bluuebunny/crossref_metadata_2025 huggingface dataset:
General Solution to the Problem of the Effect of Neighboring Groups in Polymer Reaction
Authors: Arends C. B.
Published: January 2005

An analytical solution to the problem of the kinetics of reactions on polymer chains has been derived. The solution is generally applicable within the following limits: (1) only nearest-neighbor interactions are considered, (2) the initial state of the polymer is taken to be completely unreacted (i.e., initial arbitrary sequences of reacted and unreacted sites cannot be handled). However, autocatalytic, autoinhibitory, or mixed catalytic-inhibitory systems can be handled.
Comparison of Some Exact and Approximate Results for Gases of Parallel Hard Lines, Squares, and Cubes
Authors: Hoover William G. , Poirier Jacques C.
Published: January 2005

The first seven virial coefficients for hard parallel lines, squares, and cubes, as derived from approximations of the ring and watermelon type, are compared with the exact coefficients. These approximations give no useful information as to the sign or magnitude of the virial coefficients.

A Cartesian distribution function depending upon only one space coordinate arises naturally for the line, square, and cube molecules. The first four terms of the exact number density expansion of this function are presented and compared with results obtained by iteration from the Percus—Yevick, Kirkwood, and convolution integral equations. The Percus—Yevick equation yields a distribution function which closely resembles the exact result at low densities.

Virial coefficients are obtained from the approximate distribution functions by means of the Ornstein—Zernicke relation and the virial theorem, as well as from a relation between the potential of mean force at zero separation and the virial coefficients. This last relation (which is valid for hard spheres as well as lines, squares, and cubes) has an interesting graphical interpretation and leads to correct values for the third virial coefficient from the Kirkwood equation, but not from the Percus—Yevick or convolution equations.
Theoretical Calculation of Vapor Transport of Solid in the ZnS : HCl System
Authors: Jona F. , Mandel G.
Published: January 2005

A theory has been previously developed which allows calculation of the rate of diffusion-limited vapor transport of solids in a multicomponent multireaction system which is driven by a small temperature gradient. This theory is applied to the case of ZnS(s) being transported by reaction with HCl(g). All the required parameters, i.e., gaseous diffusion coefficients, thermodynamic data, etc., are either known or independently estimated. The calculated results are found to be in quantitative agreement with the experimental results within the estimated uncertainties in the thermodynamic and diffusion coefficient data over a wide range of initial HCl pressures. Below an initial HCl pressure of 1 atm, it is seen that the experimental rate of transport drops sharply in comparison to the theoretical prediction. This has previously been attributed to kinetic limitations.

It is shown that the assumption of a single binary diffusion coefficient, applying to all pairs of component species, may lead to results in approximate agreement with the more ``exact'' theoretically predicted results.
Exciton—Exciton Interactions and Photoconductivity in Crystalline Anthracene
Authors: Choi Sang-il , Rice Stuart A.
Published: January 2005

In this paper we consider the mechanism of photoconductivity in crystalline anthracene. It is shown that two excitons may interact to form a pair of charge carriers and an unexcited molecule. The computed rate of generation of charge carriers is 3.7×108 cm—3 sec—1, in satisfactory agreement with the (approximate) experimental value of 7.2×108 cm—3 sec—1 when the exciton concentration is 1.2×1010 cm—3. Other qualitative features of the proposed mechanism are in agreement with observation if electron-hole recombination is accounted for. Recent experiments by Silver demonstrating a photocurrent proportional to the square of the light intensity, and by McGlynn demonstrating the necessity for singlet states as the kinetic intermediate in charge-carrier generation are in agreement with the model proposed.
Theory of NMR Chemical Shifts in Conjugated Fluorine Compounds
Authors: Prosser Franklin , Goodman Lionel
Published: January 2005

Ramsey's equation for the nuclear magnetic resonance screening constant is analyzed employing a Hartree—Fock ground-state wavefunction. Using the LCAO approximation, a general expression is obtained which relates the screening parameter to localized charge distribution quantities (charge and bond orders). This expression is equivalent to one given by Karplus and Das. Pertinent two-center integrals over atomic orbitals are evaluated, employing, in part, the Fourier integral folding theorem. The relative magnitudes of the integrals over atomic orbitals makes possible a simplification of the general equation for F19 shielding to a form involving quantities associated with the fluorine atom and the adjacent carbon atom. Under the assumption of an invariant sigma framework, the F19 chemical shift between two similar conjugated fluorine compounds is shown to be determined chiefly by the values of the fluorine pi-electron charge densities and the carbon—fluorine pi-electron bond orders. The latter terms are almost as important as the former. The groundwork is laid for applying the derived equations, in a subsequent paper, to several systems of aromatic fluorine compounds.
Relationship between Pi-Electronic Distributions and F19 NMR Shielding in Para-Substituted Fluorobenzenes
Authors: Taft Robert W. , Prosser Franklin , Goodman Lionel , Davis George T.
Published: January 2005

Experimental results on F19 shielding in p-substituted fluorobenzenes are combined with calculations of pi-electronic charge distribution from MO theory and are used in several procedures devised to test shielding theories. It is concluded that both —R and +R p-substituted fluorobenzenes represent a special case for which there is a reasonable degree of theoretical justification for relating the F19 shielding with the pi charge density of the fluorine atom.

