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Volume 60, Issue 3, 01 February 1974

Mass spectrometric study of the gaseous gallium monocyanide
View Description Hide DescriptionUsing the mass spectrometric and double oven technique, the gallium cyanide molecule was identified and its atomization energy was determined: . Upper limits for the atomization energies of GaN_{(g)} and Ga_{2}N_{(g)} also were established.

Kinetic theory and rheology of dilute solutions of flexible macromolecules. I. Steady state behavior
View Description Hide DescriptionFor a dilute solution of macromolecules idealized as elastic dumbbells with Brownian motion, expressions are obtained giving the stress tensor in terms of rate‐of‐strain tensors for an arbitrary, steady, homogeneous flow. The rheological equations of state are fit into a retarded motion expansion. For dumbbells with arbitrary, nonlinear, elasticconnectors, the result is given up through terms of second‐order. Stress tensor equations for two specific models, Hookean dumbbells and finitely extendible non‐linear elastic (FENE) dumbbells, are given up through terms of third order.

Kinetic theory and rheology of dilute solutions of flexible macromolecules. II. Linear viscoelasticity
View Description Hide DescriptionFor an arbitrary, time‐dependent, homogeneous flow, an expression is obtained for the stress tensor describing the behavior of a dilute solution of macromolecules idealized as elastic dumbbells with Brownian motion. The result is given in terms of the relaxation modulus from linear viscoelasticity. The general relaxation modulus found for an arbitrary, nonlinear, elastic dumbbell is specialized to that for a finitely extendible nonlinear elastic (FENE) dumbbell. Good agreement is found when the result is compared with Warner's numerical calculations for the FENE dumbbell.

Rotational relaxation of molecules in isotropic and anisotropic fluids
View Description Hide DescriptionA theory of rotational relaxation in isotropic and anisotropic liquids is presented. The Debye rotational diffusion model is generalized so as to include reorientations of arbitrary angle with the use of a nonlocal in orientation master equation for the orientational conditional probability. For isotropic media, we have previously demonstrated that spectralline shapes (Fourier transforms of time correlation functions) appropriate to, for example, Raman and ir line broadening spectroscopy, are always superpositions of Lorentzian lines. We present here an algebraic formulation which gives the linewidths of the Lorentzian lines in terms of the transition probability describing the reorientational motion. Several models and general trends for these linewidths are discussed in order to facilitate the comparison of experimental results and this theory. For anisotropic media, such as liquid crystals or small molecules ordered by liquid crystals, a nonlocal reorientational mechanism leads to a continuous spectrum and singular eigenfunctions in the eigenvalue‐eigenvector decomposition of the conditional probability. This leads to formal line shape expressions which, while certainly non‐Lorentzian, are difficult to evaluate. For a special model transition probability and for the long times relevant to line shape measurements, explicit asymptotic expressions for the time correlation functions can be obtained which also lead to non‐Lorentzian line shapes.

Exciton transport in substitutionally impure molecular crystals
View Description Hide DescriptionThe exciton transmission characteristics of a linear molecular crystal containing a nondilute concentration of substitutional impurities are studied theoretically. This model also simulates energy transport in certain long polymers. In the event of exciton scattering by the impurities, we determine exactly the energy flux resulting from the ultimate evolution of an initial nonstationary electronic state. The result is exact for an arbitrary number of impurities located at arbitrary lattice positions within the crystals. We focus attention on two cases, the randomly and the periodically substituted crystals. In the randomly alloyed crystal, we show that the exciton transport is not diffusive; the steady state exciton flux decreases exponentially as the length of the disordered region increases and does not satisfy the ordinary diffusion equation. For the special case of periodic substitution, we are able to present very simple expressions for the exciton transmission probability and flux and to show that the transport is coherent. Similarities and differences between this problem and the one of phonon transport in an isotopically substituted harmonic lattice are noted.

Effects of curvilinear motion in large‐amplitude bending of C_{3}
View Description Hide DescriptionLarge‐amplitude bending of linear, homonuclear, triatomic molecules is analyzed, with curvilinear departure of the atoms from normal coordinate bending included. The curvilinear motion is deduced from the observed variation of rotational constant with bending quantum number. The effect of this motion is to decrease the energy eigenvalues; energy states with lowest angular momentum are decreased most. These effects counteract the effects of a steeper than harmonic bending potential. A harmonic oscillator model of C_{3} is fitted to the observed rotational constant within 0.6%, and the bond distance between atoms in the linear configuration of C_{3} is found to be 1.287 Å; noticeably larger than the average internuclear distance of the vibrational ground state, 1.277 Å. First order perturbation results, including the effect of a quartic perturbation potential, approximately duplicate the pattern of energy levels observed. Square well bending potential wavefunctions are presumed to represent a limiting approximation for high vibrational levels of C_{3} since these provide the divergence of upper levels required to fit the measured vapor pressure of graphite. In this case, the effects of curvilinear motion are similar to those obtained for the harmonic oscillator model, although somewhat larger decreases in energy are obtained. In either case, the average energy decrease is relatively constant—the order of 10%—over a wide range of vibrational quantum number. This means that the usual normal mode analysis can be adjusted to approximate the effects of curvilinear motion and explains why normal mode approximations can often be extended beyond the limits of small‐amplitude bending and yet give reasonably good results.

