Volume 19, Issue 9, 01 September 1951

Diffusion through an Interface
View Description Hide DescriptionThe diffusion equation has been solved for the case of two cells of finite length with an interface between the cells. The effect of an interfacial resistance to mass transfer has been considered. It is shown that the situation where there is equilibrium (no resistance) at the interface is a special case of our solution. Several important cases are considered numerically.

Studies on the Photovoltaic Effect. II
View Description Hide DescriptionBenzaldehyde dissolved in alcohol in concentrations less than 0.1 M yields a positive photopotential and in greater concentrations the photopotential is negative. The production of the negative photopotential is attributed to the presence of peroxybenzoic acid. In general, oxygen in the peroxide linkage seems to cause negative photopotentials and oxygen in a carbonyl group yields positive photopotentials. Strong inorganic oxidizing agents produce negative photopotentials. Inorganic reducing agents and salts which are not oxidizing agents yield little or no photopotentials. A polar solvent is necessary for the production of a photopotential. A photopotential‐spectrum curve which in general follows the light absorption curve is derived for anthraquinone. High photopotentials can be obtained at wavelengths where light absorption is low if a high intensity light source is used.

Force Constants and Calculated Thermodynamic Properties for SiF_{4}
View Description Hide DescriptionUsing observed fundamental frequencies and the Wilson FGmatrix method, sets of force constants for SiF_{4} have been determined using the most general second degree potential energy function. While no unique set of force constants can be given, limits are set for the force constants. Also the calculations indicate that if the Si–F bond interaction constant is ignored, too high a value for the Si–F bond stretching force constant results. Finally, the heat content, free energy,entropy, and heat capacity for the ideal gaseous state at 1 atmos pressure were calculated for 11 temperatures ranging from 100–1000°K, using a rigid rotator, harmonic oscillator approximation.

The Asymmetric Rotor. IX. The Heavy Water Bands at 2787 cm^{−1} and 5373 cm^{−1}
View Description Hide DescriptionThe combination band (110) of the two stretching fundamentals of D_{2}O is reported and analyzed to yield ν_{0}=5373.2 cm^{−1} and the excited state moments of inertia 1.910, 3.931, and 5.929×10^{−40} g cm^{2}. The same method of analysis applied to the unsymmetrical fundamental band (100) envelope gives ν_{0}=2787.5 cm^{−1} and the excited state moments 1.881, 3.876, and 5.843×10^{−40} g cm^{2}.

Microwave Spectroscopic Investigation of the Kinetics of the Heterogeneous Ammonia‐Deuterium Exchange
View Description Hide DescriptionA method is described for analyzing a mixture of gases using microwave spectroscopy. Relatively simple microwave measurements are employed on single resolved collision broadened spectral lines. For binary mixtures, only the peak absorption coefficients need to be measured if the microwave collision diameters are known. Mixtures of isotopically substituted molecules can also be analyzed because the microwave absorption lines of the isotopic species are easily resolved.
The technique is applied to determining the mole fraction of NH_{3} in mixtures of deuterated ammonias, and to a study of the kinetics of the NH_{3}—D_{2} isotopic exchange reaction on a singly promoted iron catalyst. It is found that rates of desorption of molecules from surfaces are markedly increased on adsorption of other molecules, a fact that can be explained only in terms of strong interactions between adsorbed molecules. The rate of the exchange reaction is proportional to the square root of the deuterium pressure. With increasing ammonia pressure the rate passes through a maximum, showing that the mechanism involves reaction between adsorbed ammonia and adsorbed deuterium atoms. The activation energy diminishes significantly with increasing ammonia pressure, providing additional evidence for the existence of strong interactions between adsorbed molecules.

Nucleation in Very Rapid Vapor Expansions
View Description Hide DescriptionIn the Volmer theory, sub‐critical droplets (embryos), with vapor pressure greater than their surroundings, nevertheless, grow statistically, because they exist in sufficiently greater numbers than neighboring larger droplets. Thus the formation of nuclei against the thermodynamic barrier presupposes the presence of very large numbers of embryos of all sizes.
An approximate lower bound for the time (nucleation time) required for the formation of this system of embryos can be calculated readily by (1) neglecting the thermodynamic barrier which impedes their formation; (2) assuming that when droplets contain a certain supercritical number, Γ, of molecules they grow very rapidly because their vapor pressure is considerably lower than their surroundings; (3) assuming that the formation of the embryo system begins when the vapor first becomes saturated. The equation for the rate of formation of embryos then reduces to the heat conduction equation yielding a simple solution. The lower bound sought is found to be inversely proportional to the fourth power of the degree of supercooling. Comparison with the experiments of Wegener and Smelt indicates that in some nozzle expansions the occurrence of nucleation is determined by this process.
On this theory the thermal accommodation coefficient which determines the heat transfer and especially the accommodation coefficient for growth, which determines the probability of a molecule sticking to the surface, play a much more prominent role than they do in the Volmer steady‐state theory. Comparison with experimental time lags for the condensation of H_{2}O in air at −30 to −60°C gives the order of magnitude of the accommodation coefficient for growth as 5×10^{−4}.

