This study continues previous work that was concerned with integration errors in peaks with approximately equal sizes (small peak ratios). Chromatographic situations are created here for varying peak resolution and relative peak size. In this case, the peak size of the smaller peak ranges from 5% to less than 0.5% of the larger peak, and resolution is varied from 4.0 to 1.0. Such situations arise in trace analysis and in the determination of impurities in pharmaceutical active ingredients. All chromatograms have been integrated, using both area and height, by four baseline methods — drop, valley, exponential skim, and Gaussian skim. Integration errors are calculated using reference calibration injections. Not all combinations of relative peak size and resolution produced separate peaks. When two peaks were present, the errors for the large peak were negligible. The drop method produced large positive integration errors for a small second peak, but was accurate when the small peak was eluted first. Valley integration generally resulted in a negative peak error. The exponential skim method was accurate at resolution of 2.0 for all situations, but not at lower resolutions, where negative errors were observed. The Gaussian skim procedure was accurate at resolution equal to 1.5 only when using height. Errors were positive for greater resolution and negative when the resolution decreased. There are some situations in which none of the methods produced an accurate estimate of small peak size. As in the first study, height measurements produced less error than area measurements.
Integration of chromatographic peaks (determination of height, area, and retention time) is the first and most important step during data analysis in chromatography-based analytical methods. Peak information is used for all subsequent calculations, such as calibration or analysis of unknowns. Clearly, any error in measurement of peak size will produce a subsequent error in the reported result.
In part I of this article series (1), integration errors were evaluated when the peaks were of similar size. That is, the smaller peak was at least 5% of the larger peak. The results demonstrated that the drop method produced the least error in all situations. The valley method consistently produced negative errors for both peaks, and the skim method generated a significant negative error for the shoulder peak. Peak height also was shown to be more accurate than peak area. As the relative peak size increased (one peak became smaller), resolution at or below 1.0 generated unacceptable errors, and resolution greater than 1.5 was necessary to minimize integration errors.In the present study, this error investigation is expanded to situations in which the smaller peak is significantly different in size from the larger peak. Specifically, small peak size ratios from about 5% to less than 0.5% of the large peak are investigated at resolution values from 4.0 to 1.0. Such peak size ratios commonly occur in trace analysis, in which a solvent or major matrix component is eluted near the analyte of interest, which is present at much smaller concentrations. Similar situations occur in the determination of impurities in pharmaceutical formulations, in which regulatory requirements specify that all compounds present above 0.1% levels must be quantified.
Unfortunately, there is little available guidance on how to properly integrate small peaks when they are near a much larger peak. One previous report discussed integration errors for relative peak sizes in this range (2), noting that the drop–height method was appropriate when the small peak is eluted first. When the small peak was after the large peak, the best integration method depended upon the relative widths of the peaks. Drop–height was best for peaks of equal width, while skim–height was preferred when the peaks widths were not similar. Not all integration options were considered in this study, so conclusions could not be generalized completely.
Conventional wisdom and current chromatographic practice suggest that the minimum resolution between two peaks must be at least 1.5 to ensure complete separation. Some laboratories have even larger minimum resolution requirements. This is a prudent practice, because the effective resolution is also a function of relative peak size, in addition to retention time differences, peak width, and tailing (3). The results presented here provide some initial guidelines on the minimum separation needed and the best integration baseline method to use in each situation.
As noted in the previous report, all resolution situations described here were created using a liquid chromatography (LC) system. The peak shape observed is typical for any well-behaved chromatographic system, so application to gas chromatography (GC) separations should be valid. Although only one data system was used for this study, the author believes that all modern chromatography data systems process data using similar procedures, and only minor differences would be produced by other software packages. The general conclusions should still be valid.