ABSTRACT: Protonation of fourth-generation poly(amidoamine) dendrimers terminated with hydroxyl and amine functional groups has been studied by potentiometric pH titration. The titration data are analyzed using a multishell structural model and a Frumkin adsorption isotherm to approximate protondendrimer binding equilibria. Site-to-site correlation is ignored, and counterions are treated according to the standard Debye-Hü ckel theory. This analysis yields two binding parameters: the intrinsic proton binding constant and a constant that characterizes the strength of electrostatic interactions among occupied binding sites. For the hydroxyl-terminated dendrimers, the internal tertiary amines have an average binding constant (pK ) 6.30) 1-2 pH units lower than the value expected for a single, isolated binding site. This shift in pK is attributed to a hydrophobic microenvironment within the dendrimer interior. In contrast, no significant shift has been observed in the binding constant (pK ) 9.23) for the peripheral primary amines in the amine-terminated dendrimer because the microenvironment around the primary amines is more hydrophilic. The strength of electrostatic interactions obtained from titration data is 3 times (primary amines) and 8 times (tertiary amines) smaller than the calculated values based on the multishell model. We hypothesize that the diminished interaction strength results from ion pairing between bound protons and counterions. In addition to the Debye-Hü ckel contribution from mobile ions, ion pairing provides extra Coulomb charge screening. Introduction Because of their unique structural topology and chemical versatility, dendrimers have found applications related to catalysis, drug delivery, energy transfer, and molecular recognition. We recently developed a theoretical approach, which we refer to as the "shell model", to quantify iondendrimer binding. 12 Some of the characteristics of this model are summarized here. First, electrostatic interactions are assumed to be the sole source of site-to-site interactions. The total energy is calculated by adopting a multishell dendrimer model, and discrete charges within each shell are summed and approximated as a shell of continuous charge. This procedure makes it possible to solve the linearized Poisson-Boltzmann (PB) equation analytically within the limit of the Debye-Hü ckel approximation (i.e., a dilute electrolyte solution). Second, no distinction is made between binding configurations (or microstates) that have the same set of intrashell proton binding numbers. Instead, all degenerate configurations are averaged (mean-field approximation) so that site-to-site correlations are not considered. In contrast, such a correlation is a key aspect of the Ising model that has been used previously for modeling dendrimer binding equilibria
