ0)1−α].In this equation ε0 and ε∞ are the ``static'' and ``infinite frequency'' dielectric constants, ω = 2π times the frequency, τ0 is a generalized relaxation time and α is a constant, 0 < α < 1. The transient current as a function of the time, t, after application of a unit constant potential difference has been calculated from this expression in series form. For times much less than τ0, the time dependence is of the form (t/τ0)−α, and for times much greater than τ0, it is of the form (t/τ0)−(2—α). The transition between these extremes occurs for the range in which t is comparable with τ0. The total absorption charge, which is the integral of the exact expression, is always finite. Although many transient data for dielectrics are of the predicted form, none have been taken over a sufficiently wide range of times adequately to test the result, nor is it yet possible to determine either the relaxation time or the static dielectric constant from available data.
The Raman Spectra of the Sugars in the Solid State and in Solution I. The Raman Spectra of α- and β-d-Glucose
Authors: Spedding Frank H. , Stamm Robert F.
Published: January 2005

This paper presents data on the Raman spectra of anhydrous crystalline α- and β-d-glucose and of equilibrium aqueous d-glucose solutions containing 5, 15, and 50 moles of water per mole of glucose. Ultraviolet excitation (Hg λ2537A) was employed. A technique for photographing Raman spectra of crystalline organic powders and solutions with very poor scattering power is described. It consisted essentially of the use of complementary filters of aqueous succinic acid (saturated, 4 mm thick) and a mercury vapor absorption cell (10 cm long, 150°C). Thirty-six lines are reported for α-d-glucose, 32 for the β, and numerous new bands including measurements of maxima and shoulders are given for equilibrium solutions. Only the obvious experimental differences are discussed as the detailed discussion will be given in a later paper of this series.
Intramolecular Energy Transfer The Fluorescence of Complexes of Europium
Authors: Weissman S. I.
Published: January 2005

The characteristic line fluorescence of trivalent europium is excited in certain organoeuropium compounds by irradiation with light absorbed only by the organic part of the compound. The efficiency of excitation varies greatly with the nature of the compound, temperature, and solvent. Under optimum conditions, i.e., solution of a covalent compound at liquid-air temperature, almost unit efficiency has been obtained. The decay time of the fluorescence is independent of quenching; quenching prevents excitation of the europium ion. There seems to be a steady gradation of efficiency of transfer from covalent to ionic compounds.
The Viscosity of Certain ``Ferric Oxide'' Hydrosols
Authors: Greenstein Leon M. , Thomas Arthur W.
Published: January 2005

(1) The changes produced in the viscosities of ``ferric oxide'' hydrosols by aging, heating, and the addition of a number of electrolytes and a non-electrolyte have been studied, in some instances together with the attendant changes in the pH values and specific conductances of the systems. (2) Agreement with Poiseuille's law has been demonstrated for typical cationic and anionic hydrosols. (3) The decrease in viscosity of hydrosols on aging and heating is accompanied by an increase in specific conductance. This conductance increase in the case of cationic sols is due almost entirely to the increase in hydrogen ion activity which occurs during the reaction. This is not so for anionic hydrosols, where the conductance increase is explained by the conversion of coordinated citrato groups to citrate ions. (4) The addition of salts and acids to these hydrosols first results in a viscosity decrease, followed by an increase in viscosity at higher electrolyte concentrations. (5) The viscosity increase occurs at lower salt concentrations for those salts which are potent precipitants than for those which are weak. For cationic hydrosols, salts of both weakly and strongly coordinating anions have the same effect in depressing the viscosity; in the case of anionic hydrosols, potassium citrate is less effective in this respect than potassium sulfate and nitrate. (6) The effects of acids in decreasing the viscosity of a sol, either cationic or anionic, was found to be the same for all acids used, when compared at the same pH values. The more powerful precipitants caused the subsequent viscosity increase to occur at lower electrolyte concentrations. (7) Acids are less effective than salts in decreasing the viscosities of cationic hydrosols. (8) Large concentrations of acetone produced a decrease in the relative viscosity of cationic hydrosols; this effect is, however, negligible in comparison with the magnitude of the changes caused by electrolytes. (9) The viscosity decrease produced by aging, heating, and the addition of electrolytes may be attributed in each case partly to the increase in electrolyte concentration of the system. (10) The viscosity resulting from these reactions is considered to be dependent also upon the micellar charge: the lower the charge, the lower the viscosity. (11) The viscosity increase at higher electrolyte concentrations may be ascribed to agglomeration of dispersed particles. (12) A mechanism based upon a Donnan equilibrium between the dispersed particle and the dispersion medium has been proposed to account for the effects observed.
The Decomposition of Methane in Glow Discharge at Liquid-Air Temperature
Authors: Yeddanapalli Lourdu M.
Published: January 2005

