bluuebunny/crossref_metadata_2025 huggingface dataset:
The Host Crystal Luminescence of Zinc Sulfide Phosphors
Authors: Bube Richard H.
Published: January 2005

Effects produced on the host crystal luminescence of zinc sulfide phosphors by increasing the preparation temperature without any additives in the preparation, are compared with effects produced by adding halide in the preparation at a fixed temperature.

Both methods of altering the luminescence properties of the phosphors produce qualitatively the same results on (1) intensification of the host crystal emission for excitation by 3650A ultraviolet and by 6 kv cathode rays, and for phosphors of both cubic and hexagonal crystal structure, (2) glow curves after excitation by 3650A ultraviolet, (3) diffuse reflectivity for light in the wavelength range from 3400 to 4200A, and (4) the variation of the emission intensity during excitation as a function of operating temperature.

Data on the variations, with preparation procedure, of the emission intensity during excitation and of the glow intensity during thermostimulation show that a possible correlation exists between shallow traps and isolated omission defects, and between deep traps and pairs of omission defects; and that a correlation is suggested between luminescence centers and particular perturbed (SZn4) groups in the crystal.

At least a part of the intensification caused by adding halide in the preparation must be attributed to a classical ``flux'' action.
Disproportionation in Deuterated Ammonia
Authors: Stedman D. F.
Published: January 2005

Infrared absorption spectra indicate that in NH3 containing equal molar proportions of D and H, the proportions of the various molecular species appear to depart very seriously from what would be expected if all configurations are intrinsically equally probable.
A Molecular Orbital Theory of Reactivity in Aromatic Hydrocarbons
Authors: Fukui Kenichi , Yonezawa Teijiro , Shingu Haruo
Published: January 2005

In the search for a quantitative correlation between reactivity and electronic configuration of aromatic hydrocarbons, the electron density, at each carbon atom, of the highest occupied π-orbital in the ground state of the molecule is calculated by means of the LCAO method. Comparing the result of such a calculation on fifteen condensed aromatic hydrocarbons with their chemical reactivities, we find that the position at which the electron density is largest is most readily attacked by electrophilic or oxidizing reagents.

It is, therefore, concluded that distinct from other π-electrons the pair of π-electrons occupying the highest orbital, which is referred to as frontier electrons, plays a decisive role in chemical activation of these hydrocarbon molecules. The theoretical significance of this discrimination of the frontier electrons in relation to the chemical activation is discussed.
The Microwave Spectra and Molecular Structures of Methyl Bromoacetylene and Methyl Iodoacetylene
Authors: Sheridan John , Gordy Walter
Published: January 2005

Pure rotation spectra of H3CCCBr79, H3CCCBr81, and H3CCCI have been measured. For H3CCCBr79, B0=1561.11 Mc/sec, IB=537.379×10−40 g cm2, and DJK=+11.4 kc/sec; for H3CCCBr81, B0=1550.42 Mc/sec, IB=541.082×10−40 g cm2, and DJK=+11.1 kc/sec; for H3CCCI, B0=1259.02 Mc/sec, IB=666.316×10−40 g cm2, and DJK=+7.2 kc/sec. The nuclear quadrupole coupling factors (eqQ) for the halogens are: for Br79, +647 Mc/sec; for Br81, +539 Mc/sec; for I127, −2230 Mc/sec. On the basis of reasonable assumptions for dC≡C, dCH, and ∠HCH, it is shown that the C–C and C–Br bonds in H3CCCBr are shortened to extents comparable with those found in methyl acetylene and cyanogen bromide, respectively, while the IB of methyl iodoacetylene is consistent with a similar shortening of both C–C and C–I. This is supported by the force constants for the stretching of the C–Br and C–I bonds. Bond lengths and nuclear quadrupole couplings are discussed in relation to the structures of these molecules.
Theoretical Considerations Concerning Hammett's Equation. II. Calculation of σ-Values for Toluene and Naphthalene
Authors: Jaffé H. H.
Published: January 2005

The electron distributions in toluene and naphthalene are calculated by the LCAO MO method. The Coulomb integrals of the methyl carbon atom in toluene and the central atoms in naphthalene are assigned small increments which are justified by qualitative reasoning. These increments are treated as empirical parameters and adjusted to give the best correlation between electron densities and Hammett's σ-values. The parameters so derived are shown to obey the expected qualitative relations and lead to a good correlation of electron densities and σ-values.
Note on the Flow of Vapor Between Liquid Surfaces
Authors: Plesset Milton S.
Published: January 2005

The mass flow of vapor from a liquid surface at temperature T0 to another surface of the same liquid at temperature T1(T1<T0) may be very readily determined in the case of one-dimensional flow from the conservation relations for mass and momentum. These relations involve both the coefficient of evaporation and the coefficient of condensation. It is therefore possible to determine the condensation coefficient which has heretofore not been accessible to measurement. A new method for determining the evaporation coefficient is also made available. The temperature of the vapor between the liquid surfaces may also be found when viscous effects in the vapor flow are neglected.
Directed Valence in P4 and As4
Authors: Mashima Mitsuo
Published: January 2005

