Self-assembly by mutual association: basic thermodynamic properties.

Many natural and synthetic self-assembly processes involve the mutual association of molecules or particles with complementary interactions (e.g., antigen-ligand binding of proteins), which in turn polymerize into larger scale structures. We develop a systematic Flory-Huggins type theory for this hierarchal assembly by combining descriptions of the mutual association of the molecular and particle species A and B and the subsequent polymerization of the ApBq complexes. In particular, basic thermodynamic properties (order parameter, concentration profiles, average cluster mass, etc.) are computed for the mutual assembly process as a function of temperature, the initial relative composition of A and B, solvent concentration, and the ratio of the stochiometric indices p and q. Calculations are performed for the single-step (i.e., without subsequent polymerization) and multistep mutual association models. The main characteristics found for these mutally associationg systems are compared to those reported previously by us for self-association. For instance, we find that the average cluster size (mass) becomes considerably enhanced at the "critical" stoichiometric volume fraction (phi(angstroms))* = p/(p + q), consistent with the observation of a peak in the shear viscosity of mutually associating fluid mixtures exhibiting polymerization at equilibrium.