Showing papers in "Journal of Applied Physics in 1946"

Particle Size Determination from X‐Ray Line Broadening

Abstract: The x‐ray line broadening method of determining particle size was compared with direct measurement on electron micrographs. By controlled heating of the carbonate, magnesium oxide particles were prepared from 50 to 1000A in diameter. Particle size calculated from x‐ray data taken on a Geiger counter spectrometer agreed to ±10 percent with the microscope measurements. Mechanical mixtures of two different sizes were examined by the x‐ray method, but the particle sizes could not be determined unless the two maxima of the distribution curve were completely resolved.

A New Method for Measuring Dielectric Constant and Loss in the Range of Centimeter Waves

Abstract: In 1940, dielectric measurements in the centimeter range were considered as difficult and not very accurate. The authors, therefore, developed a ``hollow‐pipe'' method which overcame these objections and required only a weak oscillator and small amounts of the dielectric material. The theory and its practical applications, as perfected by March 1941, are presented in this paper.

Theory and Application of the Parallel Plate Plastometer

Abstract: A method has been established for the measurement of the viscosity of high polymers at low rates of shear in the range 104 to 109 poises using a parallel plate plastometer. This is based on a mathematical criterion for separating the viscous portion of the deformation from the ``elastic'' and ``delayed elastic'' components. Experimentally, the plate separation is measured at a given temperature as a function of time. The theory furnishes a relation, which is also the criterion for predominantly viscous deformation, between viscosity, plate separation, applied load, and time. This relation, a modified form of Stefan's equation, is used for calculating the viscosity from the experimentally observed quantities. The method has been applied to polyethylene and vinyl chloride‐acetate resin compounds. The viscosity‐temperature behavior of these materials is shown to be simple over the temperature range studied; that is, log viscosity varies linearly with the reciprocal of the absolute temperature. Data are prese...

The Flow of Gases in Pipes at Low Pressures

Abstract: Data are presented on the flow of air at low pressures in copper pipes of radius 0.795 and 1.30 cm; iron pipes of radius 2.64, 5.12, and 10.1 cm; and for hydrogen in a copper pipe of radius 1.30 cm. Data are also given for the resistance to flow of air in 1½‐ and 3‐inch nominal pipe size elbows, for 1½‐inch Kinney bellows valves, and for short sections of 1‐inch nominal pipe size iron pipe connecting large gas chambers. The data on straight iron and copper pipes, together with the data from the literature on glass capillaries, are correlated by the introduction of a correction factor F in Poiseuille's equation. F is correlated graphically in terms of a dimensionless group representing the ratio of mean free path to pipe radius, with separate curves for iron pipe and for copper and glass pipes or capillaries.

The Permeability of Different Rubbers to Gases and Its Relation to Diffusivity and Solubility

Abstract: As the permeability of rubber‐like substances to gases stands in relation to the solubility and rate of diffusion of the gases in those materials, these individual values should be known. The permeability of a membrane was measured manometrically and the diffusivity was derived from the time‐lag of the permeation. The solubility of the gas was computed from the permeability and the diffusivity, in addition to which the solubility was also found by direct measurement. In this way eight different gases were tested with nine elastomers at different temperatures. It appeared that the permeability of a membrane to a given gas is not affected by the presence of a second gas. The differences in permeability of different elastomers to a given gas are caused mainly by differences in rate of diffusion and only in a very minor degree to differences in solubility. The differences in permeability of the same elastomer to different gases are caused not only by differences in rate of diffusion but also by differences in solubility. A linear relationship is found between the logarithm of the solubilities of different gases in natural rubber and their critical temperatures, so the higher the critical temperature of a gas, the better does it dissolve. The presence of polar groups in an elastomer reduces the solubility of non‐polar gases and increases the solubility of polar gases in the elastomer. The various rubbers behave towards gases like organic liquids. The activation energy of the diffusion and the heat of solution were calculated from the temperature function of the diffusivity and the solubility. As the diameter of the molecule of the gas increases, the rate of diffusion decreases, while the activation energy of the diffusion becomes greater. The presence of polar groups and methyl groups in elastomers causes low rate of diffusion, which involves a great activation energy of diffusion. It is presumed that the activation energy of the diffusion is required to separate the rubber molecules for the displacement of the gas molecules. The attempt to elucidate the constant D0 in the equation D=D0 exp (−E/RT)—which proves to be a function of the activation energy of the diffusion E— by reference to one of the formulas published in the literature failed. An empirical formula was drawn up, by which D0 is directly related to the activation energy E.

