Volume 50, Issue 8, 15 April 1969

Dynamics of a Long Polymer Backbone
View Description Hide DescriptionFor the study of the dynamics of a polymer molecule in dilute solution a continuous wire model is proposed and investigated. This model is a refinement of the wormlike chain model introduced by Kratky and Porod such that the configurational energy depends not only on the curvature but also on the torsion , both of which may be considered as functions of the arc lengths measured from one end. The physical basis of considering such energy dependence is given from a general differential–geometrical viewpoint, and also by the explicit calculation of the elastic energy of an ideally thin wire, which is found to be , where and are Young's modulus and the modulus of rigidity of the wire material; is the radius of the circular cross section of the wire; and are the curvature and torsion of the space curve characterizing the wire of minimum energy. The dynamics of the model is formulated with the aid of Hamilton's principle of least action. In particular the wave propagation along the axis of a helical coil is investigated in detail. It is shown that the measurement of the propagation speed of a longitudinal wave along a polymer chain can lead to the quantitative estimate of the bending and twisting characteristics of the chain.

Theory of Trapped‐Hole Centers in Rare‐Gas Solids
View Description Hide DescriptionExperimental evidence suggests that self‐trapping of holes occurs in rare‐gas solids. Formation of an intrinsic diatomic center, similar to the center, is investigated as a possible mechanism. The energy of trapping a valence‐band hole is discussed on the basis of a simple model for the rare‐gas hole center. A method of calculating the relaxation and polarization energies is developed, appropriate parameters for the model estimated, and the method applied to solid argon, krypton, and xenon to determine the degree of relaxation and the contributions to the trapping energy. The results suggest stable trapped‐hole centers at 0°K associated with only small lattice relaxations. The internal molecular binding of the center is found to be the overwhelming factor determining its configuration on this model.

Neutralization of Isolated Ion Pair in Polar Media. I. Theory for the Yield of Solvated Electrons
View Description Hide DescriptionMotion of an isolated ion pair in a polar medium is described here through the Smoluchowski equation with a time‐dependent dielectric constant. The time dependence is taken as appropriate to constant charge rather than to constant external field. Explicit solution of the problem is obtained in the framework of prescribed diffusion. This solution, in the infinite time limit, gives the escape probability. The yield of escaped electrons is identified with the solvated electron yield. Known yields in various polar media are used to calculate the respective thermalization distances and effective dielectrc constants. Dielectric relaxation time is explicitly used in the present formulation. Two diffusion constants are used, one prior and one after relaxation. Calculated results are compared with experiment. Physical concepts derived from the present model relate to thermalization length, effective dielectric constant, and diffusion–relaxation length.

Neutralization of Isolated Ion Pair in Polar Media. II. Evolution of the Neutralization Process
View Description Hide DescriptionIn this paper we discuss the neutralization rate of an isolated ion pair in a polar medium as obtained from the prescribed diffusion solution of the Smoluchowski equation. Specifically, we consider the cases of water, methanol, and ammonia. A specific model with two diffusion constants and a time‐dependent dielectric constant has been employed. The time dependence of the dielectric constant is taken, as in the previous paper, for the situation of fixed charge rather than for fixed external field. Numerical results have been obtained for the probability that the ion pair remains unneutralized at a given time and for the rate of change of this probability with time. A critical review is presented for the time–distance relationship.

Equation‐of‐State Measurements in Compressed Argon
View Description Hide DescriptionA weighting technique used in obtaining experimental data for argon at high pressures is described. The data for fluid argon at pressures from 0.2 to 6.3 kbar and temperatures from 95° to 210°K are presented, along with melting data for argon in this range. The entropy and energy of argon are derived from these data. Recent theoretical calculations are compared with the results, and a discrepancy between the calculated and experimental values for the energy is discussed.

Mössbauer Spectra of Tetrahedral Alkali Dithioferrates (III)
View Description Hide DescriptionMössbauer spectra were taken of a series of compounds with tetrahedrally coordinated iron (III) having a general formula AFeS_{2}, where A=Na, K, Rb, Cs, over a temperature range 77°–300° K. The molar susceptibilities were also examined over the same range of temperatures. The almost temperature independence of indicates that level separation is larger or . In contrast to the observations in the case of octahedral compounds, the increasing electronegativity of the cation increases the isomeric shift (I.S.) value. This is explained by the fact that the decreasing electronegativity of the cation increases the partial character at iron in the compound. Furthermore, it is pointed out that the Walker, Wertheim, and Jaccarino (WWJ) plot is applicable to the compounds having tetrahedrally bonded iron. The internal magnetic field in KFeS_{2} at − 28°C is considered to result not from any magnetic transition, but from relaxation effects, whereas in the case of Na, Rb, and Cs dithioferrates it has been averaged to zero.

