Volume 39, Issue 9, 01 November 1963
Index of content:
39(1963); http://dx.doi.org/10.1063/1.1701409View Description Hide Description
The problem of protonmagnetic resonancelinewidths for molecules that are taking part in one electron transferreactions is re‐examined, and it is concluded that the ``weak‐pulse'' limit (aH τ p ≪1) is more generally applicable than the ``strong‐pulse'' limit (aH τ p ≫1) that was discussed by McConnell and Berger. Density matrix equations are set up using the formalism of Alexander in order to calculate line shapes from the hyperfine splitting constants and the lifetimes of the diamagnetic and paramagnetic species; and it is shown that when more than one absorption line are observed, under certain conditions, the bimolecular rate constant for electron transfer may be determined without a knowledge of the concentration of unpaired electrons. These equations are applied to the electron transferreaction between NNN′N′‐tetramethyl‐p‐phenylene diamine and its monocation radical in acetonitrile, and we find that the rate constant for electron transfer is (2.0±1.0)×108 liter mole−1 sec−1.
39(1963); http://dx.doi.org/10.1063/1.1701410View Description Hide Description
The coupling of a shock tube to a time‐of‐flight mass spectrometer for the determination of kinetic data is described whereby analysis is performed every 25 μsec. The rate of dissociation of Cl2 has been measured over the temperature range 1700°—3200°K under essentially isothermal and isobaric conditions with the observed rate constants in fair agreement with those obtained by the spectroscopic technique. The observed temperature dependence is less than predicted by simple collision theory with an apparent activation energy of 41±5 kcal/mole.
39(1963); http://dx.doi.org/10.1063/1.1701411View Description Hide Description
The decomposition of hydrazine diluted in argon has been studied over the temperature range 1200° to 2500°K and pressure range 0.04 to 0.25 atm using a shock tube coupled to a time‐of‐flight mass spectrometer. The time‐resolved mass spectra (25 μsec) enable the simultaneous identification and determination of N2H4, NH3, N2, H2, and the NH2 radical, the five major species observed. The material balance is within the experimental error (10%) during reaction up to complete decomposition.
The primary process in the dissociation of hydrazine is shown to be the rupture of the N–N bond to give NH2 radicals. The observed rate constants for the disappearance of hydrazine are those expected of a unimolecular reaction: at or near the second‐order region where the collisional activation (1) is rate controlling. At the higher temperatures, the results are consistent (within experimental error) with the very simple reaction scheme of Reaction (1) and (2) followed by At the lowest temperatures the reaction NH2+N2H4→N2H3+NH3 appears to become important.
From the experimental concentrations, a value ofis obtained. An order‐of‐magnitude estimate gives
39(1963); http://dx.doi.org/10.1063/1.1701412View Description Hide Description
The energy levels of the Er3+ ion in LaCl3 are calculated by finding the eigenvalues of the matrices for the combined Coulomb, spin—orbit, and crystal‐field interactions within the f 11 configuration. For suitably chosen values of the three Slater integrals and the spin—orbit coupling constant the root‐mean‐square deviation between the calculated and the experimental positions of 20 terms is 140 cm−1. Crystal‐field parameters can be chosen which reduce the root‐mean‐square deviation between the calculated and the measured splittings of 72 levels to 3.84 cm−1. Zeeman splitting factors in the direction parallel to the crystal axis are also calculated. The results for Er3+ in LaCl3 are compared with those for Nd3+ in LaCl3.
39(1963); http://dx.doi.org/10.1063/1.1701413View Description Hide Description
The energy levels of the Nd3+ ion in LaCl3 are calculated by finding the eigenvalues of the matrices for the combined Coulomb, spin—orbit, and crystal‐field interactions within the f 3 configuration. By judicious choice of the three Slater integrals and the spin—orbit coupling constant, the standard deviation between the calculated and the experimental positions of 22 terms can be reduced to 87.5 cm−1. Crystal‐field parameters can be chosen which yield a standard deviation of 0.91 cm−1 between the calculated and the measured splittings of 31 levels in seven terms. The calculated Zeeman splitting factors in the direction parallel to the crystal axis are in good agreement with the measured values.
39(1963); http://dx.doi.org/10.1063/1.1701414View Description Hide Description
The applicability of simple molecular orbital theory as a basis for determining approximate empirical wavefunctions useful for correlating molecular properties is examined for the methane molecule. It is found that LCAO molecular orbitals provide a fairly good approximation to the molecular wavefunction of methane in its equilibrium configuration, but represent the changes in the wavefunction produced by molecular deformation too crudely to provide an interpretation of its dipole‐moment derivatives determined by infrared intensity measurements on methane.