The tests devised for p-substituted fluorobenzenes do not clearly distinguish between the shielding equations of Prosser and Goodman and those of Karplus and Das. Also, the tests do not critically distinguish which of the following may be taken as the better estimator of the pi charge density of the fluorine atom: the shielding parameter based upon unsubstituted fluorobenzene as the standard of comparison or the shielding parameter based upon the meta isomer of the p-substituted fluorobenzene.

Data are presented on F19 shielding of the acid fluoride atom of p-substituted benzoyl fluorides and benzenesulfonyl fluorides. These results show that the special shielding relationship derived for p-substituted fluorobenzenes does not apply.
Dielectric Properties of Some Powdered Organic Semiconductors
Authors: Huggins C. M. , Sharbaugh A. H.
Published: January 2005

The use of electrical conductivity measurements to characterize the charge density and/or mobility parameters of a material is discussed. The common practice of using simple, pressed electrodes with dc measurements is felt to be grossly inferior to four-probe techniques. Even this refinement, however, is subject to considerable error for powdered samples. Many workers have used fairly simple ac techniques to eliminate interparticle contact resistances in organic semiconductors; this approach is shown to have been misapplied. It is possible, however, to measure what appears to be a specific conductivity (independent of packing pressure or filling factor) by more elaborate ac analysis. Measurements of the effective parallel resistance and capacitance are given for anthracene (powder and single-crystal), metal-free β-phthalocyanine, and a β-carotene tri-iodide complex for a frequency range of 0.05 cps to 300 Mc/sec.
NMR Spectra of Some Cyclohexyl Derivatives
Authors: Neikam W. C. , Dailey B. P.
Published: January 2005

In order to determine the C–C bond chemical shift in a new series of substituted hydrocarbons, the chemical shifts of the α protons in a series of monosubstituted cyclohexanes have been studied. Where possible each sample was frozen into its individual conformers in order to account for varying stereochemical influences. The derived values of the C–C bond shifts are in good agreement with the values found for corresponding ethyl and isopropyl derivatives.
Mass Spectrometry of Ions in Glow Discharges. IV. Water Vapor
Authors: Knewstubb P. F. , Tickner A. W.
Published: January 2005

Ions from the negative glow and Faraday dark space of discharges in water vapor have been analyzed with a mass spectrometer. The ions observed are of the form H3O+·(H2O)n with n=0 to 5. It is shown that the observations are altered by the sampling process to an extent which depends on discharge conditions and is sometimes quite large. This effect may be important whenever loosely bound ions are sampled from a plasma.

The sequence of hydration reactions is examined in an approximate manner and it is concluded that the bond strength decreases as successive water molecules add to H3O+, falling sharply beyond n=3. The rate constants for the first few stages of the hydration process appear to increase with the size of the reactant ion.
Analysis of A2B2 High-Resolution NMR Spectra. I. Furan, Thiophene, and Disubstituted Benzenes
Authors: Grant David M. , Hirst Robert C. , Gutowsky H. S.
Published: January 2005

The features of certain classes of A2B2 spectra are investigated systematically relative to the parameters involved, and these characteristic spectra are given as an aid to future interpretation. The effects upon the spectra of the relative signs of the coupling constants are discussed. Examples are provided by the analysis of spectra for the aromatic protons in furan, thiophene, three symmetrical ortho disubstituted benzenes, two nonsymmetrical para disubstituted benzenes, and a symmetrical 4,4′ disubstituted biphenyl. Better resolution than was obtainable in previous studies permitted a more detailed analysis for compounds cited earlier. In most examples the 24 main spectral lines expected for four spin systems of this symmetry were observed.

It is found that all four of the H–H coupling constants are of the same sign in thiophene, and Jαβ and Jαβ′ in furan. Appreciably different values, 1.55 and 2.85 cps for Jαα and 1.8 and 4.7 cps for Jαβ, are found in furan and thiophene, respectively, while Jββ and Jαβ′ are virtually identical: 3.53 and 3.35 cps, and 0.8 and 1.0 cps. In the substituted benzenes, the values found for J0, Jm, and Jp fall in the ranges 7.4 to 8.8 (9), 1.24 to 3.05 (9), and 0.3 to 0.6 cps (6), the number of cases being given in parentheses. The disubstituted benzenes studied have two nonequivalent ortho or meta coupling constants; they are found to differ by as much as 0.6 cps. The spectra of these substituted benzenes show that the coupling constants J0, Jm, and Jp are all of the same relative sign.
Molecular Geometry and the Vapor Pressure of Isotopic Molecules. The Equivalent Isomers cis-, gem-, and trans-Dideuteroethylenes
Authors: Bigeleisen Jacob , Ribnikar Slobodan V. , Van Hook W. Alexander
Published: January 2005

The vapor pressures of trans-, cis-, and gem-dideuteroethylenes have been intercompared directly by mercury manometry over the temperature range 120°—180°K. The trans isomer has been compared with ordinary ethylene over the same temperature range. The vapor pressures of cis- and gem-dideuteroethylene are equal to within a few hundredths of a percent. The trans compound has a greater vapor pressure than either the cis or gem compounds (about 0.1% at 130°K and 0.05% at 180°K). At these same temperatures the trans-dideuteroethylene has a vapor pressure 1.2% and 1.6%, respectively, greater than ordinary ethylene.

