Equilibrium effective molarity as a key concept in ring-chain equilibria, dynamic combinatorial chemistry, cooperativity and self-assembly

The growing interest towards cyclizations under thermodynamic control is witnessed by the large number of papers dedicated to ring-chain equilibria, dynamic combinatorial chemistry, cooperativity and self-assembly. No doubt, in all these topics, cyclic or polycyclic molecular entities play a dominant role. In this chapter, the concept of equilibrium effective molarity (EM), which gives a quantification of the ease of formation of a cyclic compound, is presented as a fil rouge that allows a quantitative analysis of the phenomenology related to the title matters. Initially, the physicochemical bases on which the concept of EM is founded are described together with connections to the Jacobson–Stockmayer theory on intramolecular reactions in linear systems. Distributions of the species in ring-chain and ring–ring systems in terms of the EM, and conditions to obtain a selected macrocycle (self-assembly macrocyclization) are discussed. The EM concept is further applied to dynamic combinatorial libraries based on a single monomer, and two different monomers. The case of a templated dynamic library is also considered. Finally, after a due discussion of the methods for the evaluation of statistical factors, the phenomenon of cooperativity in binding processes is analysed by dissecting it into three contributions, namely, allosteric, chelate and interannular cooperativity. It is shown that the chelate effect, as measured by the EM, plays a key role for the quantifications of the latter two contributions, which are crucial for the assessment of multivalency, and the stability of molecular assemblies.