Volume 28, Issue 10, 01 October 1957
 SPECIAL ISSUE ON HIGH‐POLYMER PHYSICS


Nuclear Magnetic Resonance, Radiation Damage, and Rigidity in Branched Polyethylene as a Function of Temperature
View Description Hide DescriptionMolecular motions and microstructure are studied as a function of irradiation damage and temperature in branched polyethylene. The methods of proton magnetic resonance, specific volume and density percent crystallinity, mechanical rigidity and loss, and x‐ray determined crystallinities are employed. The samples were subjected to irradiation doses ranging from 0 to 8.3×10^{18} nvt in the Brookhaven reactor. Significant changes in the proton resonance line shape at 295°K occur for an irradiation of 0.3×10^{18} nvt. Second moments and intensity ratios indicate that the first effect of irradiation on the line shape can be interpreted as due to the destruction of crystallinity or order. This effect however is offset at higher doses by the restrictive influence of radiation induced crosslinks on molecular chain motion. Estimates of the percent crosslinking aid in the interpretation of the temperature variation of proton resonance line shapes and allow some estimate to be made of the lengths of chain associated with a given type of molecular motion. Activation energies are calculated from NMR and mechanical loss data for these molecular motions.
With increasing temperature the proton resonance and mechanical properties are associated first with rotational oscillations, over energy barriers, of short segments (of the order four methylene groups in length) of a chain (activation energy ∼6 kcal/mole) and also with the γ peak of the mechanical loss data. At temperatures exceeding the ``glass transition temperature'' the molecular movements are also described by neo‐Brownian diffusional motions involving chain lengths of about 10 methylene groups (activation energy ∼12 kcal/mole). These latter ``neo‐Brownian'' motions are associated to some extent with the β peak of the mechanical loss data and probably also involve some branch point motion. The majority of the motion occurs principally in the amorphous regions of the branched polyethylene until temperatures above 290°K are reached and the microstructure begins to change due to the ``melting'' of crystallites.
The intensity ratio for the complex line shape exhibited by polyethylene at temperatures greater than 200°K are associated with the high‐frequency rigidity of the sample.

Nuclear Magnetic Resonance Studies of Polyethylene
View Description Hide DescriptionNuclear magnetic resonance(NMR) studies of three polyethylenes have been made over the temperature range −190°C to 120°C. Two components of the NMR line are observed—a narrow one identified with the ``amorphous'' regions and a broad one identified with the ``crystalline'' regions. Differences between polyethylenes in the shape of the narrow component are observed and discussed.
The variation of line width of the two components with temperature indicates two motional transitions occurring in the ``amorphous'' regions and one in the ``crystalline'' regions over the temperature range studied. Energies of activation inferred for one of the ``amorphous'' transitions agree well with those determined from melt viscosity studies implying a similarity of molecular processes controlling the two measurements and allowing an interpretation of the one observed by NMR to be made.
The NMR data are used to interpret (in terms of molecular motions) the three dispersion regions observed by dynamic mechanical measurements, with the following results: in the vicinity of −100°C, the amorphous regions undergo a transition involving mainly the onset of rotation of linear segments of the polymer chains. Between −35°C and 0°C (depending on the sample), the motion of amorphous chain segments containing branch points leads to a transition. In the neighborhood of 60–100°C (depending on the sample), there are the beginnings of observable motion of the chain segments within crystallites.
Using a new method of decomposing the NMR line into its two components (based on the experimental line shape at low temperatures), the relative intensities of the two components (hence, the relative amounts of fixed and moving nuclei) are determined. This ratio, previously held to be identical with the ``percentage crystallinity,'' is shown to be inconsistent with this view and to support the molecular interpretation presented.

