Volume 27, Issue 7, 01 July 1956
 SPECIAL ISSUE ON RHEOLOGY OF POLYMERS


Stress Analysis in Viscoelastic Materials
View Description Hide DescriptionThe problems of stress analysis for linearly viscoelastic materials are considered. This is the simplest group of materials which exhibit the general stress‐strain characteristics found in polymers and plastics. Three basic aspects are considered: measurement of material properties, determination from these of the operator equations between stress and strain or equivalently of the viscoelastic model, and use of this in the theoreticalanalysis of stress distributions. Quasi‐static analysis, in which inertia forces are negligible, is treated quite generally. The wave problems which arise when inertia effects are included are restricted to one‐dimensional space variations. A series of typical solutions of these types is discussed.

Stress Relaxation Studies of the Viscoelastic Properties of Polymers
View Description Hide DescriptionExtensive studies of the viscoelastic properties of polymers undertaken in the author's laboratory by means of the method of stress relaxation are here reviewed. The discussion is divided into four parts: chemical stress relaxation,stress relaxation in amorphous polymers,stress relaxation in crystalline polymers, and stress relaxation in certain natural polymers and polyelectrolytes. Mathematical description of the phenomena are presented in simple form. The relation between structure and viscoelastic properties of polymers are discussed and a rather complete over‐all picture of these phenomena seems to be emerging.

Stress Relaxation in Concentrated Solutions of Polymethyl Methacrylate: Molecular Weight Dependence
View Description Hide DescriptionThe measurement of stress relaxation in concentrated solutions of polymethyl methacrylate has revealed a relation between the spectrum of relaxation times, the weight average molecular weight, and the molecular weight distribution. The spectrum of relaxation times and the essentially identical theories developed by Rouse, Bueche, and Zimm are used to calculate an average relaxation time which is directly proportional to the weight average molecular weight. It is then shown that a first approximation to the distribution of molecular weights may be calculated if one assumes that the friction factor increases with the 1.5 power of the molecular weight. This distribution for selected samples of polymethyl methacrylate is compared with the Schulz distribution in which the parameters were obtained from light scattering and osmotic pressure experiments. The ratios M_{z}/M_{w} calculated from the theory and stress relaxation data on a rough fraction, a whole polymer, and a blend of two whole polymers are found to be 1.3, 1.7, and 1.9, respectively.

Theory of the Non‐Newtonian Rheology of Raw Rubbers Consisting of Supermolecular Rheological Units
View Description Hide DescriptionA theory of the viscosity of raw rubbers is developed on the postulate that raw rubbers, when subjected to continuous shear in the non‐Newtonian region of flow, consist of microscopic rheological units which are semipermanent aggregates of many rubber molecules [M. Mooney and W. E. Wolstenholme, J. Appl. Phys. 25, 1098 (1954)]. The theory treats these units as tacky, elastic solids, whose relative movement and slippage constitute the macroscopic flow of the rubber. The resulting theoretical flow curve differs little from that given by H. M. Smallwood [J. Appl. Phys. 8, 505 (1937)], but the interpretation of the parameters is radically different. The new theory leads to expressions for the number of temporary point attachments per unit area between two touching rheological units and for the mean life of these attachments.
Agreement with experimental data is slightly better than in Smallwood. Two types of observed deviation from the theory can be interpreted as due to two plausible phenomena not included in the mathematical treatment.
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 REGULAR ARTICLES


Scattering of High‐Energy Gamma Rays
View Description Hide DescriptionThe scattering of 16‐Mev bremsstrahlung by 3, 6, and 9 in. of iron was measured for small angles using a thallium‐activated sodium‐iodide scintillation counter. The experimental results closely fitted a theoretical curve calculated on the basis of single scattering.

