Volume 36, Issue 8, 15 April 1962

Magnetic Resonance of Strongly Coupled Nuclear Spin Systems. I. Refined Analysis of Complicated NMR Spectra
View Description Hide DescriptionA method which is useful for a refined analysis of the high‐resolution NMR spectra is presented. The method is based on the method of least squares. Before refinement of molecular constants, it is necessary to make a rough assignment of multiplet lines in a spectrum. Then the spectrum will be analyzed systematically with high precision. The ways to find a rough assignment are also discussed briefly. Although the method is applicable to any spin system, examples of analysis are shown by the spectra of three spin systems, the vinyl protons of acrylic acid, ethyl acrylate, and vinyl sulfonic acid. From these results, the method appears to be suitable for an analysis of the spectrum which is composed of superposed lines.

Heat Capacity of Critical Mixtures
View Description Hide DescriptionA theory is given of the heat capacity of liquid mixtures in the critical region. The entropy density is taken to be a function of the local composition and is expanded to quadratic terms in the composition fluctuation. The anomalous heat capacity computed from the average entropy fluctuation is very large because of the extreme sensitivity of the large composition fluctuations to the temperature. An application to a cubic lattice shows that the theory is equivalent to a ring diagram or random phase approximation in the theory of the Ising lattice. The heat capacity goes to infinity as (T—T_{c} )^{—½} in the critical region, for a mixture at the critical composition. Fair agreement with experiment is obtained; the one parameter which enters can be obtained, in principle, from x‐ray or light scattering.

Absorption and Dispersion of Sound in Critical Mixtures
View Description Hide DescriptionThe entropy previously associated with the long wavelength spectrum of composition fluctuations in the critical mixing region is studied under the supposition that the temperature varies harmonically with time. Relaxation effects in the response of the long range part of the radial distribution function to the temperature variation produce a complex heat capacity. The consequent sound absorption rises to a maximum at the critical point, in good quantitative agreement with experiment. The equation of motion for the radial distributions function is the modified diffusion equation previously used in a theory of the anomalous viscosity rise in the critical mixing region.

Correlations at the Critical Point
View Description Hide DescriptionAn extension of the Ornstein—Zernike approach to the determination of the radial distribution function function g (r) in the critical region is given. Nonlinear terms in the equation for the local pressure as a function of local density are introduced, the significant terms being determined from the shape of the coexistence curve. For a two‐dimensional lattice gas, g2(r)—1=G _{2}(r)∼0.86r ^{—¼} at the critical point, in reasonable agreement with the Kaufman—Onsager result: G _{2}(r)∼0.78r ^{—¼}. In a three‐dimensional lattice gas at the critical point,G _{3}(r)∼r ^{—1}(lnr)^{—½} if the coexistence curve has a quadratic top; otherwise G _{3}(r)∼r ^{—1}.

Determination of the Molecular Structures of CF_{3}NO_{2} and CBr_{3}NO_{2} by Electron Diffraction
View Description Hide DescriptionThe structure of the halopicrins is of particular interest since these compounds are not very stable. Of interest also is the orientation of the threefold group at one end of the C–N bond with respect to the —NO_{2} group at the other end. The quantitative sector‐microphotometer method in electron diffraction was employed for studying the structures of bromopicrin and fluoropicrin. In both molecules, the —CX_{3} group and N–O bond have the expected values for bond lengths and angles. On the other hand, the C–N distance is very long, 1.59 A in CBr_{3}NO_{2} and 1.56 A in CF_{3}NO_{2}; the ONO angle has values of 134° and 132°, respectively; the —CNO_{2} group is not planar; and the molecule assumes a staggered configuration similar to that found in ethane compounds (with one position vacant).

