Volume 18, Issue 9, 01 September 1950
Index of content:
18(1950); http://dx.doi.org/10.1063/1.1747899View Description Hide Description
18(1950); http://dx.doi.org/10.1063/1.1747900View Description Hide Description
The thermodynamictheory of non‐isothermal systems of liquid solutions is treated by the method of Tolman and Fine, which method includes consideration of the irreversible processes in calculating the conditions of the steady state.
The concept entropy of transfer of a dissolved molecule is discussed in terms of the interaction of the molecule with the solution. The method of Tolman and Fine is then applied in the derivations of the Soret ``equilibrium'' and the e.m.f. of a thermocell. It is shown that the irreversible transport of heat down the temperature gradient has no effect upon the steady‐state conditions, even for finite values of the gradient.
18(1950); http://dx.doi.org/10.1063/1.1747901View Description Hide Description
18(1950); http://dx.doi.org/10.1063/1.1747903View Description Hide Description
The pyrolysis of organic bromides in a stream of toluene is described as a method for the determination of the C–Br bonddissociation energies. The technique used makes it possible to discriminate between two mechanisms of decomposition: It was found that both benzyl and allyl bromide decomposed according to mechanism (a), the bromine atoms reacting readily with toluene to give hydrobromic acid. The rate of the primary dissociation process was measured by the rate of formation of HBr. It was proved that the thermal decompositions of benzyl and allyl bromide were homogeneous gas reactions obeying first order kinetics. The activation energies were calculated at 50.5±2 kcal./mole and 47.5±2 kcal./mole, and identified with D(C6H5.CH2–Br) and D(CH2:CH.CH2–Br), respectively.
The fate of the allyl radical is discussed, and a rough estimate of the activation energy for the reactionleads to a value of 14–17 kcal./mole.
The problem of ionic contribution in the C–Br bonds is discussed.
The estimation of the dissociation energies of the C–Br bonds of various organic bromides is of great interest since the values for these dissociation energies, combined with the heats of formation of the relevant bromides in the gaseous state, make it possible to determine the heats of formation of various organic radicals. Furthermore, the latter data in conjunction with the heats of formation of hydrocarbons enable us to calculate the various C–H and C–C bonddissociation energies and the resonance energies of the relevant radicals.
18(1950); http://dx.doi.org/10.1063/1.1747904View Description Hide Description
The process of synapsis of chromosomes in meiosis and the process of self‐duplication of genes in mitosis reveal the existence of a highly specific attraction between pairs of large molecules provided they are identical and rigid. We shall investigate the quantum‐mechanical behavior of a pair of molecules which interact with each other by means of vibrating electric dipole moments which are thermally excited. Because of resonance between equal frequency modes or commensurable modes of vibration, each one of the molecules shows a statistical preference for certain phase relations between these modes (using the language of the correspondence principle). A pair of molecules interacts strongly if it is an identical pair because of these phase preferences.
18(1950); http://dx.doi.org/10.1063/1.1747905View Description Hide Description
The chemical effects of x‐rays on aqueous solutions of chloral hydrate (CCl3CH(OH)2) have been studied. The primary reaction is the conversion of the organic halogen to HCl and the resulting changes in electrical conductance have been used for the determination of x‐ray dosage. The change in conductance is linear with x‐ray dose and independent of dose‐rate over a wide range. This compound has been used to determine the total output and depth‐dose curves from a high intensity beryllium window x‐ray tube.
18(1950); http://dx.doi.org/10.1063/1.1747906View Description Hide Description
The energies of the first two to five electronic transitions of 16 conjugated molecules are predicted as simple one‐electron LCAO molecular orbital transitions (with overlap included). Assignments of the observed levels to the predicted levels are made. Qualitative agreement is good when S=0.25 and β=23,000 cm−1 for ring systems.
It is shown that configuration interaction must be introduced to modify these energy predictions and to account for the intensities in some molecules (``round‐field'') such as benzene, triphenylene, coronene, and porphine. This interaction is less important in other molecules (``long‐field'') such as pyrene, biphenyl, and tetrahydroporphine.
Empirical groupings of intensities and luminescence lifetimes are shown for the different singlet‐singlet and singlet‐triplet band types of round‐field hydrocarbons and for related molecules containing conjugated hetero‐atoms. The alteration of these groupings in long‐field molecules, and under jj‐coupling, is described.