Turbulent Mixing Theory Applied to Radio Scattering
View Description Hide DescriptionObukhoff's statistical theory of turbulent mixing is proposed as a replacement for the heuristic theories of Gallet and Villars‐Weisskopf, and is applied to the problem of the scattering of radio waves by refractive indexfluctuations. In the case of ionospheric scattering, order‐of‐magnitude agreement with the observed scattered power is obtained if the refractive indexfluctuations are attributed to electron density fluctuations produced by turbulent mixing in the lower edge of the E layer. In the case of troposphericscattering, it appears that order‐of‐magnitude agreement with the observed scattered power can be obtained, except during the summer months, by attributing the refractive indexfluctuations to temperaturefluctuations. During the summer months and at low scattering heights, humidity and its fluctuations are expected to play a prominent role. Experimental and theoretical evidence is cited in favor of perennial fractional‐degree temperaturefluctuations in the troposphere. A comparison of the Obukhoff, Villars‐Weisskopf, and Booker‐Gordon models is given, and it is found that the Obukhoff model predicts the most scattered power.

Upper‐Air Density and Temperature by the Falling‐Sphere Method
View Description Hide DescriptionUpper‐atmosphere air densities and temperatures have been calculated from the measured trajectory data of a falling sphere. Densities were calculated from the equation for the drag force on the falling sphere, and temperatures were then obtained by using the hydrostatic equation and the equation of state of a perfect gas. The aerodynamic background and instrumentation are described; the method of calculation and the errors are discussed. The results of four rocket flights which carried the experiment are given. Comparison with the average of other rocket measurements indicates agreement with these results.

Effects of Neutron Irradiation upon the Young's Modulus and Internal Friction of Copper Single Crystals
View Description Hide DescriptionMeasurements of neutron irradiation effects upon the Young's modulus and logarithmic decrement of a set of coppersingle crystals of 99.999% purity have been made at room temperature. Interpretations of the results can best be given in terms of an oscillating dislocation line mechanism in which the oscillations are suppressed by the presence of interstitial atoms, vacancies, or some combination thereof. Comparisons of the results with the predictions of impurity line pinning are given. It is shown that an interpretation in this sense leads to generally accepted values for the dislocation densities and average segment lengths.

Nickel Copper Ferrites for Microwave Applications
View Description Hide DescriptionFerrites having both high relative density (∼98%) and high dc resistivity (>10^{9} ohm‐centimeters) can be prepared by properly sintering nickel copper ferrites which have both an iron deficiency and a small amount of manganese or cobalt present. Magnetic saturation at room temperature shows a linear dependence upon copper content in this system varying from 3150 gauss for NiFe_{1.9}Mn_{0.02}O_{4±} to 2400 gauss for furnace cooled CuFe_{1.9}Mn_{0.02}O_{4±}. Direct current resistivity remains high for mixtures of these two ferrites if 2Cu<Ni. An anomalous break in the curve relating dc resistivity with copper content occurs when the copper to nickel ratio exceeds this 1:2 value.

Some Recent Studies of Random Noise between Metals and Dielectrics
View Description Hide DescriptionThe purpose of these studies was to investigate the source of noise which is generated when thin dielectrics are subjected to relatively low dc voltages as reported by Boyer. It has been suggested by J. H. Mason that this phenomenon may be caused by the ionization in small voids due to poor electrode contact. Tests reported in this paper show that the application of 300 volts dc to dry films having a total resistance between test electrodes of 1.5×10 in. ohms was sufficient to give rise to a steady noise voltage if the electrodes were not in intimate contact. During some of the experimental work a two phase dielectric was subjected to dc voltage up to 1425 volts with no pulses. As expected, when the polarity was reversed, the dc current momentarily increased many‐fold, and then during its decay, noise was measured simultaneously. The noise ceased when the dc current became constant. A similar phenomena has been observed during the decay of the hetero‐change on a polarized dielectric. The test methods used provide a very sensitive method for detecting ionization in extremely small voids.

