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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 Å. 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)/(931.7−T)+(0.12−1.6×10−3T+7.8×10−6T2)/l2in which V is in cm3 g−1, T is °K and l2 is the long period expressed in angstroms. It is concluded that the interaction of the molecules at the surface of the crystal is not as important as the length of the molecular stems between the folds in affecting the dimensions at higher temperatures. The stems probably alter the dimensions through their effect on the thermal energy. The dependence of crystal specific volume on crystal size is estimated to reduce the heat of fusion of small crystals by about 2% in the normal range of long period. Neglecting this in analyzing melting-temperature-lamella-thickness data can lead to errors of the order of 3% in the surface free energy and 0.3 K in the equilibrium melting temperature. The variation of crystal specific volume accounts for about 5% of the variation of macroscopic specific volume and constant pressure specific heat with long period.

The thickening of polymer crystals during isothermal annealing is usually observed to be an irreversible process. Phenomenological laws that govern such processes take the form of simple proportionalities-flux being proportional to force. For polymer crystals, a thermodynamic force capable of driving the thickening phenomenon arises from the unequal free energies of the fold and lateral surfaces. By analogy with other irreversible phenomena, the rate of crystal thickening is taken to be proportional to the derivative of the surface free energy with respect to crystal thickness. After certain assumptions, integration yields an equation in which three parameters characterize the system: an initial thickness 1 0 , an equilibrium thickness I *, and a relaxation time T which is a function of the "undercooling". The theory provides a basis for considering the effects of parameters such as time, temperature, thermal history, pressure, and liquids on the thickening rate. In particular, the theory adequately describes the time and temperature dependence of crystal thickening in random copolymers of tetrafluoroethylene and hexafluoropropylene which exhibit thickening behavior completely analogous to that of homopolymers. During thickening, the unit cell dimensions of these quenched-crystallized copolymers decrease in a manner that is consistent with the concept of complete comonomer inclusion upon crystallization.

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In polymers with a lamellar morphology, crystallization in the presence of a temperature gradient can result in oriented lamellar crystals. Although the orientation is imperfect because of the helical [twisted] nature of the lamellae, shear stress applied by a torsion pendulum can be oriented with respect to the long lamellar dimension. Data of this type have been obtained to provide insight into the mechanical relaxation of polyethylene. The data assist the interpretation of experiments in which samples of the same density are obtained by different thermal histories.

Polyethylene with a low concentration of deuterated methylene groups displays an infrared band in the frequency region 646–651 cm−1. This band is attributed to a rocking normal mode of a CD2 group with one of the adjacent dihedral angles approximately trans and the other approximately gauche (tg). This mode vibrates at 620 cm−1 when the dihedral angles adjacent to the CD2 group are both trans (tt). In polyethylene crystals tg sequences can occur only in defects where constraints cause some of the dihedral angles to be approximately trans or gauche. Calculations of the rocking mode vibrational frequencies of CD2 groups in model chains which incorporate some of the typical defects showed that the bands were broadened but not completely disrupted by the distorted dihedral angles. Measurements of the relative intensities of the CD2 rocking bands show an increase in the concentration of tg sequences consistent with the thermal generation of defects which may be involved in transport of the polymer chain through the crystal. Confidence in the particular values of the concentration ratio is limited by uncertainties in the determination of the base line for the infrared bands of interest. Quantitative measurements of the concentration ratio tg/(tg+tt), determined from the integrated band intensities, fall between limits set by reasonable independent estimates of the concentration of folds and point dislocations.

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