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1 Nov 1961

Volume 32, Issue 11, pp. 2305-2495

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Method for Measuring Dynamic Mechanical Properties of Viscoelastic Liquids and Gels; the Gelation of Polyvinyl Chloride

Meyer H. Birnboim and John D. Ferry

J. Appl. Phys. 32, 2305 (1961); http://dx.doi.org/10.1063/1.1777064 (9 pages) | Cited 19 times

Online Publication Date: 11 June 2004

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An apparatus has been developed to determine the components of the complex shear modulus of viscoelastic liquids and dilute gels over a continuous frequency range from 0.01 to 5 cps by amplitude‐phase shift measurements and from 2.5 to 400 cps by single coil transducer impedance measurements. The temperature range is from −40° to 150°C. The sample is deformed in very small strains with annular pumping geometry, as in the earlier apparatus of Smith, Ferry, and Schremp. Preliminary results on 2.29 and 3.00% solutions of polyvinyl chloride in di‐2‐ethyl hexyl phthalate provide the dynamic storage and loss moduli and the relaxation spectrum as they change during the process of gelation. The moduli of the ungelled solutions, at an early stage of the aggregation process, follow the Zimm theory rather closely, and the local effective viscosity derived therefrom lies between the solvent viscosity and the solution viscosity. The loss compliance of the aged gels is approximately represented by the Bueche theory for cross‐linked networks. However, it is evident that the gels contain a large proportion of sol fraction (polymer species unattached to the network).

Isothermal Crystallization Kinetics of Polyethylene. III. Influence of the Sample Preparation

J. Rabesiaka and A. J. Kovacs

J. Appl. Phys. 32, 2314 (1961); http://dx.doi.org/10.1063/1.1777065 (7 pages) | Cited 36 times

Online Publication Date: 11 June 2004

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Isothermal crystallization in bulk has been compared dilatometrically with linear polyethylene samples which have been molded in different ways, including melt orientation and sintering of precipitated powders from dilute solutions. These experiments show significant differences in the crystallization kinetics, which in some cases cannot be removed even by prolonged heating of the melt prior to crystallization. The data have been analyzed by an empirical expression in terms of nucleation and growth processes, according to the theoretical approach of Avrami. The results suggest that, in general, the melted polyethylene is not in a true thermodynamic equilibrium and includes some ``quasi‐indestructible'' clusters, which act as heterogeneous nuclei in the crystallization process. The nature and the amount of these nuclei depend on the molding, melting, and mechanical history of the sample, so that the semicrystalline material may have a wide variety of structure.

Origins of Characteristic Bands in the Infrared Spectra of Isotactic Polystyrene and Isotactic Poly (Ring‐d5 Styrene)

T. Onishi and S. Krimm

J. Appl. Phys. 32, 2320 (1961); http://dx.doi.org/10.1063/1.1777066 (6 pages) | Cited 14 times

Online Publication Date: 11 June 2004

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The origins of characteristic bands in the infrared spectrum of isotactic polystyrene have been studied with the aid of the spectrum of isotactic poly (ring‐d5 styrene). It is found that these bands can be classified into three types according to their experimental behavior upon crystallization of the specimen. Assignments show that the bands in any one group are associated with a specific kind of normal vibration, either of the chain or of the benzene ring. Analysis of one of these band types indicates that rotational disordering of the benzene rings may occur, and that crystallization of the polymer is probably correlated with the growth of regions which maintain statistical variability at the local chain level.

Non‐Newtonian Viscosity of Polymers

Roger S. Porter and Julian F. Johnson

J. Appl. Phys. 32, 2326 (1961); http://dx.doi.org/10.1063/1.1777067 (6 pages) | Cited 11 times

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The rheology of concentrated and bulk polymer systems has been investigated. Studies have been made on a low molecular weight series of several polymers using capillaries and a high shear concentric cylinder viscometer. The compositional and shear conditions for non‐Newtonian flow have been closely defined. Limiting high and low shear viscosities and the path of non‐Newtonian flow may be consistently correlated for concentrated systems of linear, flexible polymers. The minimum molecular weight for non‐Newtonian flow is related to the transition at low shear in log viscosity vs log molecular weight correlations. For non‐Newtonian systems, changes in apparent activation heat for viscous flow are reported as a function of shear. The conditions for laminar flow shear degradation of polymers are also given.