The decomposition of methane in the glow discharge at liquid-air temperature has been investigated under different experimental conditions. Contrary to the earlier conclusion of Brewer and Kueck that the reaction products are only hydrogen and ethylene, they are invariably found to be hydrogen, a polymer of composition (CH2)n, and ethane, ethylene, and acetylene, the last three resulting presumably from the mutual interaction of the primary active species CH4+, CH3+, CH2+, CH+ formed from methane. In the absence of hydrogen, ethane predominates; in its presence, ethylene and acetylene proportions increase due, it is suggested, to the dehydrogenating action of atomic hydrogen. In the negative glow, the rate of methane decomposition is directly proportional to the current, and the electronic efficiency, i.e., the number of methane molecules decomposed per electronic charge, is ∼10 both for alternating and direct current. In the positive column, the rate is directly proportional to current only if pressure and field strength are constant; with constant current, the rate increases with pressure and field strength but in a manner which does not lend itself at present to a quantitative expression; the electronic efficiency is ∼0.2 for alternating and ∼0.6 for direct current. The results lead to the conclusion that a 60-cycle alternating current discharge approximates closely to that with direct current. These may be explained by considerations of the electrical energies involved. No marked difference in reaction rate or products is observed by substituting iron for aluminum electrodes, or by variation in current density. A certain chemical activity might be attributed to the Faraday dark space.
Note on Statistical Forces
Authors: Goldstein Louis
Published: January 2005

It is shown that a two-particle force acting in coordinate space represents with a very good approximation the apparent coupling in space between two spinless atoms of ideal symmetrical or antisymmetrical assemblies at all temperatures higher than, or equal to, their transition temperature.
The Radial Distribution Function in Liquids
Authors: Kirkwood John G. , Boggs Elizabeth Monroe
Published: January 2005

In accordance with the general methods of an earlier paper (reference 1) an integral equation is evolved for the radial distribution function for pairs in a liquid, and an approximate solution is effected for a system of ``hard spheres.'' The form of the function depends on a single parameter λ which can be related to certain observed physical properties of the liquid and to the diameter of closest approach. The theoretical function has been calculated for a value of λ appropriate to liquid argon at 90°K, and compared to experimental radial distribution functions derived from x-ray scattering data.
Valence and Central Forces in Bent Symmetrical XY2 Molecules
Authors: Shaffer W. H. , Newton R. R.
Published: January 2005

Appropriate generalized coordinates and potential functions are set up for studying the zero- and first-order vibration problem of the best symmetrical XY2 molecular model under the assumption of valence and central forces. The force constants in the quadratic and cubic parts of the potential function of the water vapor molecule are evaluated for these two types of forces by using the data of Darling and Dennison.
Variation of Reaction Mechanism with Surface Conditions in the Reduction of Silver Salts by Hydroxylamine
Authors: James T. H.
Published: January 2005

Silver bromide oxidizes hydroxylamine at pH 10.2–10.8 to nitrogen and water. Under comparable conditions, silver thiocyanate yields a mixture of nitrogen and nitrous oxide as the gaseous products. By varying the surface conditions of the thiocyanate, the composition of the reaction product may be varied over a wide range. Small additions of bromide or iodide greatly decrease the nitrous oxide yield. With initial partial coverage of the precipitate surface by gelatin, the nitrous oxide yield increases to a maximum. Further gelatin additions progressively decrease the yield. Aging a fresh precipitate increases the nitrous oxide yield. The results are explained by the effects of adsorption upon the relative rates of two competing reaction mechanisms.
The Electrostatic Influence of Substituents on Reaction Rates III. Solvent Effect
Authors: Westheimer F. H. , Jones W. A. , Lad Robert A.
Published: January 2005

The magnitude of the electrostatic effect of substituents on reaction velocity depends on the solvent in which the reaction is carried out. In order to investigate the influence of solvent, the first and second saponification constants of diethyl malonate and diethyl adipate have been measured, both in water and in 80-percent alcohol, in solutions of varying ionic strength. The saponification constants have been extrapolated to infinite dilution. The ratio of the first to the second velocity constant at infinite dilution in any one solvent is a measure of the effect of a charged substituent on the rate of saponification. The results obtained in water are compared with those for 80-percent alcohol, and it has been shown that they are in good qualitative agreement and in fair quantitative agreement with the predictions of the Kirkwood-Westheimer theory.
Vibration-Rotation Energies of Planar ZXY2 Molecules Part I. The Vibrational Modes and Frequencies
Authors: Silver Samuel , Ebers Earle S.
Published: January 2005

The normal modes and frequencies of planar ZXY2 molecules are investigated using the most general potential function consistent with the symmetry. The equilibrium configuration has the symmetry of the group C2v and consequently the frequencies are all non-degenerate. By developing a set of generalized coordinates having the same symmetry properties as the normal coordinates, the secular determinant is factored directly into one third-order determinant, one linear factor, and one second-order determinant.
The Near Ultraviolet Absorption Spectrum of Monodeuterobenzene
Authors: Beck C. A. , Sponer H.
Published: January 2005

The analysis of the ultraviolet absorption spectrum of monodeuterobenzene has been given. The spectrum is, as in benzene, a forbidden transition which is made allowed by the 603 vibration corresponding to the 606 ε+g benzene vibration. The 0,0 band is calculated to be 38,124, and it occurs with extreme weakness.
Statistical Thermodynamics of High-Polymer Solutions I. Theory for Dilute Solutions
Authors: Alfrey Turner , Doty Paul
Published: January 2005

Previous theoretical treatments of the thermodynamics of high-polymer solutions have assumed that the entropy of mixing is independent of the magnitude of the heat of mixing. The present treatment considers energy interactions on a molecular scale and includes these in the configurational partition function. This leads to the derivation of expressions for the heat of mixing and the entropy of mixing which reflect the effect of solvent-solute interaction. One result of particular interest is an explicit expression for the temperature dependence of osmotic pressure.