The difference between the dideuteroethylenes is correlated with differences in molecular geometry. It is shown that the trans is the most volatile of the dideutero isomers, because it has the smallest moment of inertia about the C=C axis. The vapor pressure data are then direct evidence for hindered rotation in the liquid.
Molecular Geometry and the Vapor Pressure of Isotopic Molecules. C2H3D and C12H2=C13H2
Authors: Bigeleisen Jacob , Stern Marvin J. , Van Hook W. Alexander
Published: January 2005

The isotopic vapor pressure ratio between monodeuteroethylene and ordinary ethylene has been measured in the temperature range 120°—180°K by differential manometry. The inverse isotope effect with C212H3D is less than one-half the effect observed with the dideuteroethylenes. This deviation from the rule of the geometric mean gives further support to the structural theory of isotopic vapor pressure effects and confirms the importance of quantum corrections of the order of (ℏ/kT)4 and higher. Vapor—liquid equilibrium studies of C212H4 and C12H2=C13H2 were made in a packed column under total reflux using C212H3D as an internal monitor to calibrate the column. Whereas C212H3D goes to the top of the column, C12H2=C13H2 concentrates in the boiler. Absolute values of the carbon-13 effect were calculated from the measured relative effects and the manometric data for C212H3D, and the vapor pressure ratios were checked by analysis of the kinetic behavior of the column. A test of the data was made in the framework of the applicable theory. The temperature dependencies of the isotope effects are predicted from the theory within the experimental error. The relative deuterium and carbon-13 isotope effects as well as the differences between the dideuteroethylene isomers are discussed in terms of the structure of the ethylene molecule.

It is shown that there is a large normal A/T2 dependence due to hindered rotation in the liquid. The zero-point energy change on condensation leads to a term of the form B/T and accounts for the higher vapor pressures of the deutero-compounds. The zero point energy changes obtained from the vapor pressure data are in quantitative agreement with theoretical calculations.

A new type of effect is found, namely a perturbation of the internal vibrations by the hindered rotation. This perturbation is different for the different molecules and a strict correspondence is established with the molecular symmetry.
High-Velocity Molecular Beam Scattering: Total Elastic Cross Sections for L-J(n, 6) and Exp-6(α) Potentials
Authors: Bernstein Richard B.
Published: January 2005

Explicit expressions are derived for the total elastic scattering cross sections in the high-velocity region for molecules interacting according to L-J (n, 6) and exp-6(α) potentials. Cross sections are presented in tabular and graphical form.
Trapping and Energy Transfer in Atomic Collisions with a Crystal Surface
Authors: McCarroll Bruce , Ehrlich Gert
Published: January 2005

The condensation of atoms on a solid is examined by calculating the critical energy for trapping of a particle of arbitrary mass and force constant colliding with a linear lattice. In the harmonic approximation and using classical mechanics, the maximum kinetic energy for trapping is found to depend strongly upon the well depth, in qualitative agreement with experiment. For a gas atom colliding with its own lattice (that is, force constant ratio β=1 and mass ratio μ=1) capture occurs at translational energies up to 25 times the binding energy. For β=0.2, this critical energy has diminished to 1.3 times the dissociation energy Q of the homogeneous lattice. The dependence of the critical energy on force constant is not monotonic, however—there is a maximum at β∼0.75. At β=0.75 and μ=1, for example, the incident energy must exceed ∼31Q to prevent trapping.

Most of the energy exchange occurs during the repulsive part of the collision. For this part of the collision interval, the presence of a trapping potential has little effect. However, the energy exchange occurring when the particle rebounds through the attractive part of the potential is sensitively dependent upon the force constant. For β<0.5, the incident particle loses energy equal to ∼0.5 times its binding energy. As β increases, the energy loss diminishes and after β∼0.75 the incident particle actually gains in total energy.

The accommodation coefficient for systems with repulsive interactions only does not show such specificity; for β>0.2 the energy exchange is dictated primarily by the mass ratio. The coefficients calculated for hard-sphere collisions provide an acceptable approximation when β>∼0.5.
1,2-Difluorobenzene: Chemical Thermodynamic Properties and Vibrational Assignment
Authors: Scott D. W. , Messerly J. F. , Todd S. S. , Hossenlopp I. A. , Osborn Ann , McCullough J. P.
Published: January 2005

Thermodynamic data were obtained for 1,2-difluorobenzene and correlated by methods of statistical mechanics to derive values of the chemical thermodynamic properties in the ideal-gas state from 0° to 1500°K. A vibrational assignment consistent with the calorimetric data was obtained. The experimental studies provided the following information: values of heat capacity for the solid (14°K to the triple point), the liquid (triple point to 357°K), and the vapor (355° to 500°K); the triple-point temperature; the heat of fusion; thermodynamic functions for the solid and liquid (0° to 370°K); heat of vaporization (327° to 367°K); parameters of the equation of state; and vapor pressure (304° to 403°K).
Internal Rotation in Completely Asymmetric Molecules. I. A General Theory and Analysis of the Microwave Rotational Spectrum of CH2DCOH, CD2HCOH, and CHOOCH2D
Authors: Quade C. R. , Lin Chun C.
Published: January 2005

A theory for the internal rotation in molecules where the internal rotor is not a symmetric top has been formulated. The principal feature of the theory is the expansion of the rotational constants for the molecule in a converging series of sinnα and cosnα. This allows for the straightforward evaluation of certain integrals appearing in the development of the theory.