Theory of Multicomponent Fluid Mixtures. III. A Pseudo Pair Potential
View Description Hide DescriptionThis article considers some further consequences of the exact statistical mechanical theorem (given in article I of this series) which relates the thermodynamic properties of a mixture to those of a fictitious pure fluid by defining an intermolecular potential function (called the pseudopotential) for this pure fluid. Starting with the perturbation series for the pseudopotential all terms which can be written as a sum of pairwise interactions are collected and summed to give a simple closed expression for a pseudo pair potential function for the mixture.
Retaining only these pair terms and neglecting all triplet and higher‐order interactions in the pseudopotential gives an approximation which is a rigorous lower bound to the correct pseudo‐potential for all configurations. For mixtures of molecules with rigid cores this pseudo pair potential is also a potential with a rigid core, but with a diameter equal to that of the smallest molecule. The extreme nature of this approximation, which severely limits the application of the theory at high densities and pressures, is shown to be a direct consequence of neglecting triplet interaction terms in the pseudopotential. The nature of the limitations inherent in any approximation of the pseudo‐potential by a sum of pair‐wise interactions is clarified by comparing these results with the random mixing approximation to the pseudopotential which is known to give an upper bound for all configurations. The free‐volume theory for the pseudo pair potential, resulting from summing the pair terms, for mixtures of rigid spheres is developed. The results of this calculation are compared with recent Monte Carlo calculations for binary mixtures of rigid spheres to illustrate the extremely ``soft'' equation of state which results when triplet interactions are neglected.

Double‐Minimum Potentials in Hydrogen‐Bonded Solids
View Description Hide DescriptionUsing a simple one‐dimensional model of H bonds, vibrational‐energy eigenvalues, eigenfunctions, transition moments, and absorption intensities are calculated for a series of symmetric and asymmetric double‐minimum (D.M.) potentials. On the basis of the results obtained, the necessary requirements for observing doublets in the infrared spectra of H‐bonded solids are given. In most cases an asymmetric D.M. potential does not give rise to such doublets. Attention is drawn to the rapid ``switch‐over'' from even‐odd, odd‐even to ``left‐left,'' ``right‐right'' selection rules when a slight asymmetry is introduced into a symmetric D.M. potential. Also, a very rapid uncoupling of resonance interaction between accidentally coincident ``left'' and ``right'' levels of strongly asymmetric D.M. potentials is predicted. The importance of obtaining accurate relative intensity values and of determining the infrared and Raman spectra of both the H‐bonded solids and their deuterated analogs at several temperatures is emphasized.

Preparation of Semiconducting Diamonds
View Description Hide DescriptionP‐type semiconducting diamonds can be formed at high pressures and temperatures out of mixtures of graphite and catalyst metal (Ni, Fe, etc.) to which small amounts of B, Be, or Al have been added. The crystals may have resistivities of as low as 10^{3} ohm‐cm with activation energies for conduction ranging between 0.1 and 0.35 ev. Semiconducting crystals may also be prepared by allowing B or Be to diffuse into diamond crystals at high pressures and temperatures. The crystals prepared with high concentrations of boron are blue. No n‐type crystals have been prepared so far.

Preparation of Semiconducting Cubic Boron Nitride
View Description Hide DescriptionSemiconducting crystals of cubic BN may be prepared at high pressures and temperatures by adding small amounts of selected impurities to the synthesis mixture (hexagonal boron nitride plus lithium or magnesium nitride). P‐type crystals, blue in color, can be prepared by adding Be; they may have resistivities of about 10^{3} ohm‐cm and activation energies for conduction of about 0.2 ev. N‐type crystals can be prepared by adding S, Si, KCN, and other impurities; they were found to have resistivities of 10^{3} ohm‐cm or higher and activation energies for conduction of 0.05 to 0.20 v. The diffusion of impurities into cubic BN crystals was not found to proceed as rapidly as with diamond. Point‐contact rectification effects have been observed among semiconducting cubic BN and diamond crystals.

Charge States of Molecular Fragments from CCl_{3}Br Following Nuclear Decay of Br^{80m } and Br^{82}
View Description Hide DescriptionA comparison of the positive ionic fragments from dissociation of trichlorobrommethane by β^{—}, γ decay of 35.9‐hr Br^{82} and from isomeric transition of 4.4‐hr Br^{80m } was made by mass spectrometric techniques. Virtually all the products following beta decay are singly charged, while distributions of multiply charged atomic species dominate the fragmentation pattern after the isomeric transition. The results indicate that negative beta decay affects the molecule rather mildly, while the effect is violent following isomeric transition with internal conversion. In the latter mode of nuclear decay the molecule apparently explodes as a result of multicenter Coulombic repulsion.

Molecular Dimensions in Crystalline Polymers
View Description Hide DescriptionIn this paper we calculate from theoretical considerations the molecular dimensions of polymer chains in partially crystalline polymers existing in any state of orientation. Our theory also applies to isolated molecules in solution which have helical and random coil regions within the same molecule.
The treatment is based on two probability parameters and the mathematical method of the Markoff chain.