39(1963); http://dx.doi.org/10.1063/1.1701415View Description Hide Description
Electron spin resonance methods have been used to observe alkyl radicals in liquid hydrocarbon systems during irradiation with 2.8‐MeV electrons. These investigations provide detailed structural, radiation chemical, and kinetic information about a large number of radicals.
In general, in these studies the ESR lines are found to be narrow; considerable fine structure is observable, permitting positive assignment of the radical species. Accurate hyperfine constants are reported for 21 alkyl and cycloalkyl radicals (including several deuterated species), vinyl, 1‐methylvinyl, 3‐butenyl, allyl, and cyclohexadienyl radicals, and hydrogen and deuterium atoms. Except for cyclopropyl radical, all the alkyl and cycloalkyl radicals have α coupling constants in the range 21–23 G. The β coupling constants in cases where they have been rotationally averaged isotropically are found to decrease with increasing substitution of alkyl groups on the α carbon atom. In general the values for primary, secondary, and tertiary radicals appear to be represented by the splittings observed for the methyl protons in ethyl (26.87 G), isopropyl (24.68 G), and tert‐butyl (22.72 G) radicals. A possible explanation for this trend is discussed. A number of examples showing a significant departure from the above isotropically averaged values have been found. In several cases this departure, and the resultant strong temperature dependence of the β coupling constants, is taken as evidence for a barrier hindering rotation about the α‐carbon—β‐carbon bond. Splittings caused by γ protons and which range from 0.4 to 1.1 G have been resolved in five cases. A pronounced angular dependence of this coupling constant has been demonstrated in the case of propyl radical. This angular dependence is important in considerations of the mechanism of the γ hyperfine interaction. Three radicals which do not have the usual π‐electron configuration have been observed: vinyl, 1‐methylvinyl, and cyclopropyl. The splittings by the α protons of vinyl and cyclopropyl radicals are 13.39 and 6.51 G. These small values indicate that as the orbital associated with the unpaired electron acquires s character the coupling constant increases from ∼−23 G. The coupling constants for the two conjugated radicals, allyl and cyclohexadienyl, support the theoretical prediction of negative spin density at the unstarred positions of these odd‐alternant radicals. Spectra with relatively narrow lines are reported for transient species in a number of solid hydrocarbons.
The radicals observed in various hydrocarbons are discussed in terms of the radiation chemical reactions expected in these systems. In most cases the radicals represent fragments which result from rupture of a single bond. In certain cases secondary reactions, such as the addition of hydrogen atoms to unsaturates, are also found to be important. The use of ESR methods in obtaining information concerning the rate of radical reactions is illustrated by two studies. In the first an activation energy of 3.3 kcal/mole is estimated for the addition of vinyl radicals to ethylene from measurements on the temperature dependence of the relative vinyl and 3‐butenyl radical concentrations in liquid ethylene. In the second the kinetics of the disappearance of ethyl radicals in liquid ethane are examined in detail. The absolute second‐order rate constant for this disappearance as obtained from absolute concentration and dose rate measurements is found to be 3×10 liters mole−1 sec−1 at −175°C. The activation energy for the reaction of ethyl radicals in liquid ethane is 780 cal/mole, or essentially that for the diffusion‐controlled process.
39(1963); http://dx.doi.org/10.1063/1.1701416View Description Hide Description
The spherical model of Berlin and Kac is applied to an antiferromagnetic interaction. The critical‐field curve, magnetization‐field curves, specific heats, and long‐range order are calculated. The problem is translated into lattice‐gas language, to afford a possible model for the solid—gas transition. Very unphysical behavior is found, and a probable reason is discussed. This is ascribed to a ``borrowing'' of spin from one sublattice by the other.
Analytical Expressions for Potentials of Neutral Thomas—Fermi—Dirac Atoms and for the Corresponding Atomic Scattering Factors for X Rays and Electrons39(1963); http://dx.doi.org/10.1063/1.1701417View Description Hide Description
Approximate analytical expressions for the electrostatic potentials of neutral Thomas—Fermi—Dirac atoms have been obtained by fitting a sum of three exponential terms to the tabulated values by least‐squares methods. The six different parameters used for each atom are expressed as functions of the atomic number. The corresponding expressions for the radical electron density, the mean‐square radius, the diamagnetic susceptibility, the atomic scattering factors for x rays and the atomic scattering factors for electrons according to the first Born approximation are given. The accuracy of the approximate expressions are discussed in relation to results obtained from the tabulated values of the electrostatic potential and from the corresponding electron density.
