Model-Based Determination of a Stationary Phase Gradient in Liquid Chromatography Using Optimal Control Theory

Several studies have shown that a stationary phase with a gradient of the ion exchange capacity or particle diameter can improve the column efficiency in liquid chromatography operating in gradient elution mode. However, no general method exists to obtain the optimal stationary phase gradient. This contribution closes this methodological gap by using optimal control theory. We combine control parametrization with a direct-singleshooting method to obtain optimal stratified stationary phases. We demonstrate our approach with an ion exchange chromatographic column. For the chosen case study, the optimal ion exchange capacity gradient predicts an increase of the separation efficiency by 36.3 % compared to a homogeneous column.