Volume 50, Issue 6, 15 March 1969

Extension of the Debye–Hückel Theory of Electrolyte Solutions
View Description Hide DescriptionThe Debye–Hückel theory of electrolyte solutions is extended to take account of the so‐called fluctuation potential. An oscillation in the Debye–Hückel potential for symmetrical electrolytes is predicted at approximately and the corresponding oscillation in the mean potential of the double layer pointed out. A simple derivation of the oscillation predicted by Kirkwood and Poirier is also given.

Charge‐Overlap Effects. Dispersion and Induction Forces
View Description Hide DescriptionFor nondegenerate atom–atom and atom–ion interactions the long‐range interaction energy is expressed as a sum of “nonexpanded” angular components. If charge overlap is neglected each of the nonexpanded energies goes to a well‐defined limit; namely to one of the usual R ^{−1}‐expanded induction or dispersion energies or else to zero ( is the internuclear separation). The expansions appear to be asymptotic expansions of the nonexpanded results and are valid only for large . As specific examples the H–H^{+} and H–H interactions are considered as model systems for studying charge overlap effects in induction and dispersion forces. The calculations are carried out variationally using the complete discrete Laguerre functions of degree as a radial basis set. The asymptotic nature of the expansions for these interactions is discussed by comparing the various expanded and nonexpanded results. The importance of the nonexpanded interaction energies is also discussed briefly in general.

Experimental Study of the Equation of State of Liquid Argon
View Description Hide DescriptionThe density of liquid argon has been measured at 10 temperatures from 100.9° to 143.1°K and at pressures up to 680 atm. The results have been expressed as an equation of state in the form of a double Chebyshev expansion. This equation has been used to estimate, at regular intervals of temperature and pressure, the following properties: molar volume, isothermal compressibility, coefficient of thermal expansion, thermal pressure coefficient, and configurational internal energy. Comparison is made between the present results and previous work on liquid argon, both at the saturation vapor pressure and at higher pressures.

Examination of the Adequacy of the 12–6 Potential for Liquid Argon by Means of Monte Carlo Calculations
View Description Hide DescriptionMonte Carlo calculations of thermodynamic properties of argon are reported for the temperature range between the triple point and the critical temperature at pressures up to 700 atm. It is shown that the Lennard‐Jones 12–6 potential with the parameters proposed by Michels et al., viz., and , leads to internal energies and pressures which are in fair agreement with the experimental values. The over‐all agreement with experiment may be substantially improved by reducing the depth of the potential well to . The use of other potentials, the importance of nonadditivity corrections, and the agreement between the Monte Carlo results and those obtained by the method of molecular dynamics are briefly discussed.

Computed Probability Density Functions of the Radii of Gyration of Long Random‐Flight Chains
View Description Hide DescriptionProbability density functions for the orthogonal components of the radius of gyration, , of a random‐flight chain were computed using an indirect numerical integration algorithm which was based upon a multiple convolution proposed by Forsman and Hughes. Computations were performed for relatively long chains of 100–1000 statistical segments . By using a reduced radius of gyration the distributions converged to a limiting function at about , except for extremely small radii, . Additional computations using the one‐dimensional distributions yielded the corresponding probability densities for both the two‐ and three‐dimensional (polar) radii. The computed functions were in excellent agreement with all their limiting properties previously determined by analytical methods.

Effect of Neighboring Identical Atoms on Radiative Lifetime: The Case of Three Atoms
View Description Hide DescriptionTransition frequencies (inverse radiative lifetime) are evaluated as a function of separation for a system of three identical atoms or molecules one of which is initially excited. The resulting frequencies are increased or decreased relative to the value characteristic of an isolated atom according to whether the wavefunction is symmetric or not. The results depend on the geometrical configuration of the atoms.

Rydberg Progressions in cis‐ and trans‐Butene
View Description Hide DescriptionThe far‐ and vacuum‐ultraviolet absorption spectra of cis‐ and trans‐butene and trans‐butene‐d _{8} have been recorded at low resolution. The more prominent bands are shown to be either the members of Rydberg series, (cis‐butene), and (trans‐butene), and (trans‐butene‐d _{8}), or their vibrational subbands. The band observed at 49 690 cm^{−1} in trans‐butene‐d _{8} is seen, at higher resolution, to be polarized along the molecular axis, in agreement with its assignment. Finally, from a partial vibrational analysis of the trans‐butene spectrum, the C=C and C–C bonds of the excited states are deduced to be slightly longer than in the ground state.

Transfer of Electronic Excitation Energy in Polyvinyl Carbazole
View Description Hide DescriptionThe energy transfer in amorphous polyvinyl carbazole (PVCA) has been studied by fluorescence quenching experiments using perylene, trinitrofluorenone, and hexachloro‐p‐xylene as guest molecules. The PVCA shows excimer fluorescence. The results are discussed in terms of excitondiffusion and competition between excimer‐forming sites and guest molecules for the trapping of excitons. Single‐step transfer from the excimer state by dipole resonance is considered as an alternative mechanism of energy transfer; in all three cases, however, exciton migration is the more probable energy‐transfer mechanism. The concentration of excimer‐forming sites is estimated to be 10^{−3} mole/mole basic unit of the polymer. In the pure polymer the exciton covers about a thousand basic units during its lifetime.