18(1950); http://dx.doi.org/10.1063/1.1747907View Description Hide Description
The first three electronic transitions of porphine and the first five electronic transitions of tetrahydroporphine are predicted as simple one‐electron LCAO molecular orbital transitions (with overlap included). The electron densities and bond orders in the ground states are also computed. The observed levels are tentatively assigned to the predicted levels with the help of comparisons with spectra of other aza‐amine derivatives of conjugated hydrocarbons. Probable degeneracies and polarizations are determined. The blue shift and loss of intensity of the first electronic transition, in going from tetrahydroporphine to the larger conjugated system of porphine, is typical of the change from a ``long‐field'' to a ``round‐field'' molecule (see previous paper) and is shown to occur in several other ``long‐field'' systems when additional conjugated atoms are added at the side of the system.
18(1950); http://dx.doi.org/10.1063/1.1747908View Description Hide Description
The repulsive potential between two normal helium atoms is calculated using the bond eigenfunction method. It is found that Slater's potential, V(R)=770 exp(−2.43R/a 0)×10−12 ergs, must be multiplied by a factor of 2.1 in the region of the minimum of the total potential. By extrapolating to R=0, the energy of beryllium in the ground state is found to be −29.4 Rhc units.
18(1950); http://dx.doi.org/10.1063/1.1747909View Description Hide Description
The procedure for calculating the optical rotatory power due to one electron transitions in an asymmetric field is simplified and systematized. The necessary transformations of functions to elliptic coordinates is carried through explicitly and the method of calculation is outlined. Extensive tables and graphs were prepared which greatly simplify the calculations. The method is applied to benzoin and the results are compared with the published experimental results which vary characteristically with the solvent. Representing transitions by eigenfunctions involving changes in more than one electron is the next natural but difficult improvement in this type of treatment.
18(1950); http://dx.doi.org/10.1063/1.1747910View Description Hide Description
The dielectric constant of a classical fluid, composed of spherically symmetric molecules with dipole‐dipole interactions, is calculated by a method that leads to formulas previously derived by Yvon but is more direct and yields additional results. The relations of the formulas of Lorentz, Yvon, Kirkwood, and Böttcher to one another are clarified. An accurate calculation of the deviation from the Clausius‐Mosotti formula requires knowledge of molecular distribution functions of various orders, but an approximate calculation is possible on the basis of the radial distribution function alone. It is shown that the success of Böttcher's approximation is partly the result of an approximate cancellation of errors, and that a practically equivalent formula can be obtained by another method that lends itself more readily to improvement. The distinctive feature of the present calculation is the introduction of quantities p i (h), the mean moment of molecule i when the positions of it and of h−1 other molecules are specified; Lorentz's formula corresponds to the approximation p 1 (2)=p 1 (1), and other formulas to various approximate evaluations of the difference p 1 (2)—p 1 (1).
18(1950); http://dx.doi.org/10.1063/1.1747911View Description Hide Description
Although the formulas of Part I do not apply strictly to actual gases and liquids, they suggest a possibly useful method of analyzing data on the variation of dielectric constant ε with density d under high pressure at constant temperature. The method is to express (ε+2)d/(ε−1) as a polynomial in d; the variable terms represent the deviation from the Clausius‐Mosotti formula. This method has been tested, and compared with alternative procedures based on more specialized formulas, by analysis of data on carbon disulfide (Chang, Danforth) and on carbon dioxide (Michels and Kleerekoper). It is concluded that the proposed method is an efficient one for representing the data, that the values of the coefficients are consistent with the approximate values estimated from the simplified theory, and that there is no advantage in the use of more specialized formulas. The precision of present ε vs. d data and of present knowledge of molecular distribution functions does not justify any more detailed conclusions.
18(1950); http://dx.doi.org/10.1063/1.1747912View Description Hide Description
The quantum‐mechanical calculation of the rotation‐vibration energies of the plane symmetrical X 2 Y 2 X 2 molecular model is carried out to second‐order approximation so as to include contributions arising from cubic and quartic anharmonic terms in the potential function, Coriolis interactions, centrifugal stretching, and changes in the rotational constants produced by vibration.
18(1950); http://dx.doi.org/10.1063/1.1747913View Description Hide Description
During the past several years it has been demonstrated that the light scattered from dilute solutions of macromolecules or colloidal particles is intimately related to the weight, size, and interaction of the solute species. Theoretical developments and improved techniques have made possible the determination of the molecular weight, dimension and activity coefficient of a number of polymers and proteins in solution. In these investigations the intensity of light scattered at various angles from a monochromatic beam passing through the solution has been measured by means of specially designed photometers. However, it would appear that the equivalent information could be derived from a different means of observation—that of transmission measurements at various wave‐lengths. If this possibility could be exploited the common techniques of spectrophotometry could replace the more specialized ones now used. The extent to which this is feasible is explored in this paper.