On the Thermodynamics of Solutions. VII. Critical Properties of Mixtures
View Description Hide DescriptionThe applicability of equations of state has been greatly widened by automatic computation. Algebraic relations, however, particularly strict thermodynamic relations, are apt to simplify the calculations and therefore to extend the applications much further.
Explicit general relations between temperature, pressure and composition at the critical line of a binary mixture would be useful and also theoretically interesting. Although the problem is easily formulated, it appears that a general solution cannot be found. But a partial solution can be derived: The derivatives of the variables of state along the critical line in the limits of the critical points of the pure components can be expressed by partial derivatives in these points.
The volume of a mixture increases on condensation in the range of retrograde condensation. This result may have been suspected on the basis of the principle of Braun and Le Chatelier.

Non‐Steady‐State Nucleation
View Description Hide DescriptionThe non‐steady‐state nucleation of water vapor is examined by an exact mathematical approach which solves on a computer the 100 or so simultaneous differential equations which describe nucleation. This approach avoids the numerous mathematical approximations of Kantrowitz, Probstein, and Collins. The customary kinetic and thermodynamic assumptions of the classical liquid‐drop theory of steady‐state nucleation were used. The times for the concentration of the nucleus of liquid water to reach 95% of steady state at —10°, —40°, and —60°C are 1.4, 19, and 27 μsec with supersaturations of 5, 10, and 20, respectively, and are only 10% longer than the ``time lags'' estimated by the approximate methods. Since the surface tensions of small clusters and the accommodations coefficients are unknown, the approximate methods, although incorrect by greater than 100%, are sufficiently accurate for most purposes. The results of Frisch are shown to be incorrect. The steady‐state concentrations of water clusters are equal to their equilibrium concentrations for clusters which contain up to about 15 and 5 molecules less than the nucleus at —10° and —60°, respectively. Contrary to general opinion, the equilibrium concentrations of liquid‐drop clusters do not decrease sharply in the vicinity of the nucleus.

Kinetics of Condensation of Water Vapor
View Description Hide DescriptionThe condensation of water vapor via steady‐state nucleation is examined by an exact mathematical approach which solves the kinetic equations on a computer. This approach avoids the usual assumption that nucleation abruptly stops when the parent phase becomes slightly depleted. The corrected classical theory of steady‐state liquid‐drop homogeneous nucleation and the growth law used in the classical nucleation theory were assumed. Results gave no indication of a ``critical'' supersaturation for condensation and showed that condensation via classical homogeneous nucleation would be much slower than experimentally observed in cloud chambers. Condensation in 50 msec via homogeneous nucleation theoretically requires 13 particles/cc and an initial supersaturation of 5.2 at —5°C and 3.3×10^{4} particles/cc and an initial supersaturation of 35 at —60°. Nucleation rates are sensitive to supersaturation but at —60° one‐third of the particles are formed after a 4% decrease in supersaturation, contrary to the usual interpretation of condensation kinetics in a cloud chamber. The rapid condensation rates experimentally observed in a cloud chamber may be due either to heterogeneous nucleation or to homogeneous nucleation with the surface energy of an 80‐ or 90‐molecule cluster being smaller than the macroscopic value, e.g., about 3 and 30% smaller at —5 and —60°, respectively. However, the liquid‐drop theory of homogeneous nucleation as classically formulated in terms of the macroscopic surface energy apparently cannot explain the experimental results in a cloud chamber and thus remains to be verified.

Collision‐Induced Microwave Absorption in Compressed Gases. I. Dependence on Density, Temperature, and Frequency in CO_{2}
View Description Hide DescriptionMeasurements of the dielectric loss by a resonant cavity technique at 9 and 24 kMc/sec are reported for CO_{2} for densities up to 100 amagat and 25°C. Some additional data are reported at elevated temperatures. The loss, which increases in proportion to the frequency and very nearly as the square of the density, is attributed to transient dipoles induced by the molecular electric quadrupole fields during molecular collisions. A theoretical analysis including the line shape is made to relate the loss to the pertinent molecular parameters and to permit an intercomparison with precise data available on the second dielectric virial coefficient. It is concluded that the microwave loss in quadrupolar gases may provide a sensitive method of getting information on the molecular quadrupole moments.

