Volume 47, Issue 11, 01 December 1967

Anomalous Melting Transition in the Significant Structure Model of Liquids
View Description Hide DescriptionThe significant structure theory of Eyring et al. has been used to predict the melting curve of argon at high pressure. Anomalous results were obtained, which indicate that the model may not be suitable to describe the phenomenon of melting. Possible reasons for these results are discussed.

Nuclear Magnetic Resonance Study of Molecular Motions in Hexamethylbenzene
View Description Hide DescriptionAn investigation has been made of the molecular motions occurring in solid hexamethylbenzene by measuring the proton spin—lattice relaxation time and second moment over the temperature range from helium temperatures to 450°K. The reorientation of the methyl groups is found to persist down to 2°K, presumably due to a tunneling mechanism; while the rotation of the whole molecule about its sixfold axis proceeds at a rate greater than a few kilocycles per second above 150°K. No other type of motion seems to occur at such rates, or greater, in the solid. The temperature dependence of T _{1} is used to estimate the activation energies and motional rates for the respective motions in each of the three solid phases.

Semiclassical Phase Shifts for Low‐Energy ``Orbiting'' Collisions
View Description Hide DescriptionA semiclassical expression for the phase shift in the literature which is applicable even when a maximum exists in the effective potential is re‐expressed in terms of the simple JWKB phase integrals. This expression is employed to calculate phase shifts from tables of reduced functions for a Lennard‐Jones (12–6) potential. These semiclassical calculations are compared with published exact values; excellent qualitative and good quantitative agreement is obtained. Finally, the qualitative nature of the quantal corrections to the classical total and differential cross sections and the collision lifetime is discussed.

Asymptotic Behavior for the Particle Distribution Functions of Simple Fluids near the Critical Point. II
View Description Hide DescriptionThe main purpose of this paper is to investigate the asymptotic behavior of the reduced probability density, ρ_{ p+q+s } ({p}, {q}, {s}), of p+q+s molecules when the molecules within each of the three subsets {p}, {q}, and {s}, are close together but there are large separations between the sets of p, q, and s particles. The interest is in the case where p, q, and s are unity or two. One may use the asymptotic long‐range correlation function to understand the critical singularity of the thermodynamic quantities at the critical point.

Vibrations and Thermodynamic Properties of Hexasulfur
View Description Hide DescriptionInfrared and Raman spectra of Engel's sulfur S_{6}, including complete polarization data for solutions of S_{6}, provide assignments for the fundamental modes. Force fields that have been successful for S_{8} provide good agreement with the S_{6}spectra. A force model previously used for S_{8} is shown to be incorrect. Thermodynamic properties (H_{T} °—H _{0}°, F_{ T }°—H _{0}°, S_{T} °—S _{0}°) for gaseous S_{6} are tabulated from 100° to 3000°K. The spectroscopic values S_{400}° (92.8 eu) and S_{298}° (84.6 eu) are in excellent agreement with those derived from thermodynamic measurements.

New Measurements of the Infrared and the Raman Spectrum of S_{2}Cl_{2}
View Description Hide DescriptionThe Raman spectrum of S_{2}Cl_{2} has been excited with a 6‐mW He–Ne laser, 6328 Å, and new depolarization ratios of the Raman bands have been obtained. The Raman band at 449 cm^{−1} previously reported by earlier workers is shown to be two bands corresponding to two fundamentals, one of Type A and another Type of B, at 446 cm^{−1} and 434 cm^{−1}, respectively. The Raman band at 102 cm^{−1} corresponding to the torsional mode is found to be polarized in disagreement with earlier investigations; the torsional mode is far‐infrared active at 106 cm^{−1}. Three infrared‐active fundamentals and six overtones were observed in the 3000–400 cm^{−1} region. One of these overtones at 1340 cm^{−1} has not been reported previously. One Raman overtone band and one Raman combination band have been observed at 858 cm^{−1} and 647 cm^{−1}, respectively. The Raman and infrared data have been correlated with the right‐angle configuration of C _{2} symmetry, and thermodynamic properties have been calculated for the liquid state using the harmonic‐oscillator approximation.

