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1 Oct 1968

Volume 39, Issue 11, pp. 4877-5346

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Stress Softening and Strain Softening of Poly(Methyl Methacrylate) in Yielding under Constant Load

Dieter H. Ender

J. Appl. Phys. 39, 4877 (1968); http://dx.doi.org/10.1063/1.1655880 (6 pages) | Cited 12 times

Online Publication Date: 19 November 2003

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The strain rate of poly(methyl methacrylate) during yielding under constant load was determined experimentally for various tensile loads at temperatures from 70° to 100°C. In the constant‐load test, the polymer strains uniformly beyond the yield point up to several times the yield strain. The yield point is evident as a minimum of the strain rate. Intermittent superposition of load increments affects the strain rate reversibly. The observed strain‐rate increase under constant load in the uniform‐strain post‐yield region, results essentially from strain softening with some additional softening from the stress increase due to specimen thinning. The stress influence on the strain rate is expressible as a stress‐shift factor of the strain rate. A theoretical stress‐shift factor is derived from Doolittle's viscosity equation and the assumption that Poisson's volume dilatation contributes entirely to the free volume. Good agreement between the predicted and the observed stress‐shift of the strain rate is found. An apparent anomaly of the stress‐shift factor at 100°C is probably caused by recovery from strain softening in the vicinity of the glass transition temperature.

Laser‐Excited Raman Scattering in Polystyrene

S. W. Cornell and J. L. Koenig

J. Appl. Phys. 39, 4883 (1968); http://dx.doi.org/10.1063/1.1655881 (8 pages) | Cited 22 times

Online Publication Date: 19 November 2003

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Atactic polystyrene was examined by argon ion laser‐excited Raman scattering. Depolarization measurements of oriented and unoriented polystyrene were made. An analysis is made of the depolarization measurements in terms of the orientation of the sample. Comparisons are made with dichroic measurements made by infrared. Utilizing Raman and infrared polarization data on oriented polystyrene, some changes in band assignments have been made.

Birefringence Effects in Unplasticized and Plasticized Polyvinyl Chloride

R. D. Andrews and Y. Kazama

J. Appl. Phys. 39, 4891 (1968); http://dx.doi.org/10.1063/1.1655882 (8 pages) | Cited 5 times

Online Publication Date: 19 November 2003

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Some basic birefringence effects in a PVC homopolymer have been investigated as a function of temperature, stress or strain level, and plasticizer content. The behavior of the stress‐optical coefficient (SOC) has been investigated over a broad temperature range extending down to liquid‐nitrogen temperature for both unplasticized polymer and polymer containing weight fractions of 0.1, 0.3, and 0.5 dioctyl phthalate (DOP), 0.3 dioctyl adipate (DOA), and 0.3 tricresyl phosphate (TCP). The SOC of unplasticized PVC is negative below the glass transition and shows a sign change to large positive values above the glass transition. This progressive change from negative to positive values is also observed when stress level is increased in the glassy state below Tg, or when plasticizer content is progressively increased. The SOC goes to large positive values above Tg for all plasticized polymers. A positive SOC can therefore be considered characteristic of rubbery state behavior of PVC, and a positive sign will consequently be characteristic of orientation birefringence as well. Orientation birefringence increases with increasing temperature in all cases; however, its temperature coefficient (fractional change per °C) is strongly dependent on both plasticizer content and plasticizer type. The theoretical significance of these results is discussed.

Rheo‐optics of High‐Speed Deformation. II. Polyethylene and Polybutene‐1

P. F. Erhardt and R. S. Stein

J. Appl. Phys. 39, 4898 (1968); http://dx.doi.org/10.1063/1.1655883 (5 pages) | Cited 5 times

Online Publication Date: 19 November 2003

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The photographic light scattering‐technique was used to study the relationship between sample deformation and spherulite deformation during rapid stretching of polyethylene and polybutene‐1 films. Scattering patterns are interpreted in terms of spherulite deformation theory to give the elongation ratio of the spherulite which is compared with that of the sample. At low elongations spherulite deformation is less than or equal to that of the sample indicating that an affine deformation model is a reasonable approximation. At high elongations the spherulite elongation ratio is greater than that of the sample. This is due to inhomogeneous deformation where the local deformation of the sample in the scattering region is greater than the macroscopic deformation.

