Volume 20, Issue 6, 01 June 1949
Index of content:

Propagation of Audiofrequency Sound in High Polymers
View Description Hide DescriptionVelocity and attenuation measurements were made in thin strips of rubber from 0.5 to 5 kc and from −5°C to 90°C to obtain the dynamic viscoelastic constants of butyl and GR‐S gum stocks. Above room temperature velocity and attenuation are higher in butyl gum than in GR‐S. In all cases, the velocity increases with decreasing temperature and increasing frequency. The attenuation shows a peak with temperature. For butyl the peaks are broad and occur at higher temperatures than for GR‐S. For both stocks an increase in frequency gives peaks which are higher and sharper, and shifted to higher temperatures. In some instances, there are indications of peaks in the attenuation versus frequency at frequencies beyond our range of measurement. The behavior of the dynamic modulus in the temperature and frequency range studied is similar to that of the velocity. These results combined with low temperature static measurements and very low frequency dynamic measurements indicate a U‐shaped modulus‐temperature curve whose minimum broadens and shifts to higher temperatures with increasing frequency. This may be explained by a generalization of the kinetic theory of rubber elasticity, taking into account intra‐ and intermolecular forces, and considering time effects.

Propagation of Ultrasonic Bulk Waves in High Polymers
View Description Hide DescriptionThe propagation of supersonic waves in bulk rubbers has been studied from 40 kc/sec. to 10 Mc/sec. and from −60°C to 60°C. The wavevelocity was found to increase with decreasing temperature, leveling off both at high and low temperatures, and was found to increase slightly with frequency. Peaks in attenuation as a function of either temperature or frequency were observed, the peaks occurring at lower temperatures for lower frequencies. The peaks for butyl, a high loss rubber, are broader and higher than those for GR‐S and Hevea, which are lower loss rubbers. The results are in qualitative agreement with data obtained by strip methods at audiofrequencies. However, for bulk waves the real and imaginary parts of two elastic constants, the bulk and shear moduli, determine wavevelocity and attenuation; hence, independent measurements of shear waveproperties are necessary to evaluate these constants. A three constant theory is discussed, assuming a shear viscosity only, so that an effective modulusK+4μ/3 is obtained, where K and μ are the bulk and shear moduli.Relaxation times of the order 10^{−6} to 10^{−8} second are indicated. Approximate values of the dynamic Young's modulus are obtained from the effective modulus by assuming that the high frequency dispersion is due to the appearance of a ``crystalline'' shear elasticity. These results are correlated with low frequency data, and the dynamic Young's modulus and the loss factor are plotted. The loss factor exhibits a maximum in the dispersion region. Results are plotted in the range from 1 c.p.s. to 10^{7} c.p.s., which covers a wider range of frequency than earlier investigations. The necessary distribution of relaxation times is discussed.

Dynamic Measurements of Polymer Physical Properties
View Description Hide DescriptionDynamic methods for measuring the elastic and dissipative properties of high polymers in fiber and film form over four decades of frequency (3 to 30,000 cycles per second) are described. The experimental quantities resulting from the three different techniques necessary to cover this range are unified by deriving in each case the parameters of an equivalent Voigt Model (elastic and viscous element in parallel) which would behave in the same way as the polymer sample. Examples of the application of these techniques to the characterization of high polymers are given. The effect of frequency and chemical and physical structure on the derived parameters are discussed, along with the question of heat losses resulting from cyclical differential deformation. In addition, the application of two of the methods to the characterization of the stiffness‐temperature behavior of high polymers is described.

Equation of State for Polystyrene
View Description Hide DescriptionPractical considerations emphasize the desirability of formulating an adequate equation of state for polystyrene. A fairly satisfactory one is this simplified version of van der Waals' equation,where π is the internal pressure (or cohesive energy density) and ω is the volume at absolute zero, by extrapolation. Evaluating constants from thermal expansion data and expressing P in p.s.i., V in cc per gram, and T in degrees Kelvin, this becomesAgreement with compressibility measurements, which are described in some detail, is good. Discrepancies with room temperature values of sound velocity and cohesive energy density by swelling measurements are discussed briefly.

