Volume 19, Issue 11, 01 November 1951

The Cataphoresis of Spherical Fluid Droplets in Electrolytes
View Description Hide DescriptionA theory of the electrophoresis of spherical fluid droplets in an electrolyte is developed. A general formula is given for the electrophoretic velocity in terms of the applied field, the potential distribution in and near the drops, and the dielectric constants and coefficients of viscosity of the liquid and electrolyte. It is assumed that the liquiddrop retains its spherical form in cataphoresis and also that relaxation effects in the electrolyte may be neglected.
Detailed formulas are worked out for the case of a Debye‐Hückel potential in the electrolyte, and the following charge distributions in the fluid sphere.
(a) No charge within the sphere; the whole charge is concentrated on the interface.
(b) Uniform volume distribution of charge.
(c) Ionic double layer potential in the sphere.
It is shown that sundry special cases of the theory agree with previous computations and that it is not legitimate to apply theories of the cataphoresis of solid particles to fluid drops.

Elastic Relaxation and Structure of Liquids. I. Ultrasonic Absorption in Some Halogenated Methylenes, Ethanes, and Ethylenes
View Description Hide DescriptionIn order to obtain information on the presence of structural effects in the elasticrelaxation phenomena observed in liquids, the ultrasonic absorption was studied as a function of temperature in some organic compounds whose structure is correlated in a simple way. Large differences of absorption coefficient and of its temperature dependence have been found. It is difficult, at the present time, to understand clearly the results, but they show that the liquid structure has a great importance in the relaxation phenomena present in liquids.
Moreover an increase in dipole moment of the molecules is often present with an increase of absorption, showing that the dipole moment is not related in a simple way with the characteristics of relaxation phenomena and that all the interactions among the molecules are to be taken in account.

On the Elastic Relaxation in Carbon Disulfide: The Temperature Dependence of the Ultrasonic Absorption Coefficient
View Description Hide DescriptionThe experimental values of the ultrasonicabsorption coefficient given in the literature for carbon disulfide show the presence of dispersion in the frequency range 1–100 Mc/sec, but large differences are present in the values obtained by various authors at the same frequencies so that it is difficult to analyze the behavior of this liquid. In order to discriminate among the various results more information is needed. For this reason a measurement of the absorption coefficient was performed at 30 Mc/sec. The value obtained for α is in agreement with the higher values of the absorption coefficient obtained by other authors at various frequencies and, therefore, it gives more credence to them in comparison with others.
The absorption coefficient as a function of temperature does not follow a linear law as it does in other unassociated liquids. The temperature coefficient (1/α)(∂α/∂t) goes from 7.3·10^{−3} deg^{−1} at −23°C to almost zero near the boiling point. These results can be used to examine the theoretical explanations of absorption in carbon disulfide based on the assumption that all the vibrational modes relax together or on the hypothesis that they have different relaxation times. The value of the temperature coefficient at 25°C seems to be better explained with the first treatment.

Vapor Pressures below 1 mm Hg of Several Aromatic Compounds
View Description Hide DescriptionVapor pressures of the three isomeric picolines and p‐di‐tert‐butylbenzene were determined over a pressure region of approximately 5–250 microns Hg using a Rodebush manometer and an effusion manometer for each compound. The experimental results of the two methods show good agreement. A comparison of the two manometers is made and the merits of each method are discussed.

