Combinatorial Macrocyclizations under Thermodynamic Control: The Two-Monomer Case

Dynamic libraries of cyclophane formaldehyde acetals were generated from mixtures of two different monomeric units and quantitatively analyzed for the equilibrium concentrations of the lower cyclic oligomers. Plots of equilibrium concentration versus total monomer concentration exhibited saturation behaviors analogous to those observed in the equilibration of a single monomer. However, unlike the one-monomer case, limiting concentrations in the two-monomer case no longer provide a direct measure of the effective molarity (EM) of the various cyclic oligomers. A theoretical treatment of macrocyclization equilibria occurring in mixtures of two different monomeric units, aM and bM, is presented herein. Such a theory is based on the definition of probabilities pa and pb of the two monomers at the equilibrium and allows for realistic situations in which a monomer unit of a given type shows structural bias to be incorporated into one or more specific cyclooligomers, thus causing deviations from a purely statistical distribution. The theory allows to translate equilibrium concentrations into EM data.