It has been reported that three best spd hybrid bond orbitals may be constructed at mutual angles of 73°9′ and 133°37′, but these bond orbitals have not been adapted to actual molecules. We can obtain trigonal pyramid bond orbitals which have mutual angles of 73°9′ and strength 3. When an angle between the directions of three equivalent bond orbitals is introduced as a parameter to these bond functions, variation of strength of these bond orbitals with the angle may be illustrated. These hybrid bond orbitals may be adapted to P4 and As4. It is reported that P4 and As4 molecules have bond angle 60°, the four atoms lying at the tetrahedron corners and the bonds along the tetrahedron edges. Hultgren has applied pd hybrid bond orbitals to such a configuration. Assuming that the s orbital is used in hybridization, we can obtain stronger bond orbitals than that by pd hybridization. Such spd trigonal pyramid bond orbitals have strength 2.970 (only slightly less than that of the best spd hybrid bond orbital) at bond angle 60°. It seems to be more probable that spd hybrid orbitals are used in the bond formation in P4 and As4 molecules; the unshared pair occupies the fourth hybrid orbital (containing all of the residual s parts) which has 76.5 percent s character at bond angle 60°.
The Exchange of Water between Co(NH3)5H2O+++ and Solvent
Authors: Rutenberg Aaron C. , Taube Henry
Published: January 2005

The rate of exchange of water between Co(NH3)5H2O+++ and solvent has been measured by a method involving isotopic assay of the bound water. The half-time for the exchange is independent of salt concentration and of acidity over a range of these variables and is 24.5 hr at 27°. The half-time is increased by SO4=, indicating that complex ion formation competes with the exchange process and thus supporting an SN1 mechanism as a reaction path. The equilibrium quotient [Co(NH3)5H2O18+++](H2O)/(Co(NH3)5H2O+++)×(H2O18) was measured as 1.019±0.001.
On the Determination of Rotational Line Half-Widths of Diatomic Molecules
Authors: Penner S. S. , Tsien H. S.
Published: January 2005

A simple closed-form expression is obtained for the fractional intensity of radiation absorbed by vibration-rotation bands with collision-broadened spectral lines. The resulting expressions greatly reduced the labor involved in obtaining apparent rotational half-widths from experimental measurements.
Absolute Quantum Efficiencies of Luminescence of Organic Molecules in Solid Solution
Authors: Gilmore Earl H. , Gibson George E. , McClure Donald S.
Published: January 2005

Absolute quantum yield measurements of fluorescence and phosphorescence have been made for a number of organic molecules dissolved in a transparent solid solution (E.P.A.) at 77°K. The quantum efficiencies range from nearly zero for bromobenzene to 0.6 for benzophenone. The measurements are believed to be accurate to about 10 percent. The nonradiative processes, which account for the quanta not re-emitted, are discussed. If the radiationless processes all originate in the triplet state, the triplet state lifetimes measured in solid solution can be corrected to give the natural lifetime of the triplet (phosphorescent) state. Since one cannot tell a priori that this assumption is justified, other experiments are necessary. If the singlet-triplet absorption strength is known, one can tell whether this correction should be applied or not, and infer the origin of the radiationless transition. Finally, a comparison of quantum yields in solid solution with quantum yields in other phases suggests that the mechanism of radiationless transitions, in the absence of concentration quenching and specific solvent and quencher action, is intramolecular potential surface crossing, followed by the transfer of excess vibrational energy to the solvent.
Infrared and Raman Spectra of Fluorinated Ethanes. IV. The Series CH3–CH3, CH3–CH2F, CH3–CHF2, and CH3–CF3
Authors: Smith D. C. , Saunders R. A. , Nielsen J. Rud , Ferguson E. E.
Published: January 2005

The infrared spectra of ethyl fluoride and 1,1-difluoroethane vapors have been obtained in the egion from 2 to 38μ, and the spectra of the liquids from 2 to 22μ, with the aid of LiF, NaCl, KBr, and KRS-5 prisms. The Raman spectra of both compounds were studied in the liquid phase with a three-prism glass spectrograph of linear dispersion 15A/mm at 4358A. Depolarization ratios were determined for the stronger bands. The Raman spectrum of 1,1-difluoroethane was also obtained for the gaseous phase.

A complete assignment of fundamental frequencies is proposed for each molecule and used in a detailed interpretation of the spectra and for the calculation of thermodynamic functions over the temperature range 298–600°K and at the boiling point.
Rotation-Vibration Spectra of Diatomic and Simple Polyatomic Molecules with Long Absorbing Paths VIII. The Spectra of Trideuteromethylacetylene and Diacetylene from 1.2μ to 0.7μ
Authors: Jones A. Vallance
Published: January 2005

The absorption spectra of CD3C2H and diacetylene have been investigated under high resolution (21-ft grating) in the photographic infrared with absorbing paths of up to 27-meter atmospheres obtained by multiple reflections. For CD3C2H and 3ν1 and 4ν1 bands were resolved and analyzed yielding B0(CD3C2H)=0.24566±0.00020 cm−1,and, therefore, for the moment of inertia about an axis perpendicular to the symmetry axis IB(0)=113.909×10−40 g cm2.This result, taken in conjunction with the work of Herzberg, Patat, and Verleger on CH3C2H, confirms that the C–C bond length is abnormally short in this molecule. The value obtained was rC–C(CD3C2H)=1.467±0.003A.For diacetylene the rotational structure of four parallel bands was analyzed yielding B0=0.14641±0.00013 cm−1,leading to I(0)=191.13×10−40 g cm2.The structure of the bands shows diacetylene to be a symmetrical linear molecule. By assuming values for the C–H and C≡C bond lengths the length of the C–C single bond was calculated to be rC–C(C4H2)=1.375±0.01A.
Gaseous Detonations. IV. The Acetylene-Oxygen Mixtures
Authors: Kistiakowsky G. B. , Knight Herbert T. , Malin Murray E.
Published: January 2005

