Volume 24, Issue 6, 01 June 1953
 RHEOLOGY SYMPOSIUM


Annual Meeting of the Society of Rheology at the Franklin Institute, Philadelphia, October, 1952
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Effects of Nuclear Radiations on the Mechanical Properties of Solids
View Description Hide DescriptionThe general nature of radiation effects in solids is reviewed briefly. Current theoretical understanding of the mechanical properties of solids is critically evaluated. The effect of nuclear radiation on the mechanical properties is discussed in detail. It is shown that the changes in the mechanical properties of crystalline substances (mostly metals) can be quite satisfactorily interpreted on the basis of the production of interstitial atoms and vacant lattice sites by fast particleirradiation. Isolated vacancies and interstitials may not be able to account for all the observations, and attention is called to the possible need of postulating the existence of aggregates of these lattice defects. In molecular solids (mostly high polymers) nuclear radiations bring about changes in the substance which are best described as chemical ones. Ions and free radicals are formed leading to subsequent chemical reactions thereby altering the properties of the substance. Drastic changes in the mechanical properties of high polymers are observed. Correlation with structural changes has hardly been started. Experiments are suggested which, in the writer's opinion, should give further insight into the fundamental processes involved.

A Test of the Theory of Secondary Viscoelastic Stress
View Description Hide DescriptionExperimental data published by Garner, Nissan, and Wood on secondary stresses in a viscoelastic liquid have been analyzed in terms of the superelasticity theory of secondary stresses as developed by Mooney. The theory was slightly modified to be consistent with the reported viscosity rate of shear behavior of the test liquid. With this modification the theory agreed within experimental error with observed normal stresses at various radii on a stationary circular plate mounted parallel to a rotating plate.
One reported qualitative experimental result is in disagreement with the theory, but this particular result is questioned. Other theories of secondary stress are briefly discussed.

Dynamic Mechanical Properties of the System Polystyrene‐Decalin
View Description Hide DescriptionThe dynamic rigidities and viscosities of solutions of polystyrene (number‐average molecular weight 197 000) in decalin have been measured by three experimental methods over ranges of concentration from 10 to 62 percent, of temperature from −5° to 50°C, and of frequency from 30 to 2000 cps. Similar measurements were made on the undiluted polystyrene from 115° to 133°C and 30 to 2800 cps. The data for the solutions, when reduced to a reference state of unit density and viscosity at a standard temperature, provide single composite curves for dynamic rigidity and viscosity. The distribution function of relaxation times calculated from these curves overlaps that previously derived from stress relaxationmeasurements on this system, and the combined function covers a range of time scale of ten powers of ten. It shows the three characteristic regions previously identified in the relaxation distribution function of polyisobutylene; there are no obvious anomalies associated with the fact that decalin is a very poor solvent for polystyrene. The data for the undiluted polymer, when reduced to a standard temperature, provide single composite curves for dynamic rigidity and viscosity. The temperature reduction factors provide apparent energies of activation for relaxation which agree with those for viscous flow obtained by Fox and Flory. The relaxation distribution function of the undiluted polymer is similar in shape to, but somewhat sharper than, those for other polymers in the transition from soft to glassy consistency. When reduced to a reference state of unit density and viscosity, the distribution function of the undiluted polymer lies near that reduced from data on solutions, but is considerably sharper than the latter.

Mechanical Investigations of Elastomers in a Wide Range of Frequencies
View Description Hide DescriptionA method has been found for measuring the shear moduli and losses of elastomers in a range of frequencies of about 1 to 10^{6}, from 10 cps down. This method provides for large cyclic shear stresses and deformations without employing resonance methods. Only one sample is needed for a complete study, the frequency of stress being the only variable. The method gives results that fit the ``box‐distribution function'' developed by Kuhn and Kuenzle. Results for a series of elastomers show that such investigations are important in ascertaining the mechanical properties of elastomers in practice.

Viscoelastic Properties of Dilute Polymer Solutions
View Description Hide DescriptionThe viscoelastic properties of dilute solutions of chain polymers have been measured at frequencies in the range from 200 cps to 60 kc. The data are compared with theoretical curves calculated from the steady‐flow viscosities of the solution and solvent, the molecular weight and concentration of the polymer, and the absolute temperature; this calculation made use of equations obtained from a recently developed theory. The equations contain no adjustable constants. The theory is shown to be at least a good first approximation to the viscoelastic properties of the solutions studied.
The agreement of the data and the theory implies that, up to 60 kc at least, the viscoelastic properties of dilute solutions of polystyrene and polyisobutylene are the result of the thermal motions of the segments of the polymer molecules. These segmental motions coordinate with one another to produce changes in the configurations of the molecules. The configurational changes have associated with them a series of relaxation times. These relaxation times are shown to depend upon molecular weight of the polymer, concentration, type of solvent, and viscosity of solvent.

