Volume 11, Issue 10, 01 October 1943

Atomic and Electronic Distributions in Liquid Nitrogen, Nitric Oxide, and Nitrous Oxide
View Description Hide DescriptionThe monochromatic x‐ray diffraction patterns for liquid nitrogen, nitric oxide and nitrous oxide have been obtained and analyzed by the Fourier integral method to obtain the atomic or electronic distributions. The diffraction patterns show one main peak and only faint peaks or plateaus at larger angles. The distribution curves show diatomic aggregates in liquid nitrogen and nitric oxide comparable to those found in the gaseous states. A linear molecule for nitrous oxide is consistent with the present data while a triangular molecule is not.

The Magnetic Susceptibility of Oxygen and Nitric Oxide at Low Field Strengths
View Description Hide DescriptionThe Rankine magnetic balance has been used to determine the magnetic susceptibility of oxygen and nitric oxide at atmospheric pressure in a field of about 15 oersteds. The mass susceptibility of water at 20°C is assumed to be −0.7200×10^{−6}. The mean of ten separate measurements on oxygen gives (106.3±0.2)×10^{−6} for the mass susceptibility, with an average deviation from the mean of 0.9×10^{−6}. The value of _{χMT} is 0.997±0.002; the average deviation from the mean being 0.008. The mean of six separate measurements on nitric oxide gives 47.2×10^{−6} for the mass susceptibility, and 0.0590×10^{−6} for the volume susceptibility, with an average deviation from the mean of 0.6×10^{−6} and 0.0007×10^{−6}, respectively.

Depolarization Studies of Raman Lines. A Simplified Method
View Description Hide DescriptionA simplified method for the determination of the depolarization factor of Raman lines is reported which requires only one exposure and is, therefore, independent of fluctuation of arc current and any other factors influencing the intensity of Raman lines. Two Polaroid films are placed at the front of the slit of the spectrograph, one above the other. The electric vectors of the radiation are at right angles to one another. Between the Polaroid films and the slit are introduced two half‐wave mica plates (one above the other) which orient the electric vectors of the light so that they are both vibrating in the same direction upon striking the prism faces. Thus differential reflection at these faces is eliminated. The method was checked with carbon tetrachloride.

Raman Spectra of Acetylenes. VII. Symmetrical‐Top Acetylenes
View Description Hide DescriptionRaman frequencies, relative intensities, and depolarization factors are listed for 1‐iodo‐1‐propyne, 1‐bromo‐1‐propyne, 1‐chloro‐1‐propyne, and 3,3‐dimethyl‐1‐butyne. The relative intensities and depolarization factors were obtained by use of a Gaertner microdensitometer. Assignments of the frequencies to the different vibration types and calculated values of the heat capacities for the ideal gaseous state at 1 atmos. pressure are given for 1‐iodo‐1‐propyne and 1‐bromo‐1‐propyne. Examination of the results in the 2200‐cm^{−1} region leads to the suggestion that the resonance splitting of the triple bond fundamental for disubstituted acetylenes may frequently be due to the combination frequencies (2900–700) and (1375+700); and that the doubling of the 2100‐cm^{−1} fundamental for the monosubstituted acetylenes, 3‐methyl‐1‐butyn‐3‐ol and 3,3‐dimethyl‐1‐butyne, may be due to the second overtones of the highly polarized, ``breathing'' frequencies near 700 cm^{−1} of the groups , respectively.

