Volume 25, Issue 10, 01 October 1954
 SPECIAL ISSUE ON HIGH POLYMER PHYSICS


Effect of Crystallinity on the Dynamic Mechanical Properties of Polyethylenes
View Description Hide DescriptionSix polyethylenes which differed widely in the degree of crystallinity were studied. The crystallinity was determined from density measurements. Both the density and the dynamic mechanical measurements were made over the temperature range from 25°C to above the melting point of the material.
The dynamic shear modulus drops rapidly as the melting point is approached. The mechanical damping goes through a maximum near 60°C and then through a minimum just below the melting point. It is possible to predict the density of any of the polyethylenes at any temperature below the melting point from the value of the shear modulus at the same temperature. The more crystalline materials have the higher shear moduli and the higher melting points.

The Dynamic Bulk Viscosity of Polyisobutylene
View Description Hide DescriptionThe dynamic bulk modulus of a high molecular weight polyisobutylene is calculated from measured longitudinal‐wave and shear moduli. A viscous or energy‐dissipating process associated with pure volume deformation is found, which appears to be a relaxation process. The peak in absorption of the shear and bulk moduli and the apparent activation energies associated with the two types of deformation are at least approximately the same, suggesting that the fundamental molecular mechanism involved in the two types of deformation may be the same.

Studies of Rubberlike Polymers by Nuclear Magnetism
View Description Hide DescriptionThe actual width of the protonresonance line in uncured natural rubber has been determined at room temperature to be 0.06 gauss. Curing of polymers increases the line width at a given temperature. The small increase in natural rubber is possibly compatible with a physical bonding rather than the usually assumed cross linking. For a butadiene‐styrene copolymer the increase in line width due to cure is somewhat larger. Carbon black loading increases the line width to a lesser degree than cure. This is compatible with the concept of physical bonding between the blacks and the polymer chain molecules. Variations in line width caused by changes in chemical composition and copolymerization were also investigated. Polypropylene and polypropylene oxide of roughly the same average molecular weight are compared. The polypropylene oxide exhibits a greater degree of ``rotation'' about its C–O bonds than polypropylene does about its C–C bonds. Two butadiene‐acrylonitrile copolymers also have been studied as a function of temperature. Finally, spin‐lattice relaxation timevs temperature studies are reported for a butadiene‐acrylonitrile copolymer and for raw butyl, over the temperature range from −‐50°C to 70°C. Estimates of the magnitude of the barriers hindering ``rotation'' are made.

Measurement of Orientation in Polystyrene Monofilaments by Means of Double Refraction
View Description Hide DescriptionThe molecular orientation in polystyrene monofilaments can be determined by measuring the optical double refraction, or birefringence, which the orientation produces. When the oriented filaments are observed with monochromatic light under a polarizing microscope, a pattern of interference fringes is seen which can be analyzed. The general theory of this interference pattern is discussed, including consideration of the molecular basis of optical birefringence in polystyrene. Reversals of fringe order in the interference pattern can occur, but this complication can be handled by suitable methods. A number of experimental techniques useful in these studies are described. It is found that the birefringence is greater near the outside surface of the filaments than in the center, and this can be understood in terms of the rate of cooling during the orientation process.

Theory of Orientation and Double Refraction in Polymers
View Description Hide DescriptionOrientation and birefringence in linearly oriented amorphous polymers are discussed with particular emphasis on polystyrene type chains. A system of completely uncoiled parallel zigzag chains is defined as 100 percent orientation. The variation of birefringence with orientation is assumed to follow the same expression as that for the variation of polarizationanisotropy with extension for a single random coil chain. With these assumptions and reasonable models for the completely uncoiled polystyrene chain it is possible to express any given birefringence as a percentage orientation.
Methods are developed for the experimental determination of the birefringence at a particular point in an oriented monofilament instead of the usual determination of an average birefringence through the monofilament. The application of these methods to actual examples leads to reasonable values of the orientation.
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 REGULAR CONTRIBUTED ORIGINAL RESEARCH


Transformation of Scattering Cross Sections
View Description Hide DescriptionA simple method is presented for the calculation of the transformation matrices between the Legendre polynomial expansion coefficients of the scattering cross section in the laboratory and center‐of‐mass systems. Approximate expressions for the matrices are given. Applications to transport problems involving the elasticscattering of neutrons are discussed.

