Cooperativity Effects in the Protonation of Aliphatic Polyamines

The equilibria between base A and proton H can be calculated in the probability space by means of partition functions ZA and ZH, mathematically represented by binding polynomials. The partition functions are expressed as functions of affinity constants, kj and cooperativity coefficients, bj , specific for each class j of sites. We have undertaken a series of potentiometric measurements of equilibria of polyamines with protons at 25 8C, I=0.1 KCl, in order to calculate these parameters from the experimental data by application of a special computer program. The transformation from the probability space (ZH (or ZA), kj and exp(bj )), to the free energy space (-DG=RTln ZH (or ZA)) made possible the evaluation of the cooperativity potential Dui/=-RTbi . The cooperativity potential between two amine groups separated by aliphatic chain -(CH2)n - depends on the length of the chain i.e. it decreases exponentially with the increase of the number of methylene groups. On the other hand, the cooperativity coefficient can be brought to the scale of the constants of Hammett equation by dividing bi by 2.303. It is then possible to calculate Taft constants s* for substituents in primary, secondary and tertiary amines