Reversible association and network formation in 3 : 1 ligand–metal polymer solutions

Abstract

Formation of reversible metallo-supramolecular networks based on 3 : 1 ligand–metal complexes between end-functionalized oligomers and metal ions was studied using Monte Carlo simulations. The fraction of 1 : 1, 2 : 1 and 3 : 1 ligand–metal complexes was obtained and analyzed using an analytical approach as a function of oligomer concentration, c and metal-to-oligomer ratio, r. At low concentration the maximum in the number-average molecular weight is achieved near the stoichiometric composition (r = 2/3), while the weight-average molecular weight maximum is shifted to higher r (≃ 0.75). With an increase in oligomer concentration the molecular weight maxima shift to higher metal-to-oligomer ratios (similar to the experimentally observed viscosity) due to diminished ring formation. Network formation as determined from the analysis of the molecular weight distribution and reduced average cluster size occurs in a limited range of metal-to-oligomer ratios at sufficiently large oligomer concentrations. At oligomer concentrations slightly exceeding the onset of network formation its growth occurs by means of incorporation of sol molecules into the dangling parts of the network. In the range of r close to the stoichometric composition the overall number of oligomers in the sol and dangling parts is found to remain nearly constant as a function of oligomer concentration and equal to that at the onset of network formation. The average molecular weight between effective crosslinks decreases with oligomer concentration and reaches its minimum at the stoichiometric composition, where the high-frequency elastic plateau modulus approaches its maximal value. At high oligomer concentrations the plateau modulus follows a c^1.8 concentration dependence, similar to recent experimental results for metallo-supramolecular networks.