Heat Capacity of Silver Sulfide
View Description Hide DescriptionThe heat capacity of silver sulfide has been measured over the range 50°–400°C using an adiabatic calorimeter. The heat capacity of the form, stable between 177° and about 600°C, is anomalous and has a form typical of an order–disorder transition with critical temperature at 350°C. If the sample deviates from stoichiometry by as little as one mole percent in either direction, its heat capacity is near normal at about 20 cal/mole·°C throughout the range of measurement. An interpretation of these results in terms of lattice disorder is suggested.

EPR Spectrum of Fe^{3+} in Synthetic Brown Quartz
View Description Hide DescriptionA detailed description is given of the EPR spectrum of Fe^{3+} in synthetic brown quartz (the so‐called center, presumed to be interstitial). There are three equally populated sites differing only in the orientation of their principal axes, which coincide with the three twofold axes of quartz. The values of the Hamiltonian parameters that fit the data best are: , where the are the coefficients of the Racah operators in the Hamiltonian. Lobes of the , and parts of the crystal‐field potential point 0.7°, 29.5°, and 26.8°, respectively, from the optic axis of quartz. The occurrence of irregular off‐axis extrema of the line positions when the magnetic field is directed in the vicinity of the optic axis precludes the assignment of magnetic axes of the paramagnetic center in the usual way. All features of the spectrum are predicted accurately by computer calculations based on the derived Hamiltonian. Although the data are not conclusive evidence, they are believed to be more consistent with an assignment of the center to a substitutional site.

Zero‐Field EPR of Fe^{3+} in Quartz
View Description Hide DescriptionThe zero‐field EPR transition frequencies of Fe^{3+} in synthetic brown quartz (SBQ) and natural amethyst(NA) have been measured directly. The values obtained, 7113.2 ± 0.2 and 8812.5 ± 0.2 MHz for SBQ and 24 157.5 ± 0.5 and 35 365 ± 2 MHz for NA, are in excellent agreement with those calculated from the spin Hamiltonians derived from ordinary high‐field EPR spectroscopy.

Comparison of Continuum and Discrete Lattice Results for Gas–Surface Interactions
View Description Hide DescriptionClosed‐form analytical results for trapping and gas–surface energy exchange have been derived for a simple model employing a one‐dimensional elastic continuum representation of the solid with (1) a truncated harmonic potential and (2) a Morse potential for the interaction between the gas atom and the surface of the continuum. The results consist of formulas for the thermal accommodation coefficient (a.c.) and critical trapping energy, which are compared with corresponding results of McCarroll and Ehrlich and of Trilling for one‐dimensional discrete lattices. With the truncated harmonic potential, the continuum gives practically the same values of a.c. and critical trapping energy as the discrete lattice, in accordance with Landau's 1935 prediction, for cases in which the collision frequency is considerably smaller than the cutoff frequency of the lattice. With a Morse potential, the variation of a.c. with temperature is qualitatively correct for the continuum solid model, but the a.c. values appear to be considerably larger than those predicted by Trilling for a discrete lattice. The analysis for the continuum brings out the fact that both the truncated harmonic and Morse potential formulas for a.c. can be expressed in the form of a similarity relation , where is the a.c., is a function of is the dimensionless potential‐well depth, is the gas‐atom–solid‐atom mass ratio, is the average energy per gas atom/potential‐well depth. Experimental a.c. data for several gas–solid combinations appear to be correlated fairly well on a plot of .

Rotational Properties Associated with the Heitler–London Model of H_{2}
View Description Hide DescriptionThe first‐order WBK approximation has been used to determine rotational constants and for the Heitler–London (HL) model of the H_{2}ground electronic state. Near‐equilibrium characteristics of and are discussed briefly in terms of the potential expansion about . Over‐all, the HL and experimental curves have nearly the same shape. The HL curve has negative curvature at all converging at a slightly slower rate than the experimental curve at high . This slower convergence is associated with the factor used in defining . The HL curve, like the corresponding experimental curve, rises rapidly in the vicinity of dissociation. Both increases are attributed to a breakdown in the approximation that treats the centrifugal reaction term as a perturbation of the rotationless problem. The reliability of the first‐order WBK approximation is checked and found to lead to only slight errors in the and values.

Uncoupled Hartree–Fock Calculations of the Ring‐Current Contribution to the Magnetic Susceptibilities of Conjugated Molecules
View Description Hide DescriptionUncoupled Hartree–Fock perturbation theory is used to compute the ring‐current contributions to the magnetic susceptibilities of several conjugated hydrocarbons. In the usual form of the perturbation theory this leads to an origin dependent result, but when corrections are included this origin dependence is removed. The final results agree very well with those calculated using the more complicated coupled Hartree–Fock method, and, when empirical values are used for the local contributions to the susceptibility, the theoretical values for the components, the mean value, and the anisotropy of the susceptibility are in excellent agreement with experiment.