Exact solutions of a certain set of coupled differential equations
View Description Hide DescriptionThe Schrödinger equation for N‐electron atoms has been shown to be equivalent to a denumerably infinite set of coupled, second‐order differential equations. These equations differ significantly from those usually encountered by having a strict Coulombic coupling between all functions over the entire domain of the independent variable. We consider the solution of a finite number of these. The coordinate origin is a regular singular point of the equations, and the linearly independent sets of particular solutions are expanded around that point. The solutions which are obtained are explicit for a Hamiltonian which contains only coulombic potentials, but the method is applicable to any set of equations for which the coupling persists at the origin.

Formation of excited states and ions in the radiolysis of benzyl alcohol
View Description Hide DescriptionTransient species in benzyl alcohol and solutions of benzyl alcohol were studied by means of the nanosecond pulse radiolysis technique. Neat benzyl alcohol gives a benzyl radical with G = 2.1 which is produced by dissociative electron attachment. In solutions of lithium iodide, with a G = 2.1 is observed; however, the yield of the solvent cation measured by using t‐stilbene is only 0.2. It is suggested that a radical BzCH_{2}O resulting from an ion‐molecule reaction of the primary solvent cations and solvent molecules is a probable precursor of ; therefore G = 2.1 refers to the cation yield. The yield for the excited singlet and triplet states, 0.70 ± 0.10 and 1.10 ± 0.10 were determined using solutes such as 1,1′‐binaphthyl, 1,2‐benzanthracene, pyrene, naphthalene, and benzophenone. The interplay of ionization and direct excitation in the formation of excited states are discussed.

High‐temperature series for the B‐site spinel and diamond lattices and the question of universality
View Description Hide DescriptionThe high‐temperature series for the two‐spin correlation functions on both the B‐site spinel and diamond lattices have been calculated through tenth order for the Hamiltonian, . Here is the αth component of the D‐dimensional classical spin and we define n as the spin space symmetry parameter. By <ij> we limit the first summation to nearest‐neighbor pairs of sites i and j on the lattice. The spin space symmetry parameter n is ≤D. We consider all six models resulting from D=1–3. Our analysis of the high‐temperature series indicates that while the exponent estimates for the more loosely packed diamond lattice (q=4) indicate agreement with the universality hypothesis, the B‐site spinel lattice (q=6) series are not yet displaying their critical behavior. Some conjectures concerning this peculiarity of the series for the two lattices are made.

Raman scattering in antiferroelectric ammonium dihydrogen arsenate
View Description Hide DescriptionLight scatteringmeasurements of the Raman active modes of vibration in the range 10–4000 cm^{−1} are reported for the paraelectric phase of NH_{4}H_{2}AsO_{4} in the temperature range 220–295 K. Through examination of these spectra we have identified the protonic, transverse optic, internal, and O–H–O valence vibrations and determined their symmetries.

Ion‐molecule reaction rates in Ar at 296°K
View Description Hide DescriptionThe rate constantk _{1} for the reaction Ar^{+}(^{2} P _{3/2}) + 2Ar→Ar_{2} ^{+} + Ar was found to be (2.07±0.20)×10^{−31} cm^{6}/sec at 296°K. The reaction was studied in a drift tube at pressures reduced to 0°C (P _{0}) of 1.414–3 torr. Ions effused from the drift tube and were counted with a TOFmass spectrometer. It was found that Ar^{+} in the ^{2} P _{1/2} state does not form Ar_{2} ^{+} at room temperature. This fact appears to have been neglected in previous determinations of k _{1}. Corrections were made for the collision‐induced transition Ar^{+}(^{2} P _{1/2}) → Ar^{+}(^{2} P _{3/2}), where k _{2} is the rate constant, and for side reactions with impurities. From experiments at P _{0}=6 and 9 torr it was found that k _{2,Ar}≤1.5×10^{−15} cc/sec. However, recent experiments indicate k _{2,Ar}<4×10^{−16} cc/sec, so most of the transitions were caused by collisions with an impurity in the Ar.

