Volume 34, Issue 1, 01 January 1963
 SPECIAL ISSUE ON HIGH‐POLYMER PHYSICS


Solution of Gases in Polyethylene Terephthalate
View Description Hide DescriptionThe solubilities of helium, nitrogen, oxygen, argon, methane,carbon dioxide, and ethane in glassy amorphous and crystalline polyethylene terephthalate have been studied by time‐lag and/or static sorption methods. Solubilities of all the gases but ethane were also determined in the rubbery crystalline polymer. The only deviations from Henry's law were displayed by ethane at 25°C and carbon dioxide at 25° and 40° C in the glassypolymer. Correlation of solubility constants for oxygen and nitrogen obtained by the static sorption method with values obtained dynamically indicate that the glassy crystalline polymer is an isotropic diffusion medium. Sorption in the glassy amorphous and crystalline polymers generally takes place by two processes operating concurrently: ordinary dissolution plus ``hole‐filling.'' The ``hole‐filling'' process obeys a Langmuir expression and dissolution obeys Henry's law for sorption of carbon dioxide in the amorphous polymer at 25°C. Crystallinity reduces gas solubility in the glassypolymer, but not generally in direct proportion to the decrease in amorphous volume. An exception is helium, which appears to obey the simple law, k=k*α. The glassy state of the partially crystalline polymer extends to about 80–85°C where a transition region is noted on a van't Hoff plot for solubility constants. The other extremity of this region (about 95°C) marks the onset of rubber‐like behavior in the polymer. Heats of sorption in the glassy crystalline polymer are more exothermic than in the rubbery crystalline polymer,characteristic of the transition from sorption by dissolution and void‐filling processes to dissolution alone. The heat of solution of helium is slightly positive in both the glassy and rubbery states of the crystalline polymer, with no evidence of a break at T_{g} . It appears that the major contribution to helium sorption in either state of the crystalline polymer is ordinary dissolution. In both the glassy and rubbery states, carbon dioxide shows evidence of a polar interaction with the polymer.Solubility constants are correlated with gas force constants ε/k̄ in both the glassy amorphous and rubbery crystalline polymers.

Diffusion of Gases in Polyethylene Terephthalate
View Description Hide DescriptionDiffusion of helium, oxygen, nitrogen, argon, carbon dioxide, and methane in glassy and rubbery polythylene terephthalate has been studied in the range 25° to 130°C. Despite the abnormal solution behavior of these gases in the glassypolymer, the diffusion process is evidently normal and Fickian: Correlation of solubility constants for oxygen and nitrogen, obtained by the time‐lag method, with data obtained by a static sorption method, indicates that glassy crystalline polyethylene terephthalate may be considered an isotropic diffusion medium. Diffusion is impeded purely geometrically by the presence of the crystallites, and the impedance factor is equal to the reciprocal of the amorphous volume fraction. In the rubbery crystalline state of the polymer,diffusion is Fickian and apparent activation energies for diffusion are larger than those in the glassy crystalline polymer. A model for diffusion in the glassy amorphous and crystalline polymers is proposed, assuming that the driving force for diffusion is the concentration gradient of dissolved molecules which are assumed to be in local equilibrium with molecules in the ``holes.'' The model predicts that actual diffusion constants and activation energies are larger than those experimentally measured. Thus, part of the observed difference between values of E_{Da } in the glassy and rubbery states may be reconciled. Correlations of D and E_{Da } with the square of gas molecular diameters are obtained in both the glassy and rubbery states. In the latter plots, the helium data fall above the correlations, showing evidence of partially non‐activated diffusion in both states of the polymer.

Free Vibration Experiment in the Theory of Linear Viscoelasticity
View Description Hide DescriptionAn idealized free‐vibration experiment is analyzed on the basis of the theory of infinitesimal linear viscoelasticity. The resulting motion can be expressed as a sum of terms, of which some are damped sinusoidal waves while others are negative exponentials in time. For some three parameter models of viscoelastic behavior, the results of this theory are compared with those of the usual treatment which leads to a simple damped sinusoidal wave.

