Volume 38, Issue 2, 15 January 1963

Self‐Diffusion and Impurity‐Controlled Proton Relaxation in Liquid Methane
View Description Hide DescriptionSelf‐diffusion in liquidmethane, under its own vapor pressure, has been studied between the triple point and the normal boiling point by means of the spin‐echo technique. The activation energy for self‐diffusion is approximately 0.67 kcal/mole. These results are compared with the constant‐pressure tracer results of Naghizadeh and Rice [J. Chem. Phys. 36, 2710 (1962)], which show somewhat higher (∼15%) self‐diffusion coefficients and an activation energy of approximately 0.83 kcal/mole. The temperature dependence of self‐diffusion in liquidmethane appears to be comparable on the basis of a classical reduction to corresponding states, by means of critical constants, to that in liquid Ar, Kr, and Xe.
Measurements of the proton spin‐lattice relaxation time in our sample indicate that the relaxation is predominantly controlled by the mutual diffusion of the hydrocarbon and small amounts of dissolved oxygen.

Ohmic Contact to Zinc Sulfide Single Crystals
View Description Hide DescriptionGallium‐metal electrodes have been used with ZnS and it is established that these are Ohmic. With such electrodes it has been possible to make use of theoretical work on currents in insulators to estimate that the carrier density in these crystals is in the order of 10^{6} per cm^{3} and that there is an effective trap depth of 0.9 eV. Experiments with crystals other than ZnS indicate that the mechanism of Ohmic contact formation is understood in principle.

Analysis of Weakly Coupled Nuclear Magnetic Resonance Spectra: Methyl Salicylate
View Description Hide DescriptionThe protonmagnetic resonance spectrum of methyl salicylate at 60 Mc/sec is sufficiently weakly perturbed for all the strong lines to be assigned on a ``first‐order'' basis. The frequency sweep double irradiation method has been used to demonstrate that all the spin coupling constants in the aromatic ring have the same sign. This makes possible the calculation of accurate values of the chemical shifts and spin coupling constants by iterative computeranalysis without the need for examining other sign combinations. There is an unexpected long‐range coupling (0.4 cps) between the hydroxyl proton and one of the ring protons in the meta position.

Hexagonal Close‐Packed Structures in Bi–Pb Alloys and the Polymorphism of Lead at High Pressure
View Description Hide DescriptionLattice spacings have been obtained for the hexagonal close‐packed structures in lead alloys containing 27.0 to 32.0 at.% bismuth, which were rapidly cooled from the melt. Axial ratios for these structures vary from 1.653 to 1.654. By extrapolation to pure lead of these volume/atom determinations and of some activity data, the free energy of hexagonal close‐packed lead relative to the face‐centered cubic form is estimated. It is suggested that the structure of the leadpolymorph stable at pressures greater than 0.16 Mbar is hexagonal close‐packed.

Mean Lives of Positrons in Aqueous Solutions
View Description Hide DescriptionBy measurement of the time distribution of positron annihilations in aqueous solutions,reaction rates for oxidation of positronium by the ions MnO_{4} ^{—}, IO_{3} ^{—}, and Hg^{++} have been determined. In strong oxidizing solutions the mean life of the positrons reaches a lower limit of 4.3×10^{—10} sec; the short lifetime τ_{1} in water was measured and found to agree with this value. A Pb(ClO_{4})_{2}·3H_{2}O solution reduced the intensity I_{2} with no significant change in the long life τ_{2}, an effect previously observed in nitrate solutions. This may mean that in these two cases oxidation can occur before Ps is thermalized but not afterwards. The decay distributions from a mixture of Hg^{++} and MnO_{4} ^{—} ions in solution and the Hg^{++} ion in separate solutions with Cl^{—} and ClO_{4} ^{—} indicated an association taking place between the negative and positive ions.

Calculation of Molecular Properties with Limited‐Basis Hartree—Fock Functions
View Description Hide DescriptionThe use of the limited‐basis (Roothaan) approximation to Hartree—Fock functions and its implications for the accuracy of calculations on one‐electron operators are discussed. Only for the true Hartree—Fock function does Brillouin'stheorem guarantee second‐order errors for expectation values of these operators. The mean square deviation of one Roothaan function from a second with an incremented basis set provides a measure of how closely the true Hartree—Fock function is being approached. Expectation values of one‐electron operators reflect this as well, but it is shown that the improvement or lowering of energy on addition of functions to the basis is much less suitable.