Dynamic Mechanical Properties of Chlorinated Biphenyls and Polystyrene—Chlorinated Biphenyl Solutions at 40 MHz
View Description Hide DescriptionMeasurements of dynamic shear impedance at 40 MHz and 25°C were carried out on solutions of monodisperse polystyrenes of molecular weight 2.67×10^{5} and 2.39×10^{5} in chlorinated biphenyl solvents (Aroclors). Measurements were also obtained on solutions of monodisperse polystyrenes of molecular weight 2.03×10^{3} and 1.8×10^{6} in di‐n‐butyl phthalate (DBP). In addition, measurements were obtained on one binary mixture of Aroclors and on five pure Aroclor solvents. These covered a range of 10^{6} in steady‐flow viscosity. The dynamic measurements were made by an ultrasonic reflectance technique employing pulse super‐position or by a phase‐amplitude balancing method. Results for the polystyrene—Aroclor system indicate that the effect of a solvent slightly better thermodynamically than DBP is observed as an increase in the in‐phase modulus, whereas little effect is observed in the magnitude of the polymer contribution to the out‐of‐phase modulus (G″—ωη_{ s }), where ω is the angular frequency, η_{ s } is the solventviscosity, and G″ is the modulus. Measurements on polystyrene dissolved in an Aroclor solvent for which η_{ s } is about 3 P indicate a reduced dynamic viscosity lower by a factor of 2.5 than that obtained at 73 kHz by other workers. Results for the low‐molecular‐weight polymer (2.3×10^{3}) indicate a behavior more nearly Newtonian than that predicted by the Zimm theory, while results for the high‐molecular‐weight polymer (1.8×10^{6}) conform closely to it. Measurements for the Aroclors show that viscoelastic behavior is already significant for an Aroclor with a steady‐flow viscosity of 3 P. Logarithmic plots of reduced values of G′ and G″ cross at a reduced frequency of about 10^{9.90} and both G″/ρ and η″/η exhibit a maximum at a reduced frequency of about 10^{10} Hz. The series is analyzed in terms of several theories of viscoelastic behavior.

Vapor Pressures of Isotopic Methanes—Evidence for Hindered Rotation
View Description Hide DescriptionThe liquid—vapor separation factors of CH_{3}T and ^{14}CH_{4} from ^{12}CH_{4} have been determined over the temperature range 90°—120°K by the column‐distillation technique. ^{14}CH_{4} is less volatile than ^{12}CH_{4} over the measuredtemperature range; CH_{3}T shows the cross over at 103.9°K. The reduced partition function ratios derived from the elementary separation factors are
The reduced partition functions of all the deuteromethanes and ^{13}CH_{4} in the liquid and solid are derived from known vapor‐pressure data. Comparison of the T ^{−2} dependence of species of equal molecular weight but different moments of inertia, i.e., CH_{3}D and ^{13}CH_{4}, and ^{14}CH_{4}, CH_{3}T, and CH_{2}D_{2}, with model calculations leads to the conclusion that the rotation in methane is hindered both in the liquid and the solid.

Optical Absorption Spectrum and Optical Zeeman Effect in CaWO_{4}:Yb^{3+}
View Description Hide DescriptionThe absorptionspectrum of 0.01%—0.05% ytterbium‐doped calcium tungstate is reported, observed at liquid‐helium temperature. Some of the samples contained sodium for charge compensation. The effect of Na charge compensation for Yb was found to be similar to previous results observed for Na‐compensated Ce in the same host. The spectrum was found to contain extensive complex structure that may be associated with the known lattice modes. The crystal‐field parameters have been calculated to fit the main lines of the spectrum, and the g values that are known. The calculation was made both with and without mixture of states of unequal J. Measurements of the Zeeman effect allow unambiguous identification of the symmetry of the lowest level. In terms of the free‐ion JM states this level consists of a combination of and functions. The g values for this state are g _{‖} = 1.2±0.1 and g _{⊥} = 1.5±0.1 observed at 31 kOe.

Recombination in Columns
View Description Hide DescriptionGaseous matter is considered, in which an initially inhomogeneous ionization in columns is produced by charged particles. The simultaneous processes of ionization carrier diffusion from, and recombination in, the columns are calculated for a plasmamodel considering the effects of different electron and ion mobility in the nonisothermal collective diffusion approximation. Analytical solutions of the space and time dependence of the electron and ion density fields and the electric diffusion field are given, as well as the temporal development of the effective column radius, and the critical time τ_{ H } for the ionization to become homogeneous. Based on the dynamics of the individual ionization columns, a macroscopic recombination theory is developed resulting in a quasilinear recombinative plasma decay equation for times 0≤t<τ_{ H }. The effective columnar recombination coefficient is shown to be considerably larger than the atomic recombination coefficient, α_{ N }>α for t<τ_{ H }, and explicitly time dependent due to the internal dynamics of the system, α_{ N }→α for t→τ_{ H }.