Rate of Recrystallization of Polyethylene Single Crystals

W. O. Statton

J. Appl. Phys. 32, 2332 (1961); http://dx.doi.org/10.1063/1.1777068 (3 pages) | Cited 27 times

Online Publication Date: 11 June 2004

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Platelet crystals of linear polyethylene recrystallize extremely rapidly when immersed in a bath of a hot liquid such as ethylene glycol, glycerine, or Woods metal. This recrystallization rate is much faster and to greater extent than when the heating medium is air. For example, heating in the liquids at 127°C causes the length of the chains between folds to increase 50% in 1 sec; the ultimate increase of 200% occurs in about 10 sec. No definite explanation is presently apparent for this much faster rate and greater extent in liquids. No evidence is found for reversibility when annealed crystals are reheated at a lower temperature.

Hypothesis of Voids in Semicrystalline Polymers

Shiro Matsuoka

J. Appl. Phys. 32, 2334 (1961); http://dx.doi.org/10.1063/1.1777069 (3 pages) | Cited 20 times

Online Publication Date: 11 June 2004

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The expression V=xVc+(1−x)Va, for the specific volume of a semicrystalline polymer, is a highly successful approximation; here x is the degree of crystallinity, Vc is the specific volume for the crystalline regions, and Va is the specific volume for the amorphous regions. In specimens for which x is near unity, however, this equation demands values for the parameters which are inconsistent with other experimental evaluations. We suggest that the discrepancy arises because of the presence of voids. Thus in addition to crystalline and noncrystalline regions we propose regions of zero density. The average volume of such voids is not known, but their existence can be inferred from the significant, permanent density enhancement which can be brought about by pressure‐induced crystallization.

Extension of the Eyring‐Ree Theory of Non‐Newtonian Flow

Joseph A. Faucher

J. Appl. Phys. 32, 2336 (1961); http://dx.doi.org/10.1063/1.1777070 (3 pages)

Online Publication Date: 11 June 2004

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The Eyring‐Ree theory of non‐Newtonian flow is extended to the case of a continuous distribution of flow units. This results in an integral equation of the form
math
.This equation can be solved by integral transform methods to yield the unknown distribution function G(t) when the flow curve F(ṡ) is known as an analytic function. For the case of limited empirical data, approximation methods can be used to obtain G(t). Experimental data are shown for polyethylene at two temperatures and the distribution functions calculated.

Molecular Motion in Disordered Regions of Solid Polyethylene

W. P. Slichter

J. Appl. Phys. 32, 2339 (1961); http://dx.doi.org/10.1063/1.1777071 (5 pages) | Cited 13 times

Online Publication Date: 11 June 2004

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Proton magnetic resonance studies have been made to compare the molecular motions ascribable to the disordered regions of solution‐grown and melt‐grown specimens of solid polyethylene. Studies have been made of both the spin‐lattice and spin‐spin relaxations. Restricted motion attributable to defect regions develops in solution‐grown crystals as the temperature is raised, but the number of protons in motion changes reversibly with heating and cooling, provided the maximum temperature is below ∼100°C. With higher temperatures the motion is greater in abundance and broader in frequency distribution. The increase is permanent despite annealing. Segmental motion attributed to molecules within the crystal is seen in solution‐grown crystals in the interval 50–100°C, but occurs to a much smaller degree in melt‐grown and heat‐treated samples. A model for the observed behavior is proposed.