Temperature Coefficients of Non‐Newtonian Viscosity at Fixed Shearing Stress and at Fixed Rate of Shear
View Description Hide DescriptionViscosity decreases with increasing shearing stress or rate of shear in the non‐Newtonian flow of high polymeric systems. It is shown that it follows from this fact that the variation of viscosity with temperature is greater at fixed shearing stress than at fixed rate of shear.
For such systems, it is shown experimentally that the variation of viscosity with temperature at fixed shearing stress is independent of shearing stress. However, the variation at fixed rate of shear is always less than that at very low shearing stress, and decreases with increasing rate of shear.
This behavior is reproduced by Eyring's hyperbolic sine flow equation, which is the antecedent for most other, more adequate, non‐Newtonian flow equations. However, this equation is shown to be inadequate in that it predicts incorrect values of shearing stress for the occurrence of non‐Newtonian behavior.

Effects of Rate of Shear on Inherent and Intrinsic Viscosities of Polystyrene Fractions
View Description Hide DescriptionFractions of polystyrene, varying in molecular weight from 0.3×10^{6} to 10×10^{6} approximately, were prepared by careful tertiary fractionation. Inherent viscosities were determined at various rates of shear in the approximate range 100–20 000 sec^{−1}, viscosity measurements being made at several different temperatures in benzene and toluene (good solvents for polystyrene), in butanone (an intermediate solvent), and in cyclohexane (a poor solvent). From these values intrinsic viscosities at various rates of shear were determined. These viscosity functions are sensitive to shear rate at high molecular weights; at a given temperature the shear effects are greater the higher the molecular weight and the better the solvent, and with increasing temperature they decrease in a good solvent and increase in a poor one This behavior is shown to be consistent with current ideas regarding the size and shape of polymer molecules in solution as affected by weight, temperature, and solvent power. It is concluded, among other things, that with flexible polymers (or polymer fractions) of very high molecular weight, measurements of intrinsic viscosity should be made in a poor solvent at a low temperature.

Anomalous Viscous Flow at Very Low Rate of Shear and Small Shearing Stress
View Description Hide DescriptionFluid suspensions of a solid phase in a liquid, for example, paints and printing inks, have been presumed to exhibit anomaly of flow at very low rate of shear. The consistency characteristics of such materials require an experimental shear rate and shear stress much lower than has heretofore been reported.
This paper describes a translated cylinder, or translational, viscometer of a modified Pochettino type, which possesses a shear stress sensitivity of 5×10^{−3} dyne/cm^{2}, and a shear rate sensitivity of 1×10^{−4} sec^{−1}. A rubber Latex of high solids content exhibited no anomaly of flow within this range of sensitivity. A rubber dissolved in organic solvent was observed to approximate a Bingham material of 0.05‐dyne/cm^{2} yield value, while a gum tragacanth suspension in water exhibited a yield value of 0.4 dyne/cm^{2} with marked post‐yield anomalous flow. Household paints exhibited yield value ranging from zero to 6 dyne/cm^{2}. These yield values were related to leveling‐out of brushmarks, and to sagging or ``curtain,'' except for examples exhibiting marked thixotropic behavior. Industrial organosol coatings likewise possessed yield values ranging up to 5 dyne/cm^{2} which were related to leveling characteristics. These yield values agree with those postulated by Waring from consideration of the forces of leveling of brushmarks. They are considerably smaller than those reported in the literature from extrapolation of flow curves from much higher rate of shear.
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 REGULAR CONTRIBUTED ORIGINAL RESEARCH


Signal‐to‐Noise Ratios in Band‐Pass Limiters
View Description Hide DescriptionA general analysis is made of the relations between output signal and noise powers and input signal and noise powers for band‐pass limiters having odd symmetry in their limiting characteristics. Specific results are given for the case where the limiter has an nth root characteristic, and they include the ideal symmetrical limiter (or clipper) as a limiting case. This analysis shows that, for the band‐pass limiter, the output signal‐to‐noise power ratio is essentially directly proportional to the input signal‐to‐noise power ratio for all values of the latter. This result is due to the band‐pass characteristics rather than to the symmetrical limiting action.

Space Charge Requirements in Some Ideally Focused Electron‐Optical Systems
View Description Hide DescriptionA selected set of points on the trajectories of charged particles traversing an electron‐optical system may be considered to be an object space, and another set an image space. Electron‐optical lenses are said to be ideally focused if the transformation of the points in object space to those in image space is one to one and continuous. A necessary condition for ideal focusing is used to prove that a number of electron‐optical systems require the presence of space charge in order to be ideally focused. Expressions for some ideally focused electron‐optical lenses are given, in particular those for cylindrical lenses without space charge derived from spherical lenses with space charge.

