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Volume 19, Issue 12, 01 December 1951

Statistical Thermodynamics of Rubber Elasticity
View Description Hide DescriptionTwo principal differences between the theories of rubberelasticity advanced by James and Guth and by other authors are examined in the light of certain fundamental concepts. First the distribution functions for molecular chain lengths in vulcanized rubber networks are considered from the point of view of symmetry. Assuming a relaxed network to be isotropic and a network subject to uniform stress in one direction to be transversely isotropic, it is possible to formulate very general mathematical forms with respect to which the actual distribution functions must be compatible. It is shown that the functions employed by Wall and by Flory and Rehner are consistent with the required general forms; those of James and Guth are incompatible with any degree of isotropy and suggest an aeolotropic structure for vulcanized rubber.
It is also shown that the configurational entropy of vulcanization must be zero and quite independent of the statistical nature of the chains comprising the network, providing the network is not deformed macroscopically. The negative entropy of vulcanization derived by James and Guth arises from their erroneous identification of the configurational probability with the number of configurations which a microscopically specified network structure could assume, rather than with the total number of configurations for all network structures which are consistent with the requirements of the vulcanization process. The assertion of James and Guth that the configurations of the polymer chains are altered in some systematic manner by the introduction of cross‐linkages and their concept of ``internal pressure'' originate in this error. The present article attempts to clarify the currently prevalent confusion with respect to rubberelasticity theory.

Magnetic Study of Some Inorganic Compounds of Arsenic, Antimony, and Bismuth
View Description Hide DescriptionIn the graphs of the molecular susceptibilities χ_{ m } of some salts of As, Sb, and Bi, containing the same anions against Z, the total number of electrons in them are nonlinear in each case if all the salts are taken into consideration. These graphs are, however, similar in nature and bring out the family relationship of these cations. Ikenmeyer's relation is seen to hold true only in the case of the halides of As, Sb, and Bi and the salts of these cations in combination with the same anion.
The linear relation observed between χ_{ m } of the salts of As, Sb, and Bi containing the same anion and the number of electrons N in the cations has been used to evaluate the susceptibilities of the cations and the anions in combination with them. The significance of this relation and its advantages over other methods of determining ionic susceptibilities have been discussed. The experimental susceptibilities of these cations have been compared with the theoretical values calculated by Slater's and Angus' methods and have been used to evaluate the radii of the cations.

A Study of Two‐Center Integrals Useful in Calculations on Molecular Structure. I
View Description Hide DescriptionConvenient formulas have been obtained for the overlap integrals ∫χ_{ a }χ_{ b dv }, kinetic energy integrals —½∫χ_{ a }Δχ_{ b dv }, nuclear attraction integrals Z∫χ_{ a }(1/r_{a} )χ_{ b dv } and Z∫χ_{ b }(1/r_{a} )χ_{ b }′dv, and coulomb repulsion integrals , where χ_{ a }, χ_{ a }′, χ_{ b }, χ_{ b }′ are Slater‐type AO's on the centers a and b. Explicit formulas are given for all the integrals arising from the principal quantum numbers 1 and 2, for arbitrary values of the effective nuclear charges and the interatomic distance.

A Study of Two‐Center Integrals Useful in Calculations on Molecular Structure. II. The Two‐Center Exchange Integrals
View Description Hide DescriptionThe problem of the two‐center exchange integrals is solved in the most general way for Slater‐type atomic orbitals with integral effective quantum numbers. No other restrictions are placed upon effective quantum numbers and effective nuclear charges, The integrals are expressed linearly in terms of certain auxiliary functions. A rule for finding the coefficients is given. The coefficients are explicitly computed for all cases involving orbitals with the quantum numbers 1, 2, and 3. The auxiliary functions are discussed in detail. The existing literature is reviewed, and a survey of present tables is made.

Internal Rotation in Ethylene Chlorhydrin
View Description Hide DescriptionThe Raman and the infrared spectra of ethylene chlorhydrin have been remeasured with the result that the molecules take both the trans and the gauche forms in the gaseous and the liquid states, while they take only the gauche form in the solid state. By the measurement of the temperature dependence of the infrared absorption the energy difference between these two forms has been found as 0.95 kcal/mol.

The Infrared Dichroism of Diketopiperazine
View Description Hide DescriptionThe absorption of polarized infrared radiations by diketopiperazine crystal has been measured in the wavelength region from 2.8 to 15μ. From the observed infrared dichroism the assignment of the absorption bands has been made.

Variation of Lattice Frequencies with Concentration in Molecular Mix‐Crystals
View Description Hide DescriptionAssuming a unique linear periodic lattice for a non‐ionic molecular mix‐crystal, the lattice frequencies of the translational and rotational modes have been calculated for several concentration ratios of the two components. The observed variation in frequency in such crystals has been explained. The calculations also require that additional frequencies, not yet observed, should appear in Raman and infrared spectra.

