Gradient HPLC — One Invaluable Equation

July 1, 2015
Tony Taylor
Tony Taylor

Tony Taylor is Group Technical Director of Crawford Scientific Group and CHROMacademy. His background is in pharmaceutical R&D and polymer chemistry, but he has spent the past 20 years in training and consulting, working with Crawford Scientific Group clients to ensure they attain the very best analytical science possible. He has trained and consulted with thousands of analytical chemists globally and is passionate about professional development in separation science, developing CHROMacademy as a means to provide high-quality online education to analytical chemists. His current research interests include HPLC column selectivity codification, advanced automated sample preparation, and LC–MS and GC–MS for materials characterization, especially in the field of extractables and leachables analysis.

LCGC Europe

LCGC Europe, LCGC Europe-07-01-2015, Volume 28, Issue 7
Pages: 406

An excerpt from LCGC’s e-learning tutorial on gradient HPLC at

Several mathematical relationships are useful in gradient elution reversed‑phase liquid chromatography (LC), and the webcast and tutorial from which this excerpt is taken describes many of them. Here, we concentrate on one particularly useful equation that allows us to make changes to an analytical system to improve throughput or efficiency, while retaining the selectivity of the original method. This equation can be particularly useful when developing or translating high performance liquid chromatography (HPLC) methods.   Equation 1 defines a corrected measure of gradient steepness (1) and measures the change in modifier concentration (%B) per column volume of mobile phase:   Gs = VmΔΦ/FtG    [1]   where F is eluent flow rate (in millilitres per minute), tG is the gradient time (in minutes), ΔΦ is the percent change in organic modifier over the gradient (5–95% B would be represented as 90), and Vm represents the interstitial volume (that is, the volume of mobile phase) within the column and can be simply calculated using equation 2:   Vm = π × r2 × L × W    [2]   where r is the column radius (in millimetres), L is the column length (also in millimetres), W is the column percent interstitial porosity, W (fully porous materials) ≈ 68% (0.68), and W (core–shell particles) ≈ 55% (0.55). So, for a method using a 150 mm × 4.6 mm column with 5-µm fully porous silica and a gradient of 20–60% B over 30 min at a flow rate of 1 mL/min, the value of Gs would be calculated as follows:    Vm = π × 2.32 × 150 × 0.68 = 1695 (mL) =1.7 mL Gs = 1.7 × 40/1 × 30 Gs = 2.27 %B/column volume    

    Figure 1(a) shows the initial chromatogram with a very long run time and poor signal to noise for the diffuse (broad) later eluted peaks. We can speed up this method and hopefully retain good selectivity and resolution in the simplest way by doubling the flow rate; however, to keep the gradient steepness constant then we could, for example, halve the gradient time (tG) (F = 2 and tG) = 15) (Figure 1[b]).  
    Another very convenient way to speed up the separation is to double the gradient range (ΔΦ = 80), which would mean using a gradient range of 20–100% B. This can also be compensated to keep Gs constant by doubling the flow rate (F = 2) - the result of which is shown in Figure 1(c).   When translating to smaller column dimensions, we also have a range of choices to keep the adjusted gradient steepness constant. Here we switch to a 100 mm × 2.1 mm, 2.7-µm superficially porous particle column with a Vm of 0.19 mL. We used a low-dead-volume ultrahigh-pressure liquid chromatography (UHPLC) system to rapidly mix a 20–80% B gradient in 10 min with a flow rate of 0.5 mL/min.   Gs = 0.19 × 60/0.5 × 10 Vm = 0.19, ΔΦ =60, F = 0.5 mL/min, tG = 10 min Gs = 2.28   Using the corrected gradient steepness (Gs), which allows us to maintain the %B per column volume rate of change, we were able to achieve a sixfold reduction in analysis time without compromising the quality of the separation as measured by the minimum resolution of any peak pair.   Reference   1. L.R. Snyder, J.J. Kirkland, and J.L. Glajch, Practical HPLC Method Development (Wiley, New York, USA, 1997).