E. Almansa López

The determination of stoichiometries and stability constants of complexes by means of UV-visible spectrophotometry applying traditional methods does not evaluate the quality of the values obtained, since the classic application of these methods does not provide coverage intervals. However, the use of chemometric techniques in different steps of the application of these methods makes it possible to obtain not only a real value of the characteristics of the complexes but a validation of such a value. In this paper a methodology is proposed that combines some traditional methods, three different regression models (LMSR, LSR and LSPR) and a small number of mathematical algorithms. This methodology is able to estimate, in a simple and rigorous way, the stoichiometry and stability constant of a complex and its corresponding uncertainties.

A study on using non-parametric statistical methods was carried out to calculate the binding constant of an inclusion complex and to estimate its associated uncertainty. First, a correct evaluation of the stoichiometry was carried out in order to ensure an accurate determination of the binding constant. For this purpose, the modified Benesi-Hildelbrand method had been previously applied. Then, four statistical methods (three non-parametric methods: two bootstrap approaches, the jackknife method and a parametric one: Fieller's theorem) were employed in order to compute the binding constant. The results obtained from applying these methods and the combination of the methods: jackknife after bootstrap and bootstrap after jackknife were compared. The best results in terms of accuracy were obtained from the application of a bootstrap method: the resampling residuals approach. These procedures were applied to the inclusion complex 2-hydroxil-propyl-β-cyclodextrin-2,4-dichloro-phenoxyacetic, which shows photochemically-induced fluorescence.

Sequential response surface methodology is a general procedure to re-optimize common analytical methods on the basis of the application of the response surface methodology and of a new approach to the steepest ascent method. This procedure, which is easy to apply, consists of estimating an analytical function relating the response with the experimental parameters by means of a second-degree polynomial. Thus, a 2nd order design covering the total experimental domain is used and when a maximum is obtained, the characteristics of the response surface are confirmed using a new design, which is obtained contracting the first one. In the proposed methodology, Box-Behnken designs are used because they offer advantages in comparison with second order designs more frequently used in the steepest ascent method (central composite designs), i.e. fewer experiments are needed, they are more efficient, they can be moved through the experimental domain and they can even be easily contracted or expanded.