The Relationship between Morphology and Light‐Scattering Patterns for Polytetrafluoroethylene

Marion B. Rhodes and Richard S. Stein

J. Appl. Phys. 39, 4903 (1968); http://dx.doi.org/10.1063/1.1655884 (7 pages) | Cited 12 times

Online Publication Date: 19 November 2003

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Two types of light‐scattering patterns have been observed for polytetrafluoroethylene films. It has been postulated that these patterns arise from differences in the orientation of the optic axis with respect to the morphological unit of the structure. Films studied by the light‐scattering technique have been examined by electron microscopy and the differences between the patterns are ascribed to differences in the orientation of the lamella with respect to the plane of the film.

Rheo‐optical Behavior of Polyacrylonitrile: Creep and Creep Recovery

R. D. Andrews and H. Okuyama

J. Appl. Phys. 39, 4909 (1968); http://dx.doi.org/10.1063/1.1655885 (6 pages) | Cited 4 times

Online Publication Date: 19 November 2003

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The rheo‐optical behavior of PAN homopolymer film has been investigated by means of creep and creep recovery experiments with simultaneous measurements of birefringence changes. Creep experiments were carried out at temperatures of 70°, 100°, 120°, 140°, and 160°C, at a series of stress levels. This temperature range spanned the 90° and 140°C transition temperatures. A progressive change in shape of the creep curve in a log‐log plot of compliance vs time is seen: from very flat and gradual to more S‐shaped both with increasing temperature and with increasing stress at the higher temperatures. This S‐shaped curve can be identified with the cold‐drawing phenomenon, even though no neck formation was seen. Creep recovery is more complete at lower temperatures and after lower final strains in the creep experiment. Most of the recovery is instantaneous; only a very small amount of further time‐dependent recovery is observed. At higher temperatures and higher strains, creep seems to involve permanent changes in the solid‐state structure; these produce a permanent set which is not recoverable even on heating to higher temperatures. The creep and creep recovery, therefore, cannot be properly described in terms of the laws of simple viscoelasticity. The rheo‐optical behavior of this polymer is clearly more complex than that of PVC, which has been investigated previously. Some speculations regarding the solid‐state structure of PAN are presented, based primarily on the birefringence results.

Behavior of Elastic Networks of Various Degrees of Orientation in the Kinetic Theory of Fracture

H. H. Kausch‐blecken von Schmeling and C. C. Hsiao

J. Appl. Phys. 39, 4915 (1968); http://dx.doi.org/10.1063/1.1655886 (5 pages) | Cited 10 times

Online Publication Date: 19 November 2003

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This paper describes a kinetic theory of fracture initiation using a linear elastic network as an approach to represent the strength and elastic properties of oriented materials. Emphasis has been placed on the questions as to whether the assumptions of small strains and invariant molecular orientational distribution are valid for the whole period of fracture initiation. The decrease of the modulus of elasticity resulting from the breakage of molecular elements during this period was found to be less than 1%. For brittle materials with high velocities of crack tip propagation the initiation period covers most of the lifetime of a sample. The logarithms of time to break calculated accordingly for network systems of different degrees of orientation are linear functions of applied stress over a wide range of stress. The slopes of these linear curves are inversely proportional to the modulus of elasticity of the network at zero time. Therefore, if the calculated curves of the logarithm of time are plotted versus the applied stress divided by the initial modulus of elasticity the linear portions of all curves reduce to one. For very small or large stresses the curves deviate from linearity.