Quantitative Line‐Width Measurements in the Infrared. I. Carbon Monoxide Pressurized with Infrared‐Inactive Gases
View Description Hide DescriptionQuantitative infrared‐intensity measurements on CO pressurized with gases such as H_{2}, He, and A have been carried out at room temperature. For pressures up to 100 psia the experimental absorptionmeasurements are correlated quantitatively by the use of theoretical relations derivable from the dispersion formula. Thus, for a fixed value of the total pressure, the observed absorption is a linear function of the square root of the optical density. Similarly, at constant optical density, the absorption is a linear function of the square root of the total pressure. Using Elsasser's treatment for equally spaced and equally intense rotational lines, lower limits have been determined for the rotational half‐widths of CO broadened by various infrared‐inert gases.
The determination of rotational half‐widths from spectroscopicmeasurements can be refined by allowing for the variation of integrated absorption per rotational line from one line to another in a given vibration‐rotation band. By carrying out numerical calculations, with the rotational half‐width treated as a variable parameter, a direct comparison between calculated and observed infrared absorption can be used to determine the rotational half‐width δ^{0} for pressures which are small enough to justify a treatment for nonover‐lapping rotational lines. In this manner it was found that (δ_{ F })H_{2} = 0.077 cm^{−1} atmos^{−1}, (δ_{ F })_{A} = 0.040 cm^{−1} atmos^{−1}, (δ_{ O })H_{2} = 0.063 cm^{−1} atmos^{−1}. Here the subscripts F and O denote measurements on the fundamental and the first overtone, respectively. The subscripts H_{2} and A identify the broadening agent used for study.

Quantitative Line‐Width Measurements in the Infrared. II. Unpressurized Carbon Monoxide
View Description Hide DescriptionExperimental measurements on self‐broadening of CO are correlated quantitatively by the use of a dispersion formula for line‐shape representation. Interpretation of experimental data in terms of a simplified line‐intensity distribution leads to the conclusion that the apparent rotational half‐width of CO changes with the pressure of CO at approximately the same rate as with the pressure of H_{2} for the fundamental. Similar calculations for the first overtone lead to relatively small values for the apparent rotational half‐width. Numerical calculations for a realistic line‐intensity distribution have not been carried out.

The Structure of Trifluoromethyl Acetylene from the Microwave Spectrum and Electron Diffraction Pattern
View Description Hide DescriptionMeasurements, in the microwave region, of the J = 3→4 rotational transitions of trifluoromethyl acetylene and several of its isotopic modifications have been made, and the moments of inertia, I_{B} (in a.m.u.‐Å ^{2}), have been found for the ground vibrational state: for CF_{3}CCH, 175.61_{3}, CF_{3}C^{13}CH, 177.02_{4}, CF_{3}CC^{13}H, 181.30_{2}, and for CF_{3}CCD, 187.46_{2}. Three lines corresponding to J = 3→4 transitions of CF_{3}CCH in the excited vibrational statev _{10} = 1, and two lines corresponding to v _{10} = 2 and v _{10} = 3, have also been measured and interpreted according to Nielson's theory of l‐type doubling in symmetric tops. From Stark effectmeasurements at different electric field strengths the dipole moment of CF_{3}CCH in the ground vibrational state has been found to be 2.36±0.04 Debye units. For the ground vibrational state the microwave data lead to the following bond distances: C–H, 1.056±0.005Å; C≡C, 1.201±0.002A. The C–C and C–F distances were calculated from the measured moments of inertia for several assumed values of the FCF angle. Electron diffraction experiments were also made, and the intensity curves calculated for the assumed microwave models were compared with the observed visual curve. From the combination of microwave and electron diffraction results the best agreement was obtained with the following set of parameters: ∠FCF, 107.5°±1°; C–C, 1.464±0.02A; C–F, 1.335±0.01A.

Thermodynamic Data and Some Notes on the Nature of Adsorbed Helium
View Description Hide DescriptionThe adsorption isotherms and heat capacities of helium on TiO_{2} in the rutile crystalline form have been obtained. On the basis of the observed shift in lambda‐point with coverage, the behavior of the adsorbed phase has been correlated with the behavior of the bulk liquid and solid under pressure.

