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Volume 27, Issue 9, 01 September 1956
 SPECIAL ISSUE ON HIGH POLYMER PHYSICS


Dynamic Properties of Various Rubbers at High Frequencies
View Description Hide DescriptionThe shear wavevelocity and attenuation of GR‐S, Butyl, Hevea, Hycar, and Paracril rubbers have been measured in the frequency range 0.2–7 Mc/sec and the temperature range −60°C to 20°C. To minimize errors arising from interfaces in the acoustic path, a double path technique was used. By combining the shear wave data with bulk wave data the dynamic shear, bulk, and Young's moduli, and their associated viscosities, were calculated. The results were coupled with low‐frequency Young's modulus data on the same materials to give information over many decades of logarithmic frequency, and from this the distribution of relaxation times was determined.
To a fair approximation, in the range investigated, it was found that the real and imaginary parts of the dynamic Young's modulus could be taken as equal to three times the corresponding values of the dynamic shear modulus. It was found that the classical Stokes assumption, that the bulk viscosity is negligible in comparison to the shear viscosity, was reasonable for some of the rubbers, but not for all of them.

Effect of Light Scattering upon the Refractive Index of Dispersed Colloidal Spheres
View Description Hide DescriptionThe Zimm‐Dandliker equation on the effect of light scattering upon the refractive index of colloidaldispersions of spheres is found to be in good agreement with experimental facts. It is transformed to give a new mixture rule from which the refractive index of colloidal spheres, to be expected in absence of light scattering, can be calculated. The latter is needed for particle size determinations in colloidal solutions from light‐scattering measurements to be evaluated on the basis of the Mie theory. For the same purpose, a graphical method is worked out which is less time consuming and yields very accurate results. The graphical method allows one to obtain simultaneously both the refractive index and the diameter of the particles. The method is tested successfully against data obtained by alternate procedures used heretofore.

Kinematographic Study of Tensile Fracture in Polymers
View Description Hide DescriptionHigh speed motion pictures were taken of silicone rubber, irradiated polyethylene, Plexiglas II, and aluminum foil while they were being broken. Fractures started internally in some of the silicone samples but at the edges of all of the others. The rates of crack growth and the rates of retraction of the ends of the rubber samples were measured. The velocities with which the cracks grew were compared with the results of the theories of Poncelet, Yoffe, Mott, and Roberts and Wells. Their prediction, that the velocities should be about one half those of transverse waves in the media, was found to represent the data for materials with moduli differing by five decades. After fracture, the ends of the rubber samples contracted with velocities approximately equal to the velocities of longitudinal waves in these samples.

Flow Birefringence and Stress
View Description Hide DescriptionSimultaneous measurements of flowbirefringence, shear and normal stresses on a 15% solution of polyisobutylene in decalin were performed. They proved that the extinction angle measured in birefringence is identical to the orientation of the principal tensile stress calculated from the normal stress measurements and that the birefringence was proportional to the difference in principal stresses in flow. A detailed discussion of the significance of this result is given with a possibility of a far‐reaching generalization of the mechanical behavior of high polymer solutions.

Birefringence Changes During Retraction of Oriented Polystyrene Monofilaments. I. Changes of Average Birefringence
View Description Hide DescriptionThe changes in average birefringence during retraction have been measured at 85°C for four different oriented polystyrene monofilaments. The relationship between birefringence decay and length decrease is not linear: the birefringence decay is relatively more rapid than the length decrease, in all cases. Also, the birefringence‐length relationship seems to be essentially independent of retraction temperature. Birefringence decay rate can be reduced by a factor of 1000 by not allowing the filament to retract. One of the filaments shows an interesting change in sign of the birefringence, from negative to positive, in the final stages of the retraction. The birefringence decay data for the four filaments could not be reduced to any universal curve by plotting either birefringence or relative birefringence against any simple functions of length or extension (all the filaments were made from the same polymer, so that a reduction to some such common basis should be possible). Analyzing the data in terms of a distribution of retardation times, by assuming that birefringence decay and length decrease are in some constant ratio for each retardation time (where the additional parameter, time, is introduced), also failed to reduce the data to a single common curve. Internal stress may be an essential parameter for a proper characterization of the birefringence.

