Journal of Chromatography A, 1166 (2007) 126–134 Optimisation of multilinear gradient elutions in reversed-phase liquid chromatography using ternary solvent mixtures A. Pappa-Louisi ∗ , P. Nikitas, A. Papageorgiou Laboratory of Physical Chemistry, Department of Chemistry, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece Received 22 June 2007; received in revised form 3 August 2007; accepted 7 August 2007 Available online 10 August 2007 Abstract The multilinear gradient elution theory for binary mobile phases in reversed-phase liquid chromatography presented in [P. Nikitas, A. Pappa- Louisi, A. Papageorgiou, J. Chromatogr. A 1157 (2007) 178] is extended to ternary gradients. For the evaluation of this theory and the performance of the various fitting and optimisation algorithms we used 13 o-phthalaldehyde (OPA) derivatives of amino acids with mobile phases modified by acetonitrile and methanol. It is shown that the theory can lead to high quality predictions of the retention times under gradients elutions and optimisation of ternary gradients provided that we use a six-parameter expression for the logarithm of the retention factor, ln k, and the adjustable parameters of this expression are determined from ternary isocratic data. © 2007 Elsevier B.V. All rights reserved. Keywords: Ternary gradients; Optimisation techniques; Liquid chromatography 1. Introduction The composition of the mobile phase in liquid chromatog- raphy plays an important role both in isocratic and gradient elution since it determines the possibilities offered for optimisa- tion of solvent strength and selectivity. The use of binary solvent mixtures provides the most common solution to this problem. Ternary or even higher order solvent mixtures are expected to be a more advanced and flexible solution [1]. However, in ternary mixtures experience or trial-and-error approaches can hardly lead to the determination of the optimum gradient profile that yields the best separation of the chromatographic peaks of a mixture of analytes. Thus, the use of ternary mobile phases pre- sumes the use of proper optimisation procedures, especially in gradient elution chromatography. However, the work in this area is rather limited [2–7]. In gradient elution chromatography an optimisation proce- dure usually involves the solution of the fundamental equation of gradient elution with respect to the retention time, t R , which in turn requires the dependence of the retention factor, k, upon the mobile phase composition. In recent papers [8–10] we have ∗ Corresponding author. Tel.: +30 2310 997765; fax: +30 2310 997709. E-mail address: apappa@chem.auth.gr (A. Pappa-Louisi). examined these two issues, that is, the calculation of t R from the fundamental equation of gradient elution and the dependence of k upon the composition of the mobile phase. In particular, in [8–10] we have presented a new mathematical treatment that yields analytical expressions for the retention time of a sample solute in binary mobile phases when the programmed gradient profile is linear or multilinear and ln k is not a linear function of the volume fraction ϕ of the organic modifier in the water–organic mobile phase. In what concerns the depen- dence of k upon the composition of a ternary mobile phase, we have developed an expression that allows for the calculation of k from known retention characteristics in the corresponding binary mobile phases [11]. In the present paper the optimisation of multilinear ternary gradients in reversed-phase liquid chromatography (RP-HPLC) using 13 amino acids in acetonitrile–methanol aqueous mobile phases is examined. Note that there is an increased number of publications concerning amino acids separations using linear or multilinear binary gradients [12–15]. The use of ternary solvent mobile phases attempted here is expected to improve the chro- matographic performance. In order to achieve programmable optimisation with multilinear ternary gradients, the theory of the multilinear binary gradient elution in RP-HPLC presented in [9,10] is extended to ternary mobile phases. The analytical expressions for t R derived from this treatment are used in algo- 0021-9673/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.chroma.2007.08.016