Peierls Stress for Screw Dislocations in Polyethylene

James M. Peterson

J. Appl. Phys. 39, 4920 (1968); http://dx.doi.org/10.1063/1.1655887 (9 pages) | Cited 15 times

Online Publication Date: 19 November 2003

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The Peierls stress for the motion of screw dislocations with [001] Burgers vectors in orthorhombic polyethylene has been investigated. Assumptions made are that a polymer chain moves along [001] as a unit and no intramolecular interactions need be considered, that the chains do not twist during dislocation motion, and that material displacements around the dislocation are the same as in continuum anisotropic theory. The force between chains is shown to vary nearly sinusoidally with relative displacement along the chain direction. The shear moduli C44 and C55 are derived. The Peierls stresses are expressed relative to C55. The results show that for reasonable values of C44∕C55, the Peierls stress for screw dislocation glide on a (100) slip plane is about 5×10−5 C55, while the Peierls stress for dislocation glide on a (010) slip plane is about 0.1 C55. For screw dislocation glide, it is concluded that dislocation motion on a (100) slip plane is probable, but that dislocation motion on a (010) slip plane is highly unlikely. Any slip plane other than (100) for these screw dislocations would necessitate crossing (100) planes, and Peierls stresses arising from glide on (010) slip planes would then be felt. Hence it is concluded that (100) is the only likely slip plane for the glide of such screw dislocations.

Chain‐Folding and Molecular‐Species Segregation in the Crystallization of Linear High Polymers

P. H. Lindenmeyer and J. M. Peterson

J. Appl. Phys. 39, 4929 (1968); http://dx.doi.org/10.1063/1.1655888 (3 pages) | Cited 4 times

Online Publication Date: 19 November 2003

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For linear high polymers, the assumption that chain ends are excluded from the crystal plus the existence of a reasonable width in the distribution of chain lengths is sufficient to cause a minimum in the free energy‐vs‐crystal thickness curve at temperatures well below the melting point. The predicted crystal thickness is relatively insensitive to crystallite‐surface free energy, but is sensitive to the degree of supercooling and the molecular length distribution. At temperatures lower than a few degrees below the equilibrium mp, there exists a thermodynamic driving force for molecular‐species segregation. Hence according to the theory, crystals which are composed of a variety of molecular species are thermodynamically metastable.

Tensile Deformation of Oriented Polyethylene

T. Hinton and J. G. Rider

J. Appl. Phys. 39, 4932 (1968); http://dx.doi.org/10.1063/1.1655889 (6 pages) | Cited 17 times

Online Publication Date: 19 November 2003

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Tensile test specimens have been cut from high‐density polyethylene sheet which had been fully cold‐drawn. The angle between the tensile axis and the draw direction was varied from 30° to 75°. The tensile deformation of such specimens was analyzed with the aid of a grid printing technique and was shown to be predominantly simple shear in the molecular chain direction. However, detailed analysis has shown that associated with the simple shear process there was a reorientation of the material, which is compared with the predictions of an aggregate theory for oriented polyethylene. A yield criterion and the absence of any work hardening for large deformations have been established.

Energy Contribution to Rubber Elasticity

Mitchel Shen and Paul J. Blatz

J. Appl. Phys. 39, 4937 (1968); http://dx.doi.org/10.1063/1.1655890 (7 pages) | Cited 20 times

Online Publication Date: 19 November 2003

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Stress‐temperature measurements were performed for natural rubber at both ``infinitesimal'' (<10%) and finite (<100%) strains. Data are used to calculate the internal‐energy contribution to the elastic stress fe by several thermoelastic equations. A unified derivation of these equations is given, which leads naturally to a new equation based on the temperature coefficient of shear modulus of the rubber. It is demonstrated that the dependence of the relative energy contribution fe∕f on deformation as previously reported arises because of the difficulty in obtaining extremely accurate data in the low‐strain regions. Calculation of the same data by our new equation shows fe∕f to be independent of deformation for the region of strains in which the statistical theory of rubber elasticity applies. Thus the postulate of additivity of configurational free energy, basic to the derivation of the statistical theory, is vindicated. Finally it is shown that the stress‐temperature measurements are sensitive to the sample geometry. For butt‐jointed samples, which are believed to approach uniform stress distribution, the relative energy contribution is found to be approximately 15% for natural rubber.

