Volume 23, Issue 12, 01 December 1955

Calculation of Depolarization Factors of the Raman Lines of CCl_{3}X Molecules
View Description Hide DescriptionThe depolarization factors of the totally symmetric vibrations of CCl_{3}H, CCl_{3}D, and CCl_{3}Br are computed using previously derived expressions for the spur and anisotropy of the polarizabilitytensor. The associated normal coordinate treatment uses the Wilson FG‐matrix technique with a general quadratic potential function. Calculated and observed depolarization factors agree well for stretching but not for the bending modes.

Dielectric Dispersion of Rochelle Salt in the Microwave Region
View Description Hide DescriptionThe dielectric dispersion of rochelle salt was measured at 3000∼20 000 Mc/sec using a new method. In this method ε′ and ε″ is obtained by measuring the half‐power point and the shift of resonant frequency of a rectangular TE _{01} mode cavity.
These results show that the relaxation frequency of rochelle salt exists in the decimeter wave region.

Direct Production of Spectroscopic Specimens from Single Crystals by Controlled Growth from a Vapor
View Description Hide DescriptionStudies of anisotropic infrared absorption demand quite thin sections of single crystals, having relatively large cross section parallel with one of the few spectroscopically significant planes. This article describes the principles of design, the construction, and the successful operation with benzene of an apparatus for producing such specimens of single crystals. The method involves gradual introduction of vapor into an enclosed space, supporting a gradient of temperature and having the shape desired for the specimen, until self‐nucleation occurs in a small vicinity of the colder pole of temperature. Processes of attrition among the nuclei ensue automatically and instantaneously, resulting in the survival of only those that become attached to the confining wall with a most favored orientation, an orientation that can be selected to some degree by factors of design and operation. Thereafter, vapor issuing into the enclosure accretes upon the few surviving nuclei until these seeds coalesce and develop to fill the entire volume available. The method promises to be especially useful for producing and investigating crystals that exist only at low temperatures.

Motions of Molecules in Condensed Systems. IX. Infrared Absorption Anisotropy and Induced Molecular Motion in a Single Crystal of Benzene
View Description Hide DescriptionInfrared absorption spectra were observed with radiation polarized linearly along each of the two extinction axes contained in a thin cross section from a single crystal of benzene grown especially for this purpose. The spectra indicate consistently that the cross section was the 010 plane, that they record separately the absorptions polarized along the a‐axis and the c‐axis, respectively. The anisotropies of the induced absorptions exhibited by five fundamental molecular vibrations (ones that appear only in spectra for condensed phases) are all quite similar and may even be identical. It thus appears that the induced motions, super‐imposed upon the several intrinsic ones by the perturbing intermolecular interactions, have a property of similarity independent of the differing natures of the intrinsic motions that are being perturbed.

Ionization of Strong Electrolytes. IV. Nuclear Magnetic Resonance and Dissociation of Trifluoroacetic Acid
View Description Hide DescriptionProton and fluorine magnetic resonance of trifluoroacetic acid in water reflects the influence of electrolyticdissociation below a mole fraction 0.5 and of hydration above 0.5. The dissociation constant is estimated to be 1.8.

Theory of Internal Over‐All Rotational Interactions. II. Hamiltonian for the Nonrigid Internal Rotor
View Description Hide DescriptionAn approximate Hamiltonian for a nonrigid internal rotor has been derived. The potential energy has been expanded in a Taylor's series in the displacement coordinates and in a Fourier series in the angle of internal rotation Θ. The Hamiltonian was transformed by a contact transformation, and a second‐order Hamiltonian in which vibrations and rotations have been separated has been obtained. The Hamiltonian consists of terms which constitute the usual rigid internal rotational problem, of centrifugal distortion terms involving both over‐all and internal angular momentum, and of terms that arise because of the repulsive nature of the barrier. These repulsive terms enter as a single term, 2JF_{v} (m1 — cos3Θm), in the expression for the rotational transitions of symmetric rotors, where J is the total angular momentum quantum number and m is the pseudo‐quantum number for internal rotation. The repulsive constant, F_{v} , is given by the relationwhere B_{xx} ^{(i)}+B_{yy} ^{(i)} is the derivative of the rigid rotor rotational constant with respect to the ith symmetry coordinate, and a_{i} ^{(1)} is one‐half the displacement of the equilibrium position of the ith internal coordinate in going from Θ=0 to Θ=π/3.
The dependence of the barrier height upon the vibrational motion has also been studied.