Light Scattering Study of the Annealing of Drawn Polyethylene

Marion B. Rhodes and Richard S. Stein

J. Appl. Phys. 32, 2344 (1961); http://dx.doi.org/10.1063/1.1777072 (9 pages) | Cited 11 times

Online Publication Date: 11 June 2004

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Low‐angle light‐scattering patterns are obtained for stretched polyethylene films which are annealed both with and without the constraint of constant length. The effects of stretching temperature, annealing temperature, temperature of measurement, and degree of elongation are studied. Morphological changes in superstructure are found which parallel changes in crystal orientation.

Dielectric Loss in Poly‐(Hexamethylene Adipamide) and Poly‐(Hexamethylene Sebacamide) at Low Temperatures

M. N. Stein, R. G. Lauttman, J. A. Sauer, and A. E. Woodward

J. Appl. Phys. 32, 2352 (1961); http://dx.doi.org/10.1063/1.1777073 (6 pages) | Cited 8 times

Online Publication Date: 11 June 2004

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The dielectric behavior of samples of nylon 6–6 and nylon 6–10 has been studied in the temperature region from −160° to 60°C at frequencies of 0.1 to 100 kc∕sec. The effects of thermal history, electron irradiation, and post irradiation annealing on the two dielectric loss peaks found in this frequency‐temperature range have been explored. Electron irradiation of nylon 6–6 and 6–10 and thermal quenching of nylon 6–6 lowers the γ peak (−70°C at 1 kc∕sec for 66 nylon) and raises the β peak (+15°C for 66 nylon at 1 kc∕sec). Post irradiation annealing of nylon 6–6 or 6–10 irradiated to low doses (25 to 100 mrad) removes the effect of the irradiation on the dielectric behavior, but on irradiation to high dosages (900–1000 mrad) the dielectric loss values in the region of the β maximum at 0.1 and 1.0 kc∕sec are greatly reduced. The frequency shifts of the dielectric loss maxima for all samples give activation energies in kcal∕mole which fall in the 8–15 range for the β maximum and 9–19 for the γ maximum. These absorption peaks and the effect of various variables on them are discussed in terms of the molecular structure and possible molecular motions responsible for their occurrence.

Growth of Crystals from Molten Crosslinked Oriented Polyethylene

Jane T. Judge and Richard S. Stein

J. Appl. Phys. 32, 2357 (1961); http://dx.doi.org/10.1063/1.1777074 (7 pages) | Cited 32 times

Online Publication Date: 11 June 2004

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The growth of crystals from the melt in oriented, crosslinked polyethylene was studied by x‐ray diffraction and birefringence as a function of orientation. It was found that for samples elongated more than about 200%, the crystals grow with their c axes parallel to the stretching direction. At elongations less than 200%, there is a rather abrupt transition to a mode of growth in which the b axis is perpendicular to the stretching direction with a tendency for the a axis to be aligned parallel to this direction. An interpretation is made in terms of the folded‐chain concept of crystal structure.

The Swelling of Unfilled and Highly Filled Polymers

K. W. Bills and F. S. Salcedo

J. Appl. Phys. 32, 2364 (1961); http://dx.doi.org/10.1063/1.1777075 (4 pages) | Cited 4 times

Online Publication Date: 11 June 2004

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The swelling of elastomers in solvents is a useful method for determining the effective crosslinking of the polymeric structure. However, it is now shown that this method may be applied satisfactorily to highly filled polymers. A unique method has been devised for the accurate measurement of the swelling ratio of the gel phase of the filled polymers. The method is based on the observation that the binder‐filler bond, for most filler particles, releases on swelling. The binder around the particle swells, leaving a hollow pocket which becomes filled with solvent. Corrections for this ``waste'' solvent lead to the equations from which the swelling of the polymer can be calculated. Experimental verification is given for several filled systems.
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Drift Velocity of a Charged Particle in an Inhomogeneous Magnetic Field

James Hurley

J. Appl. Phys. 32, 2368 (1961); http://dx.doi.org/10.1063/1.1777076 (2 pages)

Online Publication Date: 11 June 2004

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Alfvén and Spitzer have obtained an expression for the drift velocity of a charged particle in an inhomogeneous magnetic field. The result is correct to first order in the ratio of the drift velocity to the particle velocity. We have presented here a class of fields for which the drift velocity may be calculated exactly.

