Volume 22, Issue 5, 01 May 1954

Vibrational Relaxation Times in Gases (Three‐Dimensional Treatment)
View Description Hide DescriptionThe calculations previously made by Schwartz, Slawsky, and Herzfeld are extended to three dimensions. As before, an exponential repulsion is fitted to the Lennard‐Jones potential, with constants found from viscosity data. While the transition probability is determined directly by the short range repulsion forces, the attractive forces and the effect of the centrifugal quasi‐potential modify the effective velocity of the colliding molecules. The agreement with experiment is fairly good, although high up on the repulsion curve (O_{2},N_{2}) the Lennard‐Jones 6—12 curve seems to be not quite steep enough.

Approximation of Molecular Orbitals in Diatomic Molecules by Diatomic Orbitals
View Description Hide DescriptionThe constants necessary for the specification of the exact wave functions of the homonuclear one‐electron diatomic molecule have been tabulated for a range of relatively large internuclear distances. A method for determining upper and lower bounds of the constants is presented. The energy of the hydrogen molecule has been calculated for the ground state using the one‐electron two‐center wave functions as molecular orbitals. The results of a similar calculation by Hylleraas have been confirmed and extended. It is found that the best results are obtained if the effective nuclear charges for the molecular orbital of one electron are different from the effective nuclear charges for the molecular orbital of the second electron. Somewhat less satisfactory results are obtained if the effective nuclear charges are the same in both orbitals. The application of diatomic orbitals in the calculation of the properties of other diatomic molecules is discussed. Calculations of energy appear to be prohibitively laborious; calculations of electric dipole moments and transition probabilities may be feasible.

Infrared Absorption Spectra of Aqueous HF_{2} ^{—}, DF_{2} ^{—}, and HF
View Description Hide DescriptionStrong infrared absorption bands of KHF_{2} appear at 1233 cm^{—1} and 1473 cm^{—1} in the solid, and are observed at 1206 cm^{—1} and 1536 cm^{—1} respectively, in H_{2}O solution. Corresponding values for KDF_{2} are 888 cm^{—1} and 1045 cm^{—1} in the solid, and 873 cm^{—1} and 1102 cm^{—1} in D_{2}O solution. In saturated KHF_{2} and in KHF_{2}solutions containing excess HF, there appear new, broad absorption bands attributed to polymeric species, e.g., H_{2}F_{3} ^{—}. The HF_{2} ^{—} ion is observed in concentrated aqueous HF; in addition, there is a strong absorption at 1820 cm^{—1} which is not shifted in D_{2}O‐HF mixtures.

Statistical Mechanical Theory of Transport Processes. VII. The Coefficient of Thermal Conductivity of Monatomic Liquids
View Description Hide DescriptionA molecular theory of the coefficient of thermal conductivity is developed from the general theory of transport processes presented in the first article of this series. The thermal conductivity of liquidargon at its normal boiling point is evaluated using the Lennard‐Jones intermolecular potential and a theoretically determined radial distribution function. The theory leads to an explicit expression for the product of the thermal conductivity and the friction constant of the theory of Brownian motion. With a reasonable estimate of the friction constant, the results of the theory agree satisfactorily with experiment.

Isotope Effect in Continuous Ultraviolet Absorption Spectra: Methyl Bromide‐d _{3} and Chloroform‐d
View Description Hide DescriptionA comparison of the continuous ultraviolet absorption spectra of CH_{3}Br and CD_{3}Br indicated a nearly constant shift of +280±50 cm^{—1} upon deuterium substitution. In the case of CHCl_{3} and CDCl_{3} the shift was less than the uncertainty of ±50 cm^{—1}. These results are interpreted in terms of the Herzberg‐Goodeve picture involving the carbon‐halogen bond rupture.
The ultraviolet absorption spectra of CCl_{4}, CFCl_{3}, CH_{2}Cl_{2}, CF_{2}Cl_{2}, and CHFCl_{2} are also reported.

