Showing papers in "Journal of Chemical Physics in 1943"

Statistical mechanics of cross-linked polymer networks ii. swelling

Abstract: The interaction of solvents with cross‐linked network structures, such as occur in vulcanized rubber, is subjected to a statistical mechanical treatment based on the model and procedure presented in the preceding paper. The activity of the solvent is expressed as a function of its concentration in the swollen network, and of the degree of cross‐linking. The maximum degree of swelling of the network in contact with the pure solvent is related to the degree of cross‐linking. The heat of interaction of the solvent with the network can be calculated from the temperature coefficient of maximum swelling. The theory leads to the conclusion that the swelling capacity should be diminished by the application of an external stress. Furthermore, the modulus of elasticity should decrease inversely with the cube root of the swelling volume.

Statistical Mechanics of Cross‐Linked Polymer Networks I. Rubberlike Elasticity

Abstract: A model is proposed for the structure of a cross‐linked network, such as exists in a vulcanized rubber, which is amenable to statistical treatment. Expressions are derived for the structural entropy of the network, and for the entropy change on deformation. The latter is in agreement with the relationship derived by Wall and others by a different treatment.

Theory of Molecular Size Distribution and Gel Formation in Branched‐Chain Polymers

Abstract: The most probable distributions of molecular sizes are calculated for certain types of branched‐chain polymers. The results represent an extension of the previous work of Flory, who showed that very large polymeric molecules appear suddenly at a critical extent of reaction, which is predicted to occur very nearly at the experimentally observed gel point. This transition from liquid to gel is shown to be analagous to the condensation of a saturated vapor. It is believed that the size distributions obtained herein will aid in a study of viscosity‐molecular weight relationships in branched‐chain polymers.

Theory of the Elastic Properties of Rubber

Abstract: Previous discussions of the kinetic theory of rubber elasticity 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 su...

The Asymmetric Rotor I. Calculation and Symmetry Classification of Energy Levels

Abstract: A table of energy level patterns for rigid asymmetric rotors is given, by means of which this approximation to the rotational energies of all molecules up to J = 10 may be readily evaluated. The symmetry classification of each level is determined and expressed in terms of the K values of the limiting prolate‐ and oblate‐symmetric rotors. A simple method is developed for calculating the transformation which diagonalizes the energy matrix and is applied to the derivation of perturbation formulas.

Mechanical Properties of Polymeric Materials

Abstract: A molecular model in terms of which the elastic viscous properties of rubber‐like substances can be interpreted is presented. Experiments on stress relaxation at constant extension, creep under constant load, extrusion, vibration, and breaking are discussed in terms of a mathematical formulation of this molecular model.

Stability and Structure of Burner Flames

Abstract: It has been shown that the condition of equality of gas and burning velocities, required for stabilization of a flame above a burner, is established near the rim of the orifice or an obstruction within the stream by the effects of friction and inhibition of the explosive reaction. This condition is maintained between two critical gradients of the gas velocity at the solid surface, the lower gradient bordering on the flash‐back and the upper gradient on the blow‐off range. Values of the gradients in the range of laminar flow were determined by hydrodynamic equations from gas flow and tube dimensions; and their independence of tube diameter, except for extreme sizes, has been demonstrated both for upright and inverted flames. In the latter the critical velocity gradient for blow‐off was also found to be independent of the diameter of the centrally mounted wire within a considerable range. The effect of the surrounding atmosphere on the critical blow‐off gradient has been shown. The gas‐flow pattern was studied experimentally by photographing stroboscopically illuminated magnesium oxide dust particles. No appreciable redistribution of velocities over the cross section of the stream was observed below the combustion zone. The burning velocity was found constant over the surface of the inner cone, except at the tip, where it increases to the axial gas velocity, and at the base, where it decreases to zero. The experimental flame cone outline and flow pattern agree with the theoretical within the limitations imposed by simplifying assumptions. The temperature distribution in the flame was determined by the sodium line‐reversal method, only the center of the flame being colored, and observations of the width and emission spectrum of the luminous combustion zone were made. In natural gas‐air flames C–C and C–H bands are observed in the zone, and the temperature rises gradually behind the zone to a maximum that corresponds to the theoretical flame temperature. In natural gas‐oxygen flames no C–C or C–H bands are observed; and the temperature attains a maximum, exceeding the theoretical, immediately behind the combustion zone. Temperature distribution and flow pattern have been correlated. The flow pattern of inverted flames was also studied with particular attention to the region of flame attachment just above the central wire where the formation of an annular vortex is demonstrated. An interpretation of the formation of polyhedral flame cones, described by Smith and Pickering, has been given.