Theory of Internal Over‐All Rotational Interactions. III. Nonrigid Asymmetric Rotors
View Description Hide DescriptionThe theory of the interactions of hindered internal rotation with over‐all rotations is extended to include nonrigid asymmetric rotors. The interdependence of hindered internal rotation and vibrations and their effect upon the vibrational energy levels is considered. The theory is developed analogously to the theory developed for symmetric rotors in a previous paper. An approximate over‐all internal rotational wave function of the form 1/(2π)^{½} exp[i(P _{ z } I _{ z2}/I _{ z }—τ)]φ_{ r } is discussed, where φ_{ r } is the wave function that diagonalizes the rigid rotor Hamiltonian and τ is an integer.
While the general energy relation involves too many parameters to compute or to fit empirically, certain special cases are discussed. In particular for the 0_{00}→1_{01} transition of the CH_{3}NO_{2} type of molecule one has , where (1_{01}〈H〉_{ R }1_{01}) is the rigid rotor energy for the 1_{01} level, Θ is the angle of internal rotation, II is the internal angular momentum,m indicates a given internal rotational level, and the F's and G's are constants which can be evaluated from a knowledge of the vibrational characteristics of the molecule and of the forces that constitute the hindering barrier to internal rotation.

On the Determination of Absolute Intensities from Single‐ and Multiple‐Path Absorption Measurements
View Description Hide DescriptionThe physical principles involved in conventional absolute intensity measurements are reviewed. Experimental difficulties rule out the use of extrapolation techniques for some spectral transitions. For this reason it is of interest to re‐examine the possibility of using total absorptionmeasurements, in conjunction with the curves of growth, for making intensity estimates. Extrapolation methods yield results which are independent of spectralline shape. Use of the curves of growth, on the other hand, implies the assumption that the line contour can be described by combined Doppler and Lorentz broadening.
The curves of growth permit a unique correlation between total absorption and f‐value either for spectral lines with pure Doppler broadening or for pure collision broadening. Furthermore, a simple experimental procedure can be devised for estimating both the absolute intensity and the spectral line profile on the basis of single‐path and multiple‐path absorptionmeasurements. The suggested procedure involves absorptionmeasurements for optical densities (path lengths) under conditions in which the integrated fractional absorption is a relatively sensitive function of spectralline shape. Representative calculations referring to utilization of the proposed method have been carried out for spectral lines belonging to the ^{2}Σ→^{2}II transitions, (0,0)‐band, of OH, and also for lines belonging to the fundamental vibration‐rotation spectrum of CO.

Diffusion Coefficients of Fatty Acids and Monobasic Phosphoric Acids in n‐Decane
View Description Hide DescriptionDiffusion coefficients of the series of even‐numbered fatty acids from C_{6} to C_{18}, of three dialkyl phosphoric acids, and of 2‐ethylhexoic and benzoic acids have been measured in dilute solutions in n‐decane at 30°C. Gravity mixed diaphragm cells have been employed in making the measurements. The Stokes‐Einstein hydrodynamic relationship adjusted by an empirical coefficient represents the magnitude and variation of diffusion coefficients in the series of fatty acids if corrections are made for solute association and nonsphericity. The unmodified Stokes‐Einstein equation predicts diffusion coefficients lower than those measured by approximately a factor of two.

Thermal Diffusion in Polymer Solutions
View Description Hide DescriptionThermal diffusion measurements have been made on a series of solutions of polystyrene as follows: (1) Five molecular weights (10 000 to 336 000) in toluene; (2) 136 000 molecular weight in o‐xylene, styrene, ethyl benzene, dioxane, and pyridine; (3) Styrene dimer in toluene and styrene; measurements were also made on some binary monomeric mixtures.
The thermodynamic propertyX∂_{μ}/∂X describes adequately the concentration dependence of the thermal diffusion ratio α. It appears that that portion of the motion of the polystyrene molecule in dilute and somewhat concentrated solutions which is segmental involves 10—13 chain atoms in the moving segment. The results seem consistent with Kauzmann and Eyring's picture for motion of long chain molecules.