Ion—Molecule Reactions of Propane Ions with Benzene, 1,3—Butadiene, Hydrogen Sulfide, and Nitric Oxide
View Description Hide DescriptionReactions of the principal primary ions from propane, C_{3}H_{8} ^{+}, C_{3}H_{7} ^{+}, C_{3}H_{6} ^{+}, C_{3}H_{5} ^{+}, C_{3}H_{3} ^{+}, C_{2}H_{5} ^{+}, C_{2}H_{4} ^{+}, C_{2}H_{3} ^{+}, and CH_{3} ^{+} with benzene, 1,3‐butadiene, nitric oxide, and H_{2}S were investigated in a tandem mass spectrometer.Reaction mechanisms are deduced for these systems and it is suggested that a relatively long‐lived reaction complex is involved for most of these reactions. For the reaction of propyl ions with benzene an unstable adduct C_{9}H_{13} ^{+} was observed which could be stabilized by collision and a unimolecular rate constant of 10^{7}sec^{−1} for its decomposition was estimated from its pressure dependence. In the H_{2}S^{+}–C_{3}D_{8} and C_{3}D_{8} ^{+}—H_{2}S systems charge exchange and deuteronation of H_{2}S are competitive reactions, both proceeding via a long‐lived intermediate C_{3}D_{8}H_{2}S^{+} in which extensive isotopic exchange occurs. The results of this study are correlated with recent radiolysis experiments and it is concluded that these two methods for studing gas‐phase ionic reactions are complementary.

Photochemistry of N_{2}O Essential to a Simplified Vacuum‐Ultraviolet Actinometer
View Description Hide DescriptionThe net number of molecules generated per quantum absorbed (Φ_{Δn }) in the photodecomposition of N_{2}O with 1849‐Å light was shown to be 1.00±0.05 in the range 4 to 214 torr N_{2}O at room temperature. Direct measurement of Φ_{NO} at initial pressures of from 5 to 30 torr N_{2}O, and the constancy of Φ_{Δn } over a large N_{2}O pressure range, indicate that Φ_{NO} probably does not change with N_{2}O pressure under the above conditions. In most other respects, our results agree with those of other workers. It is shown that Φ_{Δn } should be 1.00±0.05 in the range 1380–2100 Å, and that Φ_{Δn } should be ∼0.8 in the range 1200–1380 Å.

Effect of Excluded Volume on Polyelectrolytes in Salt Solutions
View Description Hide DescriptionA recently developed theory of excluded volume, relating α to z ∝ M ^{½}βL ^{−3} by means of an integral equation, is applied to polyelectrolytes. The line describing α(M ^{½}) is the same for all polymers; the dependence of α on the polyelectrolyte parameters (ionic strength and charge density) requires, however, further elaboration. Thus, the excluded volume β is summarily identified with the high‐potential shell coaxially surrounding the charged filament, as treated in a polyelectrolyte theory presented some time ago. Distinction is made between two cases: (a) When the shell radius is smaller than the link length L characterizing the polymer and (b) when the converse holds—so that the length of free hinged links becomes determined by the shell radius. The predicted dependence of α on the molecular weight and on the ionic strength is found to agree satisfactorily with the extensive viscosity data reported by Takahashi and Nagasawa. Additional aspects of investigating α(z) are also discussed.

Partial Interference and Atomic Distribution Functions of Liquid Silver—Tin Alloys
View Description Hide DescriptionThe x‐ray scatterings from liquid Ag–Sn alloys previously measured at temperatures 100°C above the respective liquidus temperatures have been reanalyzed. The total‐interference functions (also called structure factors) I(K), where K=4π sinθ/λ, were first refined and then used to calculate the partial‐interference functions I_{ij} (K), assuming that they are approximately independent of the atomic concentrations. The least‐squares analysis with five different atomic concentrations of Sn, i.e., 18.5, 25, 36.5, 50, and 68.5 at.%, yielded three I_{ij} (K).
The Fourier transform of I_{ij} (K) leads to the partial radial distribution function (RDF)=4πr ^{2}ρ_{ ij }(r)/c_{j}, and the reduced distribution functionG_{ij} (r)=4πr[ρ_{ ij }(r)/c_{j} —ρ_{0}], where ρ_{ ij }(r) is the partial radial density, c_{j} is the atomic concentration of the j‐atoms and ρ_{0} is the average atomic density. Thus calculated I_{ij} (K) and G_{ij} (r) were used to reproduce the measuredI(K) and their corresponding G(r), and a remarkably good agreement was found between the measured and calculated values. Judging from the observed agreement, it can be concluded that for liquid Ag–Sn alloys the partial I _{SnSn}(K), I _{AgAg}(K), and I _{SnAg}(K) are not influenced by the relative abundance of the elements.
The resistivity of the alloys obtained with I_{ij} (K) and the pseudopotential elements U_{i} (K) agrees well with those measured experimentally.