Determination of relative rates for oxygen atom‐hydrocarbon reactions by reduction of oxygen atom, nitric oxide chemiluminescence
View Description Hide DescriptionRelative rates of reaction between oxygen atoms and hydrocarbons have been determined at 25°C ± 5°C. With reference to isobutene, the relative rates for ethylene, propylene, 1‐butene, cis‐2‐butene, trans‐2‐butene, 1,3 butadiene, and 3‐methylbutene‐1 are: 0.042 ± 0.010, 0.20 ± 0.05, 0.18 ± 0.07, 0.79 ± 0.25, 1.25 ± 0.35, 0.96 ± 0.35, and 0.22 ± 0.05. Hydrocarbons and oxygen atoms are mixed prior to detection of the oxygen atoms by their chemiluminescent reaction with nitric oxide. The chemiluminescent signal is simply related to the product of the gas‐phase contact time, the hydrocarbon concentration, and the reaction rate constant for the oxygen atom‐hydrocarbon reaction. With an oxygen atom concentration of approximately 10^{7} cm^{−3} at a system pressure of 10 torr, olefinic hydrocarbon concentrations as low as 1.0 parts‐per‐million are used to establish the relative rates.

Oxygen diffusion in a vapor deposited solid argon matrix at 33°K
View Description Hide DescriptionDiffusion of molecular oxygen in a vapor deposited argon matrix at 33°K was investigated by monitoring, as a function of time, the phosphorescence of a perdeuteronaphthalene‐doped argon matrix coated with an oxygen film. In pure argon, C_{10}D_{8} emits bright phosphorescence with a lifetime of 12.0 sec. In pure oxygen, emission is totally quenched. In our experiments, oxygen from the surfacefilm migrates into the matrix and quenches naphthalene impurity emission, thus decreasing the emission intensity. Diffusion kinetics are well reproducible; thus, matrices seem to have well‐defined, reproducible structure. At 33°K, in a 10^{−3} cm thick matrix containing 1 mole% naphthalene, a 50% drop in triplet intensity is observed after 35 min. The perdeutero naphthalene decay time remains unchanged at 12.0 sec and the triplet decay remains exponential at all stages of the experiment. An analysis assuming simultaneous diffusion of oxygen and argon shows that the diffusion coefficient D is a function of L, the total thickness of the sample, of γ, the oxygen to matrix ratio, and of K, the quenching constant. From the observed parameters, we compute the diffusion constant: D = 10^{−12}×10^{±2} cm^{2} sec^{−1}. Diffusion in a matrix is about 10^{11} times faster than what data for argon single crystals indicates, but it is slow enough to be discriminated against in a normal matrix experiment.

X‐ray photoelectron spectroscopy of tetraphenylporphin and phthalocyanine
View Description Hide DescriptionThe x‐ray photoelectron spectra of tetraphenylporphin, phthalocyanine and their copper complexes were measured. The copper complexes show a single nitrogen 1s photoline, whereas the metal free bases give rise to a doublet nitrogen 1s photoline. The central pyrrole and aza nitrogens in the metal free bases could be identified, whereas the central and meso‐bridging aza nitrogens in phthalocyanine could not be discriminated. Each of the central two protons in the metal free bases is localized on one of the central four porphinato nitrogens. The shifts in N 1s binding energy observed in the present work could be reproduced by the shifts in the charge density on nitrogen obtained for the bonded structure by an extended Hückel molecular orbital calculation.

Evaluation of linear chain partition functions by consideration of sequence conditional probabilities
View Description Hide DescriptionA simple, systematic treatment for the class of linear chain models whereby each unit can exist in one of several states, giving rise to a partition function that is a sum over all lengths and orders of sequences of states, is given for increasingly long range interactions between the sequences. The technique consists of constructing relations for sequence conditional probabilities which give rise to a system of linear equations for the a priori sequence probabilities and the unit partition function; matrix inversion eliminates the a priori probabilities leaving a relation for the unit partition function. When the unit partition function is calculated, one can immediately evaluate the a priori sequence probabilities from which all other average quantities can be calculated (thus making it unnecessary to calculate average quantities by taking derivatives of the partition function). A short derivation is given of the generating function method of treating independent sequences and it is shown that the partition function for finite chains can be expressed solely in terms of generating functions (circumventing the need to construct eigenvectors). The technique is then used to treat the case where there is an arbitrary interaction between adjacent sequences with application to titration and chain folding models. The extension to higher order interactions is shown to follow in a similar fashion.

