Optimizing Separation Using a Window Diagram

The illustration below shows how the mobile phase pH in liquid chromatography affects our ability to separate a mixture of four substituted benzoic acids. The retention times in (a) suggest there are many pH values where some separation is possible. To find the optimum separation, we plot α for each pair of solutes. The red, green, and orange curves in (b) show the variation in alpha (α = kB/kA where B is the later eluting solute) with pH for the three pairs of solutes that are hardest to separate (for all other pairs of solutes, α > 2 at all pH levels).


The blue shading shows windows of pH values in which at least a partial separation is possible—this figure is sometimes called a window diagram—and the highest point in each window gives the optimum pH within that range. The best overall separation is the highest point in any window, which, for this example, is a pH of 3.5. Because the analysis time at this pH is more than 40 min (a), choosing a pH between 4.1–4.4 might produce an acceptable separation with a much shorter analysis time.

The data in this illustration are from Harvey, D. T.; Byerly, S.; Bowman, A.; Tomlin, J. “Optimization of HPLC and GC Separations Using Response Surfaces,” J. Chem. Educ. 199168, 162–168.

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