Supramolecular Polymer Formation by Metal−Ligand Complexation:  Monte Carlo Simulations and Analytical Modeling

Equilibrium metal−ligand complexation leading to formation of linear or ringlike supramolecular polymers is studied by means of Monte Carlo (MC) simulations and theoretical analysis. We found that in most of the cases high-molecular-weight polymers are formed over a rather narrow composition range (near the 2:1 ligand−metal ratio). Besides the imbalance in the number of metals and ligands, the molecular weight decrease in the metal-rich area is caused by an increase in 1:1 ligand−metal complex formation. The results of simulations and theoretical modeling show that the fraction of 1:1 complexes considerably decreases for metal−ligand pairs with a high cooperativity of complexation. On the basis of our analytical model, we suggest a simple criterion for choosing the metal/ligand pair to achieve high molecular weight complexes in a broad range of metal-rich compositions. Dilution of a solution of metallosupramolecular polymers is found to decrease the average molecular weight and to enhance ring formation, which otherwise is very limited.