Physical basis of self-assembly macrocyclizations

A theoretical treatment of self-assembly macrocyclizations occurring under thermodynamic control is presented. The fundamental quantities on which the treatment is based are the effective molarity of the self-assembling cyclic n-mer (EMn) and the equilibrium constant for the intermolecular model reaction between monofunctional reactants (K-inter). Knowledge of these quantities allows the evaluation of the distribution curve of the self-assembling macrocycle. In order for effective self-assembly to take place two conditions are required: (i) the self-assembling macrocycle must have an EM much larger than that of the other cyclic oligomers; (ii) the product EMnKinter must be not lower than 185r, where r is the number of bonds that hold together the monomer units in the cyclic oligomer, the higher the better. It is shown that in the limit of an infinite value of K-inter there is a critical monomer concentration (cme = nEM(n)) below which the system is virtually composed of the self-assembling macrocycle only and above which the concentration of the latter remains constant and the excess monomer produces acyclic species only. In general the optimum monomer concentration for self-assembly is slightly more than one-tenth of the cmc. Deviation from this value is less and less important the higher the value of EMnKinter; however, the concentration of the initial monomer should not be outside the range defined by the lower self-assembly concentration and the cmc. Previous conclusions about self-assembly macrocyclizations drawn by Hunter et al. (J. Chem. Sec., Chem. Commun. 1995, 2563) are criticized in the light of the present approach.