Variation of Lattice Parameters with Fold State in the Ultralong n-Alkanes

The ultralong n-alkanes were synthesized to provide model materials for the study of polyethylene chain folding and crystallization. In this paper, results are presented from a detailed wide- and small-angle X-ray diffraction study of these materials, which have been crystallized in a range of different fold states. The trends in lattice parameter are quantified as a function of temperature, lamellar thickness, and the number of folds in each chain. For a given lamellar thickness, it is found that the unit cell expands with increasing number of chain folds. However, when the number of folds is kept constant, a contraction in the unit cell is observed on increasing the lamellar thickness, and an approximate inverse relationship exists between the a lattice parameter of the unit cell and the lamellar thickness. Above ca. 70 degrees C, increases are observed in the thermal expansion coefficients of the a lattice parameters, which appear to be associated with an a relaxation process in the n-alkane crystals. This relaxation process also appears to be related to the onset of chain tilting in the lamellae. It is found that almost all samples melt, or undergo unfolding transitions, when the a lattice parameter reaches a critical value in the range 7.660 +/- 0.005 angstrom. This value appears to mark an upper limit for the free volume in the unit cell, above which the crystals cease to be stable. The melting temperatures of the extended-chain crystals are shown to be consistent with predictions of the Flory-Vrij equation. By introducing an additional free energy term into the Flory-Vrij analysis, it is also possible to account for the unfolding temperatures of the folded-chain n-alkane crystals.