Applications of Metallic Shadow‐Casting to Microscopy

Abstract: The factors which determine image contrast in optical and electron micrographs are discussed in relation to a new metal shadow‐casting technique whereby the contrast of images is greatly increased by depositing obliquely a thin film of metal on the microscope preparations Further advantages of the use of shadow‐casting are described, and an estimate is made of the lower limit of size of objects which should be observable by shadow‐casting Examples are given and illustrations are shown of the applications of this technique to the electron micrography of particles of macromolecular dimensions, of replicas of such particles, and of surface replicas prepared in several ways

The Theory of Permanent Set at Elevated Temperatures in Natural and Synthetic Rubber Vulcanizates

Abstract: A molecular theory is developed to describe quantitatively the permanent set taking place in thin samples of vulcanized natural and synthetic rubbers held at constant extension at elevated temperatures. Permanent set is considered to be the result of the formation, through the action of molecular scission and cross‐linking reactions, of a dual molecular network in the rubber sample, in which the network chains are of two types: chains which are at equilibrium when the sample is at its unstretched length, and chains which are at equilibrium when the sample is at its stretched length. According to the theory the amount of permanent set in a rubber sample is a function of only two quantities: the relative ratio of the number of chains of the two types, and the elongation at which the sample was held. Experimental data on permanent set for various rubber types and under different conditions are presented and are shown to be in good agreement with the theory.

Viscometric Investigation of Dimethylsiloxane Polymers

Abstract: The intrinsic viscosities of an extended series of linear methyl polysiloxane fluids, having dimethylsiloxane (Me2SiO) as the repeating unit, have been determined in toluene solution. These values have been correlated with their molecular weights, determined chemically and by osmotic pressure and light scattering measurements. The Staudinger equation was found applicable only for fluids of relatively low molecular weights, i.e., up to about 2500; for the higher polymers, the best correlation of intrinsic viscosity with number average molecular weight was found to be: [η]=2×10−4Mn0.66. This held reasonably well for molecular weights from 2500 to about 200,000. The bulk viscosities of the polysiloxane fluids were found to conform to the Flory relationship for melt viscosities; the expression: log visc. (cs. at 25∘C)=1.00+0.0123 Mn12 appears to be reasonably valid for molecular weights above 2500.

A Theoretical Comparison of the Visual, Aural, and Meter Reception of Pulsed Signals in the Presence of Noise

Abstract: The present paper examines theoretically the relative sensitivity of the detection of signal pulses in the presence of noise, (a) by observation of an oscilloscope, (b) by aural perception, in which one listens to the fundamental or a low harmonic of the pulse repetition frequency (PRF), (c) and by a meter. The metering scheme may be either aperiodic, where the rectified current is fed directly to a meter with a long time‐constant, or periodic, where the rectified current is sent through an audio‐filter tuned to the PRF, given a supplementary rectification, and then passed through the meter. The dependence of the sensitivities of the different methods on various relevant parameters is studied in some detail. These parameters include the width and the shape of the IF response, the pulse length, the PRF, and in aural or meter reception, the duration of the gate, the width of the audio‐filter, and/or the time constant of the meter. The descriptive survey of the results is given in Part I and the mathematical analysis in Part II. Among the more important results are (I): The optimum IF filter is the conjugate of the Fourier transform of the pulse, not merely for visual reception, as was previously known, but also for aural or meter reception as well. (II): For very weak signals the linear detector requires only about 5 percent more input signal power than does the quadratic to achieve the same minimum detectable signal (same final signal‐to‐noise ratio). (III): The aperiodic meter has the advantage of not requiring knowledge of the PRF, and has potentially great sensitivity if spurious fluctuations in gain can be balanced out. (IV): Meter methods can be made more sensitive than the oscilloscope if long time‐constants are available. Gating is also necessary. (V): Although the best IF filter is the Fourier transform of the pulse, the best pulse is not the Fourier transform of the filter in aural reception (though it is in visual), for the best results in meter or audio‐detection are obtained by using long pulses. In visual work, the pulse length is immaterial, to a first approximation. Curves are given showing the power required to achieve a given signal‐to‐noise ratio as a function of pulse length, IF filter width, the PRF, gating time, and audio‐filter width, in some cases when the pulse and filter are not matched (i.e., are not related as Fourier transforms). Some numerical estimates of aural and meter performance relative to visual are also essayed.