Crystalline and Paracrystalline Order in High Polymers
View Description Hide DescriptionThe mathematical treatment of light scattering by regular and random arrays of points is outlined. The diffraction patterns of two‐dimensional models are compared with patterns from ideal crystals, imperfect crystals, and paracrystalline lattices. The effects of various types of crystalline imperfections and paracrystalline order on the diffraction pattern are analyzed and examples are presented. It is shown that both natural and synthetic polymers can be treated as paracrystalline materials. The diffraction patterns of polyethylene after various thermal and mechanical treatments are discussed. A detailed model of the structure of polyethylene is presented and various features of the structure of other polymers are pointed out.

Application of the Theory of Paracrystals to the Crystal Structure Analysis of Polyacrylonitrile
View Description Hide DescriptionX‐ray diffraction from single crystals of polyacrylonitrile shows that the diffuse nature of the nonequatorial scattering maxima cannot be accounted for by crystal size. The theory of paracrystals may be used to set both an upper and a lower limit to the amount of lattice distortion and yields a plausible explanation for the absence or extreme weakness of higher‐order reflections. Finally, it is shown why the diffuse maxima cannot be used directly in measuring lattice parameters and the method which must be used to obtain a more definite crystal structure for polyacrylonitrile is indicated.

Scattering of Light by Heterogeneous Spheres
View Description Hide DescriptionThe theory for the scattering of light by homogeneous spheres satisfying the Rayleigh‐Gans approximation is extended to include the effect of heterogeneous density within the spheres. These internal heterogeneities are described by a Debye‐type exponential correlation function. The resulting scattering consists of a sum of two terms: one representing the homogeneous sphere scattering contribution and the second representing the additional contribution to scattered intensity arising from the internal heterogeneities. The predicted scattering patterns bear similarities to the experimentally observed scattering patterns obtained for spherulites of high polymers.

Order and Flow of Liquid Crystals: The Nematic Mesophase
View Description Hide DescriptionLiquid crystals offer a unique opportunity for physical studies. The nematic mesophase is an aggregate, yet fluid state, which consists of anisometric, rodlike structures. The flow of three nematic‐forming compounds, p‐azoxyanisole, anisaldazine, and p‐anisal‐p‐aminoazobenzene, was studied in both their isotropic and anisotropic states. Studies were made with capillary viscometers and with a high‐shear concentric cylinder viscometer. New density, coefficient of expansion, and transition temperature data are also given. The instrumentation used is described. The results add definition to the viscosity and density anomalies at nematic‐isotropic transitions. The data for p‐anisal‐p‐aminoazobenzene are entirely new. Values for anisaldazine establish previous viscosity and density results on an absolute basis. New results on p‐azoxyanisole contribute a temperature and shear rate extension to previous studies.

Order and Flow of Liquid Crystals: The Cholesteric Mesophase
View Description Hide DescriptionThe flow properties of three cholesteryl esters have been studied in both their liquid crystal and isotropic ranges. Tests were made with low‐shear capillary viscometers and with a high‐shear rotational concentric cylinder instrument. Measurements on cholesteryl acetate are compared with relative viscosities given by Ostwald. Ostwald's viscosity data on cholesteryl propionate and butyrate are reevaluated. New flow data are also given for cholesteryl palmitate and stearate. Viscosity and flowactivation energy are reported as a function of temperature, shear, and ester molecular weight. Results indicate that all cholesteryl esters show Newtonian flow in their isotropic states and non‐Newtonian flow in their respective cholesteric liquid crystal phases. New transition temperature and density data are also given for the three esters. These values and earlier density data for the benzoate ester are discussed in terms of the aggregate size of liquid crystals. Comparisons are made between the major types of mesophase.