Rotational Relaxation in Parahydrogen and Its Mixtures with Helium, Neon, and Argon at 300°K
View Description Hide DescriptionUltrasonic‐velocity dispersionmeasurements have been performed in parahydrogen and its mixtures with helium, neon, and argon, all at 300°K. In each case the experimental dispersion curves can be matched successfully to those calculated under the assumption that the 0–2 rotational transition relaxes separately from the 2–4 and higher‐order terms. For pure pH_{2} we find a relaxation time of 1.30 × 10^{−8} sec for the 2 → 0 transition and a of 3.90 × 10^{−8} sec for the 4 → 2 transition. Comparison with the quantum‐mechanical theories of Roberts and of Davison for H_{2}–H_{2} collisions using Morse potentials shows good agreement for over the temperature range of 75°–300°K. The Morse‐potential asymmetry parameter yielding the best fit is for Roberts' calculation and 0.108 for Davison's. It is found that He–pH_{2} collisions are more effective than pH_{2}–pH_{2} in producing the to transition, but less effective for higher‐order transitions. Collisions of neon with pH_{2} are found to be more effective at room temperature for inducing the 0 → 2 and 2 → 4 transitions than either helium or argon.

Mass‐Spectrometric Investigation of the Reaction of Hydrogen with Graphite at 1900°–2400°K
View Description Hide DescriptionAn integral furnacemass spectrometer was used to directly observe the products of the reaction of hydrogen with graphite between 1880° and 2430°K at pressures up to 0.5 torr and with 80‐msec contact times. Ions observed to 140 indicate formation of an extensive high‐molecular‐weight hydrocarbon system consisting mainly of unsaturated, acyclic, nonaromatic compounds. Many of these compounds were formed in steady‐state concentrations much greater than expected for equilibrium. A reaction mechanism involving addition and insertion reactions is discussed.

Characterization of Ground‐State Wavefunctions by Measured Electronic Properties. II. Dipole Moment and Field Gradient of Nitrogen Trifluoride
View Description Hide DescriptionA particular localized‐orbital type of LCAO MO wavefunction is used to calculate the dipole moment and field gradient at the nitrogen atom in NF_{3}. Because the wavefunction is not obtained by the usual self‐consistent‐field procedure, the results for the various observables depend on the choice of calculation parameters such as the polarity of the bonds, the amount of bonding, and the hybridization of the lone‐pair orbitals on the fluorine atoms. This dependence is studied in detail and it is concluded that with reasonable choices of input parameters, good agreement with experiment can be obtained. Thus, the localized orbitals specified by setting the σ‐bond coefficient equal to 0.875, the π‐bond coefficient equal to 0.0, and the fluorine lone‐pair orbital angle equal to 112.7°, yield a dipole moment of 0.236 D and a total field gradient at the N atom of − 2.007 a.u. The experimental dipole moment is 0.234 ± 0.004 D and the experimental field gradient is − 1.505 to − 3.010 a.u. depending on the exact value of the nuclear quadrupole moment of nitrogen.

Characterization of Ground‐State Wavefunctions by Measured Electronic Properties. III. A Gaussian Basis Self‐Consistent‐Field Calculation for Nitrogen Trifluoride
View Description Hide DescriptionAn LCAO MO SCF calculation has been carried out for nitrogen trifluoride using an uncontracted (73 / 73) Gaussian basis set. Energy parameters, dipole moment, field gradient, molecular quadrupole moment, second moments of charge, and population analysis are reported. The calculation is used to evaluate earlier wavefunctions obtained by more empirical methods. Combining experimental quadrupole‐coupling‐constant data with the calculated field gradient gives a nitrogen nuclear quadrupole moment of + 0.018 ± 0.003 × 10^{−24} cm^{2} which is in good agreement with earlier, less precise, estimates of this parameter.

