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Volume 22, Issue 6, 01 June 1951

Stress‐Temperature Studies of Transitions in Rubbers
View Description Hide DescriptionThe stress‐temperature method was employed as a means of studying the apparent ``second‐order'' transition occurring in rubbers. The rubbers studied were a natural rubber gum, a butyl gum, a loaded GR‐S, and a loaded Hycar OS‐10. Pronounced stress relaxation was observed for all rubbers at temperatures not too far below the transition region, but not at temperatures a few degrees above the transition. For both the butyl and the Hycar OS‐10 rubbers the transition temperature was observed to depend strongly upon extension, the transition temperature decreasing with increasing sample extension. No such dependence upon extension was observed for the natural rubber stock. Comparison data were also obtained from volume dilatometric studies. With the exception of the data for natural rubber, the transition temperatures determined by the volume dilatometric method were somewhat lower than the lowest values obtained in the stress‐temperature studies.

Nuclear Magnetic Resonance Study of Transitions in Polymers
View Description Hide DescriptionNuclear magnetic resonance absorption line widths have been studied for several high polymers. The proton line widths were studied in a field of 7000 gauss and at a frequency of about 30 mc. Line widths obtained for Hevea and GR‐S were very narrow, indicating a large degree of ``quasi‐free rotation'' in these materials. Vulcanization, carbon loading, co‐polymerization, and crystallization produced a broadening of the lines as expected from the hindrance to internal motion introduced by these factors. Line width transitions as a function of temperature were observed for several polymers. Linear thermal expansion coefficients and specific heatvs temperature curves have breaks in the region of line transitions for the polymers studied. Swelling of polymers with benzene produced a narrowing of the absorption line throughout the line transition and lowered the transition temperature. Vulcanization broadened the transition range and shifted it to higher temperatures. Of two closely cut fractions of polystyrene, the larger molecular weight sample exhibited a line transition range at a higher temperature. The styrene monomer as well as the two fractions exhibited the same low temperature line width of about 8 gauss. The line width transitions were also studied for three butadiene styrene co‐polymers at temperatures where anomalous behavior was found in dynamic measurements. The theoretical implications of these experimental results, together with a survey of other pertinent work, indicate the possibilities of the nuclear resonance method as applied to the study of high polymers in conjunction with other methods.

Electrical Properties of Some Carbon Black‐Oil Suspensions
View Description Hide DescriptionThe dc conductivity and ac (1000 cps) properties of suspensions of R‐40 carbon black in transformer, silicone, and linseed oils, and suspensions of Shawinigan black in linseed oil, were studied as functions of time, carbon black concentrations, and rotational speed of test cell. The dc conductivity was also studied as a function of voltage. Immediately after agitating the suspension, both ac and dc conductivities increase rapidly with time, then level off and approach a saturation value. For the dc conductivity, this value increases with increasing voltage in all suspensions studied except the highest concentrations (10 percent by weight), which obey Ohm's law. The rate of approach to saturation is independent of voltage but depends on carbon black concentration. Increasing the concentration increases the conductivity. Increasing the speed of rotation decreases the conductivity. Form factors for the carbon black particles are calculated from the dynamic values of the dielectric constant by Voet's method. Agglomeration factors are then determined. At low speeds the agglomeration factor decreases rapidly with increasing speed. At higher speeds it approaches unity asymptotically.

Mechanical Properties of Substances of High Molecular Weight. IX. Non‐Newtonian Flow and Stress Relaxation in Concentrated Polyisobutylene and Polystyrene Solutions
View Description Hide DescriptionA coaxial cylinder apparatus serves to measure the apparent viscosity of a concentrated polymer solution at various shearing stresses and to follow the relaxation of stress after sudden cessation of flow. The dependence of rate of strain on shearing stress can be represented by the equation . The constant k _{2} is almost independent of temperature, and decreases with increasing concentration. The course of the stress relaxation depends on the steady‐state value of preceding cessation of flow. By assuming a logarithmic distribution function Φ of elastic mechanisms which are relaxed by hyperbolic sine flow mechanisms, it can be shown that , where t is the elapsed time. Values of Φ obtained from this equation are essentially independent of the rate of shear. The reduced distribution function, Φ_{ r }=ΦT _{0}/Tc, plotted against the logarithm of the reduced relaxation time, τ_{ r }=τcT/T _{0}η, where T is the absolute temperature, T _{0}=298°K, c is the concentration in g/cc, and η the viscosity at zero stress, is independent of temperature and concentration over the ranges studied for each of three polymer samples.

