Energetics of chain folding in polyethylene crystals

Abstract

Semi-empirical energy calculations have been used to investigate several aspects of chain folding in polyethylene single crystals. Calculations of isolated (110) and (200) folds indicate that the fold energy, relative to the planar zig-zag form of the molecule, is lower in the (200) fold than in the (110) fold. The minimum surface energies for isolated (110) and (200) folds were calculated to be 102.5 and 95.6 erg cm −2, respectively. The energetics of packing the minimum-energy folds into an array representing a portion of a single-crystal fold surface were also investigated. For fully optimized (110) fold packing, the habit corresponding to the Reneker-Geil model I (RG I) was found to be lower in energy than model RG II. However, the packing of (110) folds at experimentally observed unit-cell dimensions in RG I and RG II packing habits gave almost equal packing energies. It was also found that the setting angle was a function of the packing habit. Results of packing (200) folds into a fold surface indicate that a crystallographically reasonable ‘(200)’-type fold surface would appear to be impossible. The interaction energy of a straight-chain segment in the vicinity of a fold surface was also calculated. Not surprisingly, it was found that the lowest-energy situation finds the straight chain somewhat nestled into a groove between the {1 1 0} fold planes.