Double Refraction of Flow: Numerical Evaluation of Extinction Angle and Birefringence as a Function of Velocity Gradient
View Description Hide DescriptionThe method of double refraction of flow in systems containing large asymmetrical molecules gives experimental data which, when interpreted in light of the theory of Peterlin and Stuart, enable one to calculate molecular lengths; information about the polydispersity of the system and about the optical properties of the solute particles may also be obtained from such data. Heretofore, this theory had been developed so that the data could be interpreted only under the limiting condition of low velocity gradient where the degree of orientation of the solute particles is very small. With the aid of the Mark I computer of the Harvard Computation Laboratory, the necessary equations have been solved to provide numerical values over a much wider range of velocity gradients, greatly increasing the usefulness of flow birefringencemeasurements for the study of macromolecular systems.

Studies on Tellurium‐Selenium Alloys
View Description Hide DescriptionTellurium and metallic (hexagonal) selenium were shown to give solid solution in any concentration. The variation of the cell dimensions with composition departs only slightly from linearity: c shows a certain tendency to contraction (this corresponds to a smaller valency angle in the chains of atoms than is required by a linear variation): a varies much less (2 percent between Se and Te) and in a manner which depends upon the preparation of the alloy (as already observed for pure selenium by H. Krebs).
The presence of sharp (hk·l) lines with l≠0 in all the alloys suggests that these must be composed not of homogeneous chains (i.e., Se chains, Te chains packed together), but of composite chains, in which the homogeneous sequences must be fairly short.

Contact Distances of Ion Pairs in the Isomeric Dichloroethanes
View Description Hide DescriptionThe effective dielectric constant of ethylene chloride is calculated from known dissociation constants of various ion pairs in ethylene and ethylidene chloride according to the method of Denison and Ramsey. The average value of the effective dielectric constant is used for the calculation of contact distances of various ion pairs in ethylene chloride. The variation of contact distance with size and structure of the ions is discussed.

The Analysis of the Infrared Spectrum of Chlorine Monofluoride
View Description Hide DescriptionThe vibration‐rotation fine‐structure of the fundamental and first overtone of ClF has been resolved with grating spectrometers utilizing an 1800 lines‐per‐inch and a 3600 lines‐per‐inch grating. An analysis of the observed bands is given and the ω_{ e } and x_{e} ω_{ e } for Cl^{35}F^{19} and Cl^{37}F^{19} were found to be 786.34 cm^{−1}, 6.23 cm^{−1}, and 778.82 cm^{−1}, and 6.11 cm^{−1}, respectively.

The Oscillator Strength of H_{2} ^{+}, 1sσ—2pσ
View Description Hide DescriptionThe 1sσ—2pσ transition of H_{2} ^{+} is investigated using exact two center wave functions and using approximate wave functions based on a linear combination of atomic orbitals (with both the dipole length and the dipole velocity formulas). It is found that at the equilibrium internuclear distance, 2.00 a _{0}, the true oscillator strength of the transition is 0.319; with the dipole length formula, the LCAO approximation yields a value some 1.4 times greater, and with the dipole velocity formula it yields a value some 0.54 times smaller. Results are given for internuclear distances between 0 and 9 a _{0}.

The Outer Electron Configuration in Metallic Copper
View Description Hide DescriptionThe effect on the atomic scattering factor of metallic copper of the 3d ^{7.75}4s ^{1}4p ^{2.25} outer electron configuration, demanded by the Pauling valence of 5.50, is computed. Approximately a 6 percent lowering in intensity of the (111) reflection when compared with the atomic scattering factor computed on the basis of a Hartree‐Fock calculation for the 3d ^{10}4s ^{1} configuration is predicted if the Pauling model is the correct one. Differences for other reflections are also computed. Available intensity data for metallic copper are discussed in the light of these results.

Thermal Analysis of the System PbBr_{2}–PbO
View Description Hide DescriptionA thermal analysis of the system PbBr_{2}–PbO proved the existence of four compounds intermediate between PbBr_{2} and PbO, namely PbBr_{2}·PbO, PbBr_{2}·2PbO, PbBr_{2}·3PbO, and PbBr_{2}·7PbO. The compound PbBr_{2}·PbO was unstable above 497°C whereas the others were stable at their melting points. Pure PbBr_{2}·PbO·H_{2}O (or Pb(OH)Br) was prepared and was found to decompose into PbBr_{2}·PbO at temperatures above 150°C. This work offers an explanation for the discrepancies among data reported in the literature for the melting point of lead bromide.

