Resolution of microscopic protonation enthalpies of polyprotic molecules by means of cluster expansions.

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.