Composite knot

The great improvements in yield made it possible to study the specific properties of the knots related to their topology, to resolve the enantiomers, and also to study their coordination chemistry. It also became possible to prepare the first chemical knot composite and to prove its complex and unusual topology. The various complexes of knotted ligands display extraordinary kinetic inertness toward demetalation and, because of the proximity between the two copper ions in the helical core of the knot, novel electronic properties could be evidenced. In particular, the Cu(II)-Cu(II) oxidation state is strongly destabilized, as shown by the extremely high redox potential of the system [ 0.9V vs SCE (standard calomel electrode) in acetonitrile], which makes it almost unique in copper chemistry. 

Alternatively, the mean composition fields can be estimated only at grid-cell centers or grid nodes, and then these knot values can be interpolated to the particle locations (Wouters 1998 Subramaniam and Haworth 2000 Jenny et al. 2001). For example, using bi-linear basis functions ga x) for each grid node (denoted by a), the estimated mean composition at grid node xa is given by (Jenny et al. 2001)... 

C.C. Adams, The Knot Book. W.H. Freeman and Co., New York, 1994, p. 33. In addition to the prime knots listed we expect several dozen composite knots for n= 12. 

In the introduction we mentioned extravagant interlocked structures of higher complexity such as doubly intertwined catenane and molecular composite knots of Sauvage et al. and multicatenanes made up of 4 to 7 interlocked rings obtained by Stoddart et al. In this section, we will discuss assemblies made up of amide-based catenanes, rotaxanes and knots. Here we use the term assembly to describe covalent or... 

The knots in Figure 21 are all prime knots because they cannot be divided (factored) into smaller, nontrivial knots. Prime knots are the building blocks of composite knots and of links. Like prime numbers, which yield composite numbers upon multiplication, or like atoms in chemistry, which yield molecules upon combination, prime knots are the elementary units of knot theory. Composite knots are exemplified by the topologically achiral square knot and the topologically chiral granny knot (Figure 22). In each of these knots, a plane perpendicular to the... 

Figure 22. Diagrams of composite knots with c(K) = 6. (a) Square, or reef knot, (b) and (c) Enantiomorphs of the granny knot.

The existence of a rigidly achiral presentation suffices as proof of the knot s amphicheirality because all chiral presentations can be isotoped to their mirror images by way of the achiral one. The only possible point group for rigidly achiral presentations of prime (but not composite) knots13 is S2 , n- 1,2,. Figure 23 depicts diagrams of such presentations for a selected number of amphicheiral prime... 

Like knots, links may be prime or composite. The Hopf and Borromean links are examples of prime links because they cannot be divided (factored) into smaller, nontrivial links. Figure 30(a) is the minimal diagram of a composite link that is the abstract representative of some [3]catenanes, one of which is depicted in Figure 30(b).103b That the three-component link is a composite link is shown by the fact that a plane perpendicular to the plane of projection (dashed line) and pierced in exactly two points cuts the link in half If the open ends on both sides of the plane are now joined to form closed curves, two Hopf links result. In analogy to composite knots, the three-component link in Figure 30(a) is denoted by 2 2j, and the five-component composite link that represents olympiadane by 2 2 2 2. ... 

The evolving domain of radial, as well as linear, addition of modules to form an expanding moiety, in a manner akin to the development of polymers, referred to as "dendrimers", is examined and nomenclated The direct inclusion of topology in the description of isomers, once a very insignificant part of chemical nomenclature, is now a factor to be reckoned with, not only for the small class traditionally referred to as "topological" (including catenanes, rotaxanes, and knots), but also as new compositions of matter, such as the endothelial fullerenes, are formulated. 

The use of the metal ion template procedure for producing topologically sophisticated structures is well illustrated by the synthesis of composite molecular knots such as 105 and 106 (Figure 6.41) in this case two topological diasteromers are... 

Knot et al. (51) converted soybean oil to several monomers for use in structural applications. They prepared rigid thermosetting resins by using free radical copolymerization of maleates with styrene. The maleates are obtained by glycerol trans-esterification of the soybean oil, followed by esterification with maleric anhydride. They also synthesized several TAG-based polymers and composites and compared their properties. It was found that the moduli and glass transition temperature (Tg) of the polymers varied and depended on the particular monomer and the resin composition. They proposed that the transition from glassy to rubbery behavior was extremely broad for these polymers as a result of the TAG molecules acting both as cross-linkers as well as plasticizers in the system. 

Nevertheless, a systematic "ideal" approach toward the goal of establishing a "structure" for organites would start with the determination of the knots of the network, that is, the elemental composition (qualitative and quantitative) of the oil shales. 

Figure 34 Strategies for the synthesis of simple (a) and composite (b) knots. Complex B is a dinuclear double helicate which is then cyclized to yield the simple knot. Ligand D has sufficient binding sites to form the pre-knot E which contains the double-helicate unit which is then coupled to give the composite knots F and the meso- form G. Reproduced with permission from reference 99.

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