Poly(amidoamine) (PAMAM) dendrimers of generations G0, G1, G2, G3, G4, and G6 are investigated by potentiometric (acid−base) titrations. The data are interpreted with a site binding model, which offers the possibility to model the titration curves for all generations of the dendrimers and to describe all dendrimers within a common parameter set. These parameters involve the microscopic ionization constants for each group in the fully deprotonated state and nearest-neighbor pair interaction parameters. From this model we can further obtain all microscopic ionization constants as well as conditional microstate probabilities. The protonation of PAMAM dendrimers first involves protonation of primary amine groups at the outer rim of the dendrimer at high pH, while the tertiary amine groups in the dendrimer core protonate at lower pH. The last group to protonate at low pH is a central tertiary amine.

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Cluster expansion techniques are used to obtain microconstants and microenthalpies of protonation reactions. The approach relies on the analysis of macroscopic protonation constants and protonation enthalpies within a homologous series. Various linear aliphatic polyamines are considered, including 3,4-tri (spermidine), 3,4,3-tet (spermine), and 2,2,2,2-pent. Besides the full resolution of the microscopic protonation equilibria, one obtains information on the temperature dependence of the microstate probabilities. We find that the concentrations of the dominant microspecies increase with increasing temperature. Due to the large negative protonation enthalpies that are typical for amines, higher temperatures generally favor the less protonated species.