Synthesis of Topology

Note that here Pn,N represents the concentration at the branching catalyst CGC-Ti, P In this case in the absence of linear catalyst, For a chain 

The PDF of Eq. (178) expresses the probability of an insertion of a chain with Ni branch points under the condition that a polymer with N branch points and a terminal double bond is formed. This formula is symmetrical by definition. It turns out that this PDF (apart from round-off errors) is identical to the PDF defined in Eq. (177). This is due to the kinetics of the system, which allows the concentration of polymers with a terminal double bond to be written as a fraction of the concentration of polymers without terminal double bonds [35], as formulated in  

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The Role of Preorganization in the Synthesis of Topological Molecules. Template Reactions... 

Figure 10 Regioselective one-step synthesis of topologically chiral trans-3,trans-3,trans-3 and e,e,e [60]fullerene-cyclotriveratrylene tris-adducts.

As discussed in Section 2.2.1, metalloporphyrins or cychc peptides have been used as a template for synthesis of topologically predetermined metallopeptides and proteins. 

Valuable applications of this principle have been described by Paquette for the synthesis of topologically spheric molecules. Coates used this reductive fragmentation for the synthesis of bicy-clo[6.3.0]undecenecarboxylates, compounds which bear a structural resemblance to the a-b rings of the fusicoccin and ophiobolane natural products. Reduction of the unsaturated keto ester (164) affords an isomeric mixture of esters, the equilibration of which effects conversion to the single ester (165 Scheme 56). 

In chemistry, self-assembly is defined as a phenomenon by which molecules order themselves into a particular arrangement without external intervention. The process occurs under the guidance of numerous weak non-covalent bonding interactions that represent the core of supramolecular chemistry. It is not surprising that chemists engaged in the synthesis of topologically non-trivial structures are interested in utilizing self-assembly to direct the templation of chemical components into intermediates prone to cyclization, followed by the formation of covalent bonds. 

Scheme 1.11 Synthesis of topological polymeric isomers having manacle- and 0-shaped constructions by the ESA-CF process (Oike et al, 2000 Tezuka et al 2003b).

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