Crystallization of Low‐Molecular‐Weight Polypropylene Fractions

D. R. Morrow and B. A. Newman

J. Appl. Phys. 39, 4944 (1968); http://dx.doi.org/10.1063/1.1655891 (7 pages) | Cited 73 times

Online Publication Date: 19 November 2003

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Samples of very low molecular‐weight fractions of isotactic polypropylene have been crystallized by means of a solvent‐evaporation technique as well as by melt recrystallization. The crystalline entities obtained by these methods have been examined in terms of their internal structure and associated morphology. The particular polymorphic form observed for these fractions is dependent on both the length of the molecule and the particular crystallization conditions employed. The morphological characteristics of the samples have been found to be qualitatively similar to those previously reported for unfractionated polypropylene and high‐molecular‐weight fractions, in spite of the fact that the molecular lengths of the samples investigated are sufficiently short to prevent chain folding. Selected‐area electron‐diffraction patterns have been obtained from the γ form and from mixed α and γ form of the isotactic polymer. The diffraction data have resulted in a modification of the previously proposed triclinic unit cell for the γ phase, and a conclusion that the γ→α transformation in isotactic polypropylene is martensitic in nature. The mechanism of this solid‐solid transformation involves relative motion between the (040) planes which are found to be invariant in the two crystal phases.

Lattice‐Frequency Studies of Crystalline and Fold Structure in Polyethylene

M. I. Bank and S. Krimm

J. Appl. Phys. 39, 4951 (1968); http://dx.doi.org/10.1063/1.1655892 (8 pages) | Cited 30 times

Online Publication Date: 19 November 2003

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The assignment of the 71 cm−1 band in the infrared spectrum of polyethylene to the B1u translational lattice vibration has been confirmed by dichroism studies on an a‐axis oriented sample. This permits confident use of the Tasumi‐Krimm calculations for the dependence of this frequency of unit‐cell parameters. The results of these calculations have been applied to the analysis of the observed lattice frequency differences between odd and even n‐paraffins, and it is shown that the frequency shifts are interpretable in terms of changes in unit cell parameters resulting from different methyl end‐group packing. The variation of the lattice frequency with degree of branching observed in a series of low‐density polyethylenes can be understood on the basis of incorporation of branches in the lattice. The dependence of the lattice frequency in high‐density polyethylene on the physical state of the specimen can be correlated with different constraints imposed by the fold regions on the chain packing. These results indicate that the folds must be considered to be ``tight'' rather than ``loose.''

Structure and Thermal Behavior of Pressure‐Crystallized Polypropylene

J. A. Sauer and K. D. Pae

J. Appl. Phys. 39, 4959 (1968); http://dx.doi.org/10.1063/1.1655893 (10 pages) | Cited 20 times

Online Publication Date: 19 November 2003

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Samples of isotactic polypropylene have been crystallized at a pressure of 3.86 kbar and under a variety of crystallization conditions. These include isothermal crystallization at five different degrees of supercooling ranging from ΔT=70°C to ΔT=34°C and crystallization by slow cooling from 248°C. Each sample was studied by means of x‐ray diffraction at both room and elevated temperature, by differential scanning calorimetry, and by electron microscope observation of replicas of the fracture surface. The x‐ray diffraction results show that all the pressure‐crystallized samples have formed in the γ, or triclinic, modification. Depending upon crystallization conditions, this phase may be stable or metastable. For high values of ΔT, the triclinic phase shows a partial conversion to the α, or monoclinic, phase under elevated temperature annealing. For low values of ΔT, the γ phase does not convert to α even at elevated temperatures. The DSC measurements indicate that the melting temperatures of the pressure‐crystallized samples are dependent upon the degree of supercooling. For a heating rate of 40°C∕min, the melting temperature is at 157°C for ΔT=70°C; it rises with decrease of the degree of supercooling and occurs in two stages at 175° and at 182°C for ΔT=34°C. Fracture‐surface replicas of the slowly cooled sample show that the bulk polymer contains well‐delineated, lath‐shaped crystals, similar in morphology to those obtained from dilute‐solution crystallization. For the samples isothermally crystallized, the fracture‐surface replicas show the presence of long thin fibril‐like entities. Consideration is given to the possibility that these fibrillar elements are single‐crystal lamellas of low‐molecular‐weight polymer that have crystallized during cooling of the whole polymer from the crystallization temperature.