Collision‐Induced Microwave Absorption in Compressed Gases. II. Molecular Electric Quadrupole Moments
View Description Hide DescriptionA search for dielectric loss in the nondipolar gases, He, Ar, CH_{4}, SF_{6}, H_{2}, C_{2}H_{6}, N_{2}, and C_{2}H_{4} was made at a frequency near 24 kMc and for densities not exceeding 100 amagat. For the first six gases, the loss factor was immeasurably small, less than 2×10^{—7}, at the maximum density. The loss observed in nitrogen and ethylene is attributed to transient dipoles induced by the molecular quadrupole fields during binary collisions. From the data on the quadrupolar gases, including previous results on CO_{2}, values of the quadrupole moments (or upper limits where no loss was observed) are derived which are in reasonable agreement with other estimates.

Infrared Spectrum of CO Chemisorbed on Iron
View Description Hide DescriptionThe infrared spectrum of CO chemisorbed on iron has been obtained in the 270 to 5000 cm^{—1} range. Two absorptions were found, one at 580 cm^{—1} and one at 1950 cm^{—1}. From a vibrational analysis of five possible surface complexes, it is concluded that the observed spectra best fits the structure Fe=C=O, where the iron atom is part of the metal lattice. Force constants calculated for the Fe–C and C–O bonds, respectively, are 4.1 and 13.9 md/A. Comparison of these force constants with others suggests that both bonds are approximately double bonds. Use of empirical rules by Pauling and Badger both give an ironcarbonbond length of about 1.67 A.

Thermoluminescence of Solid Nitrogen after Electron Bombardment at 4.2°K
View Description Hide DescriptionSolid nitrogen annealed at 20°K and then bombarded with electrons at 4°K gives three glow peaks on warming, at 10°, 14.5°, and 19°K. Unannealed nitrogen gave broader peaks. A feeble, long‐lived glow followed the normal afterglow after bombardment at 4°K. Thermal effects during warming were observed in one apparatus with radiation shielding at 77°K, but they were not observed in a much more sensitive apparatus with radiation shielding at 4°K. The thermal effects are probably caused by an anomalous vapor pressure and loss of Dewar vacuum.
The data are discussed with reference to two interpretations, the storage of ^{2} D excited nitrogen atoms and the recombination of ^{4} S nitrogen atoms through diffusion. The latter explanation is preferred and a simple model is offered to account for the three diffusion activation enthalpies implied by the three thermoluminescence peaks.

Formation of Spin Centers in Carbons by Oxidation
View Description Hide DescriptionIt was found that a high concentration of electron spin centers is obtained in carbons originally heat treated to a temperature of 1000°—2400°C by heating such carbons to 700°—1100°C in an oxidizing atmosphere. The conditions for the most efficient formation of spin centers by oxidation are: a temperature of about 800°C or somewhat higher, gas pressure above atmospheric, and a proper duration of heating. The presence of spins was detected using the usual experimental techniques of paramagnetic spin resonance absorption. Spin centers were created in various types of carbons (hard, soft, and carbon blacks). The shape and width of the paramagnetic resonance line vary greatly depending on spin concentration and on the original heat‐treatment temperature of the carbon. In general the g value is close to or slightly higher than that for the free electronic spins. The experiments show that the presence of spin centers in equilibrium with an oxidizing gas is the result of the operation of two opposing mechanisms, one creating and the other destroying the centers. The creation occurs as a result of a direct chemical attack on the crystal surface. The destruction at high temperature is a result of the improvement of the crystal surface by atomic diffusion. Studies of the dynamics of formation and destruction of spin centers were carried out. The temperature dependence of spin absorption indicates a continuous change in character of spin centers with change in heat‐treatment temperature. For low heat treatments the spin centers show a localized broken edge‐bond character. With increasing heat‐treatment temperature of a carbon the spin centers gradually change in their character into ``metallic'' conduction band electrons.

Valence‐Bond Calculation of Geminal Spin‐Spin Coupling Constants in Substituted Methanes
View Description Hide DescriptionA theoretical study is presented of geminal proton spin‐spin coupling constants for a class of substituted methanes. Using a valence‐bond approach and a six electron model, consisting of a methylene group with an adjacent π electron pair, the hyperconjugation energy and the contact contribution to the geminal coupling constant are calculated. These data, which are in agreement with the experimental findings, indicate that hyperconjugative effects give larger coupling constants than would be expected on the basis of the H–C–H angular dependence alone. This is shown to arise out of delocalized structures, which in the ground state correlate the spins of the geminal protons. It is noted that the geminal coupling constant depends on the orientation of the methylene group with respect to the adjacent π electron system, and this data is reported for two values of the C–C internuclear distance.