Kinetics of Desorption. II. Cs^{+} and Ba^{+} from Rhenium
View Description Hide DescriptionThe mean desorption lifetimes (τ_{3}) of Cs^{+} and Ba^{+} on an atomically clean rheniumsurface have been measured. Under conditions of low surface coveragewas obtained for Cs^{+} in the temperature range 950<T<1080°K. This is in excellent agreement with the data obtained previously for the Cs^{+}–W system. For Ba^{+} on rheniumwas obtained in the temperature range 2100<T<2310°K. The Cs^{+}–Re, like the Cs^{+}–W bonding, can be attributed to the electrostatic image energy of a Cs^{+} ion on an electrically conductingsurface. The Ba^{+}–Re interaction, on the other hand, must include a large exchange force in addition to the electrostatic image force because of the unpaired valence electron remaining in the univalent barium positive ion. The presence of an adsorbed layer of residual vacuum gases decreased the Cs^{+}–Re binding energy by 0.4 eV and increased the pre‐exponential factor by two orders of magnitude. These results are almost identical with that reported previously for Cs^{+} desorbing from a contaminated tungstensurface.

Mass‐Spectrometric Study of Ion Profiles in Low‐Pressure Flames
View Description Hide DescriptionA mass‐spectrometric technique for determining ion profiles through low‐pressure flames (1–6 mm Hg) has been developed. Typical results are presented for hydrocarbon—oxygen flames which show that the dominant ion is H_{3}O^{+} and that the concentration of C_{3}H_{3} ^{+}, the next most abundant ion, reaches a maximum concentration in the flames ahead of H_{3}O^{+}. A large number of other ions are also identified.

Kinetics of High‐Polymer Reactions: Effects of Neighboring Groups
View Description Hide DescriptionA recurring problem in polymer chemistry is the dependence of functional group reactivities on the reacted‐or‐unreacted status of neighboring groups. This problem has been attacked by means of a closed‐loop model and an infinite‐chain model. For the latter model, an approximate solution has been developed for the general case, and an exact solution has been shown for the speical case where k _{1}=k _{2}.

General Solution to the Problem of the Effect of Neighboring Groups in Polymer Reaction
View Description Hide DescriptionAn analytical solution to the problem of the kinetics of reactions on polymer chains has been derived. The solution is generally applicable within the following limits: (1) only nearest‐neighbor interactions are considered, (2) the initial state of the polymer is taken to be completely unreacted (i.e., initial arbitrary sequences of reacted and unreacted sites cannot be handled). However, autocatalytic, autoinhibitory, or mixed catalytic‐inhibitory systems can be handled.

Reaction Kinetics of a Long‐Chain Molecule. II. Arends' Solution
View Description Hide DescriptionIn Part I [J. Chem. Phys. 37, 2584 (1962)] we considered the reaction kinetics of a long‐chain molecule, each segment of which carries a reactive group. The reactivity of each group depended upon whether zero, one, or two of its nearest neighbors had reacted. The average fractions of reacted groups and of unreacted with zero, one of two reacted neighbors were found as functions of time. Now we derive C. B. Arends' [J. Chem. Phys. 38, 322 (1963)] solution for the average fraction of sequences of unreacted groups of n for n=1, 2, ···. We start with the infinite set of differential equations for these average fractions derived by W. G. Lloyd and T. Alfrey, Jr. [J. Chem. Phys. 38, 318 (1963)]. We solve them by assuming a solution of the form derived by Arends. Thus we verify that Arends' solution satisfies the equations of Lloyd and Alfrey and we derive it more simply. In addition we show that the present results yield exactly those of Part I, thus verifying the hypothesis introduced in that work.

Comparison of Some Exact and Approximate Results for Gases of Parallel Hard Lines, Squares, and Cubes
View Description Hide DescriptionThe first seven virial coefficients for hard parallel lines, squares, and cubes, as derived from approximations of the ring and watermelon type, are compared with the exact coefficients. These approximations give no useful information as to the sign or magnitude of the virial coefficients.
A Cartesian distribution function depending upon only one space coordinate arises naturally for the line, square, and cube molecules. The first four terms of the exact number density expansion of this function are presented and compared with results obtained by iteration from the Percus—Yevick, Kirkwood, and convolution integral equations. The Percus—Yevick equation yields a distribution function which closely resembles the exact result at low densities.
Virial coefficients are obtained from the approximate distribution functions by means of the Ornstein—Zernicke relation and the virial theorem, as well as from a relation between the potential of mean force at zero separation and the virial coefficients. This last relation (which is valid for hard spheres as well as lines, squares, and cubes) has an interesting graphical interpretation and leads to correct values for the third virial coefficient from the Kirkwood equation, but not from the Percus—Yevick or convolution equations.