A Graphical Method for Determination of Mobility Ratio in the Semiconductors from Hall Effect Measurements Only

Krzysztof Pigoń

J. Appl. Phys. 32, 2369 (1961); http://dx.doi.org/10.1063/1.1777077 (3 pages) | Cited 1 time

Online Publication Date: 11 June 2004

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A method is presented for the approximate estimation of mobility ratio b=μn∕μp from the Hall constant measurements taken in the vicinity of the intrinsic region and in this region itself. It is based on the discussion of a formula giving the Hall constant of a nondegenerate semiconductor at the exhaustion. Examples of these determinations are given; the results obtained show reasonable agreement with others' estimations.

Excess and Hump Current in Esaki Diodes

Richard S. Claassen

J. Appl. Phys. 32, 2372 (1961); http://dx.doi.org/10.1063/1.1777078 (7 pages) | Cited 21 times

Online Publication Date: 11 June 2004

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The origin of the excess and hump current in Esaki diodes is described in terms of discrete defect energy levels in the forbidden band. The hump current results from equi‐energy transitions of electrons which originate in a defect level in the n side and tunnel to the valence band on the p side. Impurity conduction is required for appreciable hump currents. The position of the hump locates the defect level if the Fermi level is known for the n side. The excess current is explained in terms of energy dissipating transitions in which electrons start from a defect location within the junction, tunnel to a virtual state in a localized defect in the p region, and drop to the valence band by impact recombination. A crude derivation by the WKB method relates the logarithm of the excess current to the bias voltage where the proportionality factor contains the square root of the effective mass of the electron. From current‐voltage curves for diodes fabricated from germanium, silicon, and gallium arsenide, the effective electron masses are estimated as 0.01, 0.1, and 0.05 m, respectively. Defect levels in germanium are estimated at 0.06 and 0.24 ev below the conduction band; levels in silicon are located at 0.04 and 0.42 ev; and in gallium arsenide 0.12 and 0.5 ev below the conduction band. The simultaneous existence of two defect levels can give rise to two distinct slopes of the logI vs V curve which have been observed in silicon and gallium arsenide diodes following irradiation with 2 Mev electrons.

Effects of Phosphor Powder Dispersion in Electroluminescent Lamps

W. A. Thornton

J. Appl. Phys. 32, 2379 (1961); http://dx.doi.org/10.1063/1.1777079 (7 pages) | Cited 2 times

Online Publication Date: 11 June 2004

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The statistical distribution of phosphor crystals in the solid dielectric material of a practical electroluminescent lamp influences the observed characteristics of the lamp. Calculation on the basis of a very simple model shows that maximum efficiency is favored by high phosphor concentration, fine particles, and thick phosphor layers; the slope and intercept of the usual brightness voltage plots are affected by the same variables. Measurements on electroluminescent lamps with these variations are in substantial agreement with the predictions.

Theory and Application of a Superposition Model of Internal Friction and Creep

J. Ross Macdonald

J. Appl. Phys. 32, 2385 (1961); http://dx.doi.org/10.1063/1.1777080 (14 pages) | Cited 17 times

Online Publication Date: 11 June 2004

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Energy dissipation in solids is important in both transient and steady‐state measurements. The results of such measurements can be associated with a distribution of relaxation times provided the material is linear. In the present work, general relations are derived for the attenuation factor, phase factor, and specific dissipation function 1∕Q pertaining to transmission of small amplitude stress waves in a material describable by a distribution of relaxation times. Next, a specific, physically realizable relaxation time distribution is used to obtain a creep function and to relate transient creep and frequency response measurements. Curves of 1∕Q vs frequency are calculated with a digital computer and show a region approximately proportional to frequency at sufficiently low relative frequencies, a region of virtual frequency independence, and a final region proportional to inverse frequency at high relative frequency. The relation of the present work to other treatments of creep and internal friction is discussed, and the applicability is examined of the analytic and numeric results to creep measurements on metals and rocks, to low‐frequency wave transmission in the earth, to other damping results for the earth as a whole, and to higher‐frequency wave transmission and vibration results for geophysical and other solids. Good agreement between theory and experiment is found for frequency regions where adequate data are available, indicating that all the damping phenomena considered may be well described by a linear theory in the range of very small strain.

