Polymer knots

Kivotides D, Wilkin SL, Theofanous TG (2009) Entangled chain dynamics of polymer knots in extensional flow. Phys Rev E 80 041808... 

And how about experiments on polymer knots The most important and, luckily, also the easiest subject of such experiments is double helical DNA. One nice experiment can de done using DNA with sticky ends - a long double helix with each chain extending at one end by 15 or so unpaired nucleotides beyond the counterpart chain. If the sequences of these extending pieces are complementary to each other, they will stick upon first collision due to the random fluctuations of the double helical coil. Can we then determine the topology of the product ... 

For the present edition, we have modified the text in many places and have written new chapters on polymer synthesis, protein folding, polymer knots and new sections on molecular motors, semi-flexible and worm-like polymers, and several others. We have included many new figures. Overall, about 50% of the book is new. 

The method of preparation of polymeric photocatalytic membranes based on bi-axial stretching of a polymer extrusion containing TiOj as a catalytic hller (b) was applied for production of PTFE membranes (Morris et fl/., 2004).The obtained membranes contained 2 wt% of li02 distributed uniformly within the membrane. The SEM photographs revealed that the structure of the membrane resembled a net in which PTFE strands were knotted at multiple regions. The photocatalyst particles were primarily accumulated in the vicinity of these polymer knots. 

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.)...

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. 

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