Wide‐Line Nuclear Magnetic Resonance Studies of Poly (Ethylene Terephthalate)
View Description Hide DescriptionWide‐line nuclear magnetic resonance(NMR) studies have been made as a function of temperature and the angle between the stretch direction and the magnetic field on one‐way stretched poly (ethylene terephthalate) film. The data obtained were consistent with a structural model, the important features of which are the directions of the lines between interacting methylene and aromatic protons relative to the stretch direction. Evidence for planar orientation in one‐way stretched poly (ethylene terephthalate) film was obtained from wide‐line NMR data which were taken as a function of the angle between the normal to the filmsurface and the magnetic field. A difference of approximately 25°C has been observed in the temperature at which the sharp component appears in annealed, unoriented poly (ethylene terephthalate) film and powder phase material from the solid‐phase buildup reaction. This difference is explained as being due to a difference in the degree of crystalline perfection.

Determination of Fracture Surface Energies by the Cleavage Technique
View Description Hide DescriptionThe fracture surface energy of a material can be obtained by the cleavage technique, in which a crack is propagated along the median plane of a strip sample by forces applied at the free ends. Unfortunately, the stress distribution in a conventional sample is such that the crack tends to deviate from its original direction, so that, for isotropic materials, external constraints must be imposed to overcome this tendency. To interpret the data, relations have been derived, based on the assumption that simple beam theory can be applied to the system; this assumption is not strictly valid. The use of the constraints can be avoided by machining fine slots along the opposing faces of the sample, and the system can then be analyzed by a direct and unambiguous method. The modified technique has been applied to the glassy polymers poly(methyl methacrylate) and polystyrene for which comparative data are available from both tensile and cleavage experiments.

Rhe‐Optical Properties of Polymers. III. Dynamic Polarized Light Scattering
View Description Hide DescriptionIn a recent paper on the dynamic strain‐optical coefficient for polyethylene, it was reported that the strain‐optical coefficient displayed a relaxation‐dispersion effect. Experiments have now been carried out to measure the dynamic scattering strain‐optical coefficient as a function of frequency. Preliminary results are presented and interpreted in terms of the motion of domains within the specimen under dynamic conditions.

Crystal Habits and Morphology of n‐Tetranonacontane (n‐C_{94}H_{190})
View Description Hide DescriptionThe electron microscope has been used to study (i) the growth habits of orthorhombic (a=7.4Å, b=4.95 Å, c=122 Å) crystals of n‐tetranonacontane grown by cooling hot dilute solutions of this n‐alkane in xylene to room temperature and (ii) to examine by means of a replicating technique the surface morphology of monoclinic (a=9.0 Å, b=4.95 Å, c=122 Å, β=123°) n‐tetranonacontane crystallized from the melt in polycrystalline form. The general habit characteristics of orthorhombic solution grownsingle crystals, {110} twinned crystals, multiple {110} twins, as well as {310} twinned crystals are described. In addition, the observed dependence of the habit of {110} twinned crystals on screw dislocations situated within the constituent twin lattices as well as the twin boundary in such crystals, is considered in some detail. Polycrystalline monoclinic n‐tetranonacontane is shown to possess a distinctly stepped surface structure. The steps are of the order of 100 Å in thickness. It is deduced that the interstep surfaces are {001} faces of the constituent molecular layers and that these layers are bound peripherally by {hko} faces. Although no distinct spiral growth patterns associated with screw dislocations have been observed, the apparent presence of such dislocations in these polycrystalline samples is indicated.

Dynamic Birefringence of High Polymers II
View Description Hide DescriptionThe time‐dependence of birefringence was investigated in experiments involving relaxation at constant strain, extension at constant rate of strain, and periodically varying strain. The results of constant strain relaxation are calculated from the other two types of experiments using the linear phenomenological theory of birefringencerelaxation. Strain‐optical coefficient spectra are calculated for a number of low‐ and high‐density polyethylenes and characteristics of the spectra are correlated with sample density. A simple molecular theory is presented. The time‐dependence of birefringence is believed to principally arise from the finite relaxation time for crystal orientation.