Successive Orientational Transitions in Crystals
View Description Hide DescriptionAn extended discussion is given of a crystal model showing successive ``rotational'' or orientational transitions. This model consists of an array of classical rotators with next‐neighbor coupling, the potential energy of coupling being where θ_{ ij } is the angle between the molecular axes of symmetry. It is treated by both the internal field approximation (Bragg‐Williams approximation) and Chang's modification of Bethe's method. The internal field approximation is applied in two ways, the first involving use of consistency relations, the second involving calculations of the thermodynamic potentials. The consistency relations are shown to be equivalent to the condition that the free energy be stationary, but not necessarily a minimum, with respect to variation of the orientational distribution of the molecules. Depending on the relative values of A and B, the model shows a single second‐order transition, a single first‐order transition, two first‐order transitions, or a second‐order transition followed by a first‐order transition as T rises. The treatment by Chang's method is not as complete as that by the internal field method, but gives confidence that the latter method is sufficiently accurate to indicate correctly the general behavior of the model. Transition temperatures are computed by both methods, latent heats and specific heats by the internal field method only. The relatively complex behavior of the model can be understood in general terms. In particular, when two transitions occur, the one at lower temperature marks a change from an ordered state in which molecular axes tend to be all parallel to a preferred direction (``ferromagnetic'' case) or alternately parallel and antiparallel (``antiferromagnetic'' case) to another ordered state in which parallel and antiparallel orientations are equally probable for each molecule; the second transition is to a state of complete long‐range orientational disorder. There are suggestive similarities between the behavior of this model and the observed properties of the hydrogen and deuterium halides.

Flame Turbulence Measurements by the Method of Helium Diffusion
View Description Hide DescriptionA technique is described for measuring transverse turbulence intensity in flames which makes use of the diffusion of helium. The latter is detected by a thermal conductivity method. The effects of various experimental parameters and the reliability of the technique are discussed. Results obtained in highly turbulentflames stabilized on various baffles in a 5 cm×20 cm duct are given, and compared with results obtained under comparable cold flow conditions. It appears that, under the conditions of these experiments, the amount of ``flame‐generated'' turbulence detectable at a fixed point in the duct by this technique is probably small.

Measurement of Temperature Distribution in a Low‐Pressure Flat Flame
View Description Hide DescriptionThe temperature distribution in a very lean, flat propane‐air flame was measured by the thermocouple method, at a pressure of 0.0594 atmos. The temperature change occurred in a zone about 3 cm thick. Wallquenching was minimized by employing a burner tube diam of 25 cm. The thermocouple was made from 12‐micron wire, coated with ceramic to avoid catalytic effects. One hundred experimental traverse points were obtained, with a standard deviation of ±0.016 cm.
The burning velocity was also measured, and was found to vary with the inverse 0.30 power of pressure. This is in agreement with Egerton and Sen's result, obtained over a more limited range of pressure.
The temperature pattern was analyzed mathematically to obtain the pattern of heat release rate, taking into account the variation with temperature of thermal conductivity and specific heat. It was found that the heat release began at 300°C, attained a maximum value of 1.2 cal/cm^{3}‐sec at 1100°C, was nowhere negative, and was finite over a zone about 2 cm thick. The maximum temperature of the flame was 1332°C. The result obtained for the ``ignition point'' was found to be extremely sensitive to the exponent giving the temperature dependence of the thermal conductivity. Some calculations relating to the chemical kinetics of the flame are described.

Studies of Evaporation of Small Drops
View Description Hide DescriptionThe rates of evaporation of small droplets of diamyl sebecate (average radius R∼10^{—4} cm) were measured in a Millikan oil‐drop chamber, and observed to obey a law of the form dR/dT = a/(1+bR) which has been predicted by the theories of Fuchs and Frisch and Collins. Using a nonequilibrium distribution function of the velocities, the relationship has been rederived in a more rigorous fashion (over a limited range of conditions). Certain corrections in the constants a and b are introduced, and the validity of the Fuchs theory in this range of conditions is demonstrated. Using the formulation of Frisch and Collins, the law may be derived in the same form, subject to certain approximations.
An empirical form of the Stokes‐Cunningham law for the limiting velocity of fall in a dilute medium has been obtained for dicapryl sebecate in air.