39(1963); http://dx.doi.org/10.1063/1.1701418View Description Hide Description
The heat capacity of MnBr2 has been measured between 1.7 and 20°K. The calorimeter and carbon resistance thermometer—heater are described. There is an anomaly in the heat capacity of MnBr2, arising from the ordering of the spins of the manganous ions. The maximum heat capacity, in excess of 30 cal mole−1 deg−1, occurs at 2.16±0.01°K. The entropy associated with the magnetic ordering is R ln6 and the corresponding enthalpy is 10.84 cal mole−1.
39(1963); http://dx.doi.org/10.1063/1.1701419View Description Hide Description
The stirred‐reactor technique was used to measure the reaction rates of H2, NH3, and CH4 with mixtures of atomic and molecular oxygen (O+O2) at temperatures ranging from 350° to 600°K. A mass spectrometer capable of detecting atomic oxygen and hydrogen was used to analyze the reacting mixture in the stirred reactor. It was discovered that atomic oxygen could be quantitatively monitored by the mass spectrometer at a mass‐to‐charge ratio of 8. The reaction of H2 with the O+O2 mixture was found to be a chain reaction, with four to six atoms of oxygen consumed for each hydrogen molecule. The rate constant for the disappearance of atomic oxygen was 3×1013 exp(−8300/RT) cc mole−1 sec−1. The products of the reaction were H2O and H. The reactions of NH3 and CH4 with the O+O2 mixture were complex chain reactions, with a minimum of eight atoms of oxygen disappearing for each molecule of NH3 or CH4. Rate constants for atomic‐oxygen disappearance wererespectively. The products of the former reaction were NO, H2O, and small amounts of H2 and H. The products of the latter reaction were H2O, CO2, and small amounts of CO, H2, and H.
Primary Reactions in the Mercury‐Photosensitized Decomposition of 1‐Butyne, Propyne, and Acetylene at Low Pressures39(1963); http://dx.doi.org/10.1063/1.1701420View Description Hide Description
The mercury‐photosensitized decomposition of 1‐butyne, propyne, and acetylene was studied at very low pressures in a flow system attached to a mass spectrometer.
The primary decomposition of 1‐butyne was found to proceed by the reactions
The primary decomposition of propyne was
The presence of C2H radicals was detected in the decomposition of acetylene. These probably originate from the primary decomposition. The primary quantum yield for acetylene appears very much lower than that of the butyne and propyne. It is concluded that acetylene forms an excited molecule, but that the primary decomposition does not necessarily occur by this process but from reactions involving the formation of HgH and HgC2H.
Calculation of Heats of Vaporization and Fusion of Nonionic Liquids from the Rigid‐Sphere Equation of State39(1963); http://dx.doi.org/10.1063/1.1701421View Description Hide Description
The heats of vaporization of the rare gases, diatomic, and polyatomic molecules were calculated from the isothermal reversible work required to compress a fluid of rigid spheres from the volume it occupies at a pressure of one atmosphere to the volume of the corresponding liquid. Similarly the heats of fusion of the rare gases were calculated from the additional work necessary to compress the rigid‐sphere fluid from the volume of the liquid to that of the solid. Agreement between the calculated and observed values was, with few exceptions, very good.
39(1963); http://dx.doi.org/10.1063/1.1701422View Description Hide Description
A brief discussion of a program for evaluating the integrals which appear in the Rydberg—Klein—Rees (RKR) method of determining potential curves from spectroscopic data is given. Application is made to the ground states of H2 and I2 and the results compared to earlier calculations.
Spectroscopic Study of the Effect of High Pressures on Organic Charge‐Transfer Complexes in Solution39(1963); http://dx.doi.org/10.1063/1.1701423View Description Hide Description
The charge‐transfer solution spectra of tetracyanoethylene with benzene, hexamethylbenzene, diphenyl, and naphthalene have been observed as a function of pressure up to a maximum of 10 000 atm. The association constants and charge‐transfer transition oscillator strengths have been determined for pressures up to 4000 atm in the case of the benzene—tetracyanoethylene complex. A large increase in transition oscillator strength with pressure is observed for the benzene complex; this is in accord with the theoretical predictions of Mulliken. A small decrease in association constant with pressure for this complex is tentatively interpreted in terms of complexing between the tetracyanoethylene and the solvent, methylene chloride. The observed frequency shifts with pressure, and the band splitting of the charge‐transfer spectra of the diphenyl and naphthalene complexes are discussed. It has previously been suggested that solutions of charge‐transfer complexes contain orientational isomers of those complexes; this theory receives a measure of support from the pressure measurements.
