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1 Dec 1951

Volume 19, Issue 12, pp. 1435-1615

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Statistical Thermodynamics of Rubber Elasticity

Frederick T. Wall and Paul J. Flory

J. Chem. Phys. 19, 1435 (1951); http://dx.doi.org/10.1063/1.1748098 (5 pages) | Cited 82 times

Online Publication Date: 22 December 2004

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Two principal differences between the theories of rubber elasticity 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 rubber elasticity theory.

Magnetic Study of Some Inorganic Compounds of Arsenic, Antimony, and Bismuth

Mata Prasad, C. R. Kanekar, and L. N. Mulay

J. Chem. Phys. 19, 1440 (1951); http://dx.doi.org/10.1063/1.1748099 (5 pages) | Cited 3 times

Online Publication Date: 22 December 2004

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In the graphs of the molecular susceptibilities χm 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 χm 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

C. C. J. Roothaan

J. Chem. Phys. 19, 1445 (1951); http://dx.doi.org/10.1063/1.1748100 (14 pages) | Cited 335 times

Online Publication Date: 22 December 2004

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Convenient formulas have been obtained for the overlap integrals ∫χaχbdv, kinetic energy integrals —☒∫χaΔχbdv, nuclear attraction integrals Z∫χa(1/ra)χbdv and Z∫χb(1/ra)χb′dv, and coulomb repulsion integrals ∫ ∫ χa(1)χb(2)(1/r12)χa′(1)χb′(2)dv1dv2, where χa, χa′, χb, χb′ 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

Klaus Rüdenberg

J. Chem. Phys. 19, 1459 (1951); http://dx.doi.org/10.1063/1.1748101 (19 pages) | Cited 195 times

Online Publication Date: 22 December 2004

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The 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

San‐ichiro Mizushima, Takehiko Shimanouchi, Tatsuo Miyazawa, Koo Abe, and Masashi Yasumi

J. Chem. Phys. 19, 1477 (1951); http://dx.doi.org/10.1063/1.1748102 (2 pages) | Cited 9 times

Online Publication Date: 22 December 2004

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The 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

Takehiko Shimanouchi, Kenji Kuratani, and San‐ichiro Mizushima

J. Chem. Phys. 19, 1479 (1951); http://dx.doi.org/10.1063/1.1748103 (2 pages) | Cited 3 times

Online Publication Date: 22 December 2004

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The 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

Ram Ratan Aggarwal and B. D. Saksena

J. Chem. Phys. 19, 1480 (1951); http://dx.doi.org/10.1063/1.1748104 (4 pages) | Cited 3 times

Online Publication Date: 22 December 2004

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Assuming 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

D. W. Davidson and R. H. Cole

J. Chem. Phys. 19, 1484 (1951); http://dx.doi.org/10.1063/1.1748105 (7 pages) | Cited 705 times

Online Publication Date: 22 December 2004

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Complex 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

H. G. David, S. D. Hamann, and J. F. Pearse

J. Chem. Phys. 19, 1491 (1951); http://dx.doi.org/10.1063/1.1748106 (5 pages) | Cited 8 times

Online Publication Date: 22 December 2004

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The 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

Charles R. Mueller and Henry Eyring

J. Chem. Phys. 19, 1495 (1951); http://dx.doi.org/10.1063/1.1748107 (3 pages) | Cited 30 times

Online Publication Date: 22 December 2004

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Semilocalized 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

Charles R. Mueller

J. Chem. Phys. 19, 1498 (1951); http://dx.doi.org/10.1063/1.1748108 (2 pages) | Cited 7 times

Online Publication Date: 22 December 2004

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In 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

D. MacGillavry

J. Chem. Phys. 19, 1499 (1951); http://dx.doi.org/10.1063/1.1748109 (6 pages)

Online Publication Date: 22 December 2004

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The 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 CO2 up to 150‐Atmospheres Pressure

W. L. Robb and H. G. Drickamer

J. Chem. Phys. 19, 1504 (1951); http://dx.doi.org/10.1063/1.1748110 (5 pages) | Cited 31 times

Online Publication Date: 22 December 2004

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Diffusion coefficients have been obtained for the system CO2☒C14O2 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)

Akira Isihara, Natsuki Hashitsume, and Masao Tatibana

J. Chem. Phys. 19, 1508 (1951); http://dx.doi.org/10.1063/1.1748111 (5 pages) | Cited 20 times

Online Publication Date: 22 December 2004

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The 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

Jean T. Dubois and W. Albert Noyes

J. Chem. Phys. 19, 1512 (1951); http://dx.doi.org/10.1063/1.1748112 (4 pages) | Cited 3 times

Online Publication Date: 22 December 2004

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Attempts 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

E. J. Murphy

J. Chem. Phys. 19, 1516 (1951); http://dx.doi.org/10.1063/1.1748113 (3 pages) | Cited 4 times

Online Publication Date: 22 December 2004

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In 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 1.03×1017 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

J. S. Rowlinson and C. F. Curtiss

J. Chem. Phys. 19, 1519 (1951); http://dx.doi.org/10.1063/1.1748114 (11 pages) | Cited 28 times

Online Publication Date: 22 December 2004

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The 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

Walter Roth, P. G. Guest, Guenther von Elbe, and Bernard Lewis

J. Chem. Phys. 19, 1530 (1951); http://dx.doi.org/10.1063/1.1748116 (6 pages) | Cited 9 times

Online Publication Date: 22 December 2004

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In a capacitance spark 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 measured capacitance 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

George C. Pimentel

J. Chem. Phys. 19, 1536 (1951); http://dx.doi.org/10.1063/1.1748117 (3 pages) | Cited 15 times

Online Publication Date: 22 December 2004

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Polarized 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 B1u or B3u class.