Theoretical Calculation of Vapor Transport of Solid in the ZnS : HCl System
View Description Hide DescriptionA theory has been previously developed which allows calculation of the rate of diffusion‐limited vapor transport of solids in a multicomponent multireaction system which is driven by a small temperature gradient. This theory is applied to the case of ZnS_{(s)} being transported by reaction with HCl_{(g)}. All the required parameters, i.e., gaseous diffusion coefficients, thermodynamic data, etc., are either known or independently estimated. The calculated results are found to be in quantitative agreement with the experimental results within the estimated uncertainties in the thermodynamic and diffusion coefficient data over a wide range of initial HCl pressures. Below an initial HCl pressure of 1 atm, it is seen that the experimental rate of transport drops sharply in comparison to the theoretical prediction. This has previously been attributed to kinetic limitations.
It is shown that the assumption of a single binary diffusion coefficient, applying to all pairs of component species, may lead to results in approximate agreement with the more ``exact'' theoretically predicted results.

Electronic Spectra and Hydrogen Bonding. II. Anthrols
View Description Hide DescriptionAn investigation has been made of the effect of hydrogen bonding on the absorption and fluorescence spectra of α‐ and β‐anthrols. It is shown that, when a hydrogen bond is formed between the anthrols and dioxane, each electronic band exhibits a characteristic behavior which supplies a substantial clue as to the origin of the band. The behavior in hydrogen bonding of the low‐frequency absorption of β‐anthrol clearly indicates that the absorption consists of two overlapping electronic transitions: One at lower frequencies, which was previously assigned to the ^{1} L_{b} transition, shows a large red shift (340 cm^{—1}) upon formation of the hydrogen bond, whereas the other transition, ^{1} L_{a} , shows only a small red shift (60 cm^{—1}). The results of experiments on both the absorption and fluorescence spectra show that the proton‐donating power of the anthrols is evidently greater in the first excited state than in the ground state.

Vibronic—Spin‐Orbit Perturbations and the Assignment of the Lowest Triplet State of Benzene
View Description Hide DescriptionSecond‐order perturbation theory in electron configuration and spin space using both vibronic and spin‐orbit perturbations reveals a number of routes for bringing dipole allowed character into a spin‐forbidden transition. Apart from direct spin‐orbit interaction, there are three additional mechanisms: (1) direct spin‐vibronic coupling (a very weak, though first‐order term), (2) spin‐orbit coupling with vibronic coupling in the singlet manifold, and (3) vibronic coupling in the triplet manifold with spin‐orbit coupling. In the case of benzene, vibrational analysis alone of the phosphorescence spectrum can neither discern the route for bringing allowed singlet character into the triplet state nor can it lead to an assignment of that state. It happens that polarized luminescence data are able to show that route (3) is dominant, and, given this, vibrational analysis leads to a ^{3} B _{1u } assignment. The vibronic characteristics of the various routes are discussed. Estimates are made of the relative importance of the various routes based on energy considerations within the framework of second‐order perturbation theory. Approximate oscillator strengths are obtained and compared with the experimental value showing, independently, that route (3) is dominant and that the assignment must be ^{3} B _{1u }. Other possible examples where mixed vibronic—spin‐orbit terms are important to phosphoresence are mentioned suggesting the fruitfulness of detailed polarized phosphorescence experiments, both to aid in assigning excited states and to test vibronic theories.

Exciton—Exciton Interactions and Photoconductivity in Crystalline Anthracene
View Description Hide DescriptionIn this paper we consider the mechanism of photoconductivity in crystalline anthracene. It is shown that two excitons may interact to form a pair of charge carriers and an unexcited molecule. The computed rate of generation of charge carriers is 3.7×10^{8} cm^{—3} sec^{—1}, in satisfactory agreement with the (approximate) experimental value of 7.2×10^{8} cm^{—3} sec^{—1} when the exciton concentration is 1.2×10^{10} cm^{—3}. Other qualitative features of the proposed mechanism are in agreement with observation if electron‐hole recombination is accounted for. Recent experiments by Silver demonstrating a photocurrent proportional to the square of the light intensity, and by McGlynn demonstrating the necessity for singlet states as the kinetic intermediate in charge‐carrier generation are in agreement with the model proposed.

