Many experiments have been done to determine the relative strengths of different knots, and these show that the break in a knotted rope almost invariably occurs at the point just outside the 'entrance' to the knot. The influence of knots on the properties of polymers has become of great interest, in part because of their effect on mechanical properties. Knot theory applied to the topology of macromolecules indicates that the simple trefoil or 'overhand' knot is likely to be present in any long polymer strand. Fragments of DNA have been observed to contain such knots in experiments and computer simulations. Here we use ab initio computational methods to investigate the effect of a trefoil knot on the breaking strength of a polymer strand. We find that the knot weakens the strand significantly, and that, like a knotted rope, it breaks under tension at the entrance to the knot.

The mechanical relaxation behavior of polyimides based on a variety of 2,2'-disubstituted benzidines and rigid dianhydrides was investigated. Two transitions were observed in these polyimides. The glass relaxation process is relatively weak and occurs at high temperatures due to the linear and rigid nature of these polyimides. The subglass relaxation is very prominent in these polyimides and is due to main-chain rotational motion localized within the diamine (benzidine) segment. Changes in the dianhydride moiety have little effect on the temperature of the subglass transition and result in only minor changes in the magnitude of this relaxation. The presence of 2,2'-CF3 substituents on the benzidine moiety increases the magnitude and shifts the subglass relaxation approximately 150 °C to higher temperatures versus Cl or CHs in these positions. Incorporating a flexible ether linkage between the phenyl rings of the benzidine and the CF3 side group (e.g., OCF3) substantially reduces the temperature and to some extent the magnitude of the subglass relaxation. Replacement of the 2,2'-disubstituted benzidine unit (two phenyl rings) with one (benzene) or three (terphenyl) unsubstituted phenyl rings results in a substantial decline in both the temperature and magnitude of the subglass relaxation. Molecular modeling was used to clarify the nature of the subglass relaxation. Rotational energy barriers for the 2,2'-disubstituted benzidines, calculated from both semiempirical and density functional quantum mechanical calculations, are comparable in magnitude to the experimentally determined activation energies for the subglass relaxation.

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