Interactions between dendrimers and charged probe molecules. 1. Theoretical methods for simulating proton and metal ion binding to symmetric polydentate ligands

Binding of protons and metal ions to dendrimers is investigated using a multishell model, in which concentric binding sites are approximated by continuous and uniformly charged shells. The electrostatic interactions among the shells are assumed to be the sole source of site-to-site interactions, and an analytical formula for the total interaction energy, which includes Coulomb screening from mobile electrolyte ions, has been derived. The formula permits numerical simulation of proton and metal-ion binding equilibria using two computational methods. The first method is a statistical approach in which the partition function is simplified by a mean-field approximation. The second method is derived by considering ion binding as a surface adsorption problem, and the resulting binding isotherm is a Frumkin isotherm. In most cases, the two methods give nearly the same results, but the isotherm method requires much less computation time. Proton binding as a function of pH for an individual shell follows a trend very similar to that for the overall averaged binding. Selective protonation of alternating shells, as observed for a previously described Ising model, is not observed in this study; instead, proton binding becomes increasingly weak as one moves from an outer shell toward the center of the dendrimer.