Theory of NMR Chemical Shifts in Conjugated Fluorine Compounds
View Description Hide DescriptionRamsey's equation for the nuclear magnetic resonance screening constant is analyzed employing a Hartree—Fock ground‐state wavefunction. Using the LCAO approximation, a general expression is obtained which relates the screening parameter to localized charge distribution quantities (charge and bond orders). This expression is equivalent to one given by Karplus and Das. Pertinent two‐center integrals over atomic orbitals are evaluated, employing, in part, the Fourier integral folding theorem. The relative magnitudes of the integrals over atomic orbitals makes possible a simplification of the general equation for F^{19} shielding to a form involving quantities associated with the fluorine atom and the adjacent carbon atom. Under the assumption of an invariant sigma framework, the F^{19}chemical shift between two similar conjugated fluorine compounds is shown to be determined chiefly by the values of the fluorine pi‐electron charge densities and the carbon—fluorine pi‐electron bond orders. The latter terms are almost as important as the former. The groundwork is laid for applying the derived equations, in a subsequent paper, to several systems of aromatic fluorine compounds.

Relationship between Pi‐Electronic Distributions and F^{19} NMR Shielding in Para‐Substituted Fluorobenzenes
View Description Hide DescriptionExperimental results on F^{19} shielding in p‐substituted fluorobenzenes are combined with calculations of pi‐electronic charge distribution from MO theory and are used in several procedures devised to test shielding theories. It is concluded that both —R and +R p‐substituted fluorobenzenes represent a special case for which there is a reasonable degree of theoretical justification for relating the F^{19} shielding with the pi charge density of the fluorine atom.
The tests devised for p‐substituted fluorobenzenes do not clearly distinguish between the shielding equations of Prosser and Goodman and those of Karplus and Das. Also, the tests do not critically distinguish which of the following may be taken as the better estimator of the pi charge density of the fluorine atom: the shielding parameter based upon unsubstituted fluorobenzene as the standard of comparison or the shielding parameter based upon the meta isomer of the p‐substituted fluorobenzene.
Data are presented on F^{19} shielding of the acid fluoride atom of p‐substituted benzoyl fluorides and benzenesulfonyl fluorides. These results show that the special shielding relationship derived for p‐substituted fluorobenzenes does not apply.

Electron Spin Resonance of Titanium (III) Acetylacetonate
View Description Hide DescriptionThe ESR spectra of titanium (III) acetylacetonate present in small amounts in single crystals of aluminum (III) acetylacetonate has been investigated both at room temperature and at liquid‐nitrogen temperature. The spectra arising from the isotopes with no nuclear spin gave the following: g‖ = 2.000±0.002; g _{‖} = 1.921±0.001. The linewidths at room temperature were about 70 G, but narrowed down to less than 10 G at liquid‐nitrogen temperatures. At liquid‐nitrogen temperatures, the hyperfine spectrum due to isotopes Ti^{47} and Ti^{49} was observed and is shown to confirm previous assignments of nuclear spins. The hyperfine components of the spin Hamiltonian were found to be: A = 6.3±3.0×10^{—4} cm^{—1}; B = 17.5±0.5×10^{—4} cm^{—1}. It is shown that these results are consistent with an A _{1}ground state and with the E _{ a } state, being from 2000 to 4000 cm^{—1} above the ground state. Further, it is shown that the results suggest a considerable degree of covalent interaction involving π electrons of the ligands.

Dielectric Properties of Some Powdered Organic Semiconductors
View Description Hide DescriptionThe use of electrical conductivitymeasurements to characterize the charge density and/or mobility parameters of a material is discussed. The common practice of using simple, pressed electrodes with dc measurements is felt to be grossly inferior to four‐probe techniques. Even this refinement, however, is subject to considerable error for powdered samples. Many workers have used fairly simple ac techniques to eliminate interparticle contact resistances in organic semiconductors; this approach is shown to have been misapplied. It is possible, however, to measure what appears to be a specific conductivity (independent of packing pressure or filling factor) by more elaborate ac analysis. Measurements of the effective parallel resistance and capacitance are given for anthracene (powder and single‐crystal), metal‐free β‐phthalocyanine, and a β‐carotene tri‐iodide complex for a frequency range of 0.05 cps to 300 Mc/sec.