Theory of the Elastic Properties of Rubber
View Description Hide DescriptionPrevious discussions of the kinetic theory of rubberelasticity have dealt with individual long chain molecules, but the theory of the structure of bulk rubber has been almost entirely undeveloped. The present paper goes beyond earlier ones both in the more detailed treatment of the individual chains and in the development of a clear‐cut model of the bulk material. From the consideration of familiar properties of rubber, it is concluded that in the lightly vulcanized state it consists of a coherent network of flexible molecular chains (this involving a considerable fraction of the total material) together with other molecules not actively involved in the network, but acting like a fluid mass through which the network extends and in which it moves with Brownian motion. The idea of an effective internal pressure is advanced and discussed. A simplified model for bulk rubber is proposed, consisting of a network of idealized flexible chains extending through the material and a fluid filling it, the bounding surfaces being in equilibrium under all the forces acting on them—internal pressure, pull of the molecular network, and any external forces. For the quantitative treatment of this model the principal problem is that of computing the forces exerted by the molecular network, because of its thermal agitation, on the bounding surfaces. Two models of the flexible molecular chains have been used—one with a linear stress‐extension relation (Gaussian chain), the second with independent links of fixed length, having, like real molecular chains, a definite maximum extension. Methods for the statistical treatment of chains of independent links at all extensions are developed and applied to the computation of stress‐strain relations for the second of the above models. It is shown that an irregular network of Gaussian chains is equivalent to a simple set of independent chains; the corresponding reduction in the case of non‐Gaussian chains is only approximate. Making this reduction in all cases, the model is applied to the quantitative computation of stress‐strain curves for unilateral stretch of rubber and for stretch in two directions. A prediction is made of the change in elastic properties of rubber in the swollen state. The thermoelastic properties of rubber are worked out, and the change in slope of the nearly linear stress‐temperature curves from negative to positive values with increasing strain is explained. The location of the thermoelastic inversion point, at which this slope is zero, is shown to depend only upon the cubic expansion coefficient of unstretched rubber. The linear thermal expansion coefficient of stretched rubber in the direction of the stress is shown to be positive (and of the order of the same coefficient for unstretched rubber) below the thermoelastic inversion point. Above the thermoelastic inversion point this coefficient becomes negative and is—for appreciable extensions—of the order of the cubic expansion coefficient for a gas, independent of the composition of rubber. The linear coefficient of thermal expansion perpendicular to the direction of stress is always positive. Stress‐strain curves for bulk rubber at constant temperature have been compared with the theory for extensions up to 400 percent. The agreement is particularly good as concerns that part of the total stress due to changing entropy. In some rubber compounds minor deviations, variable from sample to sample, are found for small extensions. These are attributed to van der Waals forces not taken into account by the theory. The characteristic knee in rubber stress‐strain curves is shown to be due to change in internal pressure in the material. This varies inversely with the extended length, and in unstretched rubber is of the order of 5 kg/cm^{2}. The upward curvature of the stress‐strain curve for larger extensions, which appears even before the onset of crystallization, is explained as due to the approach of the molecular network to its maximum extension, which is of the order of 10 times its extension in the unstretched bulk rubber.Crystallization may in general enhance the S‐shape of the stress‐strain curve for natural cured rubber, Neoprene and butyl rubber. Synthetic rubber of the Buna type, while having an S‐shaped stress‐strain curve, does not exhibit any crystallization at all. It is estimated that, in the materials considered, roughly a fourth of the rubber chains are actively involved in the network. Internal pressure, maximum extensions, and the fraction of active material all change with the state of vulcanization. The general theory developed in this paper provides a basis for the treatment of many other physical properties of stretched rubber.

Frequency Spectrum of Crystalline Solids. II. General Theory and Applications to Simple Cubic Lattices
View Description Hide DescriptionAt temperatures not too close to its melting point, the molecules in a crystalline solid vibrate with simple harmonic motion about fixed equilibrium positions in a space lattice. In order to calculate the thermodynamic properties of the solid, one must know the distribution of frequencies of the normal modes of vibration of the component oscillators. On the basis of the Born‐Kármán model, the frequencies of the normal modes are the characteristic roots of a matrix. The moments of the frequency distribution can be found from the traces of powers of the matrix. Methods are developed for calculating the frequency spectrum and thermodynamic functions from these moments. The frequency spectrum of a simple cubic lattice is studied by deriving its polynomial approximation from its moments. The spectrum has two maxima, one near the middle of its frequency range and the other at the high frequency end. As the ratio of the interactions between next nearest neighbors to those of nearest neighbors increases, the height of the low frequency maximum increases and that of the high frequency maximum decreases. Specific heats are calculated from the moments of the frequency distribution.
 LETTERS TO THE EDITOR


Statistical Mechanics of Binary Mixtures
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Specific Heat Ratios in CO_{2}
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