In addition, the theory is applied specifically to CH2DCOH, CD2HCOH, and CHOOCH2D in the analysis of the microwave rotational spectra for these molecules. For CH2DCOH the height of the potential barrier hindering the internal motion is found to be V=410 cm—1, which is consistent with the barrier height for other species of acetaldehyde. To fit the spectra of CD2HCOH and CHOOCH2D a slight rotation of the effective principal axes must be made to obtain a consistent potential barrier.

The results of the calculation indicate that (1) the theory is readily applicable in the determination of the barrier heights of the more general molecules, and (2) investigation of the deuterated-methyl internal rotors could provide information on the structure of the rotor.
Thermal Conductivity of Dissociating Phosphorous Pentachloride
Authors: Chakraborti P. K.
Published: January 2005

The thermal conductivity of the dissociating system PCl5⇌PCl3+Cl2 has been measured between 145° and 175°C at a pressure below 1 atm. The thick-wire variant of the hot-wire method and an all glass apparatus has been employed. The experimental thermal conductivity values are in good agreement with the values calculated on the assumption of local chemical equilibrium.
One-Center Wavefunction for the Hydrogen Molecule Ion
Authors: Houser T. J. , Lykos P. G. , Mehler E. L.
Published: January 2005

An examination of the one-center, noninteger principal quantum number, Slater-type orbital representation applied to the hydrogen molecule ion is presented. The results give rapid convergence to the experimental value for the total electronic energy. A value of —1.09770 a.u. is obtained using only five terms in the expansion. This is 0.00207 a.u. closer to the experimental value than the fifteen term Howell and Shull calculation. The limiting energy which can be obtained using only s-type terms agrees with the Howell and Shull estimate.
Melting Curve of Ice VII to 200 kbar
Authors: Pistorius Carl W. F. T. , Pistorius Martha C. , Blakey J. P. , Admiraal L. J.
Published: January 2005

The melting curve of ice VII has been determined to 200 kbar, where ice VII melts at 442°C. The curve can be given as P=−301+2.215T−5.231×10−3T2+4.367×10−6T3 where P is the freezing pressure in kilobars at T°K. The results agree within experimental error with the Simon equation in the form (P−21.54)/5.03=(T/354.8)5.135−1,but the power series fit is better. The main uncertainty in the results is the actual pressure values at the highest pressures.
Direct Conversion of Graphite to Diamond in Static Pressure Apparatus
Authors: Bundy F. P.
Published: January 2005

Static pressure apparatus has been developed which is capable of pressures up to 200 kbar and transient temperatures up to about 5000°K, using an electric flash-heating technique. At pressures above about 125 kbar and temperatures in the 3000°K range it is found that graphite spontaneously collapses completely to polycrystalline diamond which may be retrieved quantitatively. The threshold temperature of the transformation is several hundred degrees lower than the melting temperature of graphite. The diamond/graphite/liquid triple point is found to be located at about 125 (+10, —0) kbar and 4100 (±200)°K. The shock compression results of DeCarli and Jamieson, and of Alder and Christian, are linked with the present results to construct a phase diagram of carbon extending to 5000°K and 800 kbar.
Chemical and Magnetic Enhancement of Perturbed Lines in the Violet Spectrum of CN
Authors: Radford H. E. , Broida H. P.
Published: January 2005

A chemical kinetic theory based on the quantum-mechanical properties of perturbed molecular states is developed to explain the rotational intensity anomalies observed in the CN-band spectrum emitted by an active nitrogen flame. Relative intensities of perturbed lines are calculated in terms of parameters which specify the rates of chemical formation, collisional relaxation, and radiative decay of CN molecules in the excited electronic states where the perturbed lines originate. Numerical values of these parameters are found which, inserted in the intensity expressions, predict correctly the observed pressure-dependent enhancement of each perturbed line. From this analysis the approximate value 6×10—7 sec is found for the radiative lifetime of the A2IIi, v′=10 state of CN. It is also found that nearly every gas kinetic collision changes the rotational state of an excited CN molecule, but that only about 1 collision in 100 can cause the exchange of vibrational energy for electronic energy represented by the transition A2IIi, v′=10→B2Σ+, v′=0. The theory also predicts, in agreement with recent observations, an additional selective enhancement of certain perturbed lines by a strong magnetic field.
Infrared Absorption Spectra of LiF and Li2F2 in Solid Argon, Krypton, and Xenon Matrices
Authors: Linevsky Milton J.
Published: January 2005

The infrared absorption spectra of LiF and Li2F2 isolated in solid argon, krypton, and xenon have been investigated from 2 to 35 μ. Infrared frequencies of both molecules have been obtained, and the assignment of the B2u and B3u modes of Li2F2 has been made assuming a planar rhomboid structure, (Vh). An interesting case of a so-called ``matrix effect'' is also presented.
Reactions of Nitrogen—Hydrogen Radicals. I. NH2 Recombination in the Decomposition of Ammonia
Authors: Hanes Maurice H. , Bair Edward J.
Published: January 2005

Photoelectric measurements of NH2 absorption as a function of time following an rf discharge pulse through ammonia are described. The extinction coefficient of the strong vibration—rotation line at 16725.40 cm—1 is found to be 1.02±0.10×103 liter mole—1 cm—1 as an upper limit. Under the proper conditions the kinetics of NH2 disappearance is second order with respect to NH2. Arguments attribute the initial stages of the observed reaction to NH2 recombination to form hydrazine. The recombination rate constant is 2.33±0.20×109 liter mole—1 sec—1 and is independent of the total pressure in the range 425 to 850 μ.
On the Isomerization of Isobutyl Radicals
Authors: McNesby J. R. , Jackson W. M.
Published: January 2005