Detonation velocities were accurately measured in acetylene-oxygen mixtures ranging in composition from 7 to 90 percent acetylene at 1 atmos total pressure. The velocities rise very sharply with concentration to 50 percent acetylene, then drop equally sharply to about 70 percent and from then on rise slightly to 90 percent. The thermodynamic calculations of velocities, in which no adjustable parameters were used, are in perfect agreement with experimental data in the range of 25 to 50 percent acetylene. The velocity at 7 percent, near the detonability limit, is distinctly higher than the calculated value. The calculated velocities from 50 to 90 percent acetylene lie on a smooth curve, showing no break near 70 percent acetylene as do the experimental data. They are higher than the experimental velocities, except at 85 to 90 percent acetylene, where the two curves join again. The disagreement in the intermediate composition range persists when the velocities are recalculated assuming a low heat of sublimation of carbon. A hypothesis is advanced that no solid carbon is formed in detonation waves of mixtures containing up to 70 percent acetylene, because of delays in the nucleation process. The velocities calculated with the assumptions of gaseous equilibria and of the formation of supersaturated carbon vapor, are in acceptable agreement with observations.
Chemical Kinetics of Atomic Bromine from Nuclear Isomeric Transition
Authors: Hamill William H. , Young Jay A.
Published: January 2005

Chemical evidence indicates that the nuclear isomeric transition of Br80 is completely converted. Although isomeric transition always produces C–Br bond rupture in CH3Br(g) it often fails to rupture HBr(g). Other results are consistent with the interpretation that daughter Br80 particles, following bond rupture, usually become free, thermal atoms. Their kinetic behavior with C2H4–HBr mixtures corresponds to the analogous Br79(n, γ)Br80 kinetics (R. R. Williams and W. H. Hamill, J. Chem. Phys. 18, 783 (1950)). Using daughter Br80 it is shown that bromine addition at the C=C double bond does not involve the Br3 complex. The HBr82–Br2 exchange was found to be complete in two minutes.
Polymer Formation in Hydrocarbon Flames
Authors: Thomas N.
Published: January 2005

A theory is developed to account for certain experimental phenomena occurring in hydrocarbon flames. It postulates the formation of highly unsaturated chain-polymers and their subsequent rapid breakdown to active fragments and oxidation of these. The theory is applied to a number of examples of experimental data on hydrocarbon flames. A mathematical discussion of the breakdown of chain-polymers by self-oscillation is given, using a classical model, and the relation between the theory and the experimental data is discussed with reference to earlier work on unimolecular decomposition.
Free Radicals by Mass Spectrometry. I. The Measurement of Methyl Radical Concentrations
Authors: Lossing F. P. , Tickner A. W.
Published: January 2005

A method has been developed for measuring the partial pressure of methyl radicals in thermally decomposing gases, using a modified mass spectrometer. The sensitivity of the instrument to methyl radicals has been determined by decomposing known quantities of mercury dimethyl and di-t-butyl peroxide in a stream of carrier gas and measuring the amounts of the stable products and the net height of the mass 15 peak after correction for contributions from these stable products. Assuming a 100 percent carbon balance, the sensitivity of the instrument to methyl radicals was found to be 0.47±0.07 of the sensitivity to methane under the conditions used. With the present instrument this means that an ion current of 3×10−14 ampere at mass 15 (a peak 1 cm in height) is given by a partial pressure of methyl of 0.02 micron Hg above the leak in the reactor. The rate constants for the decomposition of di-t-butyl peroxide have been measured with this instrument. Combining the values obtained with values from the literature yields a value of E=38 kcal/mole and a frequency factor of 7×1015.

The rate of decomposition of mercury dimethyl was found to be dependent on the pressure of carrier gas in the reactor in the range from 5 to 20 mm. An estimate of the collision efficiency for the recombination of methyl radicals has been made using the partial pressures of methyl radicals measured by the method presented. At 850°C this value of the collision efficiency is 2–3×10−2.
The Spatial Correlation of Electrons in Molecules
Authors: Lennard-Jones J. E.
Published: January 2005

The wave functions of molecules in their ground states can be expressed to a good approximation as single determinants made up of terms orthogonal to each other. The probability distribution for such systems can then also be expressed as a determinant. By integrating this quantity over all the spatial and spin coordinates except those of two electrons, a function is obtained which gives in effect the probability of finding a pair of electrons in assigned places with assigned spins. The properties of this function, called for short the correlation function, are examined in some particular cases. It is shown that the electrons of an inert gas atom, like neon, tend to dispose themselves so that those of the same spin subtend tetrahedral angles at the nucleus. The six outer electrons of the nitrogen molecule and acetylene tend to the same approximation to arrange themselves so that those of the same spin are in three planes through the nuclear axis inclined at 120° to each other. Similarly the eight outer electrons of the same spin in carbon dioxide tend to be correlated with each other in such a way that there are four between the carbon and the oxygen nuclei and four at the extremities of the molecule, there being two on each oxygen atom like ``lone electrons.'' In general the ``bonds'' of a molecule, when interpreted in terms of molecular orbitals, may be regarded as providing the appropriate correlation of electrons of the same spin.
A Study of Iodide-Iodine Solutions with the emf Centrifuge
Authors: MacInnes D. A. , Dayhoff Margaret Oakley
Published: January 2005