Heat Capacity of Erbium from 15 to 320°K
View Description Hide DescriptionThe heat capacity of erbium has been measured over the range 15 to 320°K and the thermodynamic functions have been calculated. Three maxima have been observed which occur at 19.9°K, 53.5°K, and 84°K. The two at the lower temperatures show a dependence on the thermal history of the sample, and this dependence was investigated. A correlation of the various contributions to the entropy at room temperature has been made and extended to the other rare earth metals.

Statistical Mechanics of Isotopic Systems with Small Quantum Corrections. I. General Considerations and the Rule of the Geometric Mean
View Description Hide DescriptionIt is shown that the differences in the thermodynamic properties of isotopic molecules subject to small quantum effects (u ^{2}/24 law) depend on the difference in the reciprocal masses of the atoms in the molecule and are, therefore, independent of all masses except of those atoms isotopically substituted. This theorem provides a rigorous proof of the rule of the geometric mean for gaseous molecules. It is shown that the partition function ratio for a pair of double‐labeled molecules, e.g., N^{15}D_{3}/N^{15}H_{3} is equal to the ratio for the single‐labeled pair N^{14}D_{3}/N^{14}H_{3}. The application of the u ^{2}/24 law to isotopic isomer equilibria is pointed out.

Scattering of High Velocity Neutral Particles. VI. Krypton‐Krypton
View Description Hide DescriptionTotal collision cross sections have been measured for krypton atoms with energies between 700 and 2100 ev, scattered in room temperature krypton, to obtain potential energy information for the interaction of two krypton atoms. The potential function may be represented byfor r between 2.42 A and 3.14 A.
The present potential appears to be consistent with potentials, valid at larger separation distances, which have been derived from measurements of gaseous compressibility, transport, and crystal properties, within the limits of uncertainty of these larger distances potentials.

Theory of Protein Solutions. II
View Description Hide DescriptionThe formal theory of the first paper of this series is extended here to include the binding of several different species of ions or molecules on a protein,aggregation in a protein solution, and solutions containing more than one type of protein molecule.

Extended Interpretation of the Boltzmann‐Maxwell Equation (A Theory of Nonstationary Random Processes)
View Description Hide DescriptionUsual theories of statistical mechanics of nonuniform state stand on the assumption of approximately stationary random processes. Generally speaking, this assumption is not reasonable when the state concerned deviates considerably from thermal equilibrium. For a system in such a state, it is difficult not only to define but also to observe a complete set of gross variables. In this case the deviations of the actual future values of the gross variables from their expected future values cannot be neglected.
A new method of coarse‐graining is proposed as available to such a state. As a concrete example of system we take a gas. We get a coarse‐grained function 〈f〉_{ D } by averaging the fine‐grained probability function of one molecule over a series of observations made on the system on different occasions where at each observation the system is initially in a common macroscopic state as determined by our incomplete set of initial conditions. It is shown that 〈f〉_{ D } satisfies the Boltzmann‐Maxwell equation. The equation is valid even when the state concerned deviates considerably from thermal equilibrium and the random processes are not stationary. In this situation, however, the interpretation of the equation is different from the usual one; i.e., the equation predicts not the result of an individual observation of the gas concerned but the result obtained by averaging over a series of observations made repeatedly on different occasions on the same gas under a common incomplete set of macroscopic initial conditions where, with the lapse of time from the start, the result of each observation deviates from the others even in the macroscopic sense. For the time being, the theory is given only in the sense of classical mechanics.