The Influence of Hindered Molecular Rotation on the Dielectric Constants of Water, Alcohols, and Other Polar Liquids

Abstract: The theory of dielectric polarization of polar liquids is used to calculate the dielectric constants of water and some alcohols. Quasi‐rigid coordination models, based upon x‐ray structural investigations, are employed in the calculation of a function g which measures the orientational correlation between neighbors in the liquid. It is pointed out that the correlation function g is closely related to the thermodynamic ``abnormality'' of polar liquids.

The Surface Recombination of H Atoms and OH Radicals

Abstract: A diffusion method of investigating surface recombination of atoms by substances of low catalytic power is presented. By this method we have evaluated the coefficient of recombination γ for H and OH on Pyrex for a temperature range of over 500°C. For smaller ranges of temperature we have found the recombination of H on a number of salts, and have found this recombination to be strongly dependent on the dryness of the surface. All salts investigated save KCl strongly recombined H when dry. Salts recombining H could not be investigated for OH recombination. However KCl, which did not recombine H, did recombine OH strongly. A number of strong dehydrogenating and dehydrating agents were tested for differences in H and OH recombination, but no difference was found.

Erratum: Frequency Spectrum of Crystalline Solids. II. General Theory and Applications to Simple Cubic Lattices

Abstract: At 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‐Karman 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.

The Quantum Yield of Diacetyl Fluorescence

Abstract: The quantum yield of fluorescence of diacetyl, excited by radiation of λ4047 and λ4358, has been measured and found to be 0.145±0.03. It is approximately independent of pressure. On the other hand, the yield with excitation of λ3650, as first observed by Henriques and Noyes, increases apparently from zero at zero pressure to nearly the value obtained for the longer wave‐length excitations at a pressure of 5 cm Hg. This marked difference in pressure effect for different energies of excitation is explained by assuming that predissociation occurs at a level between those reached upon λ3650 and λ4047 excitations. By removing vibrational energy collisions can save for fluorescence a molecule excited by λ3650, but they do not play an important role in the case of molecules with excitation energy below the predissociation limit. The observed phenomena of diacetyl fluorescence can be explained in terms of a model which involves a metastable state just below the state reached on absorption. This model is compared with McMurry's predictions of states for molecules of the type of diacetyl.

Infra‐Red and Raman Spectra of Polyatomic Molecules XVIII. Trideuteronitromethane

Abstract: The infra‐red spectrum of trideuteronitromethane has been studied in the range 3–25μ, and the Raman spectrum has been analyzed. From this data and that obtained by Wells and Wilson on nitromethane it has been possible to determine all the fundamental frequencies except that of the torsion about the C–N bond, and to carry out a normal coordinate treatment from which a potential function fitting the observed frequencies of nitromethane and trideuteronitromethane within 2 percent has been obtained.

The Magnetic Susceptibilities of Metals Dissolved in Liquid Ammonia

Abstract: Here are recorded data on the magnetic susceptibilities of potassium and of cesium dissolved in liquid ammonia at 240°K and 220°K. Also included are a few data on calcium and barium. These solutions throughout the entire range of concentrations were regarded as representing an electron gas. Such systems would permit the distributions of the magnetic moments of the electrons to be followed continuously from the degenerate region of the Fermi‐Dirac statistics to those distributions where the quantum and classical statistics are indistinguishable. The general features of the magnetic behavior of a free electron gas were recognized, overlaid, however, by interactions characteristic of the environment of the electrons in the solutions. In the light of the magnetic susceptibilities as well as of other properties, a description is proposed for the structure of the solutions with special reference to the conduction electrons. Barium was found to dissociate into two electrons per gram atom and it is inferred that ...

