Spherical coordinate representations of solvent composition for liquid chromatography method development using experimental design

One of the major techniques used for the method development of ternary and quaternary high performance liquid chromatography (HPLC) systems has been to use mixture designs, often referred to as "Glajch's Triangle". This technique does not allow for the systematic and simultaneous optimization of other factors such as gradient time, pH and temperature that affect the quality of separations. An alternative approach is to use experimental designs. The condition, however, that the composition of all components of the mobile phase must total 100% presents a problem when trying to mathematically represent ranges of each mobile phase constituent of a ternary or quaternary system. A method is described here, based on spherical coordinate representations, that adheres to the constraints of the mobile phase composition and allows experimental designs, such as central composite and factorial designs, to be applied to the simultaneous optimization of the mobile phase composition. Other factors, in particular temperature and gradient time, can then be included in the design. As a result of applying these designs to the HPLC separation of phenols and corticosteroids, it was found necessary to include three-way interactions between experimental factors in the model. The significance of these interactions shows that they need to be considered in HPLC method development.