Structure and Free Energy of the Interface between Fluid Phases in Equilibrium near the Critical Point
View Description Hide DescriptionThe theory of van der Waals and of Cahn and Hilliard, which yields the density or concentration profile through an interface and the associated interfacial tension, is generalized by replacing the equation of state assumed originally by one that reproduces more accurately the known thermodynamicsingularities at the critical point. Though the correct equation of state is not known, its presumed homogeneity of form is alone sufficient to allow most features of the interface to be determined explicitly. In particular, the maximum density gradient in the interface, the asymptotic behavior of the interface profile at large distances from the position of its maximum gradient, and the surface tension, are each obtained up to a dimensionless, and presumably universal, proportionality constant that reflects only the functional form of the equation of state. Numerical evaluation of the surface tension requires a knowledge of the limits approached by the correlation length and compressibility in the homogeneous fluid as the phase transition point is approached. These are only imperfectly known, so the surface tension calculated from the theory is subject to some uncertainty, but within its limits of uncertainty it is in agreement with experiment.

Theoretical Investigation of the Lowest Double‐Minimum State of the Hydrogen Molecule
View Description Hide DescriptionAccurate potential‐energy curve for the first excited state of the hydrogen molecule has been calculated for . The curve is known to have a double minimum, and for the outer minimum a significantly lower energy has been obtained than all previously reported results. The diagonal corrections for nuclear motion have also been computed and found to have a very sharp peak in the vicinity of the potential maximum. Vibrational and rotational levels have been calculated for all isotopes of the hydrogen molecule, and some results for H_{2}, D_{2}and T_{2} are shown and compared with experimental data. For the outer minimum, two, three, and four vibrational levels for H_{2}, D_{2}, and T_{2}, respectively, are reported which lie below the lowest levels observed experimentally. For the observed levels good agreement with experimental data is obtained; however, the agreement is significantly worse when only the clamped nuclei potential without the diagonal corrections is used in the calculation of the vibrational energies. The wavefunction is analyzed in terms of some simple functions and appears to drastically change its character in the vicinity of the potential maximum.

Absorption Spectrum of Ni^{2+} Ions in Spinel
View Description Hide DescriptionSingle crystals of Ni^{2+}‐doped spinel were made by using a large solar furnace in our laboratory, and their absorption spectra were measured in near‐infrared, visible, and ultraviolet regions. The observed bands were analyzed according to the crystal‐field theory in which the spin–orbit coupling was taken into account, and all of them were identified with the bands of Ni^{2+} ions not only in octahedral but also in tetrahedral site symmetry. The crystalline‐field parameter in both symmetries are − 1015 and 452 cm^{−1}, respectively. Their ratio amounts to − 4.008 / 9 which shows an excellent accordance with the theoretical value − 4 / 9. By adjusting the MgO concentration, the crystals with slightly different Ni–O distance could be obtained. From the measurement of and of these crystals, it was found that varies linearly as . These results are considered to show the validity of applying a point‐charge model in the treatment of the problem of this kind.

Broad‐Line NMR Study of H_{2}O and D_{2}O in Collagen Fibers
View Description Hide DescriptionThe deuterium NMRspectra of D_{2}O absorbed in parallel collagen fibers have been recorded for samples containing four different percentages of D_{2}O. In all cases, the spectra consisted of a pair of lines, the separation of which is given by , where is small compared to the rigid‐lattice value and decreases with increasing moisture content of the fibers, and is the angle between the fiber axis and the magnetic field. The splitting is ascribed to quadrupole perturbation of the Zeeman levels of deuterium caused by slightly anisotropic but rapid reorientation of D_{2}O molecules in the fiber lattice. Contrary to the interpretation by others, we have concluded from a comparison of the spectra of D_{2}O and H_{2}O in collagen: (1) that the center line in the H_{2}O spectra is not due to water, and (2) that line broadening in the H_{2}O spectra, both at high temperatures and in the presence of added salts, is due to proton exchange between the water molecules. Molecular motion causes both H_{2}O and D_{2}O splittings to be reduced to approximately the same fraction of their respective rigid‐lattice splittings.

Matrix‐Isolation Study of the Vacuum‐Ultraviolet Photolysis of Methyl Fluoride. The Infrared Spectra of the Free Radicals CF, HCF, and H_{2}CF
View Description Hide DescriptionUpon vacuum‐ultraviolet photolysis of methyl fluoride in an argon or a nitrogen matrix at 14°K, the free radicals CF, HCF, and H_{2}CF are stabilized in sufficient concentration for observation of their infrared absorption spectra. Studies utilizing carbon‐13 and deuterium substitution confirm the identification of these species. Visible‐ultraviolet absorption spectra of photolyzed Ar:CF_{3}F samples include bands which may be assigned to CH, to CF, and to HCF. The reaction of carbon atoms, produced by the photolysis of cyanogen azide isolated in an argon matrix, with HF trapped in the matrix has also been found to lead to the stabilization of sufficient HCF for infrared spectroscopic detection. Reaction of HCF with a second molecule of HF to form CH_{2}F_{2} also occurs. The force constants and thermodynamic properties of HCF have been calculated, and a partial vibrational assignment is proposed for H_{2}CF. Although these experiments do not determine the primary photodecomposition processes important for methyl fluoride, there is evidence that both H atom and F atom detachment may occur under the conditions of these experiments.