Structure of Spherulites as Revealed by Selected‐Area Electron Diffraction and Electron Microscopy
View Description Hide DescriptionTwo‐dimensional spherulites in thin films of the 6–6 nylon have been studied by selected‐area electron diffraction, bright‐field and dark‐field electron microscopy. The electron diffraction patterns were found to be comparable to studies using limited area x‐ray diffraction. In this sample they showed that the molecules were arranged in sheets with the hydrogen bonds in the plane of the film. Large field areas were used and as a result no preferred direction of orientation was seen. However, in dark‐field electron microscopy, by using only those Bragg electrons scattered into limited portions of the principle rings, the radical growth and branching of discrete crystalline regions was seen. Bright field electron microscopy showed the surface morphology of these structures.

Photoelastic Properties of Polystyrene in the Glassy State. I. Effect of Molecular Orientation
View Description Hide DescriptionThe effect of molecular orientation on the stress‐optical coefficient of polystyrene at room temperature (24°C) was measured using polystyrene monofilaments with different degrees of orientation. High degrees of orientation were obtained by cold‐stretching. The optical measurements were made using a polarizing microscope fitted with a Sénarmont compensator. The stress‐optical coefficient shows a strong dependence on molecular orientation, using birefringence as the index of molecular orientation. The stress‐optical coefficient appears to decrease linearly vsbirefringence, from a value of about +10 brewsters at zero birefringence to a value of about +4 brewsters at −0.04 birefringence. The elastic(Young's)modulus was also measured (in tension) as a function of orientation, and was found to increase nonlinearly with orientation (from 4.3×10^{5} psi at zero birefringence to 6.1×10^{5} psi at −0.04). A curve of strain‐optical coefficient vs orientation was obtained by multiplying stress‐optical and modulus values; this decreases nonlinearly and to a somewhat lesser extent than the stress‐optical curve (from about +0.03 at zero birefringence to +0.017 at −0.04). The significance of these constants in photoelastic experiments is discussed.

Photoelastic Properties of Polystyrene in the Glassy State. II. Effect of Temperature
View Description Hide DescriptionThe effect of temperature on the stress‐optical coefficient of polystyrene was measured at twelve different temperatures from −195° to +24°C using samples of unoriented polystyrene sheet. The stress‐optical coefficient appears to decrease with temperature from a value of about +17 brewsters at −195°C to a value of about +10 brewsters at room temperature. The elastic (Young's) modulus of polystyrene was also measured as a function of temperature using a flexural technique and was found to decrease linearly with temperature from 6.36×10^{5} psi at −198° to 4.65×10^{5} psi at +24°C. A curve of strain‐optical coefficient vs temperature was obtained by multiplying stress‐optical and modulus values; this curve increases with decreasing temperature from about +0.03 at +24° to +0.073 at −195°C.

Kinetics of Spherulite Growth in High Polymers
View Description Hide DescriptionSpherulite growth rates have been measured in two polyamides, 66 and 6 nylon, at temperatures ranging from 38 to 141° below the melting points using a moving photomicrographic technique. At constant temperature, the spherulite radius increases at a constant rate. This isothermal growth rate constant is temperature dependent, having low values just below the melting point, passing through a maximum on further supercooling and decreasing to negligible values at room temperature. These facts indicate that spherulite growth is not a diffusioncontrolled process. A reasonable interpretation of the data has been obtained using the concept of growth by two‐dimensional surface nucleation. A theoretical expression for the temperature dependence of the growth rate based on this concept has given good agreement with the experimentally determined values.

Mechanical Behavior of Plastics
View Description Hide DescriptionThe applicability of Nutting's equation of the mechanical behavior of some soft plasticized polyvinyl chloride preparations noted by Dyson in creep experiments is further demonstrated by force‐length measurements at constant rate of strain. This suggests new criteria for the characterization of soft plasticized PVC. For example, in a stretching experiment in which the sample is subjected to a strain (L−1) which increases linearly with time (t) at the rate (R), definition of ``modulus'' as the limit at small strains of the ratio of the force (F) to the strain is clearly inappropriate. That is, when which may be zero or infinite and also depends on the strain rate.
Some even more general force‐length‐time relationships for plastic are discussed which have been found useful for predicting the conditions of tensile failure. More complicated relationships of particular interest provide for the possibility of force‐time superposition of creep curves. Published creep data are considered from this point of view.