Asymptotic Expansion of the Partition Function of the Asymmetric Top
View Description Hide DescriptionMethods developed by Wigner and Kirkwood for the determination of the partition functions of dynamical systems without explicit knowledge of the energyeigenvalues are used to calculate the first two terms of the asymptotic expansion of the partition function of the asymmetric top in powers of Planck's constant. The result is compared with Viney's expansion for the symmetric top and with Gordon's approximate expansion for the asymmetric top.

Hydrogen Molecule Energy Calculation by Correlated Molecular Orbitals
View Description Hide DescriptionThe electronic energy of the hydrogen molecule was calculated using the correlated molecular orbital wave functionwhere a _{1}, b _{1}, a _{2}, and b _{2} are 1s atomic wave functions of electrons 1 and 2 about nuclei a and b, and r _{12} is the interelectronic distance. The p of the above formula together with z, the effective nuclear charge, used in the explicit definition of the atomic orbitals, are two parameters which are varied in minimizing the energy according to the variation method. The energy minimum was found to be 4.11 ev below the value for complete separation of the nuclei. The minimum occurred at an internuclear distance of 0.71A, and the parameters have the values z=1.285 and p=0.28 in atomic units. The energy is far better than Coulson's best molecular orbital calculation and better than any other two‐parameter calculation except for that of Gurnee and Magee.

The Entropy of Aqueous Solutes
View Description Hide DescriptionThe standard partial molal entropies of monatomic ions and of non‐electrolytes in aqueous solution can be represented by the empirical expressions,Here Z is the absolute value of the charge on the ion, r_{e} is the effective radius of the ion, and V_{M} is the molal volume.
These expressions can be interpreted in terms of the smoothed‐potential type of partition function for the system.

Theory of Anisotropic Colloidal Solutions
View Description Hide DescriptionThe appearance of anisotropic phase in the unipolar coacervations of tobacco mosaic virus or bentonite solutions are explained theoretically, and the recent theory of Onsager is confirmed. As has been emphasized already by Langmuir, the repulsive forces between solute molecules and the force arising from thermal agitation are decisive for the occurrence of the anisotropic phase. The critical concentrations where the anisotropic phase starts are explicitly determined for prolate and oblate spheroidal and also cylindrical solute molecules. It is found that the critical concentrations are all inversely proportional to the axial ratios, and therefore, it is explained why these critical concentrations are of the same order of magnitude in spite of the totally different characters of solute molecules

The Infrared Spectra of N‐Acetylglycine and Diketopiperazine in Polarized Radiation at 25° and at −185°C
View Description Hide DescriptionThe infrared absorption spectra of single crystals of N‐acetylglycine and of diketopiperazine have been observed at room temperature, and at −185°C, using polarized radiation. The spectrum of the former substance shows some remarkable changes with temperature. In both cases cooling produces a pronounced narrowing of the broad bands due to the vibration of hydrogen atoms involved in strong hydrogen bonds. The two spectra furnish examples of NH absorption in the two extremes of weak and very strong hydrogen bonding. In diketopiperazine two possible interpretations of the doublet structure in the NH valence band are offered

The Critical Field Curve in an Antiferromagnetic Crystal
View Description Hide DescriptionVan Vleck's theoretical model for the antiferromagnetic state is extended to describe the effect of applying magnetic fields so large that the Zeeman splitting is of the same order of magnitude as the exchange interaction. The intensity of magnetization, entropy, and Gibbs free energy are calculated. It is concluded that, when the field is applied parallel to the direction of the antiferromagnetic chains, the antiferromagnetic configuration (that in which there are two sublattices in the crystal possessing unequal magnetizations) is energetically favored for all values of H and T at which it is mathematically permissible. The boundary of the antiferromagnetic solution is a certain critical field curve in the H, T plane, ending at the Curie temperatureT _{C} on the T axis, and at a critical fieldH _{C} on the H axis, related to T _{C} by μH _{C}/kT _{C}=1. The case of perpendicular field, and the influence of next‐to‐nearest neighbor interaction, are also discussed. Comparison is made between the predictions of the theory and the results of recent experiments by the writer on critical field phenomena in cobalt ammonium sulfate at temperatures below 1°K. This theoretical treatment of exchange antiferromagnetism is contrasted with the theory of Sauer and Temperley on dipole‐dipole interaction cooperative effects, which also predicts the existence of a critical curve. The possibility of observing critical fieldeffects in other materials at much higher or much lower temperatures is also discussed.

The Parallel Vibrations of Linear Triatomic Molecules
View Description Hide DescriptionThe possible solutions of the valence force potential constants occurring in the potential function for the stretching modes of some triatomic molecules are found; these are found as functions of a parameter p related to the coordinates describing the parallel modes of vibration.
The form of the normal modes and the potential energy distribution corresponding to a particular set of constants for each molecule is obtained.