Gaseous Diffusion in Neon‐Noble‐Gas Systems
View Description Hide DescriptionDiffusion coefficients of all four neon–noble‐gas binary systems are reported as determined with a two‐bulb apparatus over the temperature range o°‐120°C. The experimental values, reduced to 1 atm pressure and trace composition of the heavier component, can be described by the expressions He–Ne, ; Ne–Ar, ; Ne–Kr, ; Ne–Xe, . The present data are in favorable accord with the results of other workers and with diffusion coefficient values that are derived from studies of the composition dependence of the viscosity coefficient. Values derived from the composition dependence of the thermal conductivity coefficient are in fair agreement in general, but this method does not provide nearly as reliable a means of obtaining diffusion coefficient data as does viscosity.

Triplet‐State Zero‐Field Splittings in Some Aromatic Hydrocarbons and Nitrogen Heterocycles
View Description Hide DescriptionThe SCF‐AO's expanded by Löwdin have been used for the calculation of the electron spin dipolar interactions in the triplet‐state zero‐field splittings of some aromatic molecules. Within a framework of two‐center approximation for the spin–spin interaction integrals over atomic orbitals, and adopting the Sklar‐type approximation for the exchange‐type integrals, excellent agreement with experiments has been obtained for benzene and naphthalene without invoking interactions. The wavefunctions used were obtained by means of the Pariser–Parr–Pople method, within a full single excitation configuration treatment. This approach has been extended to some aromatic nitrogen heterocycles, but the results, although promising, are poorer, possibly due to the neglect of spin–orbit coupling. Uncertainty in the choice of the C–N resonance integral and the neglect of penetration integrals in the core Hamiltonian may also be factors. Eleven molecules have been treated in all. For comparison, the single‐determinant unrestricted Hartree–Fock wavefunctions also have been employed, but these give extremely poor agreement with experiment.

Optical Properties of Tin Iodide Vapor
View Description Hide DescriptionThe optical absorption of SnI_{2}, SnI_{4}, and HgI_{2} were measured photometrically in the visible and near ultraviolet. The spectral and temperature dependence of radiation emitted by thermally excited SnI_{2} vapor was also measured and a tentative model for the electronic states of the SnI_{2} molecule deduced.

Long Radiative Lifetimes of Small Molecules
View Description Hide DescriptionIn this paper, we apply a theory of electronic relaxation in polyatomic molecules for the study of the anomalously long radiative lifetimes of NO_{2}, CS_{2}, and SO_{2}. We have classified medium‐size molecules which exhibit intramolecular vibronic coupling into two intermediate cases, which we call the sparse intermediate case and the dense intermediate case, characterized by low and high spacing of the vibronic levels relative to the radiative width. The radiative decay in the sparse intermediate case was considered in detail, taking advantage of the coarse level spacing and the extremely short intramolecular recurrence time encountered in this case. From our model calculations, we conclude that:
(a) in the sparse case, the radiative decay rate is characterized by a superposition of slowly varying exponentials;
(b) the mean radiative lifetime is expressed as a radiative lifetime calculated from the integrated oscillator strength and “diluted” by the number of states within the half‐width of the manifold of coupled levels;
(c) no intramolecular electronic relaxation processes are encountered in this case;
(d) a qualitative interpretation of the complex molecular spectra is provided.

Spectroscopic Study of Anthracene Cation Trapped in Boric‐Acid Glass
View Description Hide DescriptionThe electronic absorptionspectrum of anthracene in the boric‐acid glass, irradiated with uv light and x rays at room temperature, has been obtained in the region 2200–7000 Å. The spectrum of the irradiated film of anthracene has been attributed to the molecular monopositive ion of anthracene. The electronic energy levels of the ion of anthracene have been calculated by FE–MO method and compared with the LCAO–MO calculations of earlier workers. FE–MO calculations have been found to give satisfactory agreement with the experimentally observed energy levels. On the basis of these calculations, assignment of the observed bands is discussed and an attempt is made to remove the discrepancies in the assignment by earlier workers. The state of aggregation of anthracene in the boric acid along with the effect of temperature on the trapped ionic species is discussed.