Bonding in the Zinc Family Metals
View Description Hide DescriptionAttention is directed to the very large departures of the structures of the zinc family (IIb) metals from those produced by the close packing of spheres. This seems to indicate that cohesion in these metals differs considerably from the normal nondirectional metallic bonding. It is proposed that there is a system of covalent bonds in the basal plane resulting from bonding orbitals which are hybrids of one of the d and two of the p atomic orbitals. These absorb some of the s electrons and leave only 1.33 electrons/atom in the s band. Support for the proposed bonding scheme is provided by showing that with it one can account for many otherwise puzzling properties of the IIb metals and their alloys. The properties which are discussed in terms of the proposed scheme are (1) the abnormally large axial ratios in zinc and cadmium, (2) the effect of temperature on the axial ratios of these metals and the alloys of magnesium and cadmium, (3) the effect of alloying on the axial ratio, (4) the dependence of the axial ratio on the degree of order in MgCd_{3}, (5) the great abundance of Schottky defects in certain magnesium‐cadmium alloys, (6) the asymmetry of the heats of alloying of magnesium and cadmium, (7) the structure of solid mercury, (8) electrical conductivities of the solids, (9) the positive Hall coefficient for zinc and cadmium, (10) the poor solvent power of these metals as solids, and (11) certain unusual features of the electrical conductivities of the liquid metals and the dilute amalgams.

Photolysis of Acetic Anhydride
View Description Hide DescriptionThe photolysis of acetic anhydride has been studied using a hot mercury arc at temperatures from 60° to 160°C by analysis of the gaseous products. CO and C_{2}H_{6} are produced at equal rates which are one‐half the rate of production of CO_{2}. At 60°C, CO production is delayed initially but in time reaches the same rate as C_{2}H_{6}. Using acetone as actinometer, the quantum yield of CO_{2} is two, of CO and C_{2}H_{6}, unity. The decomposition of acetic anhydride can be photosensitized by acetone. Mass‐spectral analysis of the liquid residue at 160°C showed the absence of acetone, biacetyl, methyl acetate, acetylacetone, and acetonyl acetone. A fragment of mass 57, increasing in intensity with duration of reaction was present in amounts sufficient to account for a material balance. Some steps in the mechanism are discussed.

Study of Electrokinetic Effects Using Sinusoidal Pressure and Voltage
View Description Hide DescriptionThe electrokinetic effects streaming potential, streaming current, and electro‐osmotic pressure were studied by applying and measuring sinusoidal variations of hydrodynamic pressure and electrical voltage. Phenomenological relations between the effects were investigated, and an improved experimental method for measuring the electrokinetic coefficients, hence the zeta potential, was used. Saxen's law was verified within 6% at frequencies of 20, 100, and 200 cycles per second. The systems studied were restricted to glass‐water and glass‐salt solutions. The advantages and disadvantages of using sinusoidally varying quantities for electrokineticmeasurements are discussed.

Variational Theory of the Radial Distribution Function
View Description Hide DescriptionA variational approach to the calculation of the radial distribution function is presented. The approximations consist in the neglect of fourth‐order correlation in the entropy and the use of a constant third‐order correlation chosen to satisfy the third‐order normalization condition. The average interaction energy, containing only pair terms, does not involve correlations higher than second order. Finally, one obtains approximate expression for the excess Helmholtz free energy as a function of the radial distribution function (r.d.f.) and macroscopic parameters. This free energy, when minimized with respect to the r.d.f. at constant temperature and density, yields an integral equation for the r.d.f. This theory has a simpler structure and yields thermodynamic functions in a more direct way than earlier theories. The theory has not yet been adequately tested; however, the author speculates that it will give good results for short‐range forces but poor results for long‐range forces.

Note on Theories of Time‐Varying Space‐Charge Polarization
View Description Hide DescriptionThe nonlinearity of the differential equations governing space‐charge buildup or decay cause the principle of superposition to be inapplicable. Thus, charging and discharging curves should differ and depend strongly on applied voltage when space‐charge formation is appreciable. Two approximate theories of space‐charge formation and decay are compared, and it is found that one of their main differences is that one has been partly linearized while the other has not. Finally, it is mentioned that of the several theories of the ac response of materials with space charge, only one has not been linearized; hence, it is the only one applicable for applied voltages above about kT/e.