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.