Dielectric Relaxation in Glycerol, Propylene Glycol, and n‐Propanol
View Description Hide DescriptionComplex dielectric constants have been measured at frequencies from below 20 c/s to 5 mc/s over the temperature range −40° to −75°C in glycerol, −45° to −90° in propylene glycol, and −80° to −140° in n‐propanol. The results for n‐propanol are described by the Debye equation, but the values for the other two require a modified equation corresponding to a broader range of dispersion at higher frequencies. In all three liquids, evidence is found for a second dispersion region at still higher frequencies, which accounts for much of the difference between the radio frequency and optical dielectric constant. The relaxation times are quantitatively described over wide ranges by an empirical rate equation of a form which also fits viscosity data. The significance of the various results is discussed.

The Dielectric Constant of Ethylene at High Pressures
View Description Hide DescriptionThe dielectric constant of ethylene has been measured at pressures up to 500 atmospheres and at temperatures of 25°C and 50°C. At both temperatures the Clausius‐Mosotti function has been found to pass through a maximum with increasing density. The results have been discussed with reference to Kirkwood's theory of dielectric polarization.

Semilocalized Orbitals. I. The Hydrogen Molecule
View Description Hide DescriptionSemilocalized orbitals are defined and applied to the hydrogen molecule. The basic criteria for the analytic form of this kind of orbital is that it shall assume either molecular or atomic orbital form for certain special values of the variational parameters. A binding energy of 4.20 ev is found in comparison with 3.60 and 3.76 ev obtained from the best molecular and atomic orbital calculations. The physical interpretation of the results is briefly discussed.

Semilocalized Orbitals. II. A Comparison of Atomic, Molecular, and Semilocalized Orbital Method for Diatomic Hydrogen Fluoride
View Description Hide DescriptionIn a previous paper the method of semilocalized orbitals was developed and applied to the hydrogen molecule. This method is applied to diatomic hydrogen fluoride simultaneously with atomic and molecular orbital calculation. In contrast to the results with the hydrogen molecule, the semilocalized orbitals are closer to molecular than atomic orbital form. The semilocalized orbitals give a much better binding energy than molecular orbitals and the improvement in dipole moment calculations is especially heartening. The results with the atomic orbital method are very discouraging.

A Comparative Study of Unpolarizable and Polarizable Metal‐Solution Systems
View Description Hide DescriptionThe properties of the metal‐solution potentials of nickel in nickel free hydroxide and phosphate solutions are compared with the properties of unpolarizable electrodes and with the properties of polarizable metal‐solution systems. The electrochemical equilibria of unpolarizable systems are analyzed in terms of transfer mechanisms between the phases present. In the absence of any electrochemical equilibria, the metal‐solution potentials are interpreted as adsorption potentials.Chemisorption in the inner Helmholtz layer is discussed in connection with ``reversibility'' and polarizability of the system.

Diffusion in CO_{2} up to 150‐Atmospheres Pressure
View Description Hide DescriptionDiffusion coefficients have been obtained for the system CO_{2}–C^{14}O_{2} up to 150 atmospheres pressure and from 0°‐45°C. The coefficients are consistent with theory up to a density of 0.067 g/cc. In the range from 0.067–0.70 g/cc the coefficients are higher than predicted by theory. This may be attributed to a reduced collision diameter due to orientation of the nonspherical molecules. At higher densities the experimental coefficients are lower than the theoretical ones. This is expected as the theory breaks down at these high densities. At densities above 0.65 g/cc no measurable temperature coefficient of D was obtained. This may be explained by increased orientation at lower temperatures and in the liquid state.

Statistical Theory of Rubber‐Like Elasticity. IV. (Two‐Dimensional Stretching)
View Description Hide DescriptionThe failure, revealed by the experiment of Treloar, of statistical theories of the rubber‐like elasticity is removed. It comes from the neglection of the nongaussian character and of the nonlinear connectivity of the network structure. The theoretical formula derived here includes the semi‐empirical formula given by Treloar.

Photochemical Studies. XLVI. Photosensitization by Benzene and Pyridine Vapors
View Description Hide DescriptionAttempts to sensitize the dissociations of the following molecules by means of benzene vapor have been made: hydrogen, oxygen, hydrogen chloride, nitrous oxide, methyl chloride, methyl bromide, methyl iodide. Positive results were obtained only with methyl iodide. The decompositions of methyl chloride and methyl bromine sensitized by pyridine vapor were also studied with negative results. The reasons for the results are discussed briefly.

The Concentration of Molecules on Internal Surfaces in Ice
View Description Hide DescriptionIn this paper the experimental expression for the ``local conductivity'' of ice is given. This expression has two terms, one of which has already been discussed and brought into close relation with the structure of ice, that is, with its heat of sublimation and its lattice constant. This paper brings out another relation, deriving it from the second term of the experimental expression. It is concluded from an analysis outlined here that the second term of the local conductivity gives the concentration of molecules in ``internal surfaces.'' For the specimen of ice to which this method was applied the concentration of molecules on internal surfaces comes out as 1.03×10^{17} molecules/cc.
This is proposed as a new method of studying imperfections (internal surfaces) in dielectric crystals, and one which seems to be well suited to this purpose. It gains its advantages from the fact that it is not dependent upon the regularity of the imperfections, as in x‐ray diffraction methods, or upon the connectivity of the system of internal surfaces, as in direct current conduction.