An experimental assessment has been made of the competition between isomerization of a deuterium-labeled isobutyl radical, (CH3)2CDCH2→(CH3)2CCH2D,and the straight decomposition, (CH3)2CDCH2→CH3+CH3CD=CH2.It was found that the first reaction was never more than 1% as rapid as the second, up to 540°C. Therefore, the only measurable unimolecular reaction of isobutyl up to 540° is the straight decomposition reaction.
On Errors in Hartree—Fock Calculations
Authors: Goodisman Jerry , Klemperer William
Published: January 2005

The root-mean-square deviation of an approximate wavefunction from the true, ε, is reflected in the relative errors in expectation values calculated with this function. For operators other than the Hamiltonian, the relative error is of the size of ε, except for one-electron operators calculated with Hartree—Fock functions, where it is of the size of ε2 (Brillouin's theorem). We point out that the error in energy, while formally second-order in ε, is quite likely to be considerably better than ε2, while other expectation values reflect the size of ε more closely. It is also possible to estimate ε from configuration interaction. The discussion indicates it is unlikely that an expectation value of a one-electron operator is in error by ε2 rather than by ε with a non-Hartree—Fock function.
Covalent-Bond Asymmetries from Zeeman-Split NQR
Authors: Rehn Victor
Published: January 2005

An experimental technique is developed for the measurement of asymmetry parameters in electric quadrupole coupling of nuclei with spin I32 in covalent bonds in organic single crystals. The theoretical details of Zeeman-split nuclear quadrupole resonance spectra, upon which the technique is based, are examined and found to yield a particularly simple approximate expression for the asymmetry parameter of the electric field gradient tensor, which has been previously shown to be proportional to the double-bond character of the covalent bond. The technique is applicable to atoms bound to a single neighbor in the organic molecule. The limitations of the approximations involved in obtaining the simple formula are examined in detail, and it is found that an order-of-magnitude smaller probable error may be obtained than has been possible with previous geometrical techniques. Correction formulas are presented which may yield still another order-of-magnitude better precision if desired. Experimental results on the Cl35 resonances in para-dichlorobenzene, para-chloroaniline, and 1245 tetrachlorobenzene demonstrate the method, along with verifying the second- and third-order perturbation theoretic results which derive the maximum magnetic field—about 2400 Oe—in which the simple formulas may be used. Other experimental measurements of the asymmetry parameters of C–Cl bonds are tabulated.
Magnetic Anisotropy of Ferrocene and Chemical Bonding
Authors: Mulay L. N. , Mary Eleanor Fox S.N.D.
Published: January 2005

Knowledge of the magnetic anisotropy of ferrocene was expected to throw some light on the controversial question concerning the bonding of the iron atom to the rings in ferrocene. With this in view, measurements of the anisotropy were made on small single crystals of ferrocene by Krishnan's flip-angle method. The quartz torsion fibers were calibrated using the known crystal structure and magnetic susceptibilities of naphthalene and acenaphthene. Magnetic field strengths ranged from about 4 to 9 kG. Using the data of a complete three-dimensional x-ray study of ferrocene, the principal molecular susceptibilities were determined by the method worked out by Lonsdale and Krishnan. The susceptibility along the direction of the K3 molecular axis, normal to the plane of the rings through the center of mass of the rings, was much greater than those along the K1 and K2 directions, in the plane of the rings. The anisotropy between K3 and the average of K1 and K2 was found to be 49.5×10—6 cgs units, and is evidence in favor of a single dπ—pπ bond between each of the rings and the iron atom. Pauling's ``resonance structures'' also seem plausible; the studies do not support Fischer's ``complete π-electron donation'' structure. Theoretical calculations based on Langevin's formula for diamagnetism show a close agreement with the experimental value.
Equation of State for Binary Fluid Mixtures
Authors: Hecht Charles E.
Published: January 2005

The compressibility factor PṼ/RT for a binary fluid mixture is obtained from tabulated values of a reduced equation of state for a general pure substance assuming the law of corresponding states for pure substances.

The binary mixture is treated in zeroth order as a pseudo one-component substance obeying a Lennard-Jones 12–6 intermolecular potential with parameters so chosen that they reproduce the second virial co-efficient of the mixture. In first-order-of-perturbation theory, the difference between the actual intermolecular potentials (assuming all molecular sizes to be equal to that of the pseudo molecular size) and that of the pseudo one-component potential is introduced as a perturbation. The random-mixing assumption need not be made.

