B. Bourguignon

D-optimal designs

Abstract Many classical symmetrical designs have desirable characteristics, one of which is called D-optimality. The D-optimality concept can also be applied to select a design when the classical symmetrical designs cannot be used, such as when the experimental region is not regular in shape, when the number of experiments chosen by a classical design is too large or when one wants to apply models that deviate from the usual first or second order ones. The D-optimality concept is developed and it is also explained that D-optimality is only one possible criterion to choose a particular design. A few other criteria are also given that complement the information obtained by the D-criterion.

Simultaneous optimization of several chromatographic performance goals using Derringer's desirability function

Abstract The desirability function, a multi-criterion decision-making method proposed by Derringer, was investigated to optimize different chromatographic performance goals. This function is a measure of overall quality and provides a convenient means to compare several chromatograms obtained by high-performance liquid chromatography (HPLC) and to select the separation with the most desirable properties. Other solutions to the problem of multi-criteria optimization in HPLC, such as the Pareto-optimality, chromatographic response functions and combined threshold criteria are compared with the proposed method, and the advantages and disadvantages of each are discussed.

Application of Derringer's desirability function for the selection of optimum separation conditions in capillary zone electrophoresis

In order to obtain a set of optimal experimental conditions for the separation of rare earth metal ions in capillary electrophoresis (CE), a multicriteria approach is applied. For this purpose, the Derringers desirability function is proposed to determine conditions that will result in the most desirable combination of separation, sensitivity and analysis time. The CE separation method was optimized with the aid of a central composite design for two variables, i.e. the pH and the concentration of a complexing agent in the buffer electrolyte.

Simultaneous optimization of pH and organic modifier content of the mobile phase for the separation of chlorophenols using a Doehlert design

Abstract By optimizing the pH and volume fraction of organic modifier, the complete resolution of an isocratic separation of a mixture of phenol and thirteen of the nineteen chlorophenol isomers and of a mixture of the three tetrachlorophenols and pentachlorophenol was achieved. The effectiveness of the Doehlert design in optimizing both experimental parameters was investigated. A quadratic model was applied. For mixtures of a small number of compounds, a retention boundary map is proposed to determine limits of the concentration of organic modifier so as to elute compounds within a reasonable analysis time. The resulting three-dimensional graph of the minimum resolution as a function of the experimental parameters allows the direct visual evaluation of the ruggedness of the optimum conditions that are attainable in the selected parameter space and with a given stationary phase.

CRISEBOOK, a hypermedia version of an expert system for the selection of optimization criteria in high-performance liquid chromatography

Abstract Expert systems built in shells such as KES suffer from a lack of easy maintenance, prototyping and a user-friendly man—machine interface. To solve these problems, the feasibility of using a Hypermedia approach was investigated. The reimplementation of the expert system CRISE, and object-oriented decision tree, in Toolbook was promising as a first application. The structure and features of the reimplemented system are described and similarities and differences with the KES version are discussed.

Model building for the prediction of initial chromatographic conditions in pharmaceutical analysis using reversed-phase liquid chromatography

Abstract The development of a first guess expert system in HPLC requires a rough estimate of retention properties. This paper investigates the extent to which the simplest possible descriptor, namely the total number of carbons in a molecule, can be used. For this purpose, experimental data acquired after investigation of this parameter on the retention behaviour of various acidic, basic and neutral compounds, for a mobile phase composed of methanol-phosphate buffer and a LiChrosorb CN column, were employed. The usefulness of the descriptor log P (calculated according to Rekkers fragment system) was also studied. Similar models were derived for both descriptors. Subsequently these models were used for the selection of initial chromatographic conditions. Both models were compared through a PRESS value. The regression equation including the descriptor log P was found to be more appropriate for the present purpose.

Selectivity optimization after prediction of the migration behaviour of anions in capillary ion analysis in the presence of micelles

Abstract Above the critical micellar concentration of the modifier (cationic surfactant) anion separation in capillary ion analysis is mainly influenced by two chemical equilibria, the ionic dissociation which depends on the pH of the buffer electrolyte and the micellar partitioning in function of the modifier concentration. Experimentally obtained data were fitted to empirical and theoretical (physical) models in order to predict the migration behaviour. Both models resulted in acceptable predictions. The empirical models were second order polynomials whereas the theoretical models described the mobility of the anions in terms of physical and chemical constants of each ion (acid dissociation constant: Ka, ion association constants: km, ion partitioning constants: k′) the pH of the electrolyte, and the concentration of the modifier ([M]) available as micelles in the buffer electrolyte. The experimental domain was examined with the aid of a central composite design. After prediction of the mobility of each solute over a two-dimensional pH [M] space, a selectivity optimization was performed in order to obtain the optimum separation conditions for 10 anions.

Stationary phase degradation in reversed-phase liquid chromatography: a possible cause of bad predictions in experimental design

Abstract The degradation in function of time of cyanopropyl- and octadecyl-modified silica stationary phases, a polymer coated silica phase and a polymer phase is investigated as this could be a cause of bad predictions in experimental design. By simulating routine conditions on both types of silica columns, considerable changes of retention, peak width and asymmetry in function of time were observed when switching mobile phase pH but also when mobile phase pH is held constant. The initial column performance was best maintained on the polymer coated silica column. On most of the other columns, changes in elution characteristics are rapid enough to make them a major cause of bad predictions in experimental design.

The Oreste method for multicriteria decision making in experimental chemistry

Abstract The Oreste method, an operations research method, can be applied to optimize simultaneously different performance goals in experimental chemistry. The method is demonstrated in two examples and its weak and strong points are indicated. Oreste allows to rank the experiments in a complete order or in a partial order by considering incomparability. It can also work with data in an ordinal scale and takes into account that some criteria are more important than others.

Comparison of models and designs for optimisation of the pH and solvent strength in HPLC

Abstract Two designs, the one selected with the algorithm of Kennard and Stone and the D-optimal design, and two linear models are compared while optimising separation in RPLC by varying the pH and the solvent strength of the mobile phase. As a practical example the separation of a mixture of β-blockers is applied. To ease the selection of the number of experiments of a design while applying the algorithm of Kennard and Stone, a variant of this algorithm is proposed.