Dissolution of Polyethylene Single Crystals in Xylene and Octadecane

T. W. Huseby and H. E. Bair

J. Appl. Phys. 39, 4969 (1968); http://dx.doi.org/10.1063/1.1655894 (5 pages) | Cited 10 times

Online Publication Date: 19 November 2003

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Solution temperatures in xylene and n‐octadecane of polyethylene single‐crystal aggregates were measured by differential scanning calorimetry. Crystals were irradiated to suppress morphological changes during the heating process. The measurements, as a function of reciprocal lamellar thickness, yield values for the equilibrium dissolution temperatures Td0 and end surface free energy σe of Td0=113.7±1.2°C and σe=93±8 erg∕cm2 for dissolution in xylene, and Td0=129.4±1.6°C and σe=92±10 erg∕cm2 for dissolution in octadecane.

Variations of the Unit‐Cell Dimensions of Polyethylene: Effect of Crystallization Conditions, Annealing, and Deformation

G. T. Davis, R. K. Eby, and G. M. Martin

J. Appl. Phys. 39, 4973 (1968); http://dx.doi.org/10.1063/1.1655895 (9 pages) | Cited 40 times

Online Publication Date: 19 November 2003

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It is shown that the orthorhombic unit cell dimensions of a given polyethylene are not unique, but depend on the physical history of a sample. For polymer crystallized from a ¾% p‐xylene solution, the values of a and b measured at 23°C by powder camera technique vary up to 0.8% for crystallization temperatures of 50°, 70°, and 90°C, annealing temperatures from 50° to 127°C, and deformation. The as‐crystallized values of a and b as well as the effects of annealing and deformation are smaller the thicker the crystals. For ``undeformed'' crystals the changes correlate with the reciprocal of crystal thickness but for deformed crystals the changes occur before the thickness increases (even below the crystallization temperature). The dimensions undergo the greatest change within the first 2 min of annealing and change very little with time thereafter. The only exception observed is a slow decrease of b with time of annealing at 100°C. Crystals grown from other solvents exhibit very nearly identical effects, and the presence of solvents does not alter the cell dimensions at room temperature. Similar effects are observed when crystals grown from the melt by slow cooling, quenching in ice water, and quenching in a dry ice‐acetone suspension are annealed at temperatures from 60° to 127°C. In these crystals also the dimensions correlate with the reciprocal of the long period and extrapolate to values of 7.372 and 4.933 Å for a and b, respectively, at infinite long period. The origins of the effects cannot be assigned with certainty but changes in the fold surfaces and their concentration probably play a role; a discussion relevant to this and other mechanisms is presented. Corresponding to the maximum changes in cell dimension are changes of 1% in cell density which corresponds to an apparent change in degree of crystallinity of 6%. These changes are too small to account for the frequently reported discrepancy between the cell density and that measured by pycnometry, etc. However, the changes can account for some of the variation with crystallization temperature of the density measured by pycnometry, etc. The effects of cell variation should be considered in the detailed interpretation of the variation of physical properties with physical history of polymer crystals.

Changes in Fold Structure with Annealing in Polyethylene

D. E. Witenhafer and J. L. Koenig

J. Appl. Phys. 39, 4982 (1968); http://dx.doi.org/10.1063/1.1655896 (3 pages) | Cited 3 times

Online Publication Date: 19 November 2003

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During the annealing of quenched linear polyethylene, the ratio of the absorbance of the 1304 cm−1 band to the absorbance of the 1350 cm−1 band decreases toward the value found in single crystals and has the wrong annealing temperature dependence. Since this process takes place too slowly to be a recrystallization from the melt, this change must reflect a transformation of loose‐loop type folds to the more regular type as found in single crystals. Slowly cooled samples have the same ratios as single crystals and do not change upon annealing.

Infrared Studies of Chain Folding in Polyethylene Oxide

A. C. Angood and J. L. Koenig

J. Appl. Phys. 39, 4985 (1968); http://dx.doi.org/10.1063/1.1655897 (6 pages) | Cited 6 times

Online Publication Date: 19 November 2003

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A large number of additional peaks, some observed for the first time, appear in the ir spectra of polyethylene oxide when run at liquid‐nitrogen temperatures. These peaks are sensitive to molecular weight, thermal history of the sample, and the temperature at which spectra are run. The peaks are attributed to vibrational modes due to sequences of rotational isomers, which are present in the fold. Although presently regular and irregular folds cannot be distinguished, the possibility of these peaks arising from cilia, or interlamellar links has been discounted.
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