Conditional affinity spectra underlying NICA isotherm

The properties of the NICA (non-ideal competitive adsorption) isotherm are examined from the point of view of the underlying conditional affinity spectra (CAS), the distribution of effective affinities seen by a given metal ion at a fixed pH. It is shown that a CAS underlying NICA isotherm exists for all combinations of p- and ni-values including cases with different ni-values for the competing species (protons and metal ions). These distributions shift towards lower affinity values and change their shape as pH decreases. For instance, the conditional distributions can show two peaks within a monomodal NICA isotherm with quite negative minimum skewness, preferably for low enough p-values. Analytical expressions and a full discussion of this behaviour are reported with the aim of providing a complementary understanding of the physical meaning of the NICA parameters. Parameter p mainly influences the correlation between the binding energies of the competing ions. In general, when there is no multidimensional affinity spectrum, low p-values are usually associated with strong affinity sites for the proton tending to be involved in high affinity sites for the metal (i.e. there is correlation in a broad sense). The rate of shift of the average conditional affinity with pH is mainly determined by the proton affinities and the stoichiometric relationship, nM/nH, which determines the proton/metal ion exchange work.