The potentials, observed with a galvanic cell with two iodide-iodine electrodes, at two different radii in a centrifugal field, have been studied with solutions of potassium and sodium iodides, to which were added varying concentrations of iodine. Using a short extrapolation the transference numbers of sodium iodide have been obtained. The earlier results using potassium iodide have been confirmed. These results, when interpreted with the aid of conductance measurements, indicated the presence of the ionic complex I3−. A small deviation from the theory has been found with the results for sodium iodide-iodine solutions. The emf centrifuge used in our earlier work has been simplified, and a galvanic cell has been utilized which avoids the collection of suspended particles on the electrodes.
Radial Distribution Functions and the Equation of State of Fluids Composed of Molecules Interacting According to the Lennard-Jones Potential
Authors: Kirkwood John G. , Lewinson Victor A. , Alder Berni J.
Published: January 2005

The integral equation for the radial distribution function of a fluid composed of spherical molecules interacting according to a modified Lennard-Jones potential has been integrated in the Kirkwood approximation and in the Born-Green approximation over a wide range of temperature and density. The distribution functions so obtained have been used to calculate the equation of state and the thermodynamic functions of the fluid. The calculated thermodynamic functions are compared with the experimental values for liquid argon.
A Mechanical Theory of Spinning Detonation
Authors: Fay James A.
Published: January 2005

A review of published experimental data and theoretical discussions of spinning detonation reveals that there does not exist a consistent explanation of all the characteristics of such a phenomenon, particularly the dependence of spinning frequency upon tube diameter. In view of this, it is proposed to treat the problem principally from a hydrodynamic viewpoint by considering a possible periodic fluid motion with a characteristic frequency.

It is found that the calculated natural frequencies of vibration of the gaseous products behind a detonation wave agree closely with the measured frequencies of spinning detonation previously published in the literature. An analysis of such vibrations in the light of experimental evidence indicates that the vibratory motion is principally transverse. Of the various possible modes of vibration, the one which is observed depends upon the mixture composition and the tube size.

The observed existence of pressure waves in the wake of a spinning detonation wave is probably due to nonuniform combustion at the detonation front. It is shown how the initiation or cessation of combustion in a plane wave gives rise to compression or expansion waves respectively, and how a nonplanar disturbance excites a transverse vibration of characteristic frequency.

It is proposed that the uneven combustion of the spinning detonation wave is sustained by the heating and cooling effects of the vibratory pressure waves, which are themselves generated by such irregular combustion; i.e., spinning detonation is a self-excited vibratory phenomenon. Its appearance may thus be-attributed to the susceptibility of the reaction rate to the heating or cooling effects of pressure waves.
The Dielectric Properties of Compressed Fluoromethane
Authors: David H. G. , Hamann S. D. , Pearse J. F.
Published: January 2005

The dielectric constant, dielectric loss, and density of compressed fluoromethane have been measured at 50°C and 75°C in the pressure range 20 to 160 atmospheres. The ratio (ε−1)/d(ε+2) shows a large and regular decrease as the density increases. The theories of Debye, Onsager, and Kirkwood have been applied to the results. Evidence of the restriction of molecular rotation at high densities is adduced.
Proton Transfers in Solution
Authors: Nisonoff Alfred , Kuhn Lester P. , Gurney Ronald W.
Published: January 2005

By a spectrophotometric method the acid-base equilibrium between bromcresol green and triethanolamine was measured over the range of temperature from −6°C to +50°C in the three solvents—methanol, ethanol, and n-butanol. In each solvent the equilibrium constant was found to vary rapidly with temperature; and in methanol the value of logK was found to change sign near 0°C. This behavior is very different from the well-known results for weak acids in aqueous solution, and in the theoretical part of the paper a unified theory is presented to cover all types of proton transfer. The work required to transfer a proton consists of two parts, a part sensitive to the environment and a part insensitive to the environment; the behavior of the equilibrium constant depends on whether the two parts are of the same sign or of opposite sign. Families of curves are drawn to show the various possible types of behavior.
Application of Eller's Optical Machine to the Determination of the Molecular Structure of Gases by Electron Diffraction
Authors: Bru L. , Rodriguez M. Pérez , Cubero M.
Published: January 2005

We present in this paper a new application of the Eller's Optical Machine which allows one to reduce extraordinarily the time of calculations required in the trial and error method. We made the application to the chloride monoxide molecule.
High Concentration Limit of Unimolecular Reaction Kinetics
Authors: Johnston Harold S.
Published: January 2005

A general sum-over-states form of the Lindemann theory of unimolecular reactions is analyzed with respect to properties in the high concentration region, and results are compared with similar deductions found in the low concentration region. In a general form the theory can set a limit on the low concentration rate constant from data taken in the high concentration region alone, and it can set a limit on the high concentration rate constant from data taken in the low concentration region alone. If there are data at both the low and high concentration regions, one can compute two dimensionless parameters which are useful in interpreting kinetic data. In particular, these parameters may be used to select the number of oscillators and their frequency in the Rice-Ramsperger-Kassel form of the theory. These methods are applied to nitrogen pentoxide and nitrous oxide.
Structure of the Methyl Halides
Authors: Miller S. L. , Aamodt L. C. , Dousmanis G. , Townes C. H. , Kraitchman J.
Published: January 2005

