Volume 14, Issue 12, 01 December 1943
Index of content:
Theory of Filler Reinforcement in Natural and Synthetic Rubber. The Stresses in and about the Particles14(1943); http://dx.doi.org/10.1063/1.1714942View Description Hide Description
An attempt is made to develop a general theory of filler reinforcement by determining the stresses occurring in and about a spherical particle imbedded in a rubberlike medium subjected to an applied tension. For a system containing a single particle rigidly attached to the adjacent medium, an application of the theory of elasticity shows that, for infinitesimal deformations, the stress components within the particle are independent of the radial distance from the origin, taken at the center of the particle. The stress components at a given point in the surrounding medium depend on the elastic constants both of the particle and of the medium, on the radius of the sphere, on the distance from the origin, and on the angle between the direction vector and the applied tension. Expressions are given for the average stresses in media containing many (independent) particles. Theoretical values of the bulk moduli of the synthetic rubbers considered in the treatment are derived from sound velocity data. Curves showing the spatial distribution of radial and shear stresses are presented for a range of values of elastic constants to be expected for different kinds of filler particles and rubberlike materials.
14(1943); http://dx.doi.org/10.1063/1.1714943View Description Hide Description
Because of the mathematical difficulties involved in the treatment of large‐signal detectors, experimental methods for obtaining design data were early adopted. The procedure has been to replace the detector by a ``model'' described by a rectification or transrectification diagram. The ``model'' for a large‐signal detector is developed from practical measurement results. Formulae and results may be extracted from the ``model'' if the existing analogy with the plate‐current vs. plate‐voltage diagram for a vacuum tube is made use of. This fundamental procedure may be extended to other non‐linear devices, and in particular to frequency converters. It is shown in the following that a general theory can be developed, of which the vacuum‐tube amplifier, the large‐signal detector, the frequency converter and other devices are applications. A double‐inpout superheterodyne mixer with straight input characteristics is discussed, and it is shown how the applied general theory predicts the necessity for non‐linearity. The general theory is then used for the development of a substituting ``model,'' from which important information on the behavior of a superheterodyne converter can be secured.
14(1943); http://dx.doi.org/10.1063/1.1714944View Description Hide Description
14(1943); http://dx.doi.org/10.1063/1.1714945View Description Hide Description
A series generator in the operating range below maximum voltage possesses both d.c. negative resistance, (−V/I), and incremental negative resistance, (−dV/dI). It is shown that the incremental negative resistance is equal to Kn−R, where n is the speed, K the volts per r.p.m. per unit of field current, and R is the armature circuit resistance. Since the series generator has the incremental resistance property, it will support oscillations if the tuned circuit has the proper constants. It is shown that a generator load consisting of a separately excited motor can be represented by a condenser of sufficient size (in the order of farads), that oscillations at mechanically feasible frequencies of 0.2 to 1.5 cycles per second can be obtained. It is shown analytically that the magnitude of the capacitance varies directly with the moment of inertia of the motor armature and inversely with the square of the induction factor. It is shown experimentally that the frequency of oscillation of the circuit depends upon the motor induction factor and moment of inertia, and slightly upon the circuit resistance. The amplitude of oscillation is controlled by the circuit resistance.
14(1943); http://dx.doi.org/10.1063/1.1714946View Description Hide Description
A method is proposed for the magnification calibration of the electron microscope to compensate for the calibration errors caused by mechanical and electrical variations of the instrument. This method uses microscopic glass spheres of predetermined size, mounted directly on the specimen supporting film. A single calibrating sphere is then exposed on the same photographic plate with the sample. Any change, therefore, in the magnification of the specimen also causes a corresponding change in the magnification of the sphere, thus eliminating errors in calculating magnification arising from instrumental variations. The spheres are graded to a given size by controlled levigation and calibrated internally on a grating replica at a low magnification with a very low electron‐beam intensity. By the use of low intensity of the beam, deformation of the replica of the grating is avoided. Also at the lower magnification many more lines of the grating replica may be included in the field for greater accuracy in determining the calibrating magnification. The spheres are placed on the specimen supporting film by evaporation from a water suspension. It is estimated that an accuracy of about ±3.0 percent is attained by the measurement of the image of the calibrated sphere on the same plate as the sample.
14(1943); http://dx.doi.org/10.1063/1.1714947View Description Hide Description
Microscopic examination of surfaces developed in tantalum ribbons on heat treatment in vacuum shows a dependency of surface structure on whether a.c. or d.c. supply is used for the heating current. Further modification of surface structure results due to recrystallization over a temperature range of 1900°K to 2500°K. Grain growth is shown to increase exponentially with the temperature. An optimum amount of cold working of the samples before heat treatment results in exaggerated grain growth yielding large single crystals.
14(1943); http://dx.doi.org/10.1063/1.1714948View Description Hide Description
The jerky form of motion described as ``stick‐slip,'' which is sometimes observed in the sliding of surfaces, has been studied by means of the stick‐slip apparatus built in this laboratory. A comparative study of motion during the slip has been made for a number of combinations of unlubricated metals. The variation of friction with velocity has been determined for several typical cases. Most slip traces are symmetrical about their point of inflection indicating that the kinetic friction remains approximately constant. The static friction is greater, and a rapid drop to kinetic friction usually occurs. The kinetic friction is least at the end of slip, so that the friction‐velocity relation is not reversible. There is evidence that the friction does not return immediately to its higher static value when the sliding surfaces come to rest. These results are considered in terms of several theories of friction.
14(1943); http://dx.doi.org/10.1063/1.1714949View Description Hide Description
(1) At high temperatures (above 80°C) the specific volume of polystyrene is an explicit function of the temperature. dV/dT=0.00043. (2) At low temperatures (below 40°C) the specific volume of polystyrene depends upon its past thermal history dV/dT=0.00024, although V is not explicitly fixed by the temperature alone. (3) When a sample of polystyrene is cooled at constant rate, it contracts according to the higher expansion coefficient until some critical region of temperature, and then contracts according to the smaller coefficient. (4) The position of the critical temperature region depends upon the rate of cooling. The faster the cooling, the higher the ``transition point.'' (5) In the intermediate temperature range (say 40°C to 80°C), complex time effects can be observed. A sample heated from 20°C to this intermediate range will first expand, according to the small expansion coefficient, and then contract slowly toward a smaller volume. The rate of this contraction is greater at higher temperatures. (6) All the observations are in fair accord with the interpretation of the ``second‐order transition point'' of polystyrene as the temperature at which rate of volume change becomes comparable with the experimental time scale.