New Derivation of the Vacuum Breakdown Equation Relating Breakdown Voltage and Electrode Separation

A. Maitland

J. Appl. Phys. 32, 2399 (1961); http://dx.doi.org/10.1063/1.1777081 (9 pages) | Cited 43 times

Online Publication Date: 11 June 2004

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An analysis of the published measurements of breakdown voltage for various gap lengths for uniform and approximately uniform fields shows that the results may be represented by the breakdown equation V = Cxα and that the values of α lie in the range 0.1 to 1.1 with a mode of 0.7. A theory is developed which leads both to a breakdown equation of the same form and to a general expression to account for the range of values of α. This expression is confirmed for gaps up to 0.075 cm by direct experiment. The development is based on the postulate that an electron beam is emitted from the cathode, diverges, and bombards the anode to cause breakdown when a critical power flux is reached. The factor C is shown to include the critical power flux and to be related to both field and electrode separation. In support of the theory, the radii of craters produced on the anode are measured and shown to be related to the radius of an electron beam at the anode. Calculation shows the current carried by the beam to be of the order of 10−4 amp. Values of the critical power flux obtained from the equation V = Cxα and from anode crater data, respectively, agree within a factor of 1.5 and are of the order of 108 w cm−2. To explain the observed phenomena, a multiple electron beam system is proposed.

Excess Noise in Germanium and Gallium‐Arsenide Esaki Diodes in the Negative Resistance Region

M. D. Montgomery

J. Appl. Phys. 32, 2408 (1961); http://dx.doi.org/10.1063/1.1777082 (3 pages) | Cited 1 time

Online Publication Date: 11 June 2004

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Low‐frequency noise measurements have been made throughout the entire useful bias range of germanium and GaAs Esaki diodes. Evidence is presented in agreement with Esaki and Yajima that a near square‐law relationship exists between the mean‐square, short‐circuit noise current and excess current for bias voltages beyond the valley voltage in germanium diodes. Attempts to find a like relationship in GaAs were not conclusive. Measurements of the noise within the negative‐resistance regions of the diodes showed a nearly continuous exponential relationship between excess noise and bias for the germanium units and a similar plot was obtained for the GaAs diodes, except a well‐defined peak in the noise current was found at about 0.2 v forward bias. The evidence that the results indicate a rather continuous distribution of allowed states in the forbidden band of the germanium samples and a possible localized maximum in these states in the GaAs samples is discussed.

Physical Behavior of Photographic Grains

G. Sprague

J. Appl. Phys. 32, 2410 (1961); http://dx.doi.org/10.1063/1.1777083 (11 pages)

Online Publication Date: 11 June 2004

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A quantitative treatment of the photographic process is carried out, modeled on the Gurney Mott theory. This is extended by taking account of the distribution of photolytic silver during and after the exposure. Applications of the theory are made to some simple types of sensitizing. The most important physical parameter of a photographic grain seems to be the number of electron traps.

Transparency of Glass and Certain Plastics under Shock Attack

H. Dean Mallory and William S. McEwan

J. Appl. Phys. 32, 2421 (1961); http://dx.doi.org/10.1063/1.1777084 (4 pages) | Cited 4 times

Online Publication Date: 11 June 2004

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It is considered common knowledge by many workers in the field of detonation phenomena that transparent plastics quickly go opaque under strong shock wave attack. In this paper high‐speed photographs are shown, and it is seen that Lucite and Plexiglas do not go opaque until shattered by tension waves. The behavior of plate glass is somewhat similar. By adjustment of dimensions and lighting, events can be observed with good photographic quality through the shock front for an undetermined length of time.