Microwave spectroscopic measurements on the partially deuterated forms of CH3Cl, CH3Br, and CH3I allow a determination of the structural parameters which is less subject to zero-point vibration errors than other methods. In addition, examination of all measured isotopic species reveals that the C—D distance is shorter than C–H by 0.009A, and the D—C—D angle greater than that for H–C–H by about 12 minutes. Best values of structural parameters for the species containing the light isotope of hydrogen only are C–Cl distance 1.781, C–Br 1.939, C–I 2.139, C–H 1.11 (same for all halides), H–C–H angle 110°31′ for CH3Cl, 111°14′ for CH3Br, and 111°25′ for CH3I. Deuteration not only gives a change in the C–H bond but also a well-correlated change in the quadrupole coupling constant of the halogen.
The Gaussian Approximation for the Probability Density of a Molecule in a Cell
Authors: Careri Giorgio
Published: January 2005

Kirkwood's integral equation of the free volume theory of liquids has been used to test the Gaussian approximation for the probability density F(r) of a molecule in a cell. The approximation has been found to be good, even up to the critical point.
The Diffraction of X-Rays by Liquid Alloys of Sodium and Potassium
Authors: Gingrich N. S. , Henderson R. E.
Published: January 2005

Monochromatic x-ray diffraction patterns were taken of liquid alloys of sodium and potassium of seven different compositions at 115°C. Contrary to previous results, the present work does not show in a plot of position of main peak vs composition an inflection which had been taken as evidence for the existence of Na2K molecules in the liquid. Fourier analyses made for five of the alloys gave distribution curves which prove that there are no compact molecules in these liquid alloys, though they do not rule out the possibility that there may be weakly associated groups of atoms.
An Analysis of the Pressure Dependence of the Dielectric Constant of Polar Liquids
Authors: Jacobs I. S. , Lawson A. W.
Published: January 2005

The Onsager and Kirkwood theories of polar liquids have been used to analyze the available experimental data on the pressure dependence of the dielectric constant. It is found necessary in most cases to assume an appreciable decrease in the dipole moment arising from intramolecular distortion which may be large enough in some cases to more than compensate for the increase in effective moment caused by intermolecular compression. Quantitative estimates of these two factors are given, and their influence on binding energy and compressibility is discussed.
Self-Diffusion in Solid Sodium. I
Authors: Nachtrieb Norman H. , Catalano Edward , Weil John A.
Published: January 2005

Measurements are reported for the self-diffusion of solid sodium over the temperature range, 0°—95°C. The data fit the empirical equation D=.242 exp(−10,450/RT) with an uncertainty of ±300 cal mole−1 in the heat of activation. The entropy of activation calculated from the temperature coefficient of the elastic modulus is in agreement with the value based upon the vacancy mechanism.
Electrolytic Properties of Aqueous Solutions of Polyacrylic Acid and Sodium Hydroxide. III. The Rate of Sodium Ion Exchange between Polyacrylate and Free Sodium Ions
Authors: Wall Frederick T. , Grieger Philip F. , Huizenga John R. , Doremus Robert H.
Published: January 2005

The exchange of free sodium ions with sodium ions bound to polyacrylate ion has been investigated by an electrolytic transference method. On the assumption that there is a single exchange process, rate constants have been computed and the theory has been found to provide a moderately good representation of the data. A much better correlation is obtained, however, if it is assumed that there are two exchange processes, one very rapid and the other very slow. Presumably the sodium ions that exchange rapidly belong to the polyacrylate ion atmosphere while those that exchange slowly are located within the coiled polymer ion. The distribution of sodium ions between these two groups has been computed.
The Lowest Triplet Levels of Aromatic Hydrocarbons
Authors: Reid C.
Published: January 2005

New data for anthracene and naphthacene suggest that the lowest triplet levels of polyacenes are of species 3Lb. This makes the 39,000 cm−1 singlet band of benzene of symmetry B2u as was originally proposed and not B1u as was later suggested.
The Statistical Mechanical Theory of Irreversible Condensation. I
Authors: Reiss Howard
Published: January 2005

A theory of nucleation, based on statistical mechanics, is presented. The problem reduces to the computation of the multiple occupation, by molecules, of cells, this being accomplished through the evaluation of the configuration integral for a supersaturated assembly. The new theory does not consider the first fragments of the stable phase formed to be spherical liquid drops. In no place (not even at the nucleus) is it necessary to to consider explicitly phase equilibrium between an embryo and the mother phase. The manifold difficulties connected with this point (in view of the small dimensions of typical nuclei) are therefore obviated. Furthermore, it is possible to define an embryo unambiguously, and in such a manner that its energetic properties can, in principle, be computed. This is not possible in the classical theory.

Certain limitations on the application of Einstein fluctuation theory to supersaturated systems are demonstrated.
Some Statistical Mechanical Models of Elastic Polyelectrolytes and Proteins
Authors: Hill Terrell L.
Published: January 2005

Three statistical mechanical models are developed for use in connection with the problem of muscle action. In addition, the models should apply to certain other systems, for example, polyelectrolyte fibers or gels, fibrous proteins in general, and ion exchange resins.