Spurious Areas in Pole Figures
View Description Hide DescriptionSpurious maxima are frequently observed in pole figures determined by x‐ray diffraction techniques employing the Geiger‐counter spectrogoniometer. Their origin must be fully understood in order to avoid misleading interpretations of the pole‐figure data. By making film patterns and by the balanced filter technique—in each case with the specimen oriented for the appearance of one of the spurious peaks—these spurious maxima can be identified as diffraction of a component from the white radiation by a strongly diffracting (hkl) plane, and at a 2θ angle corresponding to K_{a} diffraction from the (hkl) plane under investigation. Spurious (110) and (112) peaks of this type may be observed in the (200) pole figure of iron and its alloys; spurious (111) and (220) peaks may appear in the (200) pole figure of face‐centered‐cubic metals such as nickel. These cannot be completely suppressed by filtering the Mo radiation used or by modifying the operating conditions such as tube voltage, spectrometer resolution, or counter type. Spurious (101̄1) peaks may appear in the (0002) pole figure of titanium and zirconium as the result of CuK_{ a } diffraction, and they can be avoided by increasing the resolution of the slit system.

Radiation from a Point Dipole Located at the Tip of a Prolate Spheroid
View Description Hide DescriptionThe radiation patterns of prolate spheroidal conductors, excited by an electric dipole in its tip, are calculated, for a number of spheroids of varying thickness, the wavelengths being equal to roughly π, π/2, and π/3 times their major axes.

Effect of Uniform Displacement on the Stress Distribution of a Wood Plate
View Description Hide DescriptionThe principle of virtual work was employed to determine the stress distribution in a wood plate subjected to a load distribution such as to effect a uniform displacement in the y direction.
The displacement u along x=±a developed an unexpected contour. The average value of u appears to occur near the ends. This cautions against the common practice of placing the instruments for measuring Poisson's ratio near the middle. In the case of isotropic material the unexpected contours still prevail but are barely perceptible.
The work was carried out for a fourth approximation (not presented) with sufficient accuracy to assure that the same contour was developing. These unexpected results were first observed in the laboratory of the U. S. Forest Products Laboratory, Madison, Wisconsin—an experience which prompted this theoretical confirmation.

Method of Averages and Its Comparison with the Method of Least Squares
View Description Hide DescriptionIt is shown, under fairly general conditions, that the standard deviation of the residuals of the straight line fitting a set of points with uniformly spaced abscissas by the method of averages is at most times as great as the standard deviation of the least‐squares line. Theorems of significance in the practical use of the method of averages are proven in the course of the analysis.

Effects of Cathode and Anode Resistance on the Retarding Potential Characteristics of Diodes
View Description Hide DescriptionAs a result of the processes of manufacture of tubes having oxide cathodes, high resistance layers often exist in the cathode and tube elements. This can produce anomalous retarding potential characteristics such as, for example, an apparently high electron temperature in diodes. By accounting for the effect of these resistances the apparent anomalies can be explained. Also given are the conditions required to minimize these errors and a method for evaluating the sum of these resistances.

Theory of Strong Electromagnetic Waves in Massive Iron
View Description Hide DescriptionA rigorous solution of Maxwell's equations is carried through for the case of a rectangular magnetization curve. Formulas for the depth of penetration and the wave impedance are derived yielding a theoretical power input formula which relates to the popular quasi‐theoretical formula of Rosenberg by just the factor 4/π.

