The Jacobson-Stockmayer Cyclization Theory

The theory of cyclization developed by Jacobson and Stockmayer describes the following equilibrium  

reactivity of all reaction sites along the chain is the same  

Based on these assumptions the concentration of the macroring of a given size is governed solely by the probability of attaining a conformation which enables the closure of this particular macrocycle. 

The final equation derived from the mathematical treatment5,9), is 

for each individual macrocycle a certain thermodynamic equilibrium concentration exists having the same physical meaning as the equilibrium monomer concentration. Increasing the ring size n, the equilibrium oligomer concentration decreases according to Eq. (3-2). 

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The Jacobson-Stockmayer cyclization theory is based on the assumption that all rings are strainless and that the conformational probability of ring closure is given by Eq. 3-2, i.e. conformational restrictions or preferences are absent. This assumption apparently cannot be fulfilled in real systems for small rings (as shown in Sect. 3.2.2). In some systems this leads to a lowering of the concentration of cydics when compared with their equilibrium concentration. This is because the probability of small ring closure is reduced due to the strain caused not only by bond angle deformation but also by bond opposition and transannular interactions. In such a case, as in the discussed earlier l,3-dioxolane-BF3 system, the concentration of small cycles (up to 25-30 bonds) is lower than the calculated one 141... 

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