The Thermodynamics of Boron Nitride; Low‐Temperature Heat Capacity and Entropy; Heats of Combustion and Formation
View Description Hide DescriptionThe low‐temperature heat capacity of microcrystalline boron nitride has been measured up to 300°K. It has been found that in the range from 20 to 65°K the heat capacity follows a T ^{2} relationship rather than the usual Debye T ^{3} law, and this has been explained as resulting from the layered, quasi‐two‐dimensional lattice of boron nitride. The Debye‐type characteristic (two‐dimensional) temperature is θ_{2}=598°K. At 298.16°K C_{p} =4.78_{3} cal/mole deg and S ^{0}=3.67_{3} eu, of which 0.034 has been extrapolated below 20°K. Derived thermodynamic functions have been tabulated at 10° intervals between 20 and 300°K. The heat of combustion of boron nitride in a conventional bomb calorimeter to yield amorphous boric oxide and elemental nitrogen has been determined to be 90.2±0.5 kcal/mole. From this value and other established thermal data the heat of formation of boron nitride is exothermic 60.7±0.7 kcal/mole.

The Intermolecular Potentials for Some Simple Nonpolar Molecules
View Description Hide DescriptionExperimental data on the crystal properties, second virial coefficients, and viscosity coefficients of Ne, A, Kr, Xe, CH_{4}, N_{2}, CO, O_{2}, and CO_{2} were analyzed for the purpose of obtaining values of the parameters in the exp‐six intermolecular potential,. For gases whose molecules are spherical, it was possible to reproduce, with a single set of potential parameters, not only the crystal, second virial, and viscosity data, but also data on other transport properties with fair accuracy. For gases whose molecules deviate appreciably from spherical symmetry it was necessary to choose at least two different sets of potential parameters in order to reproduce different types of properties. Such behavior was taken to indicate the inadequacy of the assumptions, made in the fundamental gas theories, that intermolecular forces are central and that intermolecular collisions are elastic.

Determination of Adsorption Energy Heterogeneity of Solid Surfaces
View Description Hide DescriptionA revision of the theory for the distribution of adsorption energies among the surface sites of a solid is presented. It is postulated that the distribution function for the adsorption energies is independent of the temperature. With this requirement, and a knowledge of the pressure‐temperature dependence of empirical isotherm data, it is possible to determine simultaneously the distribution function and the dependence of the partition function of the adsorbed phase on the adsorption energy. Several examples are presented in illustration of the theory.

Equilibria in the Formation of Molybdenum and Thorium Iodides from the Elements
View Description Hide DescriptionAn investigation has been made of the reaction of molybdenum and iodine to form molybdenum diiodide in the temperature interval from 1086°K to 1914°K, and the reaction of thorium and iodine to form thorium tetraiodide in the temperature interval from 1395°K to 1706°K. Thermodynamic properties of molybdenum diiodide and thorium tetraiodide were determined from measurements of the equilibria in these reactions. For the reaction Mo(s)+2I(g)=MoI_{2}(g) at 1200°K, ΔF ^{0}=—13.6 kcal/mole, ΔH ^{0}=—25.0 kcal/mole, and ΔS ^{0}=—9.5 cal/mole °K. For the reaction Th(s)+4I(g)=ThI_{4}(g) at 1500°K, ΔF ^{0}=—83 kcal/mole. Using an estimated value for ΔS ^{0} of —82 cal/mole °K, ΔH ^{0}=—206 kcal/mole. The average Mo–I bond energy in MoI_{2}(g) and the average Th–I bond energy in ThI_{4}(g) are both 89 kcal/mole.

Quenching of Mercury Resonance Radiation. IV. Unsaturated Compounds
View Description Hide DescriptionThe cross sections for quenching mercury resonance radiation by a number of mono‐ and di‐olefins, acetylenes, substituted olefins, and other compounds containing multiply bonded atoms have been measured. The quenching cross sections of mono‐olefins increase with increasing molecular weight but not with increased branching of the carbon skeleton. The position of the double bond has little or no effect on the cross section. The substitution of fluorine for hydrogen decreases the cross section of olefins. The presence of a second double bond does not alter the cross section. The double bond is more effective when between two carbon atoms than when it is between two nitrogens or carbon and oxygen. The cross sections of acetylenes are essentially the same as those of the corresponding olefins but here the substitution of N for CH does not appear to alter the effective cross section.

