R. K. Eby

Thermal Expansion of Polyethylene Unit Cell: Effect of Lamella Thickness

The unit cell dimensions have been measured at temperatures between 93 and 333 K for linear polyethylene samples with long periods of 385, 220, and 99 A. The angular positions of 6 x‐ray diffraction lines were obtained at 5–10 K intervals with a powder diffractometer and the positions corrected for beam penetration so as to agree with powder camera results obtained with more lines at 296 and 155 K. At lower temperatures, the cell dimensions are nearly independent of long period, but at higher temperatures, the basal area of the cell appears to vary linearly with the reciprocal of the long period. The value of the slope increases with temperature and at 293 K is nearly the same for sets of data obtained with a number of different molecular weight distributions, crystallization and annealing conditions as well as for n‐paraffins. The specific volume data for all three polymer samples can be represented between 133 and 333 K with a standard deviation of 2.6×10−4 cm3 g−1 by the equation V=0.8341(1055.5−T)/(93...

Glass transition of polyethylene: Volume relaxation

Data are presented to show that when linear polyethylene is quenched from room temperature to temperatures below 273 K, it exhibits a volume decrease for times long compared with that required to establish temperature equilibrium. The time, temperature, and density dependence of this decrease is shown to be consistent with a relaxation occurring in the amorphous portion (lamella boundary layers) of the samples. The data can be superposed and the shift factors follow the WLF formalism. Analysis by this method yields a Tg of 231 ± 9 K but the uncertainties preclude any correlation with specific volume over the range 1.01–1.05 cm3 g−1. The data indicate the absence of any comparably strong time dependence of the volume near 150 K. This method of detecting a glass transition in partially crystalline polymers is relatively freer of subjective judgment than most.

Crystal structure of the low temperature phase (II) of polytetrafluoroethylene

Abstract An electron diffraction pattern from polytetrafluoroethylene in Phase II was analysed to determine a chain conformation of 2.1598 CF2 units per turn of the helix. A structure was established from a combination of electron and X-ray diffraction data. The structure contains an ordered repeating pattern of a left- right-handed pair of chain stems. Although the structure is ordered in three dimensions, it cannot be described meaningfully in terms of classical space group nomenclature because very small changes in the structure result in very large changes in the cell parameters. The structure has a volume of 0.03542 nm3 per CF2 group, corresponding to a density of 2344 kg m−3.

Order—disorder transitions in polytetrafluoroethylene

Abstract The phase diagram of polytetrafluoroethylene is enlarged by differential scanning calorimetry to include the concentration of hexafluoropropylene comonomer units. The two transitions near 292 and 303 K in the homopolymer move to lower temperatures and apparently become one at small concentrations. Analysis of the data yields 295 K for the temperature and 13.2 J/g for the heat of transition of an infinitely large homopolymer crystal. The heat of transition associated with the formation of a crystal defect is 0.021 eV. The qualitative features of the transition can be accounted for by a mean-field model which involves two order parameters corresponding to planar units and helix reversals. This model yields two transitions which move closer together and to lower temperatures with increasing comonomer concentration. Decreasing lamella thickness will have a qualitatively similar effect.

Cell dimensions of hydrocarbon crystals: Surface effects

The unit‐cell dimensions of a given polyethylene have previously been shown to vary nearly linearly with the reciprocal of lamella thickness. Data obtained at 153.2 and 296.2°K are presented to show that the slope of this dependence is different for crystals of orthorhombic n ‐paraffins, melt‐crystallized polyethylene, and solution‐crystallized polyethylene. Within the limits of error, all extrapolate to the same basal area at infinite lamella thickness, and this agrees with the measured value for a sample crystallized from the melt under high pressure to yield a long period of about 3500 A. Since the effect is a surface one, it is proposed that these differences result from the differences between methyl interactions, fold interactions, different fold planes, domains, etc. It is shown that the variation of cell dimension with lamella thickness leads to a quadratic term in the variation of macroscopic density. This term permits the separation of the thickness and density of a lower‐density surface layer i...