Energetics of charged transfer in collisions of Ar^{+} ions with H_{2}, D_{2}, and CO_{2}
View Description Hide DescriptionThe energetics of charge transfer in collisions of low‐energy Ar^{+} ions with H_{2}, D_{2}, and CO_{2} molecules have been investigated in ion beam‐gas scattering experiments, which utilize a special feature of collision kinematics. The kinetic energy (KE) distributions of product ions which emerge from their collision sites at 90° with respect to the projectile beam direction were determined by electrostatic analysis, using a parallel‐plate analyzer. At this angle, exothermic transfer channels dominate the observed distributions, and the coupling between projectile and product ion kinetic energies is minimized. Information concerning the contributing transfer channels, and therefore concerning the internal states of the product , , and ions, has been deduced from the measured KE distributions. For the Ar^{+}–H_{2}, D_{2} systems, measurements were carried out at a number of projectile ion KE's, over the range 20<E _{1}<150 eV. For the Ar^{+}–CO_{2} system, runs were made at E _{1}≃6 eV and E _{1} =20.1 eV. In addition, a single distribution for the Ne^{+}–CO_{2} system was obtained, at E _{1}=50.1 eV. The distributions for Ar^{+}–D_{2} and Ar^{+}–H_{2} at the lower collision energies revealed a surprising isotope effect, in that the former showed contributions of fairly energetic ions, whereas the latter consisted solely of ions with near‐thermal energies. The Ar^{+}–CO_{2} data at E _{1}=6 eV gave evidence of ions with energies 0≤E _{3}≤∼1 eV, from which it was inferred that transfer proceeds via a number of exothermic transfer channels, having internal energy changes Q over the entire accessible range 0<Q≤2.16 eV. The effect of the thermal motions of the target particles (Doppler broadening) has been discussed in some detail. This effect is particularly important in these studies, since the kinetic energies of the product ions were small (for the most part, less than a few tenths of an electron volt).

Lattice vibrations in chlorobenzenes: Experimental dispersion curves for β‐paradichlorobenzene by neutron scattering
View Description Hide DescriptionLattice vibrational dispersion curves for the ``intermolecular'' modes in the triclinic, one molecule per unit cell β phase of p‐C_{6}D_{4}Cl_{2} and p‐C_{6}H_{4}Cl_{2} have been obtained by inelastic neutron scattering. The deuterated sample was investigated at 295 and at 90°K and a linear extrapolation to 0°K was applied in order to correct for anharmonic effects. Calculations based on the atom‐atom model for van der Waals' interaction and on general potential parameters for the aromatic compounds agree reasonably well with the experimental observations. There is no substantial improvement in fit obtained either by consideration of electrostatic forces or by further anisotropy in the dispersion forces not described in the atom‐atom model. Anharmonic effects are shown to be large, but the dominant features in the temperature variation of frequencies are describable by a quasiharmonic model.

Spatial switching in chemical reactions with heterogeneous catalysis
View Description Hide DescriptionThe qualitative properties of chemical systems with localized (heterogeneous) catalysts can depend on the relative locations of the catalysts. By considering some simple chemical systems with two catalytic sites it is shown that the number and the stability of steady states and cycles changes with intercatalytic separation. These examples indicate that geometrical considerations must be explicitly considered when analyzing the dynamics of highly structured (e.g., biological) systems.

Lifetime of electronically excited NO_{2}: Evidence for a short‐lived state
View Description Hide DescriptionThe lifetime of one spin component of the 5_{24} rotational level of some vibrational level of B _{2} symmetry of the ^{2} B _{2} electronic state of NO_{2} has been measured by observing the linewidth of the microwave‐optical double resonancespectrum of that state. The lifetime determined from the zero power, zero pressure linewidth extrapolation is less than 3.39 ± 0.36 μsec and is over an order of magnitude shorter than that usually measured in NO_{2}. This indicates that at least some electronically excited levels of NO_{2} have lifetimes approaching those calculated from the integrated absorption coefficient.

A method to estimate the critical probability in bond percolation problems
View Description Hide DescriptionA method based on the symmetry of bonding directions i = 1, 2, …, n is introduced to estimate the critical probability p_{c} in bond percolation problems. The leading terms in the critical equation Q(p _{1}, p _{2},…, p_{i},…, p_{n} ) = 1 are derived for some two‐ and three‐dimensional lattices and consequently p_{c} can be evaluated by setting all p_{i} 's equal. In two dimensions the three exact, known values of p_{c} are regained in addition to an estimate for the kagome lattice p_{c} ≃0.535. In three dimensions a one‐parameter fitting to diamond and bcc lattices gives for simple cubic lattice the estimate p_{c} ≃ 0.258 in agreement with its lower limit 1/4.