Analysis of the Near Ultraviolet Absorption Spectrum of Acetylene
View Description Hide DescriptionThe absorptionspectrum of acetylene in the region 1970—2470A has been photographed in the fourth and fifth orders of a twenty‐one‐foot gratingspectrograph with absorbing paths of 0.007 to 70 m‐atmos.
It has been possible to extend the arguments which led King and Ingold to conclude that in the upper electronic state the molecule is bent and has C _{2h } symmetry. The upper electronic state is A_{u} or, possibly A_{g}.
The effective moment of inertia I_{a} of the excited state is small, causing sub‐band separations of 50 to 150 cm^{—1}. These sub‐bands all have P, Q, and R branches, are well resolved, and have the appearance of bands of diatomic molecules. The following rotational constants of the upper state are derived: If the C–H distance is assumed to be between 1.070 and 1.090A, one finds Ground‐state combination differences are in agreement with precise values derived from infrared data. Some new lower state B values are obtained.
The O–O vibrational transition is shown to be at 42 197.69 cm^{—1}. The sub‐bands form ν_{4}″ progressions and ν_{3}′ progressions. Analysis gives two upper state vibrational frequencies The following lower state vibrational constants are obtained: The fundamental frequency ν_{4}″ is the sum of these constants, that is, 611.7_{2} cm^{—1}.

Microwave Spectrum and Dipole Moment of Pyridine
View Description Hide DescriptionThe microwave spectrum of pyridine has been studied in the region from 20 000 to 40 000 Mc. Twelve low‐J R‐branch lines have been identified. Analysis of the spectrum requires that the dipole moment lie in the a axis, and leads to the following values of rotational constants:a=6039.436 Mc, b=5804.997 Mc, c=2959.210 Mc, and κ=+0.847781. The dipole moment of pyridine vapor was found to be 2.15±0.05 D from quantitative Stark effect studies.

Thermodynamics of Equilibrium in the Ultracentrifuge
View Description Hide DescriptionAn exact equation has been derived which can be used for the determination of the ratio of the activity of substance i in a solution of molality m _{β} to the activity in a solution of molality m _{α}. Here m _{β} and m _{α} are the respective molalities observed at two positions x _{β} and x _{α} within a two‐component solution which has come to equilibrium in an ultracentrifuge. The calculation involves the densities of the solution at all positions between x _{β} and x _{α} and the partial molal volumes of i for the two molalities m _{β} and m _{α}. For each of these molalities partial volumes are required for the range of pressure between the equilibrium pressure acting on the solution of that molality and the pressure (ordinarily one atmosphere) of interest to the investigator. Some information concerning a solution containing more than two components can be derived from ultracentrifugal experiments if adequate density data are available.

Further Results on Monte Carlo Equations of State
View Description Hide DescriptionThe equation of state of three‐dimensional hard spheres has been obtained by the Monte Carlo method. Some qualitative results for a system of two‐dimensional molecules with Lennard‐Jones interaction are also given, as well as a general discussion of the usefulness and limitations of the Monte Carlo method.

Organic Photoconductors. I. The Kinetics of Photoconductivity in Rhodamine B
View Description Hide DescriptionThe behavior of rhodamine B undergoes a change at about 60°C below which temperature it is complicated by memory effects. Above 60°C the decay process is strictly bimolecular. Three activation energies were measured: for conduction, for decay, and for rise of conductivity, and each was approximately 0.55 ev. The observed second‐order character and the absolute rate of the decay process can be accounted for by a model having a large density of monoenergetic traps lying 0.55 ev below the conduction band. There is evidence that the slowness of reaching a steady state in light is to be associated with a redistribution of charge carriers from the random sites in which they are formed into preferred sites or configurations.

Organic Photoconductors. II. Crystal Violet
View Description Hide DescriptionPhotoconductivity in crystal violet is a volume effect primarily, and surface or electrode complications have not been recognized. Donor and trapping impurities may be introduced into films, but the highly purified substance shows a large photoconductivity. The thermoelectric effect is normal. On the other hand, rates are extremely slow, there is a prominent long‐lived memory effect, and under certain circumstances the second‐order rate constant for a particular decay process is inversely proportional to the initial conductance. A hypothesis is proposed to account for the last‐mentioned peculiarity, in terms of which structures are formed in the film which have the property of maintaining a constant initial density of charge carriers; the steady‐state conductance being no longer a measure of their density but only of their total number.