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Volume 38, Issue 5, 01 March 1963
38(1963); http://dx.doi.org/10.1063/1.1733798View Description Hide Description
The vapor‐phase photochemistry of both 1,3‐cyclohexadiene and 1,3,5‐hexatriene can be treated as a single system since the photolysis of one gives rise to the other and the remaining products are common to both systems. In the present study, the pressure dependence of the products has been used to demonstrate that a classification of the reactions in this system as those that are common to both photochemistry and thermochemistry and those that occur only in the photochemistry parallels the behavior with pressure. It is argued that the first class of reactions which includeoccurs from a vibrationally excited ground‐state molecule which originates from the initially formed excited singlet state by internal conversion. These reactions have been found to decrease with an increase in the pressure of the parent olefin or with the addition of inert gases such as xenon, carbon dioxide, propylene, or ether. Such data when coupled with the calculated lifetimes of the excited singlet states show that collisional quenching of the excited singlet‐state molecules is unimportant at pressure below ∼8 mm. The trends observed with an increase in temperature support this general picture.
38(1963); http://dx.doi.org/10.1063/1.1733799View Description Hide Description
A method is presented by which the effects of pressure on the absorption and emission spectra of a luminescent center can be used to provide the parameters necessary to construct a configurational coordinate diagram of the center. Pressure shifts of the 2470‐Å absorption and 3050‐Å emission bands of KCl:Tl have been measured and are used to calculate the parameters for the appropriate configurational coordinate diagram; the results are in good agreement with those obtained from purely theoretical considerations. Values for bandwidth and compressibility are also calculated and are found to agree with experimental observation.
38(1963); http://dx.doi.org/10.1063/1.1733800View Description Hide Description
The integrated infrared intensities of the acetylenic carbon—carbon and carbon—hydrogen stretching bands have been measured for a series of meta and para substituted phenylacetylenes. The C≡C band intensity is very strongly dependent on the substituent, whereas the ≡C–H band is relatively insensitive to substitution. The C≡C band intensity is insensitive to solvent effects; the intensity of the ≡C–H band is increased slightly in basic solvents.
A simple π‐electron molecular orbital model for the phenylacetylenes yields results for the dependence of the C≡C band intensity on substituent which are in good agreement with experiment. The analysis shows that most of the intensity in the C≡C stretching band results from transfer of π electronic charge between ring and ethynyl groups during vibration.
38(1963); http://dx.doi.org/10.1063/1.1733801View Description Hide Description
The relative rates of hydrogen and deuterium abstraction by chlorine atoms from H2–D2, CH4–CD4, and C2H6–C2D6 in direct competition have been studied by a mass spectrometer technique permitting direct determinations of rates. The pair CHCl3–CDCl3 was investigated by a substitution—addition competition with C2Cl4. Data were obtained between 300° and 475°K, and values of k H/k D ranged between 3.64 and 10.9 for CH4/CD4, 2.37 to 2.69 for C2H6/C2D6, 1.58 to 2.26 for CHCl3/CDCl3, and 4.7 to 8.9 for H2/D2. For the family of reactions involving C–H–Cl, an extensive series of model calculations were made by the ``bond‐energy—bond‐order'' method. The expected variation of activation energy with heat of reaction was computed and compared with experiment. The expected variation of kinetic isotope effect with both temperature and heat of reaction was computed for a range of conditions much wider than these experiments. Simple activated complex theory predicts several strong trends of kinetic isotope effect with heat of reaction. The data, in a general semiquantitative way, follow these predicted trends, but in terms of fine details the data do not fit the theoretical lines. In view of the known simplifications in activated complex theory, this agreement with broad trends is all that anyone should expect.
38(1963); http://dx.doi.org/10.1063/1.1733802View Description Hide Description
This calculation applies the theory of Kirkwood to the determination of the rotatory diffusion constant of stiff‐chain macromolecules. The rotatory diffusion constants of a wormlike coil and of a weakly bending rod are calculated in terms of molecular parameters. The calculation refers only to the mode of relaxation associated with rotation of the entire segment distribution.