Creep and Damping Properties of Polystyrene
View Description Hide DescriptionThe anelastic behavior of polystyrene has been studied by means of creep tests under long‐time load application and by means of damping capacity tests under rapidly varying repeated loading. Tensile creep data taken at various stress amplitudes reveal that the log of the creep rate (at 1000 hours) varies linearly with the log of the stress amplitude. A similar type of variation is obtained when damping capacity or energy absorbed per cycle is plotted against stress amplitude. From these two sets of data, the creep rate is found to be proportional to the square of the damping capacity. It would thus appear possible, for polystyrene at least, to predict 1000‐hour creep rates from short‐time measurements of absorbed energy under dynamic loading conditions.
The data obtained from the creep and damping tests, together with additional data from short‐time tension and compression tests, seem to be consistent with an internal structure in which the linear polymer chains and groups of chains are in ordered or partially extended positions, but in which, in the absence of stress, no preference is shown for any particular direction. Under the action of stress—particularly if the stress is maintained for a long period of time—a tendency exists for the ordered regions to orient in the direction of the applied stress. The so‐called ``crazing'' condition which has been observed to occur in the creep specimens is probably a manifestation of this orientation. X‐ray evidence appears to support this point of view.

Scattering by an Inhomogeneous Solid
View Description Hide DescriptionA general treatment of the scattering of radiation by an inhomogeneous material is developed. It is shown how scattering measurements can be used to obtain the average square of the fluctuations in refractive index or electron density and a correlation function which measures the degree of correlation between two fluctuations as a function of their distance of separation.
The scattering of visible light by Lucite and two glass samples has been investigated. The data are analyzed in terms of the quantities mentioned above. It is found that the extensions in space of the inhomogeneities in the Lucite sample are much greater than those in the optical glass samples investigated. The magnitudes of the fluctuations in refractive index are found to be dependent on the composition of the sample.

Relationship between Gough‐Joule Coefficients and Moduli of Vulcanized Rubbers
View Description Hide DescriptionThe Gough‐Joule coefficients (a) at constant stress and (b) at constant strain are defined and methods of measurement of each on vulcanized rubbers are given. It is shown mathematically and experimentally that the ratio of (b) to (a) is equal to the ``tangent'' modulus. The quotient of the Gough‐Joule coefficient at constant stress divided by the stress and the quotient of the Gough‐Joule coefficient at constant strain divided by the strain are shown to be constants which are independent of the stress‐strain‐temperature conditions of the test. Experimental data are given for stocks based on Hevea, GR‐S, Neoprene GN, Butyl Rubber, and Butaprene.

Polymerization in the Solid State
View Description Hide DescriptionThe melting point of ε‐carbobenzoxy‐α‐carboxyl‐l‐lysine anhydride stored at room temperature for one year (I) rises considerably above that of the freshly prepared compound (II) (m.p. 100°). X‐ray diffraction studies indicate: (II) is probably monoclinic, a≃90A, b=5A, c≃10A; (I) suffered disorientation giving diagrams similar to those of bulk polymer (III); threshold conditions for the disorientation process are heat‐treatment of (II) at 70° for 24 hours; the change appears to be complete when (II) is heat‐treated at 85° for 24 hours since the diagrams are similar to those of (III) and no further change is observed in the diagrams of samples treated under more severe conditions below the melting point. The largest Bragg spacing of 29A observed for (II) is of the same order of magnitude as the over‐all length of a fully extended hydrogen‐bonded dimer of (II). The smallest refractive index of (II) is parallel to the b axis. The structure of (II) is concluded to be a triple dimer layer arrangement which would involve a relatively small entropy change on polymerizing in the solid state to give (I) and (III).

Time and Stress Effects in the Behavior of Rubber at Low Temperature
View Description Hide DescriptionThe stiffening of rubber‐like materials at low temperature involves several different phenomena, sometimes with their effects superimposed. One of these is crystallization. This is a rate process which is generally very fast at high stresses and very slow at zero stress. In these experiments at temperatures near −25°C and under a shear stress of about 148 p.s.i. the dynamic modulus of the rubber increased at a rate convenient to study. Correlation with x‐ray data showed that crystallization was very likely responsible for the increase in stiffness. The rate of change of stiffness increased rapidly with increase in applied stress, and there was no optimum rate at −25°C as has been found for unstressed rubber. The degree of vulcanization influenced the rate of change, tighter cures giving smaller changes. Neoprene FR, GR‐S and polybutadiene, which ordinarily show little evidence of crystallization showed very definite, but small increases in stiffness. Mixing GR‐S with natural rubber seems to limit the crystallization of the natural rubber rather effectively, but apparently Neoprene FR does not mix intimately enough with natural rubber to affect the crystallization of the latter appreciably.