Adsorption of Cs on Tungsten: Measurements on Single‐Crystal Planes
View Description Hide DescriptionThe adsorption of immobilely deposited and thermally equilibrated Cs layers has been studied on the (110), (211), (100), (111), (103), and (115) regions of a tungstenfield emitter. The work‐function‐vs‐coverage data permit resolution into adsorbate charge and effective dipole length, at least on the high work‐function planes. The results indicate ionic adsorption on (110) and probably (211) at low coverage, with charge diminishing on all planes as increases. Dipole lengths exceed the ionic radius of Cs by 1.4–2 Å, indicating the effect of finite screening at the metal surface. The adsorption energies and their change with can be interpreted in terms of the “metallet” model.

Anisotropic Molecular Reorientation in Methyl‐d _{3}‐acetylene in the Liquid State
View Description Hide DescriptionThe temperature dependence of deuteron and proton spin–lattice relaxation times,, has been measured in methyl‐d _{3}‐acetylene and methylacetylene‐d _{1} using the adiabatic fast passage method. The difference in activation energies obtained from deuteron data for acetylenic deuteron and methyl‐d _{3} deuterons demonstrates that the reorientation is anisotropic without assumption of any model for reorientation. Assuming the validity of the rotational diffusion equation the deuteron 's due to quadrupolar interactions were analyzed in terms of rotational diffusion constants and . At −30°C and in methyl‐d _{3}‐acetylene. The applicability of the rotational diffusion mechanism for the description of the reorientation about the main symmetry axis is questionable as is shown by a comparison of with the time for the mean period of rotation of a free rotor. At temperatures above the bp the spin–rotation interactions contribute to the relaxation rates of protons, in addition to dipolar interactions which are predominant at lower temperatures. The spin–rotation interaction constants were approximately estimated to be 0.6–4.0 kHz for the acetylenic proton in methyl‐d _{3}‐acetylene and 6–25 kHz for the methyl group in methylacetylene‐d _{1}. The results indicate the importance of inertial effects.

Asymptotic Evaluation of WKB Matrix Elements
View Description Hide DescriptionA procedure is given for the analytic asymptotic evaluation of certain integrals which arise in the quantum‐mechanical theory of inelastic molecular collisions. The integrals are evaluated using WKB wavefunctions and the saddle‐point method. The method is equivalent to Landau's but is considerably more transparent and is easily applied to vibrational and rotational transitions for which there is no crossing of potential‐energy surfaces, as well as to electronic transitions near a crossing point. The special case of resonance collisions is discussed, and the method is illustrated with an example.

Spectral Study of NO_{2} Fluorescence Excited by 11 Lines of Argon and Krypton Ion Lasers
View Description Hide DescriptionHigh‐resolution spectra of the fluorescence of NO_{2} excited by 11 Ar^{+} and Kr^{+} laser lines between 4579 and 5208 Å, have been obtained at NO_{2}pressures from 10^{−3}–10 torr. Rotational lines as well as vibrational bands are observed superimposed on a continuum extending from the exciting line to the observation limit of 7500 Å. Vibrational assignments of the fluorescent bands have been made, and vibrational constants of the gound electronic state have been determined. The pressure dependence of absorption coefficients of NO_{2} at the laser wavelengths also was measured; an excited‐state lifetime near 10^{−5} sec was estimated from these absorption coefficients. In addition, the lifetime of excited NO_{2} was measured to be 5 × 10^{15} sec from the observation of the increase in visual size of the fluorescence beam at low pressure. Preliminary values of (square of collision diameter times lifetime) of the fluorescence excited by the 4880‐Å line were measured to be approximately 7 × 10^{−20} cm^{2}·sec for line emission and 0.5 × 10^{−20} cm^{2}·sec for the integrated continuum emission, respectively; this difference is attributed to the difference in rates of rotation–vibration collisional transfer and electronic quenching.

Rice–Allnatt Theory of Transport for Rough Spheres
View Description Hide DescriptionThe Rice–Allnatt theory for liquids of monoatomic molecules is extended to rotating hard cores surrounded by symmetrical soft potentials. The kinetic equation is solved by the Chapman–Enskog method. Numerical values for the thermal conductivity, the shear viscosity, and the bulk viscosity coefficients are evaluated and tabulated to show the dependence on molecular moment of inertia.

Magnetic‐Susceptibility Anisotropy, Molecular Value, and Molecular Quadrupole Moment of ^{15}N^{15}N^{16}O
View Description Hide DescriptionThe high‐field rotational Zeeman effect has been observed in ^{15}N^{15}N^{16}O to give an absolute value of the molecular value of and an anisotropy in the magnetic susceptibility of . Arguments are given which show conclusively that the molecular value is negative. The molecular quadrupole moment in the center‐of‐mass coordinate system is . The values of the second moment of the electronic charge distribution in NNO are and . The results are compared with similar results for CO_{2}, O_{2}, and N_{2}.