38(1963); http://dx.doi.org/10.1063/1.1733803View Description Hide Description
A mechanism is proposed to explain the ``stereoblock'' structures which occasionally result from homogeneous anionic polymerizations [cf. J. Am. Chem. Soc. 80, 1768 (1958)]. The mechanism postulates that a growing polymer chain has two reactive states in dynamic equilibrium, both capable of adding monomer, but each with its own stereospecificity. The resulting diastereosequence distribution is calculated and it turns out to be non‐Markoffian. It is shown that our ``two‐state'' polymerization mechanism yields predictions about the dependence of NMR spectra on polymerization conditions, and as such is capable of experimental test. The case of more than two states is also discussed.
38(1963); http://dx.doi.org/10.1063/1.1733804View Description Hide Description
Bloch functions are not good basis functions for molecular crystals in high electric fields. When the interaction with the electric field is large with respect to next‐neighbor interactions, it is better to use wave‐functions which are localized over molecular sites as basis functions. A treatment of electronic mobility and diffusion in molecular crystals using quantum mechanical transition probabilities between localized energy levels and considering only nearest‐neighbor interactions is developed. The asymmetry of the potential function, caused by the electric field, and the conservation of energy during transport are considered. The mobility is found to be independent of temperature, and the diffusion constant proportional to temperature. The magnitude of the diffusion constant calculated from phonon‐induced transitions is quite reasonable (4.6×10—3). Photon‐induced transitions do not appear to be important.
38(1963); http://dx.doi.org/10.1063/1.1733805View Description Hide Description
The electric dipole transition matrix element of a molecular crystal in the presence of an electric field is calculated. It is found to be proportional to the matrix element of the zero‐field Hamiltonian between nearest neighbors and inversely proportional to the electric field strength for the limit of strong fields.
38(1963); http://dx.doi.org/10.1063/1.1733806View Description Hide Description
The vapor pressure of liquid bismuth in the temperature range 800°—1050°K has been measured by the torsion‐effusion method. The values obtained are represented by the equation: log10 p (mm Hg) = 8.579— (10 108/T). A few separate Knudsen measurements have been performed in the same temperature range and the results used to calculate the molecular weight of bismuth vapor, and thus the heat of dissociation for the reaction ½ Bi2→Bi.
Relative Signs of Nuclear Spin Coupling Constants: A Refinement of the Double‐Irradiation Experiment38(1963); http://dx.doi.org/10.1063/1.1733807View Description Hide Description
The application of a very weak perturbing radio‐frequency field in nuclear magnetic double‐resonance experiments in such a way as to irradiate just a single resonance transition is shown to give information about the relative signs of the spin coupling constants in systems of three or more spins. The method is not restricted to near first‐order spectra and may be used even when several multiplets overlap. It has been applied to the determination of the relative signs of the couplings in 1,2‐dibromopropane, and the results agree with those of Finegold, who used conventional analysis methods. The sign of a long‐range coupling is reported.
38(1963); http://dx.doi.org/10.1063/1.1733808View Description Hide Description
The intensity distribution in the 1Σ—3II transition of SiO, observed by Verma and Mulliken, is discussed. The appearance of the subband 1Σ—3II2, which violates the selection rule ΔΩ=0, ±1 and the appearance of the Q branch of the 1Σ—3II0 subband, which violates the selection rule that ΔJ=0 is forbidden for Ω=0→Ω=0 transitions, are explained by the mixing of the 1Σ state with a 1II state as a result of the rotation of the molecule. The effect of spin‐orbit interaction is considered only insofar as it mixes singlet functions with the multiplet components of 3II r . Some indication is given as to why this explanation is inapplicable to the a 3II—X 1Σ+ transition of AlCl where the selection rule for Ω is apparently rigorously obeyed.
38(1963); http://dx.doi.org/10.1063/1.1733809View Description Hide Description
Slater's ``New Approach to Rate Theory'' [N. B. Slater, Theory of Unimolecular Reactions (Cornell University Press, Ithaca, New York, 1959), Chap. 9; J. Chem Phys. 24, 1256 (1956)] is used to analyze in detail two simple gas‐phase photochemical mechanisms. Quantum yields are calculated as functions of pressure, and the qualitative nature of the plots is discussed. Statistical methods are used to develop consistency theorems for checking experimental plots of quantum yield versus pressure against the theory.