The Kinetics of the Oxidation of Isopropyl Alcohol by Chromic Acid

Abstract: The oxidation of isopropyl alcohol by chromic acid is a reaction first order with respect to the acid chromate ion, HCrO4−, first order with respect to the alcohol, and second order with respect to hydrogen ion Evidence has been obtained that the reaction proceeds by way of a compound of tetravalent or of pentavalent chromium On the basis of these facts, a mechanism for the oxidation has tentatively been suggested

The Transmission Coefficient in the Theory of Absolute Reaction Rates

Abstract: The activated complex theory of reaction rates is discussed critically. The transmission coefficients for a number of idealized energy surfaces have been computed quantum mechanically. It appears that curvature of the reaction path may introduce activation energy in addition to that caused by constriction and elevation of the energy valley. Except at low temperatures, this additional activation energy is almost negligible. However, it may contribute to the separation of isotopes, where small differences in activation energy are important. For systems in thermal equilibrium at room temperatures and above, the average quantum mechanical transmission coefficient is found to differ insignificantly from that calculated by classical mechanics.

Errata: ``Vibrational Frequencies of the Isotopic Water Molecules; Equilibria with the Isotopic Hydrogens''

Abstract: The fundamental frequencies, anharmonicities, and vibrational modes for the molecules HDO, HTO, DTO, and T2O are calculated on the basis of Dennison's and Darling's recent analysis of the vibrational spectrum of the H2O molecule. The equilibrium constants for nine equilibria involving these molecules are given. Experimental values for the reactions HD+H2O=H2+HDO and HT+H2O=H2+HTO are compared with those calculated. It is concluded that the vibrational potential function is essentially unaltered by isotopic substitution.

Distance Correlations and Bose‐Einstein Condensation

Abstract: The correlation effect on the molecular distance distribution in a Bose‐Einstein gas is calculated as a function of volume and temperature, particularly for the case of degeneracy (condensation) of the gas. It is shown that, under certain conditions in the condensed state, the density as seen from any one molecule appears, over a rather extended region around it, to be considerably larger than the true density. This result seems to have direct relation to the fact that the low temperature modification of liquid helium has a negative coefficient of thermal expansion.

Statistical Lengths of Rubber‐Like Hydrocarbon Molecules

Abstract: The root mean square lengths of trans‐, cis‐, and random rubber‐like hydrocarbon molecules are calculated. These results are compared with the maximum possible lengths of the trans‐ and cis‐varieties and interpreted from the point of view of recent theories of rubber elasticity. It is found that the cis‐structure should be more elastic than the trans‐structure but the calculated difference is not large. The theory is probably sufficient to account for the properties of polychloroprene as compared to natural rubber, but stearic forces are necessary to explain the lack of elasticity in balata or gutta‐percha.

The Crystal Structure of Silver Oxalate

Abstract: An x‐ray diffraction study reveals that silver oxalate is monoclinic, having the symmetry of the space group P21/c—C2h5. The unit cell has the following dimensions: a=3.46±0.02A, b=6.16±0.02A, c=9.47±0.04A, β=76°±1°. There are two molecules of Ag2C2O4 per unit cell. All atoms are located in sets of fourfold general positions. The parameters of the silver and oxygen atoms are determined from two‐dimensional Fourier syntheses, using the experimental crystal structure factors for the h0l and 0kl planes. The positions of the carbon atoms are approximately determined by requiring that the carbon‐carbon and carbon‐oxygen bond distances be reasonable. The silver oxalate structure may be considered to be made up of chain molecules of composition (Ag2C2O4)x extending through the lattice parallel to the b axis. These chains appear to be held together by longer silver‐oxygen bonds to form the three‐dimensional structure.

The Vibration-Rotation Energies of the Linear X-Y-Z Type Molecule

Abstract: The vibration‐rotation energies of the linear X‐Y‐Z type molecule are derived according to a method suggested by Professor Harald H. Nielsen in a recent paper. By the proper substitutions the energy expressions are reduced to the ones appropriate for the XY2 type molecule, and a comparison with the work of Professor D. M. Dennison is effected.

Infra‐Red and Raman Spectra of Polyatomic Molecules XIX. Acetaldehyde and Acetaldehyde‐d4

Abstract: The infra‐red spectra of acetaldehyde and acetaldehyde‐d4 have been measured between 3μ and 25μ. An analysis of the spectra has been made and values are suggested for the fundamental vibration frequencies of these molecules. These values are compared with the assignment for the propylene molecule, and a strong similarity is shown. The results have been used to calculate the height of the potential barrier restricting internal rotation in acetaldehyde, and a value of about 2000 cal. is deduced.

