Limits of multi-linear gradient optimisation in reversed-phase liquid chromatography

The concept of limiting peak purity was applied to quantify the degree of completion of the separation capability of a chromatographic system using multi-linear gradients. The objective was to check whether the complexity of a gradient program deserves be increased to enhance resolution by inserting more linear segments, or on the contrary, no significant improvements can be expected under more complex gradients. A set of 19 isoindole derivatives of primary amino acids was selected to test the performance of isocratic, single linear and multi-linear gradients. Accurate simulated chromatograms were obtained via numerical integration of the general equation of gradient elution, using pre-established start and end conditions of the gradient program. The overall peak purity was selected as objective function. Good—although not baseline—resolution was achieved with an optimal trilinear gradient. Excellent agreement between experimental and predicted optimal chromatograms was found. With the proposed approach, a degree of completion of the separation capability of the chromatographic system of 21.2, 49.7, 81.5 and 88.5% was accomplished with optimal gradients with one, two, three and four segments, respectively. More complex gradients did not enhance the latter figure significantly. Also, multi-linear gradients gave rise to more benefits than complementary gradients.