The Diffusion of Copper in Cuprous Oxide

Walter J. Moore and Bernard Selikson

J. Chem. Phys. 19, 1539 (1951); http://dx.doi.org/10.1063/1.1748118 (5 pages) | Cited 32 times

Online Publication Date: 22 December 2004

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Cuprous 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 copper oxidation. It is suggested that parabolic rate constants with large negative entropies of activation and low heats of activation may be due to grain boundary diffusion.

The Vibration Spectrum of Rutile

Frank Matossi

J. Chem. Phys. 19, 1543 (1951); http://dx.doi.org/10.1063/1.1748119 (4 pages) | Cited 21 times

Online Publication Date: 22 December 2004

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Raman effect data for rutile are evaluated for the force constants. It is shown that quasi‐molecules TiO2 are formed with strong Ti☒O bonds although every Ti atom is surrounded by 6 O atoms in about equal distances. The main force constants are (in 105 dynes/cm) 1.7 for the Ti☒O bond of the quasi‐molecules, 0.06 for the other Ti☒O bonds, 0.2 for O☒O bonds. The spectrum can be interpreted as that of coupled modified TiO2 molecules whose effective bond strength is a combination of the actual bond strengths.

Fourier Analysis of the X‐Ray Scattering from Soap Solutions

G. W. Brady

J. Chem. Phys. 19, 1547 (1951); http://dx.doi.org/10.1063/1.1748120 (4 pages) | Cited 2 times

Online Publication Date: 22 December 2004

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A Fourier analysis of the x‐ray diffraction of sodium dodecyl sulfate has been made on the basis that the micelles formed by aggregation of the long‐chain molecules are spherical. The radial distribution of the micelles has been determined at two concentrations; the distribution functions show definite peaks indicating a preferred distance for neighboring micelles. It is concluded that the spherical micelle is compatible with the x‐ray evidence. The deficiencies of the lamellar micelle are discussed.

The Effect of Ultrasonic Radiation on the Electrolytic Separation of Deuterium

Donald F. Mason, Royce E. Biddick, and Charles A. Boyd

J. Chem. Phys. 19, 1551 (1951); http://dx.doi.org/10.1063/1.1748121 (3 pages)

Online Publication Date: 22 December 2004

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The application of ultrasonic radiation to the polished platinum cathode of an electrolysis cell increases the coefficient for the electrolytic separation of deuterium. The radiation also decreases the temperature dependence of the separation coefficient. This is thought to be due to the rapid removal of the discharged gases by the ultrasonic radiation. This prevents the surface‐catalyzed exchange reaction between the discharged gases and the electrolyte.

Vibrational Intensities. III. Carbon Dioxide and Nitrous Oxide

David F. Eggers and Bryce L. Crawford

J. Chem. Phys. 19, 1554 (1951); http://dx.doi.org/10.1063/1.1748122 (8 pages) | Cited 79 times

Online Publication Date: 22 December 2004

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Experimental intensity measurements can be combined with known harmonic and anharmonic potential constants of molecules to determine the variation of dipole moment with displacement. We have used a finite Taylor's series for both potential energy and dipole moment. The effect on intensity of frequency variation over the band is included explicitly for both parallel and perpendicular bands as in Fermi resonance between several bands. Intensities of two fundamental and four combination bands in carbon dioxide were measured. A complete second‐order perturbation treatment of intensities was carried out for several bands, and the possible relation of the results to resonance structures is mentioned. The relative importance of electrical and mechanical anharmonicity is indicated.
Two cubic potential constants were determined for nitrous oxide from measured intensities, known rotational convergence, normal coordinates, and bond distances. Using these constants a first‐order intensity treatment was carried out for several combination bands. The intensities of three fundamental and three combination bands were measured. Discrepancies in measured rotational convergences are mentioned, and possible lines are suggested for further work on nitrous oxide.

Substituted Methanes. VII. Vibrational Spectra, Force Constants, and Calculated Thermodynamic Properties for CH3I and CD3I

Paul F. Fenlon, Forrest F. Cleveland, and Arnold G. Meister

J. Chem. Phys. 19, 1561 (1951); http://dx.doi.org/10.1063/1.1748123 (5 pages) | Cited 9 times

Online Publication Date: 22 December 2004

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Raman displacements for the liquid, and infrared absorption wave numbers for both liquid and gas, have been obtained for CH3I, together with quantitative depolarization factors for the Raman lines and semiquantitative relative intensities for both the Raman and infrared bands. The present and previous data were critically compared, and probable values of the wave numbers corresponding to the fundamental vibrational frequencies were determined for both liquid and gaseous states. Force constants in a modified valence force potential function, containing all possible quadratic interaction constants, were calculated; these then were used to calculate the fundamentals of CD3I. Finally, the heat content, free energy, entropy, and heat capacity for both CH3I and CD3I were calculated for 11 temperatures from 200° to 1000°K, for the ideal gaseous state at 1 atmos pressure.
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