Data for a total of 25 mixtures in 7 different binary systems are compared with the theory. The perturbation is seen to be unimportant. Theory holds to within about 15% if reduced densities less than 0.3 are considered.
Padé Approximant Studies of the Lattice Gas and Ising Ferromagnet below the Critical Point
Authors: Essam John W. , Fisher Michael E.
Published: January 2005

The Padé approximant procedure is used to study the low-temperature series for the Ising problem. The critical behavior of the spontaneous magnetization of an Ising ferromagnet and of the liquid-vapor coexistence curve of the corresponding lattice gas is found to be I0(T)∼|ρliq−ρga5|∼|Tc−T|β where (in three dimensions) 0.303≤β≤0.318. It is conjectured that β=5/16=0.31250. The low-temperature initial susceptibility and the compressibility of the lattice gas at condensation are found to diverge as χ0(T)∼κ0(T)∼|Tc−T|−γ′ where in two dimensions γ′=1.75±0.01 while in three dimensions γ′=1.25 (+0.07, —0.02). Consideration of a heuristic model partition function suggests the identity α′+2β+γ′=2 where α′ is the index of divergence of the specific heat below Tc. The amplitudes of the singularities are derived and extrapolation formulas are presented for the plane triangular, square, and honeycomb lattices and the three-dimensional face-centered, body-centered, and simple cubic lattices. The results are compared briefly with experimental evidence.
Cluster Expansion Methods for Systems of Polar Molecules: Some Solvents and Dielectric Properties
Authors: Jepsen Donald W. , Friedman Harold L.
Published: January 2005

General methods are developed for evaluating Mayer cluster diagrams for systems of molecules with orientation-dependent forces. These methods are particularly useful for obtaining chain and ring contributions. Simplification occurs for ordinary two-body forces in the absence of external fields because of invariance under rotation of the two-body complex as a whole. Using these methods we adapt Mayer's rearrangement procedure to calculate the cluster expansion of the potential of the average force between two ionic or dipolar solute molecules that are immersed and fixed in a gas of dipolar molecules. The comparison of this potential with the corresponding macroscopic quantity leads to a cluster expansion for the dielectric constant of the dipolar gas.
Kinetics of Potassium Chloride and Chlorine on Tungsten
Authors: Silver M. , Witte Robert S.
Published: January 2005

The kinetics of adsorbed layers of potassium chloride on tungsten and of chlorine on tungsten have been investigated in the range 300°—1900°K by means of the field electron microscope. Data are interpreted as showing that KCl in the presence of tungsten at room temperature forms a W–KCl complex to which the potassium is weakly bound. Activation at approximately 500°K results in the desorption of potassium leaving a tungsten chloride (WClx) layer which is stable to about 1100°K. Work functions, patterns and critical temperatures for KCl on tungsten and chlorine on tungsten are indistinguishable in the range 1100°—1900°K. Limiting processes above 1100°K are believed to be the formation and subsequent desorption of tungsten chloride and atomic chlorine. Temperature-dependent processes, such as migration, desorption, and structure change, associated with experimentally determined activation energies of ∼10 to 80 kcal, are discussed. The behavior of chlorine on tungsten is shown to be similar to that of oxygen on tungsten in the temperature range studied.
Kinetics of Addition of HI to Isobutene and Vinyl Chloride
Authors: Bose A. N. , Benson Sidney W.
Published: January 2005

The addition of HI to i-butene above 200°C proceeds homogeneously and quantitatively to yield i-butane+I2 in accordance with the equation 2HI+i−butene→i−butane+I2.It is shown that the rate-determining step is the formation of the intermediate t-BuI which is present in vanishingly small stationary concentration HI+i−butene→ lim k2t−BuI(slow),  t−BuI+HI→i−BuH+I2(fast).The second-order rate constant k2 is given by (units of liter/mole-sec) logk2=6.50−18 000/4.575T.From the known thermodynamic data the reverse, first-order rate constant k1 is given by (units of sec—1) logk1=12.52−36 400/4.575T.

Comparisons with similar data for EtI and i-PrI show that the substitution of Me groups for H lowers the Eact by about 6 kcal/Me group and also the A factor by about a factor of 5. This can be explained on the basis of a loss of internal rotational entropy in the transition state.

Qualitative observations indicate that C2H3Cl adds HI at a rate intermediate between C2H4 and C3H6. The principle products are C2H5Cl+I2 above 290°C, but sufficient C2H6+HCl appear to vitiate simple kinetic studies. Qualitative observation of the system EtCl+I2 indicate an I-atom-catalyzed elimination of HCl with an Eact∼43 kcal/mole.
Isotope Effect in the Solution of Oxygen and Nitrogen in Distilled Water
Authors: Klots Cornelius E. , Benson Bruce B.
Published: January 2005

The isotopic fractionations of nitrogen and oxygen in water have been measured in the range 2°—27°C. The extrapolated values at 0°C of k′/k, the ratio of Henry's Law constants, are 1.00085 (±0.00010) for nitrogen and 1.00080 (±0.00015) for oxygen in the sense of the heavier species being more soluble. Several possible sources are recognized for the observed effects which are, however, of the magnitude to be expected from the motion of point masses in ``iceberg'' cavities of reasonable dimensions.
Exciton Impurity Levels in Molecular Crystals
Authors: Merrifield R. E.
Published: January 2005

Impurity levels for excitons in molecular crystals are discussed in terms of the wavefunctions and energy levels of a crystal containing a single substitutional impurity molecule. The problem is formulated in general terms and is found to be soluble in the special case in which the transition dipole moment of the impurity molecule is parallel to those of the host molecules. A simple criterion for the existence of localized bound states is derived, from which it is concluded that such states should be of widespread occurrence. In particular, it is found that bound states can arise even where the impurity molecule has a higher excitation energy than the molecules of the host crystal if its transition moment is sufficiently large. Bound states can also arise where the ``impurity'' is a host molecule at a site of localized strain. The specific case of a one-dimensional crystal with nearest-neighbor interactions is treated in some detail as a numerical example.
Non-Gaussian Character of Real Polymer Chains
Authors: Nagai Kazuo
Published: January 2005