Crystallization of Unvulcanized Rubber at Different Temperatures

Abstract: The crystallization and melting of unvulcanized natural rubber in the unstretched state have been investigated at different temperatures. Change of volume has been used as a quantitative measure of the extent of crystallization, and mercury‐filled dilatometers containing the rubber have been used for the volume measurements. Crystallization was observed to occur at temperatures between −50° and +15°C and to be most rapid at about −25°C. The final decrease of volume on crystallization was usually found to lie between 2.0 and 2.7 percent. The melting of the crystalline rubber was found to occur over a range of temperature and to be strongly dependent on the temperature at which the crystals were formed. The temperature at which the beginning of melting occurs is from 4° to 7° above the temperature of crystallization. The range of melting is about 35° at the lowest temperatures and decreases to about 10° at the highest. The same range of temperature of melting is obtained regardless of the extent of the crystallization.

Fatigue of Glass under Static Loads

Abstract: Static loading tests were run on glass and porcelain rods732 inch in diameter for times ranging in duration from 0.01 second to 24 hours, by using specially designed apparatus. It was found that glass can support for 0.01 second about 3 times the stress that would break it in 24 hours. The effects are generally the same for all glassy materials. Porcelain showed the effect somewhat less than glass. It appeared that adsorbed moisture and gases reduced the strength.

Non‐Uniform Transmission Lines and Reflection Coefficients

Abstract: A first‐order differential equation for the voltage reflection coefficient of a non‐uniform line is obtained and it is shown how this equation may be used to calculate the resonant wave‐lengths of tapered lines.

Theoretical Physics in the Metallurgical Laboratory of Chicago

Abstract: Dr. Darrow has suggested that a short introduction may enhance the usefulness of the more specialized papers to be presented to the Society by members of the old Theoretical Physics group of the Metallurgical Laboratory (Plutonium Project). Because the presentation of these papers will have to be very brief and because some of our collaborators could not present abstracts in time for the meetings, I was most happy to follow our Secretary’s invitation to summarize our work in general terms.

The Production of High Centrifugal Fields

Abstract: High centrifugal fields were produced by spinning small solid steel spherical rotors up to their bursting speeds. The rotors were supported magnetically in a vacuum by an improved method and spun by rotating magnetic fields. The peripheral velocities at which the rotors of various sizes, made of the same (flaw free) steel and having the same shapes, exploded, were roughly the same and of the order of 105 cm/sec. A centrifugal field of 2.4×108 times gravity was obtained with a .795‐mm spherical rotor which was the smallest diameter tried. Calculations indicate that in some cases plastic flow probably occurred in small regions near the centers of the spherical rotors somewhat below their bursting speed.

A Photoelectric Instrument for Light Scattering Measurements and a Differential Refractometer

Abstract: The method of determining particle sizes and molecular weights by light scattering measurements on solutions is finding increasing fields of application. In order to obtain the necessary data quickly and conveniently, an instrument has been developed which allows the required light scattering measurements to be taken on a routine basis. This apparatus is described. It measures transmission and the scattering of light at 90°; two different schemes can be employed to obtain the angular intensity distribution of the scattered light. A description is also given of a compensating refractometer which is used to determine the difference in refractive index of solvent and solution. The instrument, which is simple in design, gives a direct reading of the refractive index difference and has an accuracy of better than 10−5. The light scattering instrument has been tested using polystyrene of known molecular weight, and has been applied to study the change of apparent molecular weight (or particle size) of a series o...

