Strength and deformation of rigid polymers: structure and topology in amorphous polymers

Glassy polymer is formed because the irregular chain architecture prevents crystallisation. Computer simulations allow Voronoi tessellation of atomic groups (for example monomers) to be carried out and measured along the molecular chain, which reveals significant density fluctuations. A Voronoi polyhedron is constructed for each particle according to a unique mathematical procedure [J Reiner Angew Math 134 (1908) 198]. When measured in terms of Voronoi polyhedra, amorphous structures show wide variations in packing density on the atomic/monomer scale, with a characteristic skewed distribution. The Voronoi method can be applied to all polymers; however, in this paper only uncrosslinked amorphous polymers are considered. Constriction points around a chain segment are defined as a locally specific configuration and arrangement of adjacent chains such that the local density within a sphere of radius approximately equal to two monomer diameters comes close to or below the hypothetical crystalline density. The topological theory of molecular structure developed by Bader defines the concepts of atoms and bonds in terms of the topological properties of the observable charge distribution [Rep Prog Phys 44 (1981) 893]. In polymers the high density regions become an even stronger topological feature, and are referred to as the constriction points.