I. Normal Frequencies of a One‐Dimensional Crystal. II. An Approximation to the Lattice Frequency Distribution in Isotropic Solids
View Description Hide DescriptionI. The accurate expression for the individual frequencies of a linear crystal of any number of particles is derived.
II. It is shown that, for an isotropic three‐dimensional array of uniform masses, the root‐mean‐square frequency is easily evaluated and the maximum square must always be less, but not much less, than twice the mean square. For two commonly studied simple cubic systems, the maximum square is evaluated and shown to be twice the mean square. The Debye expression for the frequencies in terms of standing wave components is modified empirically to give the correct maximum and mean squares by substituting linear crystal frequencies for the components and introducing a second force constant.
The resulting expression, a simplified form of the factored secular equation, should yield a more realistic and probably therefore a more widely useful distribution function than the Debye equation.

Small‐Angle X‐Ray Scattering from Argon
View Description Hide DescriptionA correlation function as introduced by Debye in the case of light scattering is used to characterize the inhomogeneities in liquid argon for those cases showing excessive small‐angle x‐ray scattering. This method of characterizing the inhomogeneities is compared with the method of characterizing the inhomogeneities as droplets. Curves showing the correlation functions for the various cases are also presented.

Rotational Temperatures of OH in Methane‐Air Flames
View Description Hide DescriptionRotational line intensity distributions in emission and absorption of the 0↔0 band of the ^{2}Σ↔^{2}Π transition of OH have been measured in methane‐air flames. The number of electronically excited OH radicals in the inner cone greatly exceeds the equilibrium concentration, and the intensity distribution of the high quantum numbers gives a temperature of 5200°K. However, OH radicals in the ground state were in thermal equilibrium at 2000°K. A break in the intensity distribution indicates a two stage combustion reaction. It is suggested that the excessive amount of excited OH is due to its formation in the intermediate reaction steps. Line reversal temperatures using Na,Hg, and OH have been measured in the same flame for purposes of comparison. Also the rotational temperature of excited OH in a methane‐oxygen flame was measured.

On the Electron Affinity of Fluorine
View Description Hide DescriptionThe hamiltonian for systems isoelectronic with neon is treated by perturbation methods. The energy of ionization of such systems is represented by a four‐term expression (i.e., to third order of perturbation); the two leading terms are calculated, spectroscopic data for isoelectronic systems are used to evaluate the constants in the two remaining terms. The electron affinity of fluorine is estimated to be 73±3 kcal/g atom. The corresponding dissociation energy of fluorine, as inferred by the Born‐Haber cycle, is estimated to be 18 kcal/mole, to an accuracy believed better than ±12 kcal/mole.

The Ultraviolet Absorption Spectra of Gaseous Diazomethane and Diazoethane. Evidence for the Existence of Ethylidine Radicals in Diazoethane Photolysis
View Description Hide DescriptionThe absorption of gaseous diazoethane begins at about 5400A, increases to a broad maximum of ε=3.5 at 4500A and falls to a minimum of ε=0.15 at 3200A. At wavelengths shorter than 3000A a second region of rapidly increasing absorption is found. The absorption curve of diazomethane is similar in general shape to this curve but shifted somewhat toward shorter wavelengths. The absorption of diazoethane is continuous over its entire region while in the visible region diazomethane shows a number of broad and very diffuse bands from about 4300A to 3200A which probably overlie a continuum. The presence of 2‐butene in the photolysis products of diazoethane is explained by the combination of ethylidine radicals formed by the primary photochemical process

A Note on the Quantum‐Mechanical Perturbation Theory
View Description Hide DescriptionThe solution of the quantum‐mechanical eigenvalue problem is discussed for cases when a series of approximate eigenfunctions is known. If these ``unperturbed'' states are divided into two classes, a perturbation formula is derived giving the influence of one class of states on the other in the final solution. The formula contains as special cases: (i) the Schrödinger‐Brillouin formula for the eigenvalue of a nondegenerate state, (ii) a new simple formula for treating a class of degenerate states, and (iii) the splitting of the secular equation in cases where the system naturally consists of two independent parts in mutual interaction.

