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 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 $${\text{V=0.8341(1055.5−T)/(931.7−T)+(0.12−1.6×10}}^{\text{−3}}{\text{T+7.8×10}}^{\text{−6}}{T}^2{\mathrm{)/l}}_2$$ in 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.