Specific Heat of Atactic and Isotactic Polypropylene and the Entropy of the Glass
View Description Hide DescriptionThe specific heat of atactic and isotactic polypropylene has been measured from 80° to 490°K. The isotactic sample was 64.9% crystalline, as determined by specific volume, and the atactic sample was 2–3% crystalline, as determined by the specific heat measurements. Below the glass temperature, which was found to be 259°K, and above the melting point, which was found to be 447°K, the specific heats are very nearly the same. From the data, the entropy,enthalpy, and free energy referred to absolute zero were computed. The heat of fusion of pure isotactic polypropylene crystal was found to be 45 cal/g. On the basis that the thermodynamic functions for the two materials above the melting point are the same, the residual entropy of the glass at absolute zero is calculated to be 0.62±0.2 eu/mole. The behavior of the thermodynamic functions is such that a lowering of the glass temperature by 53±20°K would produce a glass of zero configurational entropy. A lowering of 150±15°K is necessary to make the enthalpy of the glass equal that of the crystal. It is deduced that underlying the observed glass transition is a second‐order transition in which the entropy of the supercooled liquid is a primary factor.

Nuclear Magnetic Resonance Studies of Molecular Motion in Natural Rubber
View Description Hide DescriptionNuclear magnetic resonance measurements have been made on natural rubber to examine how frequency, temperature, and crystallinity influence the nuclear relaxation. Molecular motions were studied by observing NMRlinewidths and spin‐lattice relaxation times at temperatures between −100° and 100°C, and at radio frequencies between 2 and 60 Mc. The influence of crystallinity was seen in measurements on stark rubber. The relation between frequency and temperature in the spin‐lattice relaxation process is examined in terms of the Arrhenius equation and the WLF expression. The importance of using frequency as a variable in NMR studies of molecular motion is stressed.

NMR and Dilatometric Studies of Polyethylene Recrystallization
View Description Hide DescriptionPolyethylene samples with different thermal history were annealed at temperatures slightly below melting point. The chain immobilization as revealed by NMR shows first a decrease corresponding to a partial melting and a subsequent slow continuous increase as a consequence of progressive recrystallization. Dilatometric measurements demonstrate two different mechanisms of crystal growth.Primary crystallization with an Avrami coefficient n=3 and a long induction period for nuclei formation characterizes the initial solidification from melt during which the bulk of the sample crystallizes. The volume reduction at subsequent crystallization of the remaining amorphous areas completely blocked by spherulites produces a negative pressure and hence a local melting point depression strongly hampering further crystal growth. This effect is still enhanced by increased concentration of rejected impurities, e.g., short chain or branched macromolecules contained in the sample, which being intrinsically noncrystallizable at a given temperature also reduce the maximum attainable crystallinity. After this transition period during which n drastically drops and soon loses any physical meaning the secondary crystallization begins, where the change in density is no longer due to an increase in crystal‐to‐total‐volume ratio but only to the increasing thickness of the initially formed crystals accompanied by a reduction of the surface‐to‐volume ratio. The slow density increase with annealing time is fully accounted for by the better order and density in the growing core of lamellar crystals as compared with the less dense surface layers, and by the time dependence of lamellar thickness at the annealing temperature.

An Approximate Relation Between Elastic Moduli and Thermal Expansivities
View Description Hide DescriptionA large number of polycrystalline and amorphousmaterials ranging from pure metals to glassypolymers have been found to obey the relations α^{2} E=150 [dyn cm^{−2}°K^{−2}]s at normal temperatures. The linear coefficient of expansion is denoted by α, Young's modulus by E, and s is a dimensionless spread factor (0.5<s<2). The spread of about ±0.3 decade is small compared to the three‐decade range of E covered by the data. Notable exceptions to the relation are certain alloys, some inorganic glasses, cellular materials (e.g., wood), granular materials (e.g., cement), and rubbery materials. The variations with temperature of α, E, and heat capacityC_{p} are compared for representative materials and implications of the α^{2} E relation are discussed. An empirical approach in which generalized Grüneisen numbers are utilized and a preliminary statistical mechanical attempt to relate α to C_{v} and the elastic properties of polymers are discussed. Both lead to the conclusion that for polymers, perhaps even more so than for metals, it would be of interest to make separate measurements to very low temperatures of α, C_{p} , and various elastic moduli.
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 REGULAR ARTICLES