Use of Corona Discharges for the Study of Ion—Molecule Reactions
View Description Hide DescriptionLow‐pressure positive corona discharges have been developed for studies of ion—molecule reactions at pressures which exceed those used in conventional high‐pressure mass spectrometry by several orders of magnitude. The reactions occurring within the discharge are studied by means of a mass spectrometer, sampling the ionic species which arrive at the cathode. Studies made in a system of nitrogen and trace quantities of either water vapor or oxygen have shown the importance of both ion—molecule reactions and charge‐exchange processes which occur in atomspheric gases. The cross sections for a number of these processes with ions of near thermal energies have been measured.

Compressibility of Solid Iodine
View Description Hide DescriptionA large discrepancy exists between the recently published, static, x‐ray‐determined compressibility of solid iodine and previously published shock‐wave compression data. In order to resolve this discrepancy, static piston displacement compression measurements have been made on iodine up to 40 kbars. The agreement of these measurements with shock data indicates that compressions calculated from x‐ray data on iodine are in error.

Shock‐Tube Study of the Recombination Rate of Hydrogen Atoms with Oxygen Molecules
View Description Hide DescriptionMeasurements have been made of the rate of chain branching during the induction period of the H_{2}–O_{2}reaction. Mixtures of H_{2}–O_{2}–CO–Ar were shock heated and the ``blue continuum'' emission from the O+CO→CO_{2}+hvreaction was monitored using an end‐on technique for sensitivity. Experiments performed at different densities were analyzed to yield the rate coefficient k _{4} ^{Ar}=3.3×10^{9} liters^{2} mole^{−2}·sec^{−1} at 1100°K for the reactionThis value when combined with other literature values for k _{4} ^{Ar} yields the temperature‐dependent expressions and . In addition values of k _{1} for the reactionwere obtained from the data between 975° and 2060°K and combined in the Arrhenius expression accurate to ±20% over our range. A value for at 1500°K was obtained for the reactionThe end‐on technique is shown to be a useful tool to study recombination reactions involving only one free radical.

New Scaled Atoms‐in‐Molecules Theory for Predicting Diatomic Potential‐Energy Curves. I. General Theory and Application to H_{2} and He_{2} ^{+ +}
View Description Hide DescriptionAn exact scaled atoms‐in‐molecules theory for predicting potential‐energy curves and other properties of diatomic molecules is developed. The basis consists, in the first place, of linear combinations of antisymmetrized products of atomic substate eigenfunctions. Each such basis function ψ_{ n } can be modified by introducing variational scaling parameters s_{n} ^{A} and s_{n} ^{B} into its component atomic eigenfunctions. Exact equations are developed for determining, by reference to experimental atomic properties, all intra‐atomic contributions to the energy matrix elements. All remaining parts of the energy matrix elements are interatomic in nature, and these parts are computed using previously determined approximate atomic eigenfunctions; as the latter are successively made more accurate, results of the diatomic calculation should converge to experiment. A restricted orbital model, which reduces the number of independent nonlinear variational parameters, is also proposed. Initial applications to ground and excited electronic state of H_{2} and He_{2} ^{+ +} are presented. A potentially useful approximate calibration technique is suggested and tested.

Sudden Approximation Applied to Rotational Excitation of Molecules by Atoms. III. Angular Distribution and Energy Dependence of the Inelastic Scattering
View Description Hide DescriptionThe sudden approximation for rotational excitation of diatomic polar molecules by atomic impact is applied, yielding semiclassical angular distributions of rotational transition cross sections and their energy dependence. The results for a model system (intended to approximate TlF–Ar) are not inconsistent with the experimental findings of Toennies. The dominant excitations are those allowed by first‐order time‐dependent perturbation theory, but the strong coupling (due principally to the large long‐range anisotropy in the potential) produces extensive excitation to remote open channels, i.e., those forbidden by low‐order perturbation theory. The main prediction of the present work is the presence of a single major peak in each of the various differential polar inelastic cross sections; with increasing collision energy, these maxima trend to smaller angles and increase in peak intensity.

Statistical Thermodynamics of Self‐Avoiding Random Walks
View Description Hide DescriptionThe statistical thermodynamics of self‐avoiding random walks on the diamond lattice with nearest‐neighbor interaction energy ε is examined. If the probabilities per step of nearest‐neighbor formation are taken as fundamental quantities, it is possible under a reasonable and simple assumption about the form of such probabilities to derive an expression for the canonical partition function. The partition function of a walk of σ+l steps relative to a single walk of length σ is , where a=exp(—ε/kT) and the p_{n} are suitably defined nearest‐neighbor formation probabilities.