Birefringence Changes During Retraction of Oriented Polystyrene Monofilaments. II. Changes in Radial Distribution of Birefringence
View Description Hide DescriptionThe radial distribution of birefringence, Δ(r), has been measured in Filament # 16 at a series of time values up to 600 hrs, during retraction at 85°C. The birefringence distribution was obtained by cutting wedges on the end of the filament samples and analyzing the optical interference pattern down the center line of the wedges, under a polarizing microscope. The rates of birefringence decay at different points along the radius are not the same, or even proportional; the interrelationship is apparently fairly complex. Birefringence values near the center of the filament change from negative to positive sign in the long‐time region, while values near the exterior surface remain negative throughout. Values of the diameter average birefringence calculated from Δ(r) are in close agreement with values obtained from direct experimental measurement. A cross‐sectional‐area average birefringence was also calculated from Δ(r); this quantity decreases monotonically toward zero, with no transition to positive values in the long‐time region, and therefore corresponds more closely than the diameter average birefringence with the observed length changes. The area average is nearly proportional to the diameter average, however, except for values near zero.

Detailed Structure of Copolymers from Dielectric Measurements
View Description Hide DescriptionThe effective dipole moment of each polar group in polar‐polar or polar‐nonpolar copolymers is expressed in terms of the moment of an equivalent isolated polar group and the average of the vector sum of the moments of all of the polar groups surrounding it. If effects of short‐range forces leading to angular correlations of dipole pairs are neglected except for interactions between nearest neighbors along the chain, an expression for the average of the effective moments of the two types of polar groups present can be written as a function of the composition of the copolymer in the form .Here, x _{1} is the mole fraction of one of the monomers in the copolymer, (μ_{1} ^{2})_{eff} and (μ_{2} ^{2})_{eff} are the squares of the effective moments of the two polar groups. L, M, and N are constants involving the dipole‐moments of the equivalent isolated groups and the average cosines of the angles between nearest‐neighboring dipole pairs of types 1 − 1, 1 − 2, and 2 − 2. The quantity P _{11}(x _{1}) is the probability of a monomer of type 1 adding to a free radical of its own kind at the end of a growing chain in the polymerization mixture. It can be calculated from r _{1} and r _{2}, the reactivity ratios of the two monomers, and the composition of the monomer feed mixture. Interactions extending farther along the chain than nearest neighbors introduce terms in higher powers of P _{11}(x _{1}).
Onsager's equation for the dipole moments of molecules in mixtures of polar liquids has been modified to express the average of the effective moments of the polar groups present in terms of the dipolar contribution to the dielectric constant,. Using this equation, values of 〈μ^{2}〉_{Av} have been calculated from measurements of for several copolymers of poly‐(p‐chlorostyrenestyrene) representing the whole range of copolymer composition. Measurements were made on bulk copolymers at temperatures above the glass‐transition temperature. A curve of the form L+Mx _{1}+Nx _{1} P _{11}(x) has been fit within experimental error to the calculated values of 〈μ^{2}〉_{Av} over the whole range of copolymer composition. This indicates that within the limits of error of this work only nearest‐neighbors on the polymer chain contribute to the effective moments of the polar groups. The average cosines have been calculated for the angles between each of the three kinds of dipole pairs in the copolymer.

 REGULAR ARTICLES


Radiation Induced Conductivity in Polyethylene and Teflon
View Description Hide DescriptionThe conductivity induced in polyethylene and Teflon by bombardment with x‐rays from a 2‐Mev Van de Graaff and gamma rays from Co^{60} has been investigated as a function of time, temperature, geometry, exposure rate, and applied electric field. Within the range of the variables studied, the observed photocurrents were directly proportional to the exposure rate and the applied electric field. The photocurrent could be divided into three components, the current due to the action of monodirectional photons, the increase in this current due to the influence of the electric field, and a component of less than 10% made up of all other possible charge carriers. During irradiation, the conductivity increased by a factor of about 10^{3}. Between 78°K and 273°K the photocurrent was nearly independent of temperature. In general, the conductivity of Teflon was greater than that of polyethylene.