Fine Structure of Viscose Rayon

Abstract: Quantitative x‐ray diffraction methods have been used to study the orientation of the cellulose chains and lateral ordering around the long chain axes in various commercial and experimental rayons. Lateral order can vary independently of orientation in cellulose, as is the case with other linear polymers such as the polyamides. The degree of lateral order obtainable by aqueous annealing of regenerated cellulose appears to be restricted by the structure originally set up. As noted by Sisson, the well‐known relations between yarn tenacity and orientation and elongation to break and orientation are not unique. At a given orientation, a range of tenacities and elongations are possible, depending upon the influence of other variables. Study of a series of yarns prepared under constant mechanical conditions showed that elongation to break increased with lateral disordering of the cellulose chains at constant orientation. The data support Baker's proposal that local chain disordering in any linear polymer favors higher extensibility. Some yarns of essentially the same orientation and lateral order have shown different properties indicating that other as yet undefined structural variables also have an important effect on physical properties.

Problems in Non‐Elastic Deformation of Metals

Abstract: In this article an attempt is made to examine the goals of current and of possible future types of research concerned with the non‐elastic deformation of metals. It is found that an understanding of non‐elastic deformation would be enhanced by research upon the following topics: 1. The anelasticity associated with the viscous behavior of grain boundaries and the at least temporary viscous behavior of slip bands. 2. The mechanics of the initiation and growth of twin bands. 3. The mechanics of the initiation and growth of slip bands, including the drop in resistance to deformation which accompanies the initial slip bands. 4. The mechanics of the segregation of solute atoms in solid solution, such as of carbon and nitrogen in iron. 5. The conditions under which strain hardening is not removed by recovery or by recrystallization, and hence under which a mechanical equation of state exists, i.e., under which a relation exists between strain rate, strain, stress, and temperature. 6. Variation of the heat of activation for plastic strain rate upon stress and upon the microstructure. 7. Anisotropy introduced by deformation.

The Effect of Water on the Strength of Glass

Abstract: The strength of glass was measured in various surrounding media. It was found that glass is 20 percent stronger when dry than when wet, and two to two and a half times as strong when baked in vacuum than when tested wet (on tests of ten seconds duration). Apparently, the chief cause of the loss of strength, as compared with that in vacuum, is moisture, but gases, especially CO2, seem to have some effect. It was found that fatigue of glass disappears when the glass is tested in a vacuum.Autoclaving tests showed that glass is rapidly etched by water at higher temperatures, and that even silica glass is considerably attacked. It appears that the attack of water on glassy surfaces produces gels, and this attack goes on inside the flaws, thus considerably complicating the problem of the strength of glass.

Thermal Expansion and Second-Order Transition Effects in High Polymers: III. Time Effects

Abstract: It has been suggested that the so‐called second‐order transition in high polymers is not an equilibrium phenomenon, i.e., a true thermodynamic singularity, but rather a rate effect. Confirmation of this point of view has been obtained by determining the equilibrium volume‐temperature curve of polystyrene. Such equilibrium curves exhibit no transition within the range of from 20° to 140°C, whereas the same material shows a transition at about 82°C for rates of heating usual in thermal expansion measurements. Two facts appear in agreement with the viscous flow interpretation of the thermal expansion process: First, two mechanis ms were found to operate, at markedly different rates. One gave almost instantaneous expansion, even at room temperature, whereas the other was quite temperature‐dependent in this region, being extremely slow at room temperature. Second, the activation energy for the slower mechanism was found to be of the order of magnitude of that for viscous flow, considerably lower than the activation energy for rubber‐like elasticity. Volume‐temperature curves at finite rates of heating are discussed in light of these findings.

Liquid Rise in a Capillary Tube

Abstract: A theory of the dynamics of capillary rise is developed by making certain assumptions as to the nature of the motion of the liquid in the tube. The most important assumptions are that the same forces act on the liquid when it is in an accelerated state of motion as when it is in a steady state, that the surface tension is constant, that the angle of contact between the meniscus of the liquid and the tube wall is constant, and that the wetting of the tube is not a rate‐determining factor of the motion. This theory leads to a second‐order non‐linear differential equation, the solution of which represents the motion of the liquid in the tube. A formal solution of the differential equation is obtained in the form of a double Dirichlet series. Approximations to the series are compared with experimental data, and it is concluded that the agreement between theory and experiment is satisfactory.