39(1963); http://dx.doi.org/10.1063/1.1701424View Description Hide Description
The vibrational and the electronic spectra of the nitrate ion change with concentration in aqueous solutions of metallic nitrates M (NO3) n , and the changes vary with the cation M n+ present in the solution. The position, size, shape, and polarization of the ν1 Raman band of the nitrate ion and the position of the nearultraviolet absorption band of that ion have been measured as functions of concentration in solutions of the nitrates of Li, Na, K, NH4, Mg, Ca, Zn, and Al. Three correlations emerge from these data. (1) The changes in the peak frequency and in the half‐width of the Raman band are inversely related, and both appear to depend on the degree of hydration of the cation. (2) The changes in the specific intensity of the Raman band are paralleled by shifts in the ultraviolet absorption band and are resonance Raman effects. (3) In solutions of ammonium nitrate the spectral changes are very small, apparently because of the similarity between the ammonium ion and the water molecule.
39(1963); http://dx.doi.org/10.1063/1.1701425View Description Hide Description
In the classical analysis of nucleation of a crystalline phase from a fluid phase it is assumed that the nucleus is a perfect single crystal. In the present paper it is shown that ZnO fourlings almost certainly nucleate as fourfold twins. Alternative nucleation mechanisms are described which would account for a polycrystalline nucleus.
39(1963); http://dx.doi.org/10.1063/1.1701426View Description Hide Description
A recent calculation by Salem of the attractive forces between two long parallel hydrocarbon chains was based on two assumptions: (1) pairwise additivity of dispersion forces between individual groups on each chain, and (2) isotropy of the polarizability of a group on the chain. The validity of these assumptions is examined here by means of a Drude model calculation of the interaction between two parallel linear lattices of dispersion oscillators. We describe an exact calculation on this model, and also a calculation based on applying Salem's assumptions to the same model. We conclude that the assumptions are not valid for the Drude model, because of strong induced‐dipole interactions between neighbors along the lattice. Salem's procedure leads to essentially correct numerical results, however, due to use of an experimentally determined bond polarizability at a crucial stage of the calculation. This allows for the effects of interactions between neighbors. Our results are applicable to real hydrocarbon chains only to the extent that the Drude model is valid.
39(1963); http://dx.doi.org/10.1063/1.1701427View Description Hide Description
The mechanism of production of line radiation in a thick target differs from that of bremsstrahlung radiation. As a result the effective depths of formation of the two types of radiation, under identical conditions, are not the same. With relatively low voltage across the x‐ray tube, the average change in the depth of production with voltage was found to be 300 A/kV for the continuum while the line data gave a value of 440 A/kV, in anodematerial having an atomic number of about 30. The dependence of the two quantities on the takeoff angle has also been investigated.
39(1963); http://dx.doi.org/10.1063/1.1701428View Description Hide Description
A theory is presented to explain the rotational perturbations experienced by a molecule trapped substitutionally in a rare‐gas lattice at low temperatures (4°—20°K). The nonbonded repulsive interaction due to the Pauli exclusion principle between the molecule and the host lattice has been ignored in preference to the multipole charge interaction. In the case of an octahedral substitutional trapping site the dominant interacting term is the rotation of a permanent molecular hexadecapolar charge distribution interacting with the fourth gradient of the electric potential at the molecular center of mass due to all of the lattice charges. A general method of computing the fourth gradient of the potential due to the rotational independent induced‐dipole—induced‐dipole effect is given in the Appendix in terms of the molecular and atomic polarizabilities and ionization constants. Matrix elements are given for linear, spherical‐top, symmetric‐top, and asymmetric‐top molecules.
The theory for a trapped linear molecule is applied to the vibration—rotation data of HCl trapped in an Ar lattice yielding a value of the single molecular hexadecapole moment in HCl of 3.9×10−42 esu cm4. Other effects discussed are: (1) higher‐order terms in the potential expansion, (2) isotopic substitution in the molecule, and (3) the rotation of HCl in the other rare‐gas lattices.