Tridirectional X‐Ray Patterns of Oriented Film at Wide and Small Angles
View Description Hide DescriptionDrawn, oriented film of polyethylene terephthalate was studied by means of an x‐ray diffraction technique in which the x‐ray beam was directed in three mutually perpendicular directions: (1) through the film, (2) and (3) in the plane of the film, parallel and normal to the direction of draw. Patterns were obtained in each of these directions for the diffractions occurring at both small and large angles. This combination of patterns provides a picture of the film'spolymer texture with these parameters: size, orientation, and arrangement of crystallites; extent of amorphous material; shape of microvoids. In this film the crystallites have planar orientation and are 45 A wide in the plane. A long period of 125 A exists in the direction of draw and is comprised of 75‐A crystallite length and 50‐A amorphous material. There is evidence that the film is composed of lamellae about 60 A thick; these lamellae are stacked in a staggered arrangement such that the crystallites in one lamella are adjacent to the amorphous regions in the lamella below. The small angle diffraction evidence cannot be reconciled with the ``coiled ribbon'' arrangement recently proposed in the literature to explain off‐meridional diffraction spots.

Lattice Energy of Crystalline Polyethylene
View Description Hide DescriptionThe heat of sublimation of linear paraffin chains from the crystalline form to the gas at 0°K is calculated from heats of fusion, heats of vaporization, and heat capacities of solid,liquid, and gaseous hydrocarbons. The heat of sublimation, which is defined as the lattice energy of the crystalline phase of linear polyethylene, is 1.84 kcal/mole of CH_{2} groups. The heat of fusion of crystalline linear polyethylene is 0.922 kcal/mole of CH_{2} groups.

Flow Birefringence and Stress. V. Correlation of Recoverable Shear Strains with Other Rheological Properties of Polymer Solutions
View Description Hide DescriptionThe correlation of normal stress with the shear stress and flowbirefringence of flowing solutions has been extended to include the recoverable shear strain s which can be measured directly by a rotational viscometer in ``recoil.'' This has been shown experimentally with solutions of a high‐viscosity nitro‐cellulose in n‐butyl acetate and a viscous polyisobutylene. These results show that the principal axes of the tensors of stress, strain, and optical anistropy coincide, even when no constant shear modulus (shear compliance) exists.

Effect of Irradiation On Dynamic Mechanical Properties of 6–6 Nylon
View Description Hide DescriptionMeasurements of elastic modulus and mechanical loss at audio‐frequencies have been obtained on irradiated and nonirradiated specimens of polyhexamethylene adipamide over a broad temperature range extending from 80°K to 600°K. The irradiations were carried out at the Brookhaven and Penn State Reactors. The internal friction spectrum of unirradiated nylon 6–6 contains at least four peaks corresponding to different mechanisms being invoked as the temperature is raised. With irradiation doses from 0.3×10^{18} nvt to 5.5×10^{18} nvt, significant changes in the dispersion regions occur. At temperatures above the main softening region, an increase in modulus with temperature is found. This is evidence of rubber‐like behavior and is accounted for by the introduction of cross‐links resulting from ionization and free radical formation produced by the irradiation. At high irradiation doses the percent cross‐linking appears to become independent of dose. The various effects found are discussed in terms of molecular forces and mobility of chain segments.
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 REGULAR ARTICLES


Temperature Consideration in Solar Battery Development
View Description Hide DescriptionSemiconductor materials of band gap appreciably greater than that of silicon may prove useful for photovoltaic solar energy converters operating at elevated temperatures. Such operation is of interest for applications where solar energy concentration can be employed to reduce the photovoltaic surface area required to produce a desired amount of electrical power.