It is shown that the distribution function of the end-to-end vector of a polymer chain at its free state as well as the partition function of the polymer chain subjected to an external force, may be expressed in terms of even moments of the end-to-end distance of the chain at its free state. In looking over these functions it is seen that the quantities g2k and g2k' (k≥2) in the text, representing the non-Gaussian character of a polymer chain, are related in definite ways with even moments. As a main contribution of this paper, a mathematical method is presented for calculating the even moments just described and in particular, the fourth moment 〈R4〉, by taking into account the interdependent internal rotation. For the sake of simplicity, polyethylene is employed to illustrate the method. The expression for 〈R4〉 is obtained as a simple function of the (1, 1) elements of several matrices. The N (N is the number of skeletal bonds) dependence of g2k and g2k', and thereby also that of every term in a series expansion of the distribution function, are discussed in full detail.
Exciton—Phonon Interaction in Crystalline Benzene
Authors: Maria H. , Zahlan A.
Published: January 2005

The uv crystal spectrum of benzene is investigated in the region 4°—80°K. The intensity of the a-polarized and c-polarized components of the 0–0 band are temperature dependent. The intensity of the a 0–0 component is found to be proportional to the density of phonons with a frequency of 16 cm—1. The half-width of the a and c axis-polarized 0–0 components are also studied as a function of temperature. The half-width of the band at 38 786 cm—1 0–0+925 is similar to that of the purely electronic components, while for the 38990 cm—1 band 0–0+1155, the half-width is temperature independent. The mean phonon-perturbing frequency is 12 cm—1. The a-c 0–0 band splitting is studied as a function of temperature.

Sample line shapes are reported, and the results are discussed briefly on the basis of the theoretical work of Toyozawa.
Reactions of O Atoms with Isobutane
Authors: Wright Franklin J.
Published: January 2005

The reaction of isobutane with oxygen atoms produced by a titration technique has been studied in the gas phase at 30°C. The experimental evidence leads to the conclusion that hydrogen abstraction by the oxygen atoms plays only a minor role and that the reaction products are formed in a more direct manner by the simultaneous replacement by an oxygen atom, of two groups on the parent hydrocarbon.
Electron Spin Resonance of S-State Ions in Barium Fluoride
Authors: Drumheller John E.
Published: January 2005

The electron spin resonance of manganese and gadolinium impurities in barium fluoride have been studied at room and liquid-nitrogen temperatures. The normal hyperfine interaction constant A is found to be —97.0±1.0 G at 300°K and —101.6±1.0 G at 77°K. The low-temperature data reveals the ``super'' hyperfine interaction of the 3d manganese electrons with the fluorine nuclei and the contributions from s and p orbitals are approximately | As|=5.7 G and | Ap|=1.1 G, respectively. The spectroscopic splitting factor g is measured to be 1.9998±0.0010. No crystalline electric field splitting is detectable. The gadolinium data reveals significant crystalline electric field splitting of both fourth- and sixth-order cubic and possibly some lower symmetry. These are found to be C=159.3 G and D=—5.5 G, respectively and the g factor is 1.984±0.020. Some of the low field, higher order transitions of gadolinium are also reported. Where possible, comparison with results on similar crystals is presented. Measurements were made at 8.6 Gc with impurity concentration at about 0.2% ionic concentration.
Pressure-Effect Model for a Luminescent Center: KCl:Tl
Authors: Alers P. B. , Dolecek R. L.
Published: January 2005

A method is presented by which the effects of pressure on the absorption and emission spectra of a luminescent center can be used to provide the parameters necessary to construct a configurational coordinate diagram of the center. Pressure shifts of the 2470-Å absorption and 3050-Å emission bands of KCl:Tl have been measured and are used to calculate the parameters for the appropriate configurational coordinate diagram; the results are in good agreement with those obtained from purely theoretical considerations. Values for bandwidth and compressibility are also calculated and are found to agree with experimental observation.
Photon-Induced Electronic Transitions in Molecular Crystals
Authors: Sage Martin L.
Published: January 2005

The electric dipole transition matrix element of a molecular crystal in the presence of an electric field is calculated. It is found to be proportional to the matrix element of the zero-field Hamiltonian between nearest neighbors and inversely proportional to the electric field strength for the limit of strong fields.
Vapor Pressure of Liquid Bismuth
Authors: Aldred A. T. , Pratt J. N.
Published: January 2005

The vapor pressure of liquid bismuth in the temperature range 800°—1050°K has been measured by the torsion-effusion method. The values obtained are represented by the equation: log10p (mm Hg) = 8.579— (10 108/T). A few separate Knudsen measurements have been performed in the same temperature range and the results used to calculate the molecular weight of bismuth vapor, and thus the heat of dissociation for the reaction ½ Bi2→Bi.
Intensity Distribution in the Forbidden 1Σ—3IIr Transition of SiO
Authors: James Thomas C.
Published: January 2005

The intensity distribution in the 1Σ—3II transition of SiO, observed by Verma and Mulliken, is discussed. The appearance of the subband 1Σ—3II2, which violates the selection rule ΔΩ=0, ±1 and the appearance of the Q branch of the 1Σ—3II0 subband, which violates the selection rule that ΔJ=0 is forbidden for Ω=0→Ω=0 transitions, are explained by the mixing of the 1Σ state with a 1II state as a result of the rotation of the molecule. The effect of spin-orbit interaction is considered only insofar as it mixes singlet functions with the multiplet components of 3IIr. Some indication is given as to why this explanation is inapplicable to the a 3II—X 1Σ+ transition of AlCl where the selection rule for Ω is apparently rigorously obeyed.
Photochemical Reactions in the Gas Phase and Slater's ``New Approach to Rate Theory''
Authors: Wilson David J.
Published: January 2005