Mechanical Properties of Substances of High Molecular Weight. X. The Relaxation Distribution Function in Polyisobutylene and Its Solutions
View Description Hide DescriptionPrevious twin transducermeasurements of the dynamic rigidity and viscosity of a polyisobutylene sample of viscosity‐average molecular weight 1.2 million have been extended over a wider temperature range, and previous wave propagation data on solutions of this polymer in xylene have been extended by transducermeasurements at lower concentrations. Values of the relaxationdistribution function are derived from all these data and are compared with values obtained from stress relaxationmeasurements on solutions of the same polymer in Decalin, as well as stress relaxation data of Andrews and Tobolsky on solid polyisobutylene and dynamic measurements on butyl rubber from several sources. When reduced to a common reference state at 25°C by the assumption that all relaxation processes depend identically on temperature, the data for solid polyisobutylene provide a picture of the distribution function over eleven cycles of logarithmic time. It appears to have a plateau from 0.1 to 10^{4} sec with a sharp rise at shorter times and a sharp drop at longer times. From 10^{−5} to 0.1 sec the functions for polyisobutylene and butyl rubber are similar in shape, the latter being somewhat higher. When data for polyisobutylene solutions from 5 to 25 percent concentration are reduced to the reference state of the solidpolymer by the assumption that all relaxation processes depend identically on concentration, a single distribution function is obtained which from 10 to 10^{6} sec is similar in shape to that derived from direct measurements on the solidpolymer but lies somewhat below it.

Relation of Tensile Strength to Brittle Temperature in Plasticized Polymers
View Description Hide DescriptionSince both the second‐order transition temperature and the tensile strength of plasticized polymers decrease linearly with plasticizer content, and frequently in inverse proportion to the molecular weight of the plasticizer, it was predicted that a linear relationship should exist between tensile strength and transition temperature for plasticized polymers, independent of the nature of the plasticizer. Tensile strength versus heat distortion for four different plasticizers in polystyrene follows this prediction very well. However, tensile strength versus brittle temperature for plasticized Vinylite VYNW gives a different straight line for each plasticizer. It is suggested that the diffusion rate of a plasticizer molecule is important in the fast brittle point test. The hypothesis is proposed that the brittle temperature of a plasticized polymer represents an isodiffusion constant state. It follows on the basis of some semi‐empirical equations that the brittle temperature should decrease linearly with plasticizer content, and inversely as the activation energy for diffusion of the plasticizer molecule in the plasticized polymer. This latter prediction appears in accord with existing data. This diffusion concept allows one to predict that the brittle temperature should increase linearly with logarithm of frequency of the test, but inversely as the activation energy for diffusion.

Visco‐Elasticity of Rubber
View Description Hide DescriptionA theory has been obtained for the visco‐elastic behavior of rubber in the frequency range above that at which creep is important and below that at which it behaves like a hard solid. The rubber chains are treated as springs in a viscous medium, and a general expression is obtained for the contribution to modulus of a single section of chain as a function of its length and terminations. A statistical estimate is made of the number of chain segments having given length and terminations. A modulus function is found for the group of chains with each kind of termination and these are added in the proper amounts to give the form of the modulus vs frequency curve for any amount of cross‐linking.
Measurements of shear modulus were made on one apparatus at frequencies between 0.0125 and 750 cps. Agreement is good if a pure viscosity is added to the theory. However, at low frequencies the imaginary part of modulus does not decrease as much as predicted.

Sedimentation Equilibrium in Concentrated Polymer Solutions
View Description Hide DescriptionIt has been shown that sedimentation equilibrium can be obtained in polymer solutions of concentration as high as 20 percent by weight. This equilibrium has been approached from both sides, with identical results. The virial coefficients for the osmotic pressure may be calculated from experiments of this kind. The results are in good agreement with the osmotic pressure data of other investigators for polystyrene in butanone and polyvinyl acetate in butanone.

