A model for self-assembly in solution

A model treating the competition, under thermodynamic control, between self-assembly and nonlinear random polymerization is presented. The fundamental quantities on which the treatment is based are the effective molarity (EM) of the assembly 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 complex. In order for effective self-assembly to take place, the product KinterEM must be no lower than a limit value easily computable on the basis of simple structural parameters such as the number of molecules in the assembly (N), the number of bonds joining them (B), and the number of interaction sites in the monomers. This limit decreases on decreasing N and on increasing B, and the most obvious way to realize this condition is by increasing the degree of cyclicity of the assembly (B − N + 1). The yield of an assembly with a high degree of cyclicity is very sensitive also to modest changes of KinterEM about its limit value. Depending on the value of the monomers concentration, the assembly could undergo either sharp disassembly (denaturation) or conversion into gel.