Physical Basis of Self-Assembly Macrocyclizations

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Abstract

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 (Kinter). 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 Kinter there is a critical monomer concentration (cmc = nEMn) 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. Soc., Chem. Commun. 1995, 2563) are criticized in the light of the present approach.

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