An Investigation of Boron Carbide
View Description Hide DescriptionMixtures of boron and carbon were heated at approximately 2000°C; the reaction products have been studied by x‐ray diffraction and by density and electrical measurements. The existance of a wide range of homogeneity of ``boroncarbide'' has been established. No evidence of compound formation corresponding to B_{4}C could be detected. Similarities between the structures of boron and ``boroncarbides'' indicate that the latter may best be described as solutions of varying amounts of carbon in a slightly distorted boron lattice.

The Creep of Zinc Single Crystals under Direct Shear
View Description Hide DescriptionRoom temperature measurements on very pure specimens verify the Tyndall law, s=at^{m} , which was determined by tensile measurements. The value of m is approximately 0.6. Discrepancies in tensile creep tests reported by other observers are shown experimentally to be caused most probably by bending of the specimen during the creep process. The Bauschinger effect has also been investigated and creep at the very small stresses needed appears to follow the same creep law.

Tolerance Coefficients for R‐C Networks
View Description Hide DescriptionA method is presented for the calculation of the departure of actual network behavior from design characteristics attributable to the use of nonideal components. The method yields a set of tolerance coefficients relating percentage changes in the positions of the zeros and poles of the network function to percentage changes in the network components. Once this information is available, changes in gain or phase are easily determined.

Simplification for Mutual Impedance of Certain Antennas
View Description Hide DescriptionThe formula for mutual impedance by the generalized circuit method is reduced to a form which greatly reduces the number of integrations required in determining the mutual impedance of various combinations of open wire and terminated wire antennas. The application is illustrated by finding the mutual impedance of the legs of an open wire X‐antenna, the latter being equivalent to the radiation impedance of a biconical antenna, and for small angle cones reduces to a form from which Schelkunoff's inverse terminal impedance may be determined.

Mutual Impedance of Rhombic Antennas Spaced in Tandem
View Description Hide DescriptionUpon examining the formulas for self‐ and mutual impedances of antennas, it is found that while the mutual impedance formula for separately driven collinear standing wave antennas may be used directly in determining the radiation impedance when such antennas are connected in cascade, certain modifications must be made in the case of traveling wave antennas under similar circumstances. Accordingly, formulas are derived for rhombic antennas spaced in tandem and are modified to permit the determining of the radiation impedance of two identical rhombic antennas connected in cascade.

Slot Coupling of Rectangular and Spherical Wave Guides
View Description Hide DescriptionA dominant‐mode wave guide radiating through a slot into a half‐space may be regarded from a network viewpoint, with the half‐space represented by a number of spherical transmission lines, the wave‐guide feed by a single uniform transmission line and the slot by a coupling network. This paper contains (a) an investigation of how many spherical transmission lines are necessary to represent adequately the far field (gain pattern) of the slot antenna, and (b) an approximate theoretical evaluation (by a variational calculation) and experimental check of the equivalent circuit parameters of a slot‐coupled junction of a rectangular and spherical wave guide, when the far field can be well represented by the dominant spherical mode. The results are useful in connection with a method of measuring the electromagnetic scattering properties of obstacles located in a half‐space illuminated by a wave‐guide‐fed slot antenna.

Determination of the Drag on a Cylinder at Low Reynolds Numbers
View Description Hide DescriptionDrag coefficients for a cylinder were measured at Reynolds numbers from 0.06 to 6.0 by observing the deflections of thin wires suspended in an air stream. The results confirm a theoretical equation proposed by Lamb and are consistent with experimental data of other investigators.

Charged Disk in Cylindrical Box
View Description Hide DescriptionThe mixed boundary value problem of the potential inside a cylindrical conducting box of radius a and height 2c in which is mounted coaxially and concentrically a thin flat charged conducting disk of radius b is solved approximately. A formula for the coefficients in the Bessel function potential series is derived which is valid for c>¼a and b<¾a. The boundary conditions are met rigorously except that the disk is not quite flat. Figures show its deviation for twelve parameter values. A formula for narrow gaps is derived. Upper and lower limits for the capacitance for twelve parameter values are tabulated.

The Darlington Problem
View Description Hide DescriptionAny RLC transfer function with an even or odd numerator is realized as the transfer voltage ratio of a Darlington network, where such a network is defined as one containing lossless elements plus only one resistance. The single resistance appears within the network, and the termination is thus lossless. An unbalanced network that contains no mutual inductance is achieved by the procedure. The method makes use of Norton's theorem, zero shifting, and the paralleling of ladder networks. The number of ladders and elements required in the realization is kept small by a technique demonstrated in the paper.