The first model is a statistical mechanical version of the ``autone'' model of Varga, Szent-Gyorgyi, Gergely, and Laki, but we extend the theory to include the effect of an adsorbed substance (e.g., ATP) on the length of the elastic element.

The second model is a charged rubber-like cylindrical fiber. The charges on the molecular chains of the network may be permanent or may result from the adsorption of ions from solution (e.g., hydrogen ions, or ATP). The approximate free energy of the system is computed by combining the Flory-Rehner swelling theory, the Fowler-Langmuir adsorption model, and an electrostatic free energy based on a ``smeared'' uniform charge density inside the fiber (electrolyte is also present), as suggested by the work of Hermans and Overbeeck. If the radius of the cylinder is large compared to the radius of the Debye-Hückel ionic atmosphere, it is not necessary to linearize the Boltzmann factor in the Poisson-Boltzmann equation. From the free energy of the system one obtains the interconnected pressure-volume, length-tension and adsorption isotherm relations. Important special cases are isotropic swelling (zero tension) with the gel under pressure or not, and the elasticity of the fiber (with adsorption) under zero pressure. When the fiber is constrained to a constant radius, it is possible to get a phase change in the length-tension curve (see below).

The third model is an equilibrium statistical theory of the well-known α—β transformation in fibrous proteins (such as keratin and myosin). Adsorption of ions from solution and electrostatic effects can be included here as well as in the preceding model, but the discussion is concerned primarily with an analysis of the elasticity of a sheet of polypeptide chains with α- and β-units statistically scrambled, taking into account as a nearest-neighbor problem in statistical mechanics (using the quasi-chemical method) lateral β—β hydrogen bonds and vertical α—α hydrogen bonds. From the theory it would appear that critical phenomena, phase changes (for example, a considerable increase in length at constant tension, representing a phase change from primarily vertical α—α crystallization to primarily lateral β—β crystallization) and hysteresis are to be expected. These phenomena are observed experimentally, though modified in most cases by superimposed non equilibrium effects. It is pointed out that a fiber operating (on stretching and retraction) between the two ``ends'' of a phase change would be particularly suitable in the muscle problem, because of the sensitivity of the length of the fiber at constant tension to small changes in environment (e.g., pH).

Although a few illustrative examples are given, further applications are reserved for a later paper.
The Absolute Quantum Yields of the Fluorescence of Chlorophyll Solutions
Authors: Forster Leslie S. , Livingston Robert
Published: January 2005

An integrating sphere has been adapted to the measurement of the quantum yield of the fluorescence of solutions of pigments. The intensities of the fluorescence and of the absorbed light were determined separately with a thermopile.

Chlorophylls a and b dissolved in various solvents have been studied with this apparatus over a range of concentrations, and the measured yields corrected for autoabsorption. The yield for chlorophyll a is 0.25 and is in general independent of solvent and excitation wavelength. The yield for chlorophyll b is 0.11 for ether solutions and 0.06 for methanol solutions. The absolute fluorescent yields of solutions of fluorescein, eosine, magdala red, and rubrene were also measured. These results are in reasonable agreement with the published values of the yields for the same compounds.
Dipoles on a Lattice : the Spherical Model
Authors: Lax Melvin
Published: January 2005

The statistical treatment of a lattice of classical dipoles, electric or magnetic, has been intractable because of the ``strong'' condition that all dipoles have a fixed length. The spherical model consists in replacing the above strong condition by the weaker condition that the sum of the squares of the dipole vectors have the correct value, thus permitting some, but not much, fluctuation from the true situation.

The previous work of Berlin and Thomsen using the spherical model and nearest neighbor interactions is generalized to include a mixture of long and short range interactions. The evaluation of the partition sum in the presence of long-range forces requires care because some of the eigenvalues depend on specimen shape. A formula has been derived for the susceptibility, however, in which the shape dependence is explicitly shown to cancel. In fact, it is proven that in the spherical model a permanent dipole lattice is equivalent to an induced dipole lattice with a certain effective polarizability. Expansion of this polarizability in inverse powers of the temperature shows precise agreement to terms of order (1/T)3 with an exact evaluation of the corresponding expansion coefficients.

All qualitative results are in agreement with those of Berlin and Thomsen. One- and two-dimensional lattices show no transition. A simple cubic lattice (the case they treat) shows an antiferroelectric transition bounded by a critical field curve E=Ec[1—(T/Tc)]½.

The effective field and its application to an elementary quantum mechanical treatment of the ferromagnetic problem are described.
The Excluded Volume of Polymer Chains
Authors: Hermans J. J. , Klamkin M. S. , Ullman Robert
Published: January 2005

The ``random flight'' distribution function for the relative positions of two segments of a linear polymer chain is based on the assumption that the space occupied by a single polymer segment is relatively small and may be neglected. In this paper, the space requirements of a real polymer chain are taken into account. A generalized Fokker-Planck equation is formulated, and the distribution function, the average square distance, and the average inverse distance between two chain segments are calculated.
Kinetics of OH Radicals from Flame Emission Spectra V. A Study of the Acetylene-Oxygen Flame
Authors: Shuler K. E. , Broida H. P.
Published: January 2005

