Appendix to Chapter 23. Calculation of Maximum Possible Conversion for Intramolecular Cyclization Reactions

Appendix to Chapter 23, Calculation of Maximum Possible Conversion for Intramolecular Cyclization Reactions 

Since Ni = 1 and N2 = 0, this gives = 2/3. In a pentamer, pair 1-2 can react first, and then pair 3-4 (substituent 5 does not then react), or pair 4-5 (substituent 3 isolated). The situation is analogous when pair 4-5 is the first to be formed. For the reaction of the second pair, therefore, the situation is a double repeat of that of the trimer, whereas if pair 2-3 or 3-4 is formed first, then a monomer and a dimer always remain. 

The analogous term X — 2) A + A 2 = can be subtracted from this equation, which then gives, after transforming, 

for an individual molecule with the (high) degree of polymerization X , the number of unreacted groups obtained is N, i.e., 

Analogous arrangements give the following for shorter chains  

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