Linked-ring polymers

Figure B3.3.11. The classical ring polymer isomorphism, forA = 2 atoms, using/ = 5 beads. The wavy lines represent quantum spring bonds between different imaginary-time representations of the same atom. The dashed lines represent real pair-potential interactions, each diminished by a factor P, between the atoms, linking corresponding imaginary times.

It will be noted here that such polymers have few single bonds in the repeating unit and contain a substantial proportion of linked ring structures. This has been taken further by the reaction of tetramines with tetra-acids, as indicated in Figure 29.18. 

Exercise 31-9 Explain how an alkene-metathesis catalyst might convert a cyclo-alkene into (a) a long-chain unsaturated polymer, (b) a mixture of large-ring polymers, and (c) a catenane (interlocking carbon rings like two links in a chain). 

The so-called Jones polynomials [38] are even more strongly invariant than the Alexander ones. However, their calculation requires far more computer capacity calculation of an Alexander polynomial takes in the order 0(/3) operations, where / is the number of selfintersections of contour projection on the plane on the other hand, the calculation of a Jones polynomial takes in the order 0(e ) operations. This is why the existing attempts to use Jones polynomials in computer experiments with ring polymers have not been successful as yet Nevertheless, the construction of algebraic polynomial invariants of knots and links seems to be of great importance in principle, and we shall consider it in the next section. 

Ring polymers are synthesized by linking two reactive ends of linear polymers in dilute solution. The cyclization probability can be defined as the... 

Copolymerization reactions also yield polycyclic borazines with directly linked rings. The reaction of N-lithiated borazines with B-chloroborazines gives polymers ... 

The reaction mechanism was assumed as follows first linear intermediates (I) and subsequently bridged, branched, or ring polymers (II) are formed (for a detailed discussion, see Ref. 43). Because of the high degree of cross-linking, high ceramic yields are obtained. 

Williams et al. [208] have presented crystal data for 7 ew-deciphenyl and me/(7-undeciphenyl as models for poly(7Pi-phenylene). The oligomers have a helical confonnation. Their diffraction patterns agree very well with that of the polymer. me7(7-Linked rings are not expected to form a conducting system upon charging, unless they become part of a polycyclic structure as a result of cross-linking such aspects are not considered in the jraper. 

The observed high cyclization is attributed to an interaction between the double bonds in the transition state, since a strong bathochromic shift of the absorption due to the double bonds is observed in the uv spectrum. Six-membered rings as well as five-membered rings have been observed experimentally in the polymerization of 1,6 dienes. As expected, the extent of cyclization in this case depends strongly on the thermodynamic quality of the solvent (Table 16-10). In such polymerizations, soluble products are obtained, even at highest yields, because of the strong cyclization, whereas extensive reaction as for Equation (16-54a) would lead to cross-linked, insoluble polymers. 

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