The Compatibility, Efficiency and Permanence of Plasticizers
View Description Hide DescriptionThis paper attempts to interrelate three important aspects of plasticizer behavior: compatibility or how much plasticizer can be added without causing phase separation;efficiency, or how much a given amount of plasticizer lowers the brittle temperature; and permanence, or how well a plasticizer is retained by the polymer on heat aging or solvent treatment.
Compatibility is discussed in terms of the Flory‐Huggins theory of the thermodynamics of polymer solutions, which relates the activity of the plasticizer to its concentration in the polymer. Efficiency is measured by how the plasticizer lowers the melt viscosity of the polymer. An empirical relationship between efficiency and μ (the Huggins polymer‐solvent interaction constant) is shown. Loss of plasticizer at elevated temperatures depends in part on the effective vapor pressure of the plasticizer, and in part on how rapidly diffusion of plasticizer from the interior of the sample replenishes that lost from the surface. From the fact that diffusion constant times viscosity is a constant, it is possible to correlate measureddiffusion rates with plasticizer content and with plasticizer efficiency. A linear relationship is predicted and found experimentally between logarithm of the diffusion constant and the brittle temperature. In this sense, the more efficient a plasticizer is, the more rapidly it can diffuse out of the polymer and be lost. Consideration is given to the effect of plasticizer on electrical resistance and tensile strength. A preliminary discussion of polymeric plasticizers is presented.

X‐Ray Diffraction Studies of the Stretching and Relaxing of Polyethylene
View Description Hide DescriptionThe orientation of the crystallites when polyethylene is stretched at 96°C is normal in that, from the onset of stretching, the preferred orientation is that wherein the long chain axis is parallel to the direction of stretch. At low extensions the preference for this orientation is weak, but it progressively becomes stronger as stretching proceeds.
When polyethylene is stretched at room temperature, the crystallite behavior is more complicated. The first 20 percent extension produces no preferred orientation of the crystallites. From 30 percent to 200 percent extension the preferred orientation is that wherein the 011 ``axis'' is parallel to the direction of stretch, and the long chain axis therefore inclined to this direction at an angle of 64°. From 200 percent extension to the break (about 600 percent extension), the tilt of the crystallites in the preferred orientation progressively lessens and almost vanishes at the break. The stress‐strain diagram of polyethylene is interpreted in the light of these findings. The preferred orientation of the crystallites in the region of the shoulder in necked‐down polyethylene is also that wherein the 011 ``axis'' aligns with the stretching direction.
When stretched polyethylene is relaxed by shrinking at elevated temperatures, the crystallites become disoriented but in a non‐random manner. This behavior is described qualitatively.

Infra‐Red Absorption Spectra of Some Polymers at Liquid‐Helium Temperatures
View Description Hide DescriptionInfra‐red absorption spectra of polythene, rubber, polystyrene and polyvinyl chloride have been obtained at 4° absolute, in the rocksalt region, in a specially designed transmission cell containing liquid helium. No unusual changes occur on cooling which considerably alter the absorption. Some sharpening and improvement in resolution occurs, but the widths of most bands in polymers remain wide.
In polythene one component of the doublet at 720 cm^{−1} becomes very sharp (possibly even less than the experimental value of the slit width, 1 cm^{−1}). Its companion remains broad, about 4 cm^{−1}. The two components are interpreted as CH_{2} wagging in trans‐ and cis‐configurations of the hydro‐carbon chain.

Dilatometric Studies of High Polymers. I. Second‐Order Transition Temperature
View Description Hide DescriptionBy means of a density balance, the relationship between intrinsic viscosity and dilatometric properties is established for polyethylene terephthalate. The most pronounced property change associated with increasing intrinsic viscosity was observed to be the second‐order transition temperature. The relationship between crystallinity and dilatometric properties is presented for 3 aromatic polyesters. In every case, increased crystallinity in the polymers is associated with higher second‐order transition temperatures, larger transition range, higher density, and lower volume coefficients of expansion. Second‐order transition temperatures, densities at 0°C, and volume of coefficients of expansion are presented for a number of polyesters and vinyl polymers to illustrate the effects of chemical structure as well as physical state on these dilatometric properties. Illustration of the effect of copolymerization on second‐order transition temperatures is made with a copolyester system.

Dilatometric Studies of High Polymers. II. Crystallization of Aromatic Polyesters
View Description Hide DescriptionBy means of both a density balance and gradient tube, experimental density data are obtained to illustrate the thermal crystallization behavior of 3 aromatic polyesters at temperatures from 90°C to 150°C. The data are discussed with reference to both amount and rate of crystallization and density curves are presented to show qualitative similarity between kinetics of polymercrystallization and the kinetics of chemical reactions. From the experimental data, a temperature, for convenience labeled the minimum crystallization temperature, is described and is shown to be 30° to 50° above the second‐order transition temperature for the polyesters. In addition to thermal crystallization, data are presented to show that immersion media may initiate crystallization below the minimum temperature associated with thermal crystallization of polymers.Liquids used as immersion media for polyethylene terephthalate were water, methyl alcohol, acetone, benzene, nitromethane, and nitric acid. The last four liquids initiate crystallization of the polymer at room temperature.