Slater's ``New Approach to Rate Theory'' [N. B. Slater, Theory of Unimolecular Reactions (Cornell University Press, Ithaca, New York, 1959), Chap. 9; J. Chem Phys. 24, 1256 (1956)] is used to analyze in detail two simple gas-phase photochemical mechanisms. Quantum yields are calculated as functions of pressure, and the qualitative nature of the plots is discussed. Statistical methods are used to develop consistency theorems for checking experimental plots of quantum yield versus pressure against the theory.
Measurements of the Viscosity of Krypton
Authors: Clifton David G.
Published: January 2005

The viscosity of krypton has been measured over the temperature range 297° to 666°K by the oscillating disk method using helium for calibration. The viscosities obtained were used to get the parameters for a Lennard-Jones 12–6 potential function and they were found to be ε/k=162°K and σ=3.734 Å. Calculation of the viscosity, thermal conductivity, self-diffusion coefficient, second virial coefficients in the moderate temperature range, and the heat of sublimation at 0°K from the L. J. 12–6 function gives very good agreement with experimental values. Calculated values for the second virial coefficient at low temperatures, the reduced thermal diffusion factor, and the lattice spacing at 0°K are in fair agreement with experiment.
Thermoluminescence in Quartz
Authors: Medlin W. L.
Published: January 2005

X-ray- and uv-excited thermoluminescence in natural quartz has been investigated by studying the properties of synthetic samples. The results for a large number of natural samples, including single crystals, outcrop specimens, and core-hole samples showed that most of them had four prominent glow peaks in common. One of these is due to the presence of Ti and the others are apparently associated with a defect center. The effects of annealing at temperatures up to 900°C were found to be important in well-crystallized samples but unimportant in others.

The emission spectrum of the Ti glow peak shows that a number of levels are involved in the luminescent transitions. All of the defect-center glow peaks have the same emission spectrum which consists of a single maximum with a long wavelength tail. Direct-current electrical measurements on single crystals showed that the trap-emptying processes for the defect center were nonlocalized. Optical absorption measurements at room temperature indicated that none of the common absorption bands are associated with peaks in the glow curve. From phosphorescent-decay measurements it was determined that the trapping levels associated with the defect center have very narrow energy distributions whereas the trapping level due to Ti is discrete.

The glow peaks for ordinary quartz are not excitable by uv irradiation, but in samples annealed at 900°C all of the glow peaks due to the defect center are excited by uv. The annealed samples show absorption in the uv region which is not present in unannealed specimens. The results suggest changes in the trap-filling mechanism, but the effects can also be explained by alterations in the luminescent levels.

Luminescence can be excited in all of the samples at fixed temperatures by x rays but not by uv. At low temperatures the effects of transitions through trapping levels are unimportant, and the emission is due only to x-ray excitation of the luminescent centers. The spectral response of the emission is the same as that for the Ti glow peak. The intensity is about the same in all samples and is not affected by impurity content. This indicates that the luminescent levels involved are due to a crystal defect center and that the same center is involved in the thermoluminescence due to Ti.
Sequence Selection Problem in the Crystallization of Polymers
Authors: Gornick F. , Jackson J. L.
Published: January 2005

The crystallization of linear polymer chains is considered as a process involving the selection of crystallizable sequences from the melt. If, owing to the requirements of thermodynamic stability, such sequences must exceed in length some critical value less than the chain length, and if the selection process is random, then the melt will be increasingly subdivided into uncrystallized sequences of varying length. Some of these may be expected to be less than the critical length, so that the segments comprising them are ``wasted'' insofar as participation in further crystallization is concerned.

An approximate sequence length distribution function for the uncrystallized sequences in the system is derived and utilized in connection with the problem of retardation in crystallization kinetics.
Energies of, and Transition Intensities Associated with, the Rotational Levels of Nearly Degenerate A1A2 Pairs of Vibronic States in Molecules of Symmetry C3v
Authors: Hougen Jon T.
Published: January 2005

Expressions for the energies of the rotational levels associated with a nearly degenerate A1A2 pair of vibronic states in a molecule of symmetry C3v are presented. These expressions take into consideration Coriolis interaction between the levels associated with the A1 vibronic state and the levels associated with the A2 vibronic state. Expressions for the intensities of rotational lines in transitions involving such a nearly degenerate A1A2 pair of vibronic states are also presented. In certain cases transitions involving a (accidentally) degenerate A1A2 pair of vibronic states will have the same appearance as transitions involving a (necessarily) degenerate E vibronic state. A loose analogy between the problem discussed in this paper and the problem of spin uncoupling in a 2Π state of a diatomic molecule is pointed out.
Weight-Average and z-Average Degree of Polymerization for Polymers Undergoing Random Scission
Authors: Inokuti Mitio
Published: January 2005

Closed expressions are derived for the weight-average and the z-average degree of polymerization for polymers undergoing random scission processes. These expressions are applicable to any initial molecular size distribution. Application is made to the case where the initial distribution is the generalized Poisson type. In particular, numerical results are given for some initially broad molecular size distributions of this type.