Observations of Dislocation Glide and Climb in Lithium Fluoride Crystals
View Description Hide DescriptionIt is shown that reagent CP‐4 plus ferric ions can be used to detect the positions of dislocations in LiF crystals. The technique is highly selective and both edge and screw (110) [11̄0] dislocations can be detected and distinguished. A double etching method is used to observe, for the first time, the glide and climb of individual dislocations in LiF.

Effect of Magnetic Field Strength During Condensation on the Coercivity and Form of Vapor‐Deposited Iron
View Description Hide DescriptionThe coercivity and form of iron deposited from the vapor were found to be influenced by the strength of a magnetic field applied during condensation. The intrinsic coercivities of powders deposited at −196°C and at −78°C in fields of 800 to 900 oersteds were about 120 oersteds. The greater fraction of particle diameters ranged from 10 to 20μ. No appreciable quantity of submicron particles was detected in several samples examined by electron microscopy. Line‐broadening in the diffraction patterns of the vapor‐deposited iron was attributed to strain, the magnitude of which was theoretically sufficient to account for the observed coercivities.

Transit Time Transistor
View Description Hide DescriptionIt is shown that, by utilizing transit‐time effects, an appropriately designed transistor can be operated as a three‐terminal amplifier in certain special frequency bands which lie far above the α‐cutoff frequency. The criteria for the existence of such frequency bands are similar to those for the existence of a negative‐resistance band when the structure is operated as a diffusion delay diode; if such a negative‐resistance band exists, there are also two narrow bands, one on each side of it, where transit‐time transistor action is available. The existence of these bands is in general independent of the magnitude of the base resistance, but their width decreases with increasing base resistance.

Instability in Hollow and Strip Electron Beams
View Description Hide DescriptionA thin strip or hollow electron beam drifting in a magnetic field directed parallel to the direction of motion is in an unstable condition. As a result of initial nonuniformities the beam breaks up into a series of ``spiral nebulae.'' This paper is written to describe some experimental observations which are of help in understanding the phenomenon, and to show that it can be applied to give useful amplification.

Solutions of the Reactor Kinetics Equations for Time Varying Reactivities
View Description Hide DescriptionThe solutions of the reactor kinetics equations for constant (step‐function) reactivities are straight‐forward and well known. For time dependent reactivities, however, only approximate solutions (excluding machine results) peculiar to the individual need are generally available. To obtain solutions for time dependent reactivities, the reactor kinetics equations are combined into a single integral equation of the Volterra type. The kernel of the integral equation characterizes the particular reactor through the decay properties of the six groups of delayed neutrons plus the prompt neutron generation time. A simple iterative procedure for hand computation of the solutions for general time dependent reactivities is given. Curves for two types of such reactivities (linear and are included.

First Correction to the Geometric‐Optics Scattering Cross Section from Cylinders and Spheres
View Description Hide DescriptionThe total scattering cross section in the short wavelength limit is considered in this paper. The problems treated include diffraction of a plane electromagnetic wave by a conducting cylinder (two possible polarizations) or a conducting sphere, acoustic scattering by a rigid sphere, and quantum‐mechanical scattering by an impenetrable sphere. The first correction term to the geometric optics result is computed. In each case, this term is proportional to (ka)^{−2/3}. The constant of proportionality depends on the specific geometry.

Neutron Diffraction Study of Titanium‐Zirconium System
View Description Hide DescriptionTitanium and zirconium alloy system consists of a continuous series of random substitutional solid solutions of solvent and solute atoms. Titaniumscatters thermal neutrons in the opposite phase from those scattered by zirconium, the scattering amplitudes being: b _{Ti}=−0.38×10^{−12} cm and b _{Zr}=0.62×10^{−12} cm. An alloy containing 62 atomic percent titanium and 38 atomic percent zirconium is developed that gives no coherent scattering reflections in its neutron diffraction pattern, and is extremely useful in constructing devices in which scattering of thermal neutrons is not desired. Based on negative and positive scattering amplitudes of different isotopes of the same element for thermal neutrons, development of isotopic alloys is suggested.

Neutron Flux Spectra in Air
View Description Hide DescriptionApplication of the moment method of L. V. Spencer and U. Fano is made to the penetration and slowing down of neutrons in infinite media. General considerations are restricted mainly to those modifications of the method necessary for the neutron problem; in particular, a special technique is given for reducing the integral term of the neutron transportequation. Calculations are carried out for point isotropic monoenergic neutron sources of 1, 100, 500 kev, 1, 2, 5, and 14 Mev in an infinite atmosphere of air. Best available numerical values of the cross sections are used, and the effects of absorption,anisotropicangular distributions, and inelastic scattering are included. Distances out to 10 mean free paths are considered.