Energy calculations of the crystal structure of the low temperature phase (II) of polytetrafluoroethylene

Abstract Energy analysis is used to determine the low energy crystal structure for polytetrafluoroethylene molecules in the 13 6 and 54 25 conformations. The structure for the 54 25 conformation contains an ordered repeating pattern of a left- and right-handed pair of molecules in a unit cell having projected parameters, a′, b′, and γ′, of 9.60 A, 5.62 A, and 91.4 degrees, respectively. These results, the relative orientations of the molecules, and the relative translations of the molecules are in good agreement with results obtained in a concurrent and independent analysis of diffraction data. Energies calculated for rotational and translational displacements in various modes suggest that a range of structures and a fairly large amount of disorder may be present, also in agreement with experiment.

Theory of polymer crystal thickening during annealing

A previous theory of thickening has been extended to encompass the possible dependence of cooperative chain transport on lamella thickness and crystallinity changes during annealing. These have marked effects on the thickening rate leading to changes in slope and departures from straight‐line behavior of the plots of lamella thickness versus the logarithm of time. The resulting curves bear a resemblance to many exprimental ones in the literature. Also brought out by the analysis is the important fact that the volumes of the coherently thickening domains are not known from experiment.

Disorder in the crystal structures of phases I and II of copolymers of tetrafluoroethylene and hexafluoropropylene

Abstract X-ray diffraction patterns for oriented and unoriented copolymers of tetrafluoroethylene and hexafluoropropylene are presented. They show a transition between 229 and 243K for a copolymer with about 3.4 CF 3 per hundred main chain carbon atoms. The lower temperature phase (II) appears to be similar to that of the homopolymer. A primary difference is the presence in the copolymer crystals of small longitudinal displacements of the molecules caused by the randomly located CF 3 groups. The displacements increase with increasing CF 3 concentration. The higher temperature phase (I) is similar to that of the homopolymer with a difference again being the longitudinal disorder of the copolymer. The difference disappears at higher temperatures as longitudinal disorder is introduced thermally in the homopolymer. At 296K (phase I) the molecular stems in a copolymer with about 3.4 CF 3 per hundred main chain carbon atoms are at an angle of 37.1 degrees with respect to the normal to the basal plane of the lamellas. In phase II, this number is the same within the limits of error.

Melting Temperatures of Copolymers

The melting temperatures (532° to 580°K) of copolymers of tetrafluoroethylene and hexafluoropropylene have been measured on a microscope hot stage. The copolymers had concentrations of perfluoromethyl groups between 0.0275 and 0.075 groups per carbon atom and lamella thicknesses which varied from 340 to 500 A independently of comonomer concentration. An equation based on the concept of inclusion of the groups within the lamellar crystals as defects has been fitted to the data. The constants of fitting yield the equilibrium melting temperature, 616.6°±4.9°K, the surface energy, 4.5×10−13±1.6×10−13 erg/fold, and the perfluoromethyl defect energy, 0.047±0.003 eV/defect. Within the limits of error, these values are shown to be satisfactory by the possible comparisons with previously reported values or with values deduced from physical models. Neglecting the effect of lamella thickness yields a significantly poorer fit of the data.

Methyl branches in hydrocarbon crystals: Calculation of relaxation effects

A two‐site model for a relaxation process has been used in conjunction with the results of illustrative potential‐energy calculations on a model system to examine the effects of isolated methyl branches on the chain packing and mechanical relaxations of a linear hydrocarbon host crystal. The results indicate that a branched molecule can be accommodated in an array of linear chains in two different modes of packing and that each mode has two orientations. For one of the modes, the two orientations have nearly equal energies. Upon mechanical deformation of the array, this mode gives rise to a relaxation. The relative strengths are evaluated for different deformations, some of which yield values of the order of those observed experimentally. This relaxation is much weaker for unbranched chains in the planar zigzag conformation.