Determination of Field Strength for Field Evaporation and Ionization in the Field Ion Microscope

Erwin W. Müller and Russell D. Young

J. Appl. Phys. 32, 2425 (1961); http://dx.doi.org/10.1063/1.1777085 (4 pages) | Cited 31 times

Online Publication Date: 11 June 2004

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The field strength required for field evaporation of tungsten and for best image conditions in the field ion microscope is measured by comparison with field electron emission of the same emitter. The evaporation field is independent of emitter radius except for radii below 150 A where the influence of free surface energy becomes noticeable. The field for the best conditions of a helium ion image of a typical emitter of 1000 A radius is 440 Mv∕cm. This field increases gradually with decreasing tip radius, so that the ratio of evaporation field to best image field for tungsten decreases from 1.27 at 1000 A radius to 1.0 at about 40 A radius. The radius dependence of this ratio can be calculated by assuming that the time a hopping atom spends in the critical ionization zone is a constant fraction of the ionization time. Practical implications are that large tip radii are preferable for easily evaporating emitter materials, and small radii may be useful when field evaporation is to be studied under best image conditions.

X‐Ray Measurement of Stacking Fault Widths in fcc Metals

B. E. Warren

J. Appl. Phys. 32, 2428 (1961); http://dx.doi.org/10.1063/1.1777086 (4 pages) | Cited 25 times

Online Publication Date: 11 June 2004

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A generalized derivation of the broadening of powder pattern lines by stacking faults has been carried through allowing for fault planes of arbitrary dimensions. A minimum dimension for the fault plane Tmin is obtained from the measurable effective particle sizes De(111) and De(200). Values of Tmin of the order of 200 A are obtained for samples of filings of copper, α brass, and silver. The results suggest that, in the drastic cold work involved in filings, the stacking faults tend to extend over rather large distances comparable to the coherent domain dimensions.

(110) Nickel Surface

L. H. Germer, A. U. MacRae, and C. D. Hartman

J. Appl. Phys. 32, 2432 (1961); http://dx.doi.org/10.1063/1.1777087 (8 pages) | Cited 35 times

Online Publication Date: 11 June 2004

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Nickel (110) surfaces, in clean and nearly clean conditions, have been studied by low‐energy electron diffraction. When free from foreign atoms, the surface (110) plane of atoms has the normal arrangement expected for such a plane. Very slight contamination by oxygen (and perhaps other atoms) results, in some cases, in an arrangement of the topmost layer of atoms in which nickel and oxygen (or another atom) alternate along each [100] line and also along each [110] line. Study of such a surface has shown that the superficial half‐layer of nickel atoms is displaced toward the bulk of the crystal by about 0.10 A.

Production of High Ion Densities in Helium by Means of High Explosives

G. E. Seay, L. B. Seely, and R. G. Fowler

J. Appl. Phys. 32, 2439 (1961); http://dx.doi.org/10.1063/1.1777088 (9 pages) | Cited 5 times

Online Publication Date: 11 June 2004

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Temperatures of about 20 000°K with ion densities ranging from 1017 to 1018 cm−3 have been produced in helium by means of explosive‐driven shocks. Helium was used because of its relatively simple structure, but this choice eliminated usual shock methods because of the high sound speed and high ionization potential. Shock waves having sufficient strength and planarity were obtained by reflecting against a glass plate initially strong shock waves produced by high explosives. Equilibrium calculations based on smear camera velocities of accurately plane shocks were used to determine the state of the gas behind the reflected shock wave.
The light emitted consisted of a continuum on which were superimposed shifted and broadened lines of the normal helium spectrum and forbidden lines as well. Time‐resolved spectrograms showed evidence of a measurable relaxation time at the shock front but no evidence of significant radiative cooling of the gas behind the shock.
Under the conditions of these experiments, it was demonstrated that a quantitative prediction of the behavior of the helium states with principal quantum numbers 2, 3, and 4 requires consideration of the effects of electrons as well as ions.
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