Crystal Interfaces. Part I. Semi‐Infinite Crystals
View Description Hide DescriptionThis paper presents a calculation of the stresses and energies for interfaces between different crystals. Only simple cases corresponding to interfacial dislocations of pure screw or edge type are treated. The difference between the two crystals is expressed in terms of different elastic constants and variable interfacial bondings. Two kinds of interfacial forces appear: tangential forces with a periodic character and normal forces. The latter are induced by different normal displacements of the two contact surfaces of the crystals due to the equal and opposite tangential interfacial forces and are accounted for by assuming a linear relation between force and relative displacement. By using a periodic parabolic model to represent the periodic potential associated with the tangential forces, it is shown that the contribution of the normal force to the interfacial energies is negligible for the approximation used. When these normal forces are neglected, the Peierls‐Nabarro representation of the interfacial forces yields simple results in terms of an interfacial rigidity modulus μ and an effective elastic constant λ_{+} defined by , where σ is Poisson's ratio and the two crystals are designated by a and b. It is seen that ½λ_{ a }≤λ_{+}≤λ_{ a }, where λ_{ a } is the smaller of λ_{ a } and λ_{ b }. Apart from being proportional to μc, the interfacial energy E depends only on a parameter β=2π(c/p)(λ_{+}/μ), where p is the dislocation spacing and the lattice constantc of the reference lattice is given by 2/c=1/a+1/b. The dependence on β is such that below a poorly defined value of the order of unity the variation of E is very rapid while beyond this it remains practically constant. It is further shown that the elastic energies stored in the two crystals are in the ratio λ_{ a }/λ_{ b } and that less than 2% of these energies is stored at distances from the interface greater than half the distance between dislocations. Similar results are shown to hold for simple twist and tilt boundaries.

Crystal Interfaces. Part II. Finite Overgrowths
View Description Hide DescriptionA calculation of the interfacial energy between a crystalline film and a crystalline substrate of a different substance for the simple case in which the lattice parameters differ in one direction only, is presented. The results are expressed in terms of film thickness h, interfacial misfit η, interfacial bonding, and relative hardness of film and substrate. A parabolic interfacial potential has been used to investigate the effect of h showing that it is only a significant factor when either or both h and η are small. It is further shown that, in the minimum energy configuration of the system, the film is homogeneously strained. According to the calculations, a critical value of misfit η_{c} exists below which the film is strained to fit the substrate exactly and above which the required strain is an order of magnitude less than η_{c}. The misfit η_{c} is estimated to vary from as much as 13% for a ``soft'' monatomic layer which is tightly bound down to practically zero for thick films which are loosely bound. It is shown that the interfacial energy associated with an infinitely thick film as calculated with a Peierls‐Nabarro type of interfacial force, is a useful approximation for many purposes. Approximate expressions for the strains in terms of the relevant parameters are deduced from this result.

Right‐Angle Bends in Thin Strip Conductors
View Description Hide DescriptionCurrent density and resistance expressions are obtained by means of a conformal transformation for a strip conductor which contains a right‐angle bend. The approach, similar to that applied by Cockcroft to the problem of rectangular coaxial capacitors, is sufficiently general to take into account the effects arising both from a width change at the bend and from a small radius on the inside corner. It is suggested that the current density expressions can be applied in some cases to superconducting thin film strips, and the effect of a right‐angle bend on the supercurrent‐carrying capacity of such a strip is discussed. A typical result is that the critical current of a bent superconducting strip may be only 1/6 that of a similar but straight strip if the radius of the inside corner of the bend is 1% of the strip width. A specially shaped right‐angle bend is then described, the critical current for which is identical to the corresponding straight strip. Current density nonuniformity somewhat away from the corner is also discussed. For example, a 4% variation across the strip is found two strip widths from the corner. The design of a thin film cryotron gate element is then discussed in the context of these current density results. The resistance expression, which naturally applies only to normal conductors, relates the resistance of the bent film strip to the strip dimensions and the bulk resistivity. It is shown that a radius on the inside corner as large as several percent of the strip width will decrease the resistance by an amount which is generally negligible.