Lattice Theories of the Liquid State
View Description Hide DescriptionThe assumptions underlying the lattice theory of liquids of Lennard‐Jones and Devonshire are examined. Four modifications of this theory have been proposed which avoid some of these assumptions. These modifications are (a) by Cernuschi and Eyring, (b) by Ono, (c) by Peek and Hill, and (d) one suggested in this paper. It is shown that they may all be deduced as special cases of one mathematical treatment. They are intuitively more attractive than the original theory and avoid any mention of the so‐called ``communal entropy.'' They give reasonable values of the second virial coefficient. None of them, though, shows much improvement over the original theory in calculating the critical constants and vapor pressure curves.

Heat Generation by Electric Sparks and Rate of Heat Loss to the Spark Electrodes
View Description Hide DescriptionIn a capacitancespark the gas between the electrodes is heated almost instantaneously; subsequently, the spark‐generated heat flows from the gas to the material of the electrodes. In the present experiments sparks of 0.1 to 2 millijoules were passed between Pt electrodes in a bulb containing helium or argon or xenon, and either the pressure change, Δp, at constant volume v or the volume change, Δv, at constant pressure p was recorded, the former by means of a sensitive diaphragm and the latter by the movement of a droplet in a capillary tube attached to the bulb. The spark‐generated heat H residing in the gas at any instant was computed from the equations H=1.5vΔp and H=2.5pΔv, which apply to constant volume and pressure, respectively, and are derived from the gas law and the energy equation, using the heat capacity of monoatomic gases. From the values of H and the discharge energy corresponding to the measuredcapacitance and breakdown voltage, the percentage of spark‐generated heat residing in the gas was obtained. Immediately after discharge the percentage was found to exceed 95. The rate at which the percentage decreases with time was found to be independent of total energy and vessel diameter above a critical value of the latter. It was found to become smaller with decreasing heat conductivity of the gas, decreasing diameter of the spherical electrodes, and increasing gap length, as expected on the basis of heat loss from the gas to the electrodes. With electrode diameters of 1 mm, the heat loss after about 30 milliseconds ranged from a few percent for xenon and 10 mm gap length to 75 percent for helium and 1 mm gap length. An increase of the electrode diameter to 3 and 4.6 mm caused a substantial increase of the rate of heat loss; for example, for xenon and 10 mm gap length the heat loss after about 30 milliseconds was 28 percent and 35 percent, respectively. It was found that for constant electrode diameter the data for the several gases and gap lengths could be combined in a plot of percentage heat loss against a dimensionless parameter, θ, representing the product of thermal diffusivity and time elapsed since discharge, divided by the square of the gap length. By means of the latter parameter, one may estimate an upper bound of the heat loss during the formation of a combustion wave from a spark in an explosive gas, i.e., during the process of spark ignition, on the basis that the combustion wave is formed in a time interval smaller than the time required for the wave to travel a distance equal to its width. It is found that the loss of spark energy during the ignition process is always rather small.

Infrared Studies of Mixed Crystals: Naphthalene in Anthracene
View Description Hide DescriptionPolarized infrared studies have been made using single crystals of dilute solid solutions of naphthalene in anthracene in the spectral region 755 to 830 cm^{−1}. The ab plane at normal incidence was studied with the plane of polarization either parallel or perpendicular to the b axis. The mole fraction of naphthalene was varied from 0.009 to 0.029. The contour of the naphthalene band at 787 cm^{−1} shows a dependence upon concentration, approaching the contour observed in pure naphthalene. There is an increasing dichroic splitting of the band which is attributed to space group coupling as the number of nearest identical neighbors increases. It is likely that the magnitude of this splitting in naphthalene is only about 5–10 cm^{−1} and that the crystal forces in naphthalene as well as in the mixed crystals of naphthalene in anthracene are sufficiently weak that the ``oriented gas'' model is applicable. Using this model, the 787 cm^{−1} band of naphthalene is assigned as a single fundamental of either B_{1u } or B_{3u } class.

The Diffusion of Copper in Cuprous Oxide
View Description Hide DescriptionCuprous oxide strips were prepared by the oxidation of copper at 1000°C. The diffusion of radiocopper in this material at 800 to 1050° gave a self‐diffusion coefficient, D=0.0436 exp(−36100/RT). Virtually the same D is obtained from experiments in which radiocopper is plated on copper strips, and the distribution of activity measured in the cuprous oxide film formed on oxidation in air. The observed D values are in accord with a predicted relation k/D=4, where k is the parabolic rate constant for copperoxidation. It is suggested that parabolic rate constants with large negative entropies of activation and low heats of activation may be due to grain boundarydiffusion.