Thermal Expansion of Polyethylene Unit Cell: Effect of Lamella Thickness

Abstract

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.

Structural and dielectric investigation on the nature of the transition in a copolymer of vinylidene fluoride and trifluoroethylene (52/48 mol %)

“…This behavior would be analogous to the effect of amorphous surfaces on the lattice spacing of polyethylene crystals 17 18, for which it was found that this spacing decreases with increasing lamellar thickness.…”

Orthorhombic phase of crystalline polyethylene: A Monte Carlo study

“…In the work [19], lattice parameters a, b, c have been measured in the temperature range 93 -333 K, and the data are smooth enough to allow a direct extraction of thermal expansion coefficients by means of finite differences. The other chosen set of data [20] is to our knowledge the only one covering the range from helium temperatures up to T = 350 K, however, the scatter of the data is too large for a direct numerical differentiation.…”

Theory of flow-induced fibril formation in polymer solutions

“…From their work on the x-ray spacings of lamellar bulk polyethylene samples and single crystals, Davis, Eby, and Colson [15] Here A 0 is the cross-sectional area of the chain in an undisturbed lattice at a specified temperature in ,42 for polyethylene, and A o(strain) the same quantity for a sample with a finite lamellae of thickness 12 that exhibits an expanded lattice resulting from end surface stress. 6 The value of K2 in A 3 has been given by these authors for meltcrystallized polymer, solution crystallized polymer, and nparaffins, and highly precise values of Ao are available from the same source [16].…”

“…This assumption cannot be made in cases where there are no physical grounds for deciding that the surface free energy depends on the dimensions of the system considered. and in a similar way we obtain Given the free energy of formation in ergs/crystallite as (23) (20e) and inserting (T e from eq (21), there is obtained r (24) whi c h beco mes, on noting from eq (15) (25) where the volume strain parameter a is defined as…”