As a first step it is necessary to review some aspects of the scattering from small particles and the internal interference arising in the case of larger particles. This opportunity is taken to present a compilation of the scattering factors and the quantities derived from them, that is the dissymmetry and correction factor, in a more precise and convenient form than has appeared previously, because of the use to which they are put in the following sections. The calculations relating to the case of transmittance of solutions containing larger particles are then presented and in the final sections the application of both methods of observation to the determination of the molecular weight and size of samples of polystyrene and tobacco mosaic virus is reported.
Kinetics of OH Radicals from Flame Emission Spectra. I. Vibrational Transition Probabilities, Intensities, and Equilibrium in the 2Σ+—2Π Transition18(1950); http://dx.doi.org/10.1063/1.1747914View Description Hide Description
The relative vibrational transition probabilities for the first four vibrational levels of the 2Σ+—2Π system of OH have been calculated. Anharmonic wave functions derivable from the Morse potential function were used and the electronic dipole moment matrix component appearing in this formulation has been evaluated. Relative intensities for the various bands have been calculated under the assumption of thermal equilibrium. Comparison of these calculated values with the data of Dieke and Crosswhite on the oxy‐acetylene flame at one atmosphere indicate vibrational equilibrium with a vibrational temperature of ∼3750°K in the outer cone which compares with a rotational temperatue of ∼3000°K. The relationship between vibrational and rotational equilibrium for this case is discussed briefly.
18(1950); http://dx.doi.org/10.1063/1.1747915View Description Hide Description
A particular solution of the differential equation of diffusion involving a diffusion coefficient proportional to concentration is presented.
From previous experiments by Wagner and Zimens the diffusion coefficient for the exchange of lead and silver ions, extrapolated to the concentration of a saturated solution of lead chloride in solid silver chloride, is calculated to be 2.4·10−9 cm2/sec. at 270°C. Therefrom it follows that the self‐diffusion coefficient of lead ions equals 0.8·10−9 cm2/sec. In contrast, the self‐diffusion coefficient of silver ions, derived from conductivity measurements of Koch and Wagner, amounts to 9.2·10−8 cm2/sec.
18(1950); http://dx.doi.org/10.1063/1.1747916View Description Hide Description
The self‐diffusion coefficient of sodium in sodium chloride and sodium bromide has been measured as a function of temperature. A comparison of the self‐diffusion coefficient with the electrolytic conductivity reveals that the Einstein relation is satisfied at high but not at low temperatures. The temperature dependence of the diffusion coefficient may be explained by the Schottky‐Wagner vacancy theory if the presence of impurity ions is taken into account. A possible explanation for the failure of the Einstein relation in terms of association between multivalent foreign ions and vacancies is suggested.
18(1950); http://dx.doi.org/10.1063/1.1747917View Description Hide Description
The x‐ray scattering curves of five proteins in solution have been measured at small angles. The radii of gyration of the protein molecules are determined from the scattering curves. These data together with the known molecular weights, densities, and frictional ratios are used to estimate the axial ratios and hydrations of the molecules. Some possibilities and limitations of the method are pointed out.
18(1950); http://dx.doi.org/10.1063/1.1747918View Description Hide Description
The electroplating of metallic selenium from acid baths has been achieved and reduced to practice. The paper discusses in succession the polymorphism of selenium; selenium ions in selenious acidsolution; cathodic deposition as the amorphous and metallic phase; the nucleationcharacteristic and crystal growth of the metallic modification; the properties of various types of plating baths; a selenium‐carbon anode for the stabilization of the bath composition; and finally a number of influences affecting the crystallization habit of the deposit. The current density of 200 amp./ft.2 attainable in a well‐balanced plating bath compares favorably with standard baths for true metals.
18(1950); http://dx.doi.org/10.1063/1.1747919View Description Hide Description
The Lennard‐Jones and Devonshire theory of the liquid state has been modified by introduction of the quasi‐chemical method to allow for both holes in the liquid and an expandable lattice. The essential step is to minimize the free energy with respect to a lattice expansion parameter. On the whole, critical constants obtained in this way are in appreciably better agreement with experiment than those of the Lennard‐Jones and Devonshire theory. however, the equilibrium number of holes turns out to be much too small.