Starting Potentials of Positive and Negative Coronas with Coaxial Geometry in Pure N_{2}, Pure O_{2}, and Various Mixtures at Pressures from Atmospheric to 27 mm
View Description Hide DescriptionConsequent to an exhaustive study of coronas with coaxial cylindrical geometry in pure N_{2}, pure O_{2}, and mixtures over a considerable pressure range, it has been possible to obtain a consistent set of threshold values as a function of gas type and pressure for the principle current transitions signaling the accepted coronas. Thresholds for the positive wire corona should depend on gas characteristics only, while those of negative wires should reflect the second Townsend coefficients characteristic of the cathodematerial. Observations indicate that interpretation along this simple line is complicated by two factors. First, some current transitions under different conditions, which were in the past assumed to represent the same corona process, have been found to be different mechanisms. Thus, in pure N_{2} positive wire corona is not a gas determined process but a cathode dependent mechanism, while in pure O_{2} the corona is a gas dependent process but of the streamer type and not of the burst pulse type. Secondly, all thresholds of the characteristic negative wire corona transitions do not represent a secondary mechanisms characteristic of the cathode surface. These transitions are all preceded by a low order Townsend discharge whose threshold passes unnoticed but is characteristic of the initial cathode state. The commonly noted threshold is determined by a conditioning process which may depend on current density, duration of bombardment, and the composition of the gas. While the data yielded by the antecedent studies permits of interpretation in the present system of gases, this study also indicates that a correct interpretation of relative starting potentials of positive and negative wire coronas requires an extensive investigation of the basic nature of the coronas before it is attempted.

Finite Deflections of a Cantilever‐Strut
View Description Hide DescriptionA cantilever‐strut is an originally straight uniform thin rod clamped or ``built‐in'' at one end and acted on by an arbitrary force at the other end. The arbitrary force and the angle it makes with the tangent to the clamped end of the rod are regarded as independent variables. The problem of finding the deflection coordinates of the loaded end of the rod, the tangent angle of the loaded end, and the strain energy of bending in the rod is solved in terms of a newly defined function that satisfies a nonlinear partial differential equation.Solutions are given in series form. Since the cantilever‐strut is a segment of an inflectional elastica, the classical elliptic integral solution is also outlined for comparison with the more direct series solution of the problem.

A Preliminary Study of a Physical Basis of Bird Navigation. Part II
View Description Hide DescriptionThe previous paper contained a complete statement of the Magnetic‐Vertical‐Coriolis theory and the experimentation carried on from November, 1943, through July, 1945 (Experiments I through V). The present report presents the results obtained since this latter date and up to the summer of 1949 (Experiments VI through XI).

Electron Plasma Oscillations
View Description Hide DescriptionElectron plasma oscillations are excited by a beam of fast electrons in a stabilized low‐pressure mercury discharge. Probe measurements reveal that the uhf fields are localized in thin layers, the plasma density and frequency of which follow Langmuir's law. The beam of fast electrons traversing such an oscillation layer becomes velocity modulated, and excitation conditions result from drift time and bunching considerations similar to those in a klystron. A sealed‐off tube described covers a frequency range between 800 and 4000 Mc (five modes) without changing or matching any resonance circuit.

Electrical Breakdown Over Insulators in High Vacuum
View Description Hide DescriptionThe breakdown voltage of vacuum gaps depends on the electrode material, but when the gap is bridged by an insulator it is independent of the electrode material and varies with the kind of insulator. Some indication is found that the breakdown voltage increases with increasing surfaceresistivity of the insulator, but no apparent correlation is found between breakdown voltage and dielectric constant, density, or vapor pressure. It is found that a roughening of the intervening surface of the insulator in a region adjacent to the cathode increases the breakdown voltage. For electrode separations of 1 mm or greater the breakdown voltage does not increase linearly with the length of the insulator. Experiments were made in which one of the electrodes was separated from the insulator. It seems that the critical gradient at breakdown in the vacuum space between the cathode and the insulator, calculated for the case of plane electrodes from the ratio of dielectric constants, is not as large as would be required in gaps without insulators. These gradients are almost the same for copper as for stainless steel electrodes. The breakdown voltage over an insulator is raised when the edge of the insulator close to either electrode is rounded. When a layer of glass, thin compared with the separation of electrodes, is fused to the cathode,breakdowns occur at lower voltages than for an identical vacuum gap.

An Application of the Absolute Reaction Rate Theory to Some Problems in Annealing
View Description Hide DescriptionAbsolute rate theory is combined with molecular models in the study of the annealing of metals and of glass. It is thus possible to obtain expressions which are in close agreement with experimental data. Both the observed first‐order data for metals and the second‐order data for glass are predicted in this way. A virtue of the rate theory treatment is that it replaces the earlier macroscopic theories with a treatment in molecular terms.

