Approximate and exact equations for peak capacity in isocratic high-pressure liquid chromatography

In this letter, we examine an equation that had been published in Analytical Chemistry in a paper entitled "Comprehensive Study on the Optimization of Online Two-Dimensional Liquid Chromatographic Systems Considering Losses in Theoretical Peak Capacity in First- and Second-Dimensions: A Pareto-Optimality Approach" by Vivo-Truyols, G.; van der Wal, Sj.; Schoenmakers, P. J. Anal. Chem.2010, 82, 8525-8536. In that paper, the authors considered, among many issues, the effects of extra-column and column broadening on isocratic peak capacity. They developed an equation to cover all possible conditions and offered a derivation based on two Taylor-series expansions and a regression. We have found an exact equation that covers all conditions and have compared the results using our equation to the results using their approximation in predicting ratios of peak widths. Their approximation works well, as we show, but we wish to offer the exact equation which is simpler in form than the approximate solution.