## When Peaks Collide (Part 2)

In Part 1 of this two-part series, John Hinshaw discussed the resolution of a pair of symmetrical peaks and the effects that relative peak size have on area measurements. This month's "GC Connections" examines the effects of peak tailing on resolution and peak overlap.
Nov 01, 2010
Volume 13, Issue 4

Part 1 of this series1 reviewed the calculation of the resolution of two adjacent peaks, repeated here in equation 1. A version of the resolution equation commonly used in practice is given in equation 2.

Here, t R is the retention time, wb is the peak width-at-base as measured at 13.4% of the peak height, and wh is the peak width at it's half-height. The subscript numbers indicate which peak. Measurements of the peak retention times and widths for the purposes of determining resolution are shown in Figure 1 for a pair of peaks with Rs = 2.0.

 Figure 1: Peak measurements for calculation of resolution. Peak 1 and peak 2 are identical nontailing Gaussian peaks with σ = 4.0 s and τ = 0.0 s. The peaks are spaced 8σ apart (32 s), and Rs = 2.0.
These relationships are cast in terms of a pair of identical symmetrical peaks, but the definition of resolution does not limit the relative sizes of the peaks or their shapes. Resolution calculations are performed routinely on pairs of peaks that can be quite different in size and shape, yet the effects of disparities in peak shapes on quantitative measurements are rarely assessed. Part 1 of this series1 showed that increasing the size of the first peak up to 10 times the size of the second did not materially affect quantitative measurements, as long as the peak resolution was at the "baseline" level of 1.5 or greater and a simple vertical peak boundary at the valley point — I'll call this method valley integration — delineated the first peak from the second. With a less-than-baseline resolution of 1.0, however, where the difference in the retention times of symmetrical peaks is equal to the average of their widths at base, significant measurement errors of up to 10% for the smaller peak's area were incurred for valley integration. Even greater errors were caused by either tangential or exponential skimming methods of peak integration. Thus for this limited set of examples, a requirement that symmetrical peak pairs have resolution of 1.5 or greater is well justified.