Investigations on Barium Ferrite Magnets
View Description Hide DescriptionBariumferrite (BaO:6Fe_{2}O_{3}) has been investigated magnetically to test the predictions of fine particle theory in the region of grain sizes larger than the critical one for which no satisfactory theory exists as yet. Grain size and coercive force of polycrystallinemagnets (nonoriented and crystal oriented) were closely related to sintering temperatures. A comparison of theoretical and observed temperature dependence of coercive force is made and shows a close fit when certain reasonable assumptions are made.
Susceptibilities showed values attributed to rotation of the magnetization vector for samples of high coercive force only (4000 oe), while wall movements contribute more or less to the susceptibility of all other samples.
Domain patterns show wall movements in applied fields on samples with particle thickness down to 10×10^{−4} cm. Patterns on grains below 5×10^{−4} cm thickness ( _{I}H_{C} more than 2000 oe) indicate reversals of magnetization by the rotation process. On magnets of the transition particle size both processes can be observed side by side, the walls being less movable for higher coercive forces.

Surface Film Formation and Metallic Wear
View Description Hide DescriptionThe interactions between surface asperities which occur during sliding are of primary importance in both friction and wear. In consequence, many of the phenomena observed during investigations into the nature of friction should have their counterpart in wear. An experimental study is described of the way in which wear is affected by factors already known to influence friction. It is shown that when a relatively soft metal slides on a harder one, the relationship between the wear and the sliding distance may be one of three general types. Each type is associated with the formation of a surfacefilm during sliding. The extent to which these films (oxide, adsorbed boundary lubricant, etc.) prevent intermetallic contact influences the relationship between the wear rate and the applied load. With several metals there is a discontinuity in the wear rate‐load relationship, and two distinct regimes of wear are obtained. The transition between these two regimes is associated with the breakdown of a protecting surfacefilm. Finally, it is suggested that the generation of protective surfacefilms during sliding comprises an essential part of the ``running‐in'' process of machinery.

Effect of Pile Irradiation on the Dielectric Constant of Ceramic BaTiO_{3}
View Description Hide DescriptionA specimen of ceramic BaTiO_{3}, made of reagent‐grade materials at a calcination temperature of 1250°C, was exposed to pile irradiation in the amount of nvt=2.1·10^{20} at Hanford, Washington. The original ceramic showed a peak in the dielectric constantversus temperature curve usually ascribed to ferroelectricity. After irradiation this peak essentially disappeared, and the dielectric constant was reduced to a nearly constant value over the temperature range 30°C to 140°C. This reduced value is about half of the room‐temperature dielectric constant as determined before irradiation. Evidence is mentioned for a small residual peak in the dielectric constant of the irradiated specimen.

Monte Carlo Calculation of Noise Near the Potential Minimum of a High‐Frequency Diode
View Description Hide DescriptionNoise near the potential‐minimum of a high‐frequency diode has been calculated in this paper using a high speed electronic, digital computer. Random numbers were generated and used to simulate the emission of electrons at the cathode. Electrons emitted were continuously fed into the calculating process and those collected on the anode or returned to the cathode were automatically erased. In this way the electron motions computed by numerical integration followed the actual operation of a one‐dimensional space‐charge limited diode.
The results of this paper are based upon data obtained in the course of 3000 unit time intervals. In each case current and velocity fluctuations near the potential minimum were computed. This basic information permitted the calculation of the reduction in noise current caused by space‐charge smoothing. The results were then applied for a calculation of the minimum noise figure for microwave beam‐type amplifiers and show a sharp minimum of less than 2 db around 2500 Mc and a maximum of about 7.5 db near 4000 Mc. At very low frequencies the noise figure is small and agrees with existing low‐frequency theories. At very high frequencies it approaches the figure corresponding to full shot noise, namely 6.3 db. Within the accuracy of calculation, correlation between current and velocity fluctuations has not been found nor the smoothing in velocity fluctuation.