Significance of the Equation of State for Rubber

Abstract: The physical significance of stress‐strain curves and of isometrics obtained by the relaxation method is discussed and clarified. Stress‐strain curves taken at various temperatures give the correct dependence of stress upon temperature if they are taken sufficiently fast so that stress relaxation does not mask the temperature dependence. Isometrics obtained after previous relaxation of the sample are shown to depend upon duration and temperature of the relaxation by a numerical factor only. The basis for this behavior is the factorization of the stress into a factor depending upon extension and temperature only which corresponds to the equation of state and another factor depending upon the temperature T* and the duration of the relaxation process. For simple stress relaxation, the same factorization holds with T* equal to T. A general theory is formulated for time dependent elastic phenomena by generalizing Boltzmann's theory. The theory explains why factorization does not hold for creep, in agreement wi...

The Fatigue Modulus of Glass

Abstract: The decline in the breaking strength of glass with an increase in the length of time it is under stress has been noted by various experimenters. Based on the experimental results of T. C. Baker, an empirical relationship is obtained which indicates that the reciprocal of the breaking stress is a linear function of the logarithm of the duration of the stress. Certain implications of this relationship are discussed.

The Analysis of Multicomponent Mixtures of Hydrocarbons in the Liquid Phase by Means of Infra-Red Absorption Spectroscopy

Abstract: This is a general method of applying infra‐red absorption spectroscopy to the analysis of multicomponent hydrocarbon mixtures in the liquid phase. The procedure is calibrated by measuring optical densities of synthetic standard samples. A constant thickness cell is used for both standard and unknown samples. Two procedures for converting optical densities to concentrations are described. Examples are given for four‐ and five‐component mixtures. Data are presented to show the reproducibility of repeated measurements of optical density on the same sample, and results are given to show the agreement between the infra‐red analyses and the known composition of synthetic mixtures.

A Spark Shadowgraphic Study of Body Waves in Water

Abstract: Shadows of shock waves in water were photographed by means of a point‐spark of less than one‐tenth micro‐second duration; the waves were formed when high velocity spheres struck the water surface. The shock wave front had the form of an elliptical arc of small eccentricity; the ellipticity was caused by the greater strength and velocity of the wave at its center. The absence‐of‐light band had a varying width which depended on the strength of the wave. A large number of secondary waves behind the impact wave were observed; these were produced by the vibrating spherical missile as it traveled through the water. The period of vibration was determined from the spacing of the waves for 4/32″, 6/32″, and 8/32″ spheres; these agreed to within 19 percent of the periods calculated on the basis of Lamb's theory. Interference of the vibration waves was also observed when two spheres were shot into the water simultaneously. The cavity behind the missile was nearly conical in shape with the forward tip being distorted by pressure changed immediately ahead of the missile. A sphere produced a cusp at the forward tip of the cavity; cylinders and cones each produced their own characteristic shadow pattern. When a grid was placed in front of the tank, distortions in its shadowgram were observed. These were caused by the high pressures surrounding the missile and, from the shift in the grid pattern, the direction and magnitude of the pressure gradient could be inferred. When the shock waves were reflected with the wave front nearly normal to the surface there was an indication that the stem, which is characteristic of Mach reflections, was present. All other reflections were regular. Focusing of the wave by a brass mirror was demonstrated in the spark shadowgram. Waves reflected near normal incidence from substances having a lower acoustic impedance than water were reflected with a presence‐of‐light band ahead of the usual absence‐of‐light band. At glancing incidence this reversal occurred even when the reflecting substance had a higher acoustic impedance. Striations frequently appeared in the shadowgrams when waves were reflected. These striae were from 0.02 to 0.08 cm apart and represented a quasi‐stationary state. They were believed to be formed when the reflected vibration waves passed through the incident waves.

