Polymers knotted

Fig. 11.40 Distribution of strain energy is two knotted polymer chains containing 35 (left) and 28 (right) carbon atoms. The strain energy is localised and most of the bonds immediately outside the entrance point to the knot. (Figure redrawn from Saitta A M, P D Sooper, E Wasserman and M L Klein 1999. Influence of a knot on the strenght of a polymer strand. Nature 399 46-48.)...

To make this review self-contained and to provide a foundatitMi for further discussion, we have included the experimental methods and theoretical models of mechanical degradation for linear chains in the second and third sections, respectively. From the fourth to seventh sections, the mechanochemistry of cyclic polymers, graft polymers, star-shaped polymers (star-shaped polymers), dendrimers, and hyperbranched polymers is summarized. In the eighth section, we survey the mechanochemistry of supramolecular aggregates and knotted polymers, where the topology constraints are temporal. We hope our overview can serve as a guideline for the future work in the field of polymer mechanochemistry. 

So far we have only reviewed the mechanochemistry of isolated knotting polymers. In real systems, the environment should be taken into consideration. Saitta and Klein studied the rupture processes of a bulk-like PE knot [285]. In the first model, a knotted alkane is surrounded by six linear alkanes (unknotted). For the sake of comparison, a linear alkane is also surrounded by six linear alkanes in the second model. Their results show that the bonds at the entrance and the exit of the trefoil knot are more distorted than elsewhere. Quantitatively, the knot weakens the chain to which it is tied by a factor of about 15%. Indeed, the estimated force to break a knotted alkane is 3.5 nN (the value depends on the timescale), 0.5 nN smaller than that of an unknotted alkane of the same length. 

Imaging of Catenane, Eight-Shaped and Trefoil Knotted Polymer Rings Combs as Magnified Polymer Structures (Schappacher and Deffieux, 2009)... 

Figure 21.18 Elution volume dependence of the molar mass and of the radius of gyration for a linear PS comb L-2-100 (E) and of its cyclic homolog C-2-100 (C). (Reproduced with permission from M. Schappacher and A. Deffieux, Imaging of catenated, figure-of-eight, and trefoil knot polymer rings, Angewandte Chemie International Edition, 2009, 32, 5930-5933. Wiley-VCH Verlag GmbH Co. KGaA.)...

Schappacher, M. and Deffieux, A. (2009) Imaging of catenated, figure-of-eight, and trefoil knot polymer rings. 

Polymers below the glass transition temperature are usually rather brittle unless modified by fibre reinforcement or by addition of rubbery additives. In some polymers where there is a small degree of crystallisation it appears that the crystallines act as knots and toughen up the mass of material, as in the case of the polycarbonates. Where, however, there are large spherulite structures this effect is more or less offset by high strains set up at the spherulite boundaries and as in the case of P4MP1 the product is rather brittle. 

Other applications of the polymer substrate technique include the synthesis of threaded macrocyclic systems (hooplanes, catenanes, knots), the retrieval of a minor component from a reaction system, and the trapping of reaction intermediates [Frechet, 1980a,b Hodge, 1988 Hodge and Sherrington, 1980 Mathur et al., 1980],... 

Latex balloons are made of polymers. The latex near the knot and top of the balloon are not stretched as tightly as latex on the side. This can be seen by observing the transparency of the different parts of the balloon. The knot and top areas of the balloon have a greater polymer density. Therefore, the balloon in these areas has a greater ability to stretch and partially seal itself around the skewer. On the sides of the balloon, the tightly stretched latex cannot seal around the needle and the balloon pops. 

The simplest example of topological classification is the knotting of individual strands, i.e., self-entanglement. However, the effects attributed to entanglement in non-crosslinked polymers are clearly intermolecular. The simplest such case is that of pair-wise classification without self-entanglement. Consider the following three examples of strand pairs ... 

After numerous answers were brought to the synthetic challenge itself, there arose ever more insistently the quest for functions and properties of such special compounds. Already, even if still far from real applications, one can imagine, based on interlocked, threaded or knotted multi-component molecules, new organic materials, specific polymers, molecular devices or machines able to process and transfer energy, electrons or information. 

Upon cooling of solutions of long-chain polymers it may happen that only parts of the chain eventually crystallize together with parts of other polymer chains. When a number of such small crystallites are formed they operate as knots in a network of flexible polymer chains in solution and one obtains a gel. Processing of such gels into strong fibres and films is applied commercially and has been reviewed [13,14]. 

These domains are connected by hydrogen bonds, which act as knots or crosslinking centers to create flexible blocks.13 Microphase separation and the appearance of domain structure are considered to be the main factors, which determine the unique properties of this class of polymers. 

---