Convergence-optimized procedure for applying the NICA-Donnan model to potentiometric titrations of humic substances

Despite the high success of the NICA-Donnan (N-D) model to describe the interaction of protons and metal ions with natural organic matter, the large number of fit parameters is a major hindrance to its capacity to provide unique numerical solutions. This well-known difficulty is reflected in the unusually low value of the generic proton binding constant for carboxylic-type groups of fulvic acid (pK(H1) = 2.34), and to some extent of humic acid (2.93), and by the considerable covariance of the other generic N-D parameters. In some studies, the number of parameters obtained by regression is reduced by estimating some values independently with other techniques. Alternatively, the applicability of the model can be improved by devising a rigorous simulation procedure, which constrains the model-fit to converge toward chemically and physically realistic values. A procedure based on three successive iterations is proposed, and the solution is shown to be stable and invariant with the initial set of parameter values. The new generic parameters, in particular pK(H1)(FA) = 3.54 and pK(H1)(HA) = 3.87, derived from the same data set as the previous generic parameters, are in better agreement with literature data.