Notes on the Excitation of Electromagnetic Waves in Cylindrical Metallic Wave Guides
View Description Hide DescriptionIn this paper very simple formulas are deduced for calculating the amplitude of modes produced in a cylindrical guide when the currents distribution is known. One example is included.

Use of a Mechanical Harmonic Synthesizer in Electric Wave Filter Analysis
View Description Hide DescriptionA mechanical method is described for graphing the effect of the variation with frequency of the series reactance (X _{1}) and the shunt reactance (X _{2}) of a filter section. This method permits the quantities X _{1}/−4X _{2}, X _{1} X _{2}{(X _{1}/−4X _{2})−1} and X _{1} X _{2}/{(X _{1}/−4X _{2})−1}, from which the characteristics of an electric wave filter are calculated, to be graphed easily as a function of frequency. The cut‐off frequencies are located directly from the graphs of N and D (where N/D is either the ratio X _{1}/−4X _{2} or (X _{1}/−4X _{2})) as functions of frequency, and the calculation of the attenuation and phase shift at any frequency is readily made from the ratio of corresponding ordinates of the N and D curves. The image impedance is determined from the ratio of corresponding ordinates from two additional curves which are mechanical plots of the numerator and the denominator of the expression for the square of the image impedance, X _{1} X _{2}{(X _{1}/−4X _{2})−1} for the mid‐series image impedance, and X _{1} X _{2}/{(X _{1}/−4X _{2})−1} for the mid‐shunt image impedance.

Barkhausen Noise and Magnetic Amplifiers. II. Analysis of the Noise
View Description Hide DescriptionThe Barkhausen noise is calculated for ferromagnetic cores used in magnetic amplifiers. The method of analysis follows that used in the analysis of the shot effect. The signal‐to‐noise ratio for a typical magnetic amplifier circuit is calculated and compared with experiment.

Elasticity of Zinc Crystals
View Description Hide DescriptionYoung's modulus,E, has been measured by dynamic and static methods for 25 zincsingle crystals. The results fit a parabolic curve when 1/E is plotted against the square of the cosine of the orientation. From the constants of this curve and earlier data on linear compressibility by Bridgman, are derived numerical values for the coefficients of compliance of the zinc crystal, as follows: S _{11}=8.38, S _{12}=0.5, S _{13}=−7.31, S _{33}=28.4, S _{44}=26.1, all ×10^{−13} cm^{2}/dyne.
Data on three crystals were taken from room temperature to 375°C. From these may be computed Young's modulus for any orientation and any temperature in the range given. Young's modulus decreases for all orientations with increasing temperature.

Electric‐Field Modulation of Ultrasonic Signals in Liquids
View Description Hide DescriptionAn experiment is performed to determine whether the presence of a periodic transverse electric field produces modulation, either of amplitude or of phase, of a continuous progressive ultrasonicwave train passing through the liquid. One object of the experiment is to ascertain whether the application of an electric field to a polar liquid influences either the compressibility or the viscosity of the liquid through molecular orientation. The results of a related investigation in which an electric field was applied in the direction of wave travel, published in 1945 by Barone and Giacomini, were inconclusive. The present experiments reveal phase modulation in a number of conducting liquids. This is explained as a thermal effect involving the temperature dependence of velocity of sound. No evidence is found of phase modulation resulting from dipole orientation in non‐conducting polar liquids. Amplitude modulation, which would result from change of attenuation, is not found in any liquid. A variety of organic liquids is investigated. Limits of sensitivity of the apparatus are given.

Inter‐Particle Interference Effects in the Small Angle X‐Ray Scattering from Fine Powders
View Description Hide DescriptionSimple formulas for calculating the small angle x‐ray scattering from aggregates of identical spherical particles, taking into account the interference between different particles, are given. The case of independent clumps of particles and the case of a more general arrangement describable by a radial density function are considered. Calculated curves of scattered intensity vs. angle for likely arrangements of both types are presented. The assumption that each particle scatters independently is seen to be a poor approximation whenever there is a significant amount of clumping or whenever the average density of the sample is as much as one third of the density corresponding to close packing. Estimates of particle size from the small angle scattering are shown to be seriously affected.