Excluded Volume Effect in Polymer Chains. I
View Description Hide DescriptionThe number of allowed configurations of a polymer chain is considered on the basis of a random walk on an arbitrary ``regular'' lattice. Upper and lower bounds for the number of nonoverlapping configurations in various lattices have been derived by means of a recursion formula method. The probability density function and its moments for the ``head‐to‐tail'' distance for short‐range nonoverlapping chains are shown to the calculable by the use of a generating function. The order of the logarithm of the number of nonsuperposable ring polymer chains has been shown to be directly proportional to the number of segments composing the ring.

Sum Rules for the Vibration Frequencies of Isotopic Molecules
View Description Hide DescriptionThe squares of the frequencies of isotopically related molecules obey certain simple sum rules. Whenever there exists a chemical exchange reaction involving only isotopic variations of a single type of molecule, such that the reaction is balanced at each atomic position of the molecule, then a relation of identical form exists between the sums of the squares of the frequencies. ThusIf, as in the latter example, the molecules all have the same symmetry, the sum rule may be applied separately to each factor of the secular equation. When forms of lower symmetry appear (as in the example involving the water molecule), symmetry factoring may or may not be possible. In such cases it is necessary to employ certain group‐theoretical considerations; the possible factoring is not in general identical with that appropriate for the product rule.
Examples of the application of the sum rule are given, involving the acetylene, water, methane, and hydrocyanic acid molecules. The existence of higher order isotope rules, intermediate between the sum and product rules, is pointed out.

A Reduced Equation of State for Gases and Liquids
View Description Hide DescriptionAn empirical, reduced equation of state is presented which holds with reasonable accuracy for both liquids and gases. Liquid densities of non‐associated substances are predicted to within 4 percent, vapor pressures to within 25 percent, heats of vaporization to within 10 percent and gas isotherms reproduced to within 10 percent. The values predicted for the coefficients of thermal expansion and compressibility are not better than 30 percent. With the exception of the latter which are incapable of good representation by any such reduced equation, the equation represents a marked improvement over the van der Waals and Berthelot equations.

The Use of Single‐Crystal Neutron Diffraction Data for Crystal Structure Determination
View Description Hide DescriptionIntensities of neutron reflections from single crystal specimens of several substances have yielded structure factors in close agreement with calculation and with those measured by the usual powder method. Specimens whose dimensions were in the millimeter range were used. Three materials yielded low results, probably because of extinction in the single crystal specimens. The use of single crystalneutron reflections for crystal structure determination appears practical in many cases.

Experimental Determination of Even‐Odd Character of Excited Electronic States of Molecules with a Center of Symmetry
View Description Hide DescriptionEven‐even transition intensities increase with monosubstitution but decrease with opposed disubstitution. Even‐odd transition intensities which increase with monosubstitution must increase further with opposed disubstitution.
Determination of parity in this way may settle disputed assignments. Thus the ^{1} A _{1g }—^{1} E _{2g } π‐transition of benzene is probably at 1700 A. The first singlet absorption of naphthalene is ^{1} A _{1g }—^{1} B _{1u } or ^{1} A _{1g }—^{1} B _{2u } and cannot be ^{1} A _{1g }—^{1} A _{1g } even though the cancellation of transition matrix elements (from configuration interaction, in the one‐electron approximation) gives it an intensity and vibrational structure similar to those in a forbidden transition. The visible bands of porphine are even‐odd (a _{2u }→e_{g} ^{1} A_{g} —^{1} Q_{u} ^{0}).
Intensities in the 2100 A transition of phenyl derivatives are being remeasured to settle its assignment in benzene, since existing data give conflicting results.

Viscosity of Neopentane
View Description Hide DescriptionThe viscosity of neopentane has been measured between −15°C and 30°C. These results are consistent with published work covering the temperature range 30°C to 150°C. The viscosity data for neopentane have been compared with similar data for the other pentanes. This comparison has provided an example of the importance of molecular shape for viscosity behavior. The possible significance of molecular shape for the interpretation of viscosity curves of binary mixtures is noted. Finally, it has been suggested that further work on liquids composed of spherical molecules might be worthwhile.