The inner cone of the acetylene-oxygen flame burning lean (1:5), stoichiometric (2:5), and rich (4:5) at atmospheric pressure has been studied spectroscopically with the object of gaining some information about the elementary processes occurring in this flame. The rotational, vibrational, and electronic distributions of OH(2Σ+) have been determined for each fuel mixture. The analysis of the data showed a rotational Maxwell-Boltzmann distribution with a rotational ``temperature'' several hundred degrees higher than the adiabatic flame temperature. The vibrational distribution of OH(2Σ+) was distinctly nonequilibrium with an excess population in the level v′=3 analogous to that observed for the hydrogen-oxygen flame. This is attributed to the interaction of the 2Σ+ and 2Σ− states of OH. The analysis of the electronic distribution of OH indicated that OH(2Σ+) is present in its thermal equilibrium concentration in the flame at atmospheric pressure. The results of this study in conjunction with the work of Gaydon and Wolfhard on the low pressure acetylene-oxygen flame indicate that the radiation of OH(2Σ+) is to a large extent chemiluminescence so that a considerable fraction of the excited hydroxyl radicals must have been formed in the 2Σ+ state by a chemical reaction (or reactions).
Equilibrium in the Exchange of Hydrogen between Phosphine and Water
Authors: Weston Ralph E. , Bigeleisen Jacob
Published: January 2005

The exchange equilibrium PH2D(g)+H2O(l)=PH3(g)+HDO(l) has been measured at 25°C by the use of dilute sulfuric acid and buffer solutions as a catalyst. From this measurement and the ratio of the vapor pressures of H2O and HDO the equilibrium constant for the exchange PH2D(g)+H2O(g)=PH3(g)+HDO(g) is calculated to be 1.52 at 25°C. The latter experimental value is combined with a theoretical computation of the temperature independent factor of the equilibrium constant to evaluate the difference in the zero point energies of PH3 and PH2D. This leads to the equation, which is valid up to about 500°K, Kg=0.781e198/T. This equation is in good agreement with calculations based on the spectra of PH3 and PD3 and the rule of the geometric mean.
The Microwave Spectra, Structure, Dipole Moment, and Chlorine Nuclear Quadrupole Coupling Constants of Methylene Chloride
Authors: Myers Rollie J. , Gwinn William D.
Published: January 2005

The microwave spectra of CH2Cl235, CH2Cl35Cl37, CH2Cl237, CDHCl235, CDHCl35Cl37, CD2Cl235, and CD2Cl35Cl37 have been examined and effective moments of inertia have been determined for these seven isotopic species. From these data the effective bond distances and angles were determined as C–Cl distance=1.7724±0.0005A, Cl–C–Cl angle=111°47′±1′, C–H distance=1.068±0.005A (average of all species), or 1.082A (extrapolated to infinite hydrogen mass), and H–C–H angle=112°0′±20′ (average of all species) or 112°58′ (extrapolated to infinite hydrogen mass). The best value for the dipole moment of methylene chloride was found from the Stark splitting to be 1.62±0.02×10−18 esu. The chlorine nuclear quadrupole coupling constants were also determined and their relationship to the structure is discussed.
Fluorescence Studies of Some Simple Benzene Derivatives in the Near Ultraviolet. III. Benzotrifluoride
Authors: Sastri Mantrala L. N. , Sponer H.
Published: January 2005

The fluorescence spectrum of benzotrifluoride has been studied using various sources of excitation. The spectrum consists of about 36 bands for which assignments are given according to the symmetry properties of the molecule. The analysis is in agreement with that of the absorption spectrum. In the region of overlap, fluorescence and absorption bands show close coincidence.
The Dielectric Properties of Water in Solutions
Authors: Haggis G. H. , Hasted J. B. , Buchanan T. J.
Published: January 2005

Results of dielectric constant and loss measurements at λ=9.22, 3.175, and 1.264 cm are given for a wide variety of aqueous solutions of ions and organic molecules. The water relaxation time is shortened by positive ions and lengthened by hydrogen bond-forming molecules. The properties of water are treated by a statistical method in which the numbers of molecules in four, three, two, one, and zero-bonded states are estimated from dielectric and latent heat data. Fair agreement with experiment is obtained in calculating the static dielectric constant of ice at 0° and water from 0–370°C, using Kirkwood's dielectric theory and Verwey's calculation of the dipole moment of a four-bonded water molecule. The effects of temperature and solutes on the water relaxation time are discussed in terms of this statistical method. The effective number of water molecules ``irrotationally bound,'' i.e., prevented from turning in the electric field by the ion or the organic molecule, is estimated from the depression of the low frequency dielectric constant, using a dielectric theory of mixtures. This number is zero for uncharged solute molecules but is finite for organic or inorganic ions.
Nuclear Magnetic Resonance in Metals. I. Broadening of Absorption Lines by Spin-Lattice Interactions
Authors: Gutowsky H. S. , McGarvey B. R.
Published: January 2005

Magnetic resonance line shapes and widths, their temperature dependence, and the conduction electron shifts in resonance frequency are reported for the metals Li7, Na23, Al27, Cu63, Cu65, Ga69, Ga71, Rb85, Rb87, and Cs133. The absorption lines in most of these metals are broader than predicted for nuclear magnetic dipolar broadening alone. We propose that the mechanism responsible for most, if not all, of this additional broadening is the interaction between the nuclear spins and the conduction electrons, which also determines the spin-lattice relaxation time. Spin-lattice relaxation times T1 are estimated from the nondipolar broadening of the experimental absorption lines. These T1 values compare favorably with available directly measured values and with approximate T1 values obtained by Korringa's theory from the measured resonance shifts. In the case of lithium, a dipolar line-width transition was observed at 255°K; this transition results from self-diffusion, for which we determine an activation energy of 9.8±1 kcal/mole.
Influence of the Solvent on Rates of Ionization, Entropies, and Heats of Activation
Authors: Pearson Ralph G.
Published: January 2005