The Response of Biased, Saturated Linear and Quadratic Rectifiers to Random Noise

Abstract: Spectral distributions and powers associated with the output of biased, saturated linear and quadratic rectifiers are determined according to the method of Rice when the incoming disturbance is random noise. Three classes of input spectra are considered: (I), broad band noise, where the central frequency is equal to or less than the spectral width, (II), semi‐broad band noise, for which the central frequency exceeds the width by a moderate amount, and (III), narrow band noise, where the width is much less than the central frequency. Rectification of types I and II yields spectra having roughly the same distribution as that of the incoming waves, but for type III an infinite number of separate noise bands are generated and appear in the output, centered about harmonics of the central frequency. It is found that clipping, whether at the ``top'' or ``bottom'' of the incoming wave, always spreads the spectrum and reduces the output power. Further, it is shown that clipping due to cut‐off alone produces a greater spectral spread than clipping with saturation in addition, for types I and II, but not necessarily for spectra of type III. Symmetrical clipping for classes I and II yields little broadening of the spectrum, even in extreme cases, and for class III waves, the even‐harmonic regions are completely missing except for a d.c. component, and only the odd‐harmonic zones appear. The behavior of linear and quadratic rectifiers is qualitatively similar in most cases. The powers in the d.c. and continuous portions of the output spectrum are shown to be independent of the spectral shape of the incoming noise. Some examples of extreme clipping are considered, numerous curves are included, and a general analysis is outlined.

Pressure‐Volume Relation for Cylindrical Tubes with Elastomeric Walls: The Human Aorta

Abstract: The general theory of the elasticity of elastomers as developed by James and Guth (reference 9) is extended and applied to cylindrical elastomeric tubes. Data obtained by Hallock and Benson (reference 4) on human aortas of several age groups are described rather well by the resulting equations. On the basis of this analysis an interpretation of the aging process for aortas is given.

The Pulsed Properties of Oxide Cathodes

Abstract: A survey of the results obtained in an experimental study of the pulsed properties of oxide cathodes is presented. Pulsed measurements reveal that unusually large electron currents are available in microsecond pulses, and that several other phenomena are modifications of the d.c. properties, namely (a) sparking and (b) pulse temperature rise. Sparking may be either current limited or voltage limited, depending upon cathode materials and life. The pulse temperature rise also depends upon materials and life and is indicative of the nature of the cathode resistance. Evidence for a layer structure of the oxide cathode can be drawn from pulsed data.

A Study of Oxide Cathodes by X‐Ray Diffraction Methods: Part I. Methods, Conversion Studies, and Thermal Expansion Coefficients

Abstract: Two methods are described for obtaining x‐ray diffraction patterns of oxide‐coated cathodes. One method is used in the study of the conversion process in forming the oxide cathode while the other method is utilized in measuring the thermal expansion coefficients of barium, strontium, and thorium oxides. The conversion of an equal molar barium‐strontium carbonate solid solution, (BaSr)CO3, involves (1) crystal growth in the carbonate, (2) decomposition to the mixed oxides, BaO and SrO, (3) formation of the oxide solid solution, (BaSr)O, and (4) crystal growth in the oxide. A similar sequence of events is observed in the conversion of a mixed carbonate, BaCO3+SrCO3. Crystal and particle size growth of carbonates and crystal growth of oxides are investigated and possible relationships are discussed.

Analyses of Mixtures of Light Gases by Infra‐Red Absorption

Abstract: A discussion is given of the application of infra‐red absorption methods of analysis for light gases which do not obey Beer's law of absorption due to pressure broadening. Some of these gases do not obey Beer's law in the pure state or when contaminated by foreign gases. The method of analysis depends upon the nature and intensity of the pressure broadening effect of the different components in the sample upon each other. Data are presented showing the nature of some of these effects and illustrating the accuracy obtainable for certain types of analyses. The instrumentation used in routine gas analyses by infra‐red in this laboratory is described.

A Computer for Solving Linear Simultaneous Equations

Abstract: The mathematical principles of the classical iterative method of solving linear simultaneous equations are discussed. Basic electrical circuits for setting up an analog of the mathematical relations are given, and a commercial model of a 12‐equation computer is briefly described. The results of solving a number of problems on the computer are given to illustrate its accuracy and speed of operation. It is found that solving sets of 12 equations requires only 1/4 to 1/7 the time required by conventional methods.