Effect of Size and Spectral Purity of Source on Fringe Pattern of the Mach‐Zehnder Interferometer
View Description Hide DescriptionIn analysis of Mach‐Zehnder interferograms taken of the axi‐symmetric flows about supersonic projectiles, the question arises whether errors in fringe width occur because of the finite size and non‐zero spectral width of the source employed. Under the assumptions that the source is a circular area normal to the axis of the interferometer with spectral intensity function approximated by a gaussian error curve, it is shown that the deviations from ideal fringe width λ_{0}/ε caused by source size and spectral line width are negligibly small for an interferogram with 200 fringes on either side of center. The limiting factor is not deviation in fringe width but the exponential damping of fringe intensity amplitude owing to the spectral band width of the source. This reduces the fringe contrast below experimental detectability long before deviations in fringe width become appreciable.

The Cascaded Binary Counter with Feedback
View Description Hide DescriptionThe count of a cascade of binary pulse counters having any arrangement of feedback connections can be calculated. The calculation is simplified for two special connection patterns. For a particular count, one or the other of these patterns, or a modification of the two, requires a least number of connections.

Initial Conditions in Linear Varying‐Parameter Systems
View Description Hide DescriptionThe problem considered in this paper is that of determining the response of an initially excited linear varying‐parameter system to a given input. Mathematically, this problem reduces to solving a linear differential equation (with time‐dependent coefficients) subject to prescribed initial conditions. It is shown that these conditions may be satisfied by superposing upon the given input a linear combination of delta‐functions and treating the system as if it were initially at rest. Based on this fact and employing the concept of a system function, a general and yet simple expression for the response is developed. The result is similar in form to that obtained by the use of conventional laplace transformation techniques in the case of a linear differential equation with constant coefficients.

Behavior of the Resistance Ignitor in Mercury
View Description Hide DescriptionAn empiric expression has been derived for the probability of arc striking per unit time, per unit length of contact perimeter, for a resistance ignitor in a mercury‐pool tube: p′=k(E−E _{0})^{3}/ρ^{2}, where k and E _{0} are constants, E is the ``useful'' electric field strength near the mercurysurface, and ρ the resistivity of ignitor material at the junction with the mercury.
From the foregoing, a formula has been established for the probability of ignition per unit time, for the entire ignitor, in terms of the applied voltage v and ignitor ``firing resistance''R. With this formula, whose two arbitrary constants can be determined by two sets of measurements, the firing voltage of any ignitor can be predicted under a wide variety of circuit conditions, provided R remains unchanged under these conditions.
The probability formula was found to be consistent with a modification of a theory advanced by L. Tonks, whereby mercurysurface distortion and rupture permit field emission at field strengths less than those effective for smooth surfaces. The modification attributes the reduction in ignitor firing voltage by ignitor current to its extremely localized ohmic heating of the mercury. This heating reduces the surface tension and roughens the mercurysurface, thereby accelerating the process of surface rupture by the electric field.

The Epitaxy of Alkali Chlorides on Metals
View Description Hide DescriptionThe alkali chlorides were crystallized from solution on single crystals and on polycrystalline specimens of various metals. Oriented growth was obtained on Ag,Au,Cu, Zn, Pb, Sb, Bi, and Fe. Since oxide films were present on all metals except Ag and Au, it was concluded that the oxides were oriented with respect to the metallic substrate. From results with Ag and Au, it was found that the permissible misfit for epitaxy to occur was of the same order (∼10 percent) as for ionic pairs.

On the Representation of the Electric and Magnetic Fields Produced by Currents and Discontinuities in Wave Guides. I
View Description Hide DescriptionElectromagnetic scattering problems in cylindrical wave guides, including free space, involve the calculation of the fields produced in the presence of geometrical discontinuities by arbitrary currents. Such discontinuities may be replaced by equivalent electric and magnetic currents. The over‐all calculation then leads to two distinct problems: first, the calculation of the fields produced by the prescribed and induced currents in a discontinuity—free guide; second, the self‐consistent determination of the induced currents by the condition that the fields so produced satisfy the boundary conditions at the discontinuity surfaces. The first problem is treated herein by representation of the fields in terms of a complete set of vector modes characteristic of the possible transverse field distributions in the guide cross section. This representation transforms the over‐all field problem into one‐dimensional modal problems of conventional transmission line form. The eigenvalue problem of finding the characteristic modes is discussed in detail for the case of a uniform guide with perfectly conducting walls. The transformation procedure and the solution of the resulting transmission line problem are treated from an impedance point of view. A typical modal analysis and synthesis is presented for the explicit determination of the fields produced by arbitrary electric and magnetic currents in an infinite and semi‐infinite wave guide of arbitrary cross section. The connection with a corresponding dyadic Green's function representation (to be treated in Part II) is pointed out.