Analysis of Multivelocity Electron Beams by the Density‐Function Method
View Description Hide DescriptionSome mathematical techniques are presented which assist in the analysis of one‐dimensional multivelocity accelerated electron streams by the density‐function method. These techniques include methods for removing mathematical singularities from the equations. The correspondence between the density‐function method and the usual single‐velocity analysis is discussed; and a new definition of the equivalent ac voltage in terms of the density function is given. This definition is meaningful even for large velocity spread. The density‐function method and the single‐velocity theory agree for small velocity spread while, for a strongly multivelocity beam, no simple transmission‐line type of equations are to be found. Because of the latter fact, a common assumption about the noise conservation properties of the low‐voltage region of an electron gun is not valid, and the beam's ``noisiness'' is not invariant with distance in this region. These conclusions are verified by detailed noise calculations reported in an accompanying paper.

Density‐Function Calculations of Noise Propagation on an Accelerated Multivelocity Electron Beam
View Description Hide DescriptionThe propagation of noise current and voltage fluctuations through the multivelocity accelerating region immediately in front of the potential minimum has been calculated using the density‐function method of analysis. Basic assumptions made include: (a) linearized one‐dimensional analysis; (b) zero total ac current in the beam; (c) uncorrelated full shot noise in each velocity class at the minimum plane; (d) dc potential η(ξ) given by the Fry‐Langmuir analysis. Starting at the minimum, the noise fluctuations were traced out towards positive ξ by a numerical forward‐integration process using an IBM 650 electronic computer. Principal results of the computations are that Haus's noise parameters S and Π are found to vary significantly with distance between η=0 and η=4, contrary to previous assumption. The noise parameter S decreases to ∼0.7 of its initial value of kT_{c} /2π, while the noise power Π rises from zero to ∼0.3 of the initial value of S. Exact results depend slightly on frequency. Beyond η=4 both noise parameters become invariant. The theoretical minimum noise figure of a beam type microwaveamplifier, which is F _{min}=1 +(2π/kT) (S‐Π), is thus found to be reduced to ∼3½ db for a temperature‐limited cathode instead of the commonly quoted value of 6½ db which is based on the values of S and Π at the cathode.

Characteristics of the Bayard‐Alpert Ionization Gauge at Pressures above 10^{−5} mm Hg
View Description Hide DescriptionBayard‐Alpert ionization gauges were calibrated in the range from 10^{−5} to about 10^{−1} mm Hg for various gases. In this pressure range, it is necessary to operate with grid currents below 100 μa in order to minimize the effects of gauge pumping and to prevent space charge from affecting the operation of the gauge. The gauge becomes insensitive to pressure when the ion current reaches 20 to 30% of the electron current. However, linearity is preserved only up to an ion current of about two percent of the electron current. Some of the reasons for the high pressure behavior of the Bayard‐Alpert gauge are discussed.

Application of Radioactive Tracers to the Study of Shaped Charge Phenomena
View Description Hide DescriptionThe problem of determining the velocity of a given element in a shaped charge jet as a function of the position of that element in the parent liner has been attacked with the help of radioactive tracers. Radioactively tagged liners were fired into stacks of steel plates, and the depth reached by the tagged element in each case was determined by radioactive assay of the plates. The resulting depth v rsus position curve was combined with emergent jet velocity data to yield velocity as a function of position. The results are in rough qualitative agreement with those previously obtained by the somewhat unwieldy method of collecting and weighing jets and slugs. The radioactive method is more direct and appears to be capable of sufficient refinement to warrant its use as a research tool.

Explicit Formulas for Tschebyscheff and Butterworth Ladder Networks
View Description Hide DescriptionGreen found the closed‐form formulas for the element values in a resistance‐terminated ladder network that has a maximally flat (Butterworth) or equal‐ripple (Tschebyscheff) characteristic. The Green formulas apply only when all the zeros of the reflection coefficient ρ are chosen to lie in one half‐plane. In this paper we present new formulas for the element values for the case in which the zeros of ρ are chosen to alternate in the left and right half‐planes. These formulas apply for n odd, where n is the degree of the dominator of the transfer function, and for any nonzero ratio of the output to the input resistance. The networks obtained are related to the symmetrical ones given by Bennett's and Belevitch's formulas for matched networks.