A breakdown of the rates of reactions in which ions are formed from neutral molecules into heats and entropies of activation reveals the following regularities with change in solvent: the heats of activation do not change greatly and are more frequently larger in polar solvents than in nonpolar ones; the entropies of activation are always negative and become more negative as the polarity of the solvent decreases. An explanation is given in terms of solvent molecules ``frozen'' around the incipient ions of the activated complex. Nonpolar solvents suffer a greater loss in entropy in such ``freezing'' than polar solvents. An electrostatic calculation is given which is satisfactory for all solvents whose molecules contain a permanent dipole moment, but which must break down for nonpolar solvents.
Molecular Orbital and Heitler—London Methods
Authors: Slater J. C.
Published: January 2005

The historical connection between the molecular orbital and Heitler—London treatments is traced, with particular attention to the contributions of Mulliken. Early discussions of the self-consistent-field problem, the relations of Heisenberg's work to the antisymmetry of the wavefunction, and configuration interactions in the two-electron problem, are reviewed, with references to the heteropolar as well as the homopolar cases. Early discussions of directed valence are mentioned. The Coulson—Fischer, Hurley—Lennard-Jones—Pople, and alternant molecular orbital approaches to bonding are discussed, with mention of recent work on correlation energy.
Approximate Self-Consistent Molecular Orbital Theory. I. Invariant Procedures
Authors: Pople J. A. , Santry D. P. , Segal G. A.
Published: January 2005

A general discussion of approximate methods for obtaining self-consistent molecular orbitals for all valence electrons of large molecules is presented. It is shown that the procedure of neglecting differential overlap in electron-interaction integrals (familiar in π-electron theory) without further adjustment may lead to results which are not invariant to simple transformations of the atomic orbital basis set such as rotation of axes or replacement of s, p orbitals by hybrids. The behavior of approximate methods in this context is examined in detail and two schemes are found which are invariant to transformations among atomic orbitals on a given atom. One of these (the simpler but more approximate) involves the complete neglect of differential overlap (CNDO) in all basis sets connected by such transformations. The other involves the neglect of diatomic differential overlap (NDDO) only, that is only products of orbitals on different atoms being neglected in the electron-repulsion integrals.
Semiempirical Molecular Orbitals for General Polyatomic Molecules. II. One-Electron Model Prediction of the H–O–H Angle
Authors: Cusachs Louis Chopin
Published: January 2005

A consistent one-electron semiempirical molecular orbital method based on the approximation Hij=Sij(2−| Sij |)(Hii+Hjj)/2has been used with atomic data to predict the equilibrium geometry of the water molecule. A variety of plausible parameters predict an equilibrium H–O–H angle in the range 95°—105°. Success and limitations of the method are attributed to the fidelity with which it reproduces important one-electron effects. In less critical cases, this model resembles the Wolfsberg—Helmholz and other non-Hückel semiempirical MO treatments.
Lower Bounds to Energy Eigenvalues for the Stark Effect in a Rigid Rotator
Authors: Choi Jong H. , Smith Darwin W.
Published: January 2005

Upper and lower bounds have been calculated for the energy levels of a rigid rotator in an electric field, in order to study the problems associated with the use of the partitioning method for bracketing an eigenvalue of the Schrödinger equation. Results of arbitrarily high accuracy are possible in this example.
Electronic Spectra of Polyatomic Molecules—A Brief Survey
Authors: Ramsay D. A.
Published: January 2005

A brief discussion is given of the early contributions of R. S. Mulliken and his school to the study of the electronic spectra of polyatomic molecules. An up-to-date summary of the polyatomic molecules and free radicals for which high-resolution studies of their band spectra have been carried out is included. Some points of likely interest to the theoretical worker are discussed, including the Renner effect in AH2 and BAC molecules, predissociation in HAB molecules, and some recent experimental results on the allyl and vinoxy radicals.
Upper and Lower Bounds to the Eigenvalues of Double-Minimum Potentials
Authors: Bunge Carlos F. , Bunge Annik
Published: January 2005

Several methods of obtaining upper and lower bounds to the eigenvalues of self-adjoint operators bounded from below have recently been developed by Löwdin. All these procedures are based on a bracketing theorem. We mention them and discuss one of the variants that makes use of intermediate Hamiltonians. To illustrate the power of the method, an application is made to various forms of double-minimum (D.M.) potentials, both symmetric and asymmetric, which have already been studied by Somorjai and Hornig. The new results show the importance of obtaining these lower bounds in connection with the resonance interaction between accidentally coincident ``left'' and ``right'' levels of weakly asymmetric D.M. potentials. An agreement between upper and lower bounds of 12–15 significant figures is obtained.
Approximation of Expectation Values
Authors: Hirschfelder Joseph O. , Sanders William A.
Published: January 2005

The general problem of calculating expectation values for properties other than energy by the use of perturbation theory is considered.