Strain‐Amplitude Dependent Internal Friction Studies of Dilute Alloys of Copper
View Description Hide DescriptionThis paper presents an investigation of the room temperature decrement in dilute polycrystalline alloys of copper as a function of strain amplitude and annealing at a frequency of about 1 cps. The characteristics of the internal frictionmeasured are:
(1) The internal friction and strain amplitude dependence of the internal friction decreases with increasing solute content.
(2) The internal friction is reversibly dependent upon the preanneal temperature.
(3) The internal friction is hysteretic with strain amplitude.
From the effect of the solute concentration and annealing temperature on the decrement, values for the binding energy for Al and Si solute atoms to dislocations in copper were calculated. These values are compared to theoretical values calculated on the basis of strain and electrical interaction energies. The experimental binding energy is in good enough agreement with the theoretical values to conclude that the onset of a strain amplitude dependence of the internal friction is caused by the freeing of sufficient dislocations from their pinning solute atoms.

X‐Ray Study of the Local Atomic Arrangement in Partially Ordered Cu_{3}Au
View Description Hide DescriptionThe atomic arrangement present in Cu_{3}Au in a state of equilibrium partial long‐range order has been investigated by measuring with x‐ray techniques the short‐range order existing below the critical temperature. A single crystal of Cu_{3}Au, cut parallel to a (100) face was quenched into water from 380°C, just below the critical temperature for ordering. Using monochromated CuKα radiation and a Geiger counter spectrometer, the diffuse scattering from this crystal was measured in the (h _{1} h _{2}0) plane of reciprical space. From these data, short‐range order parameters and a first‐neighbor size effect coefficient were obtained. The measurements show that there is a marked short‐range order among the wrongly occupied sites below the critical temperature. It is shown that the measured short‐range order parameters can be predicted by assuming that the wrongly occupied sites coalesce into tiny antiphase domains, and that these domains are one atomic plane in thickness, lie parallel to any one of the three sets of (100) planes in the crystal, and contain, on the average, about nine atoms each.

Formation of p‐n Junctions in Semiconductors by the Variation of Crystal Growth Parameters
View Description Hide DescriptionThe fluid transport theory of Burton et al. for the variation of the effective distribution coefficient with growth rate and stirring is applied to the growth of semiconductor crystals from a melt containing both donor and acceptor impurities. ``Rate growing,'' or the formation of p‐njunctions by varying the growth rate, is considered and the importance of the ratio of melt concentrations is demonstrated. Junction formation by varying the degree of stirring in the melt, or ``stirring modulation'' is also described. General principles are derived and various applications are discussed.

Polarization Reversal in the Barium Titanate Hysteresis Loop
View Description Hide DescriptionIn the presence of an opposing field the polarization of tetragonal BaTiO_{3} reverses itself. Devonshire's phenomenological treatment shows that in a sufficiently large opposing field the original direction of polarization becomes unstable. The values of commonly observed coercive fields are much smaller than this, and the polarization actually reverses while the initial state is still metastable. The observed coercive field and the shape of the audio‐frequency hysteresis loop can, however, be explained in terms of the field dependence of the switching rate that was measured by Merz in pulse experiments. Measurements by Drougard, Funk, and Young, of the small signal conductivity, taken while traversing the hysteresis loop, are also explained in terms of Merz's rate. The absence of an appreciable inductive component in the small signal conductivity measurements indicates that variations in the applied field produce corresponding variations in the switching current with a time lag which is at most a few times 10^{−8} second and possibly much less. The increases in dielectric constantmeasured during switching remain unexplained.

High‐Resolution Microradiography Using Low‐Voltage X‐Rays
View Description Hide DescriptionMathematical considerations of the concept of extremely high resolution in microradiography have allowed the derivation of optimal conditions for studies of biological material. Specimen thickness must be kept below 4 microns, and as a consequence very low voltages over the x‐ray tube are needed. Using a special method for preparing the specimen for analysis, it has been possible to obtain microradiograms at x‐ray potentials of a few hundred volts. The absolute resolution of the x‐ray image is comparable to that of the light microscope.

