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 ¼ 2/3), while the weight-average molecular weight maximum is shifted to higher r (x 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.

Thermoreversible associating polymer networks. I. Interplay of thermodynamics, chemical kinetics, and polymer physics

“…Coarse-grained modelling with the goal of studying the dynamics of AP systems by analogy is the only currently feasible approach for bulk systems, so we make no attempt to mimic specific chemistries. The only published simulations of which we are aware that model AP networks with specific chemistries [84,90] are pure Monte Carlo studies that used a very coarse-grained (lattice) bond-fluctuation model [91] and focused on static properties.…”

“…The use of a hybrid MD/MC method is a powerful advantage. Pure Monte Carlo (MC) simulations have been performed with lattice [37,38,40,83,84] and off-lattice [36,44] models. These are very effective at studying static properties like percolative gelation and (in the case of solutions) phase separation, but have limited ability to capture the complex, collective dynamics which occur in bulk polymers, and thus lack properties (i) and (ii).…”

Cis-trans switchable metallosupramolecular polymers: Computer modeling

“…13 The initial configuration is brought to equilibrium during 8 ϫ 10 6 Monte Carlo steps by moving and bonding updates with the acceptance ratio reflecting the overall free energy change ͑⌬F = ⌬E + T⌬S͒. 14,15 The equilibrium properties of metallosupramolecular polymers for different oligomer concentrations, fractions of trans-isomers and different ratios of metal ions to oligomers are determined by averaging the simulation results over 2 ϫ 10 6 Monte Carlo steps following similar approaches as discussed in Ref. 15.…”

“…15 It is also worthwhile to note that in contrast to synthetic polymers or surfactants containing azobenzene ͑or analogous͒ groups, where isomerization induces reversible sol-gel transitions by altering hydrophobic association, [16][17][18][19] the isomerization of metal-ligand complexes discussed here influences the cross-linking mechanism itself so that solnetwork transition could be induced in the absence of any other interactions ͑hydrophobic, etc.͒. Indeed, 3:1 ligandmetal complexes, which play the role of cross-linkers in the network, can be formed ͑with a different association constant͒ from either cis-or trans-2:1 complexes which serve mainly as chain extenders.…”

“…The highfrequency elastic plateau modulus ͑G 0 ͒ characterizes the elastic response of the reversible metallosupramolecular networks to an external deformation and can be estimated ͑in the absence of entanglements͒ by calculating the number of effective strands of the networks N s : G 0 ϳ N s kT. 15 As is shown in Fig. 4, the elastic plateau modulus strongly depends on the metal-to-oligomer ratio, reaching its maximum at the stoichiometric composition ͑three ligands per metal͒, where the degree of cross-linking is the largest.…”