Effect of Irradiation on the Hole Lifetime of N‐Type Germanium
View Description Hide DescriptionThe minority carrier lifetime of germanium is very sensitive to certain types of irradiation. The results of irradiating large single crystal samples of n‐type germanium with fast neutrons and Co^{60}gamma rays are presented and discussed. Lifetime was determined from a transient measurement of the decay of holes following an injection pulse. The effect of initial carrier concentration has been considered. According to the James‐Lark‐Horovitz model, four energy levels are introduced by irradiation into the forbidden band of germanium, one above and three below the center of the band. Using the upper level, a one level recombination model serves to explain the experimental results approximately. The determination of the recombination level agrees well with the position of the first ionization level of the interstitial produced by irradiation at about 0.2 ev below the conduction band. On this basis, the effective cross section for hole capture by these recombination centers is found to be about 4×10^{−15} cm^{2} and 5×10^{−16} cm^{2} for neutron and gamma‐irradiated germanium, respectively. A lower level may also be responsible for the recombination process.

Equipartition of Energy and Local Isotropy in Turbulent Flows
View Description Hide DescriptionHomogeneous turbulence in which 〈v ^{2}〉 = 〈w ^{2}〉 ≠ 〈u ^{2}〉 was produced experimentally, where 〈u ^{2}〉, 〈v ^{2}〉, and 〈w ^{2}〉 are the mean‐square turbulent velocities in x, y, and z direction, respectively. The decay of turbulence and the energy transfer between 〈u ^{2}〉 and (〈v ^{2}〉+〈w ^{2}〉) were measured, and it was found that the larger components (〈v ^{2}〉 and 〈w ^{2}〉) are losing more energy due to viscosity than by transfer to the smaller component (〈u ^{2}〉). However, 〈u ^{2}〉 is receiving enough energy by transfer to compensate for its decay and is in fact slowly increasing. The measurement of mean‐square vorticity components shows that the turbulence is becoming locally isotropic at a faster rate than the equipartition of energy is taking place.
In another set of experiments it was found that when approximately isotropic turbulence is subjected to deformation, the three components of turbulentenergy become widely different in magnitude and that the turbulence is not locally isotropic. This indicates that even at high Reynolds number the deformation in a shear flow may cause anisotropy. The data on the turbulentshear flow near a solid wall confirm this conjecture.
The connection of this investigation to turbulent flows in general is discussed. In particular, it follows that neither the turbulentenergy nor the small‐scale structure of turbulence rapidly settles down statistically to quasi‐equilibrium.

Contribution to the Theory of the Contact between a Carbon Brush and a Copper Collector Ring
View Description Hide DescriptionThe main subject is the interpretation of the fluctuations, ΔU, (0.3 to 0.6 v), in the contact voltage U between a carbon brush sliding smoothly on a copper ring. A special method was used and proved very informative. Within a fraction of a second, voltage or current was varied from an initial value (often zero) to a higher value and back again. Thereby voltage vscurrent or time were registered by means of an oscilloscope. It is shown that the sudden negative ΔU's are essentially due to electrical breakdowns—frittings at about 1 v—of the collector films, which are necessary in order to let the current through. The proof is given with stationary as well as sliding contacts by comparing the features involved with those of model diagrams, the design of which is based on the concept of fritting. Besides typical frittings of the type studied earlier, the concept of widening the area of conducting spots (generated through the collector films) by frittings as the current is increased, has been worked out. It is shown that every fritting of the collector films leads to a metallic junction by proving that consecutive records with decreasing voltage exhibit the character prescribed by the electrical and thermal constants of the electrode material used.
Experimental proofs were obtained showing that ``frictional oxidation'' provided a noticeable contamination (of fritted spots) during one revolution between leaving the brush and meeting it again.