38(1963); http://dx.doi.org/10.1063/1.1733810View Description Hide Description
The theory of how a probability distribution may be estimated by sampling is applied to the problem of using approximate wavefunctions for quantum mechanical systems and estimating the errors involved. The most probable wavefunction of given mean energy is considered and some of its properties found. The energy variance, which gives a lower bound to the true energy, can be calculated. The theory is applied to the simple harmonic oscillator and the predicted relation between mean energy and variance is compared with the actual relations found using two different types of approximate wavefunction.
38(1963); http://dx.doi.org/10.1063/1.1733811View Description Hide Description
Energy evolution below 1°K has been observed in β‐phase palladium hydride (formal composition Pd2H). The rate of evolution was strongly temperature‐dependent below 0.1°K, but became temperature‐independent between 0.1° and 1.0°K. It depended upon previous specimen history and was greatly reduced by annealing of the specimen below 50°K. For specimens kept below 1°K, the rate of energy production at a given temperature diminished with a half‐life of about 8 h.
The results are explained semiquantitatively as a (spectroscopically forbidden) nuclear‐spin conversion in quasi‐molecular PdH4 units left behind in small concentrations when the lattice is cooled through the rotational transition (at 55°K) of β‐palladium hydride. The temperature‐dependence below 0.1°K appears to result from limitation in the rate at which the lattice can remove the change in librational energy associated with the conversion process.
38(1963); http://dx.doi.org/10.1063/1.1733812View Description Hide Description
The reactions producing HeH+ from gaseous mixtures of H2 and He subjected to electron impact in the ion source of a mass spectrometer have been studied. Ionization efficiency curves show practically all of the HeH+ to be formed by reaction of H2 + and He. Phenomenological cross sections were compared with values for the formation of H3 + from the H2 +–H2 present in the ion source. The maximum value of the ratio of rate constants for HeH+ and H2 + formation computed from the experimental data was 28% of the theoretical ratio. If the heat of the endothermic reaction between H2 + and He is supplied from internal energy in H2 +, then the rate constant should be computed in terms of the fraction vibrationally excited H2 + with sufficient internal energy to meet the needs of the reaction rather than total H2 + in the ion source. An estimate of the population of the excited vibrational state in H2 + produced from H2 by electron impact gives approximately 29% with enough energy to react. The translational energy dependence of the ratio of rate constants reveals a kinetic energy threshold for the HeH+reaction of about 0.35 eV, but at higher ion kinetic energy there is strong evidence for heat of reaction coming primarily from internal energy in H2 +.
An attempt was made to use the HeH+reaction as a probe to investigate the distribution of excited H2 + produced from CH4 by electron impact. A third‐order process giving HeH+ was discovered in this system. Indications of a larger yield of H2 + with sufficient energy to react with He were obtained.
38(1963); http://dx.doi.org/10.1063/1.1733813View Description Hide Description
The viscosity of krypton has been measured over the temperature range 297° to 666°K by the oscillating disk method using helium for calibration. The viscosities obtained were used to get the parameters for a Lennard‐Jones 12–6 potential function and they were found to be ε/k=162°K and σ=3.734 Å. Calculation of the viscosity,thermal conductivity, self‐diffusion coefficient, second virial coefficients in the moderate temperature range, and the heat of sublimation at 0°K from the L. J. 12–6 function gives very good agreement with experimental values. Calculated values for the second virial coefficient at low temperatures, the reduced thermal diffusion factor, and the lattice spacing at 0°K are in fair agreement with experiment.
38(1963); http://dx.doi.org/10.1063/1.1733814View Description Hide Description
X‐ray‐ and uv‐excited thermoluminescence in natural quartz has been investigated by studying the properties of synthetic samples. The results for a large number of natural samples, including single crystals, outcrop specimens, and core‐hole samples showed that most of them had four prominent glow peaks in common. One of these is due to the presence of Ti and the others are apparently associated with a defect center. The effects of annealing at temperatures up to 900°C were found to be important in well‐crystallized samples but unimportant in others.
