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 (EM n ) 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 EM n K inter must be not lower than 185 r, 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 (cmc = n EM 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 EM n K inter; 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.