PPI Light Spot Brightness Probability Distributions
View Description Hide DescriptionA mathematical study utilizing the statistics of noise theory is presented which derives light spot brightness probabilities for PPI target returns of various signal‐to‐noise ratios. An idealized model is employed which differs from similar previous ones by taking account of the cathode‐ray tube's highlight brightnessvs intensifier electrode voltage characteristic. For the 10KP7 cathode‐ray tube this characteristic obeys an approximate 2.5 power law in typical operation. This law, together with a square law second detector, combine to form an over‐all fifth power detector. The light spot brightness of the display is assumed to be formed by linear superposition of individual target returns resulting from the radarantenna scan. In the model, seven identical returns are so integrated.
Various mathematical methods of handling the problem are considered. The Edgeworth series approximation is found to give poor results compared with the Laguerre polynomial approximation. By the latter method the light brightness probabilities are found to be obtainable by interpolation from a table of the incomplete gamma function. Ancillary tables of statistical moments and selected values of the confluent hypergeometric function, _{1} F _{1}(−5n/2; 1; −x), are included in the text.

Direct Cellular Evaluation of the Density of States in Phase Space and the Accurate Calculation of Fermi Levels
View Description Hide DescriptionA new procedure for rigorously deducing the energy distribution of states, formulated upon a direct summing of cells in k space, provides a sound basis for assessing the classical approximation so familiar in statistical mechanics. It is thus established that the latter approach underestimates the density of states to the extent that the conventional Fermi energy calculation for electrons in metals is a few percent too high.

Focusing of a Long Cylindrical Electron Stream by Means of Periodic Electrostatic Fields
View Description Hide DescriptionThis paper presents a theory of focusing long cylindrical electron streams by means of electric fields which vary periodically along the stream. The use of a bifilar helix or a series of annular rings to produce periodic electric fields is considered.
The potential distribution at the position of the electrons is expanded in a power series, and an equation of electron motion is written. The solutions obtained indicate that the flow of electrons is essentially parallel, provided that the electrons enter the focusing structure practically without transverse velocities and are distributed across the stream such that the space charge fields decrease radially toward the axis in a manner similar to that of the periodic electric fields.
The method of periodic electrostatic focusing is of particular interest in connection with traveling wave tubes. The possibility of using a bifilar helix as both the slow wave and the focusing structure is discussed.

Transient Flow of Non‐Ideal Gases in Porous Solids—One‐Dimensional Case
View Description Hide DescriptionCalculations of pressure and production histories are presented for one‐dimensional flow of non‐ideal gases through porous media. The non‐ideal properties considered in this paper are the gas viscosity and deviation factor (compressibility factor) which are assumed to vary as simple functions of pressure. The effect of each of these parameters is investigated independently as well as in combination. The results demonstrate that pressure declines and production histories in linear gas‐flow systems are markedly influenced by variations in these parameters. Numerical solutions of the flow equations were obtained by solving the corresponding difference equations on an electronic digital computer.

The Effect of a Transverse Electric Field on Carrier Diffusion in the Base Region of a Transistor
View Description Hide DescriptionA solution for the density of minority carriers is obtained for a semiconductor device having a two‐dimensional rectangular geometry and a transverse field. The solution is developed for a variety of boundary conditions and the current‐gain factor α of the corresponding semiconductor devices is obtained from this solution.

Analyses of Basic Dielectric Amplifier Circuits
View Description Hide DescriptionDielectricamplifiers with high‐input impedance and low‐output impedance have high power gain and slow response. Analyses of two basic types of dielectricamplifier circuits, i.e., parallel and series, are given here. Both steady‐state and transient responses are studied.

Applications of the Dirac Delta Function to the Evaluation of Certain Integrals
View Description Hide DescriptionThe evaluation of certain integrals is attained by use of ordinary linear differential equations having inputs that depend on the Dirac delta function. The method is illustrated by several examples.

Compression Wave Velocity Experiments with Copper
View Description Hide DescriptionA method for obtaining experimental compression wave velocities in metals is described. Measurements of the compression wave velocity in copper were made and found to be in good agreement with theoretical predictions. It is suggested that the discrepancy between the velocity (4730 m/sec) reported herein and that reported by Rinehart and Pearson (3600 m/sec) is associated with the different geometries of the two sets of experiments.