The Low Velocity Scattering of H+ and H3+ in Hydrogen

Abstract: The theory of the elastic scattering of a low velocity ion in a gas is examined in some detail. More precise measurements are reported on the elastic scattering of H+ and H3+ in hydrogen in the velocity range of 2 to 135 volts. The simple exponential form of a potential law is shown to change with the velocity of the ion, i.e., with distance of closest approach of the interacting particles. For H+ in H2 this is— V=−20.37×10−32r4from 2 to 24 volts (ra>1.74A) and V=−8.68×10−14r1.74from 24 to 135 volts (ra=1.74 to 1.5A). The interaction energy calculated on this basis is 3.0 electron volts instead of the 3.5 previously reported. For H3+ in H2 an average taken from 5.4 to 130 volts is V=−1.145×10−36r4.60(ra=2.12 to 1.07A); but between 10.5 and 28 volts (ra = 1.85 to 1.48A) V=−5.98×10−32r4. Both inverse fourth‐power potential laws are compared with a similar law evaluated on the basis of the interaction being due solely to that of the charge on the ion interacting with the induced dipole of the hydrogen molecu...

A Direct Experimental Determination of the Electron Affinity of Chlorine

Abstract: The electron affinity of chlorine has been determined to be 85.84±1.0 kcal./mole by measureing the ratio of ions to electrons leaving a hot tungsten surface in contact with a low pressure of gas containing chlorine atoms. Both Cl2 and SnCl4 were used as carrier gases.

Crystal Structure of Gadolinium Formate, Gd(OOCH)3

Abstract: The crystal structure of gadolinium formate has been studied by means of Laue, rotation, and powder x‐ray patterns. It has a rhombohedral lattice. The unit cell, a0=6.17A, a=115° 30′, contains one molecule, Gd(OOCH)3. Density—(calculated) 3.85, (Berman balance) 3.77. By taking into consideration the symmetry of special positions all space groups except D37—R32 and C3v5—R3m can be excluded. A structure has been found in the latter group which yields excellent agreement of calculated and observed intensities.

Raman Spectra of Hydrocarbons I. 1‐Octene, cis+trans 2‐Octene, trans−3‐Octene, trans−4‐Octene, 4‐Octyne, and 1‐Octyne

Abstract: Raman frequencies, intensities and depolarization factors are reported for 1‐octene, cis+trans 2‐octene, trans−3‐octene, trans−4‐octene, 4‐octyne, and 1‐octyne. The experimental arrangement is described. The intensities were determined by use of a micro‐densitometer. Comparison of the relative intensities obtained in the present investigation for 4‐octyne with the estimated intensities obtained previously indicates that the so‐called ``estimated intensities'' are in reality estimates of densities rather than of intensities. The relative intensities are based upon an arbitrary value of 1000 for the strongest line in the Raman spectrum. A high speed, Hilger E−518 glass spectrograph was used in obtaining some of the spectrograms. With this instrument, a spectrogram of carbon tetrachloride, from which eight lines could be measured, was obtained in one minute.

The Activation Energy of the Reaction CH3+HBr = CH4+Br and the Carbon‐Hydrogen Bond Strength in Methane

Abstract: Mixtures of hydrogen bromide, methyl iodide, and iodine have been illuminated with ultraviolet light, and the rate of formation of methane as a function of the relative concentrations has been determined With iodine absent from the system, a maximum amount of methane is formed, due to the absence of recombining reactions of methyl radicals and iodine A comparison of the amount of methane produced with iodine present in various amounts with that produced when iodine is absent enables one to calculate the relative rates of the reactions CH3+HBr=CH4+Br,CH3+I2=CH3I+I, when the relative steric factors of the two reactions are assumed to be approximately the same as for the reactions H+HBr=H2+Br,H+Br2=HBr+Br This leads to an activation energy of 15 kcal for the methyl‐hydrogen bromide reaction, which, combined with the activation energy of the reverse reaction as determined by Van Artsdalen, yields a binding energy of 102 kcal for CH3–H