Stability of Oscillations of Superposed Fluids
View Description Hide DescriptionThe Stokes‐Taylor instability of the interface of two superposed fluids is studied. The two uniform layers of heavy fluids are of different densities and viscosities and are incompressible. Surface tension and gravity are taken into consideration. The main problem considered is the role of viscosity on the modes of decay and growth of waves, and the finding of an analytical solution more generally valid than those in existing approximate theories. The present viscoustheory is based on an approximation by interpolation exact in three regions of wave numbers (intermediate and two extreme regions). The extreme regions, being most important from the practical point of view and serving as a foundation of the present theory, are studied somewhat in detail up to the fourth order. Results are illustrated graphically and show good agreement with numerical solutions of the complete equation. For the sake of comparison, curves are also drawn according to existing theories and show discrepancies in the maximum rate of growth and decay from 12% to more than 100%.

Reverse Current and Carrier Lifetime as a Function of Temperature in Silicon Junction Diodes
View Description Hide DescriptionEarlier measurements of the reverse current and carrier lifetime in germanium have been extended to a series of silicon grown junction diodes, with measurements as a function of temperature between −190°C and 200°C. The lifetime reaches a plateau at low temperatures and can be explained in terms of the Hall‐Shockley‐Read recombination theory. The slope of logi_{r} vs 1/T, the magnitude of i_{r} , and the slope of i_{r} vs V suggests that charge generation from centers about 0.5 ev deep is responsible for most of the reverse current in these samples up to temperatures well above room temperature.

Technique for Approximate Measurement of Correlation Coefficients
View Description Hide DescriptionA new method is described for approximate measurement of the coefficient of correlation between two random variables which can be represented by time‐varying electrical voltages. This method makes use of simple analog‐computing elements to obtain the coefficient of linear regression of one variable on the other. Its use in connection with an oscilloscope display of the two variables is described, and the relation between these displays and the Lissajous figure formed by two sinusoids is discussed. A possible design for a directreading correlation meter is suggested.

Theory of Nonlinear Coupling in a Novel Ferroelectric Device
View Description Hide DescriptionA novel dielectricmodulator consisting of two pairs of mutually orthogonal plates on a block of ferroelectric material is described. Interaction between the orthogonal fields due to the nonlinear properties of the dielectric is shown to exist. The differential equation of performance is linearized to the Mathieu‐Hill type and applied to the analysis of the device when used as a frequency multiplier.

Theoretical Considerations Governing the Choice of the Optimum Semiconductor for Photovoltaic Solar Energy Conversion
View Description Hide DescriptionThe theory of the photovoltaiceffect is used to predict the characteristics of a semiconductor which would operate with an optimum efficiency as a photovoltaicsolar energy converter. The existence of such an optimum material results from the interaction between the optical properties of the semiconductor which determine what fraction of the solar spectrum is utilized and its electrical properties which determine the maximum efficiency of conversion into electricity. Considerable attention is devoted to the effect of the forbidden energy gap (E_{G} ) of the semiconductor. It is shown that atmospheric absorption causes a shift in the solar spectrum which changes the value of the optimum forbidden energy gap between the limits 1.2 ev<E_{G} <1.6 ev. Furthermore, plausible departures of the diode reverse saturation current (I _{0}) from the parametric dependence predicted by Shockley are considered, and it is shown that such departures reduce the advantage of the optimum material over others in the range 1.1 ev<E_{G} <2.0 ev. The relation between E_{G} and the load impedance for maximum power transfer from the solar converter is discussed. Finally, I _{0} is computed from the published values of the semiconductor parameters of three intermetallic compounds, i.e., InP,GaAs, and CdTe, and it is shown that the efficiencies predicted for these materials are greater than those predicted for other materials which have been proposed, i.e., Si, CdS, Se, and AlSb.