The emission spectrum of the Ti glow peak shows that a number of levels are involved in the luminescent transitions. All of the defect‐center glow peaks have the same emission spectrum which consists of a single maximum with a long wavelength tail. Direct‐current electrical measurements on single crystals showed that the trap‐emptying processes for the defect center were nonlocalized. Optical absorptionmeasurements at room temperature indicated that none of the common absorption bands are associated with peaks in the glow curve. From phosphorescent‐decay measurements it was determined that the trapping levels associated with the defect center have very narrow energy distributions whereas the trapping level due to Ti is discrete.
The glow peaks for ordinary quartz are not excitable by uv irradiation, but in samples annealed at 900°C all of the glow peaks due to the defect center are excited by uv. The annealed samples show absorption in the uv region which is not present in unannealed specimens. The results suggest changes in the trap‐filling mechanism, but the effects can also be explained by alterations in the luminescent levels.
Luminescence can be excited in all of the samples at fixed temperatures by x rays but not by uv. At low temperatures the effects of transitions through trapping levels are unimportant, and the emission is due only to x‐ray excitation of the luminescent centers. The spectral response of the emission is the same as that for the Ti glow peak. The intensity is about the same in all samples and is not affected by impurity content. This indicates that the luminescent levels involved are due to a crystal defect center and that the same center is involved in the thermoluminescence due to Ti.
38(1963); http://dx.doi.org/10.1063/1.1733815View Description Hide Description
Hexagonal, graphitelike boron nitride may be changed directly into the zincblende cubic form reported earlier or into a new wurtzite form by the application of static high pressures. No catalyst appears to be necessary. At high temperatures, between about 2500° and 4000°K, the zincblende form is favored; at lower temperatures, down to 300°K, the wurtzite form is favored; frequently both forms appear together. The minimum pressure required for the transformations is about 115 kbar at 2000°K; somewhat higher pressures, of the order of 130 kbar, suffice at higher and lower temperatures. The crystallites of the dense phases are small but give good x‐ray diffraction patterns from which the crystal structures can be determined.
38(1963); http://dx.doi.org/10.1063/1.1733816View Description Hide Description
The crystallization of linear polymer chains is considered as a process involving the selection of crystallizable sequences from the melt. If, owing to the requirements of thermodynamic stability, such sequences must exceed in length some critical value less than the chain length, and if the selection process is random, then the melt will be increasingly subdivided into uncrystallized sequences of varying length. Some of these may be expected to be less than the critical length, so that the segments comprising them are ``wasted'' insofar as participation in further crystallization is concerned.
An approximate sequence length distribution function for the uncrystallized sequences in the system is derived and utilized in connection with the problem of retardation in crystallization kinetics.
38(1963); http://dx.doi.org/10.1063/1.1733817View Description Hide Description
Radio‐frequency pulse methods have been used to measure the N14 spin‐lattice relaxation time in 25 molecular liquids, with the N14 in several types of groups. For eight of the compounds, microwave or pure quadrupole resonancemeasurements of the N14quadrupole coupling constant were combined with our T 1 results to give values for the correlation time τ q describing the molecular reorientations which govern T 1. These values for τ q at 25°C are about an order of magnitude shorter than reorientational correlation times calculated from the viscosity and molecular radius using the Debye—BPP approach. For the other compounds, τ q was estimated and used with the observed T 1 for N14 to predict values of the quadrupole coupling constant. The temperature dependence of T 1 was observed for nine compounds, leading to activation energies for molecular reorientation of 1.4 to 3.2 kcal/mole and inverse frequency factors τ q 0 of 2×10—14 to 9×10—14 sec. The temperature dependence of the protonT 1 was observed in CH3CN and it is compared with that of N14. It appears that the relaxation of some quadrupolar nuclei affords considerable promise for studying molecular reorientations in liquids and for separating diffusional and rotational processes. These possibilities, as well as that of estimating quadrupole coupling constants not otherwise readily accessible, are discussed.