Generalized rank annihilation method : II. Analysis of bimodal chromatographic data

When confronted with the problem of overlapped peaks, the chromatographer's approach is to change the chromatographic process. However, this may entail considerable time in methods development, with no guarantee of achieving adequate resolution. The “generalized rank annihilation method” (GRAM) utilizes multivariate statistical methods to process a matrix of calibration data with a matrix containing the test data, and can be applied to the problem of completely overlapped peaks in chromatography. Chromatographic analyses (both calibration and test) are carried out on either two (or more) columns of different stationary phases or on columns of similar stationary phase, but with different mobile phases. The results of each set of analyses are combined to create single, bilinear matrices (again, calibration and test). Rank annihilation is then performed on the combined matrices, and both the resolved elution profiles and spectra are generated, as well as quantitative information. The presence of components in the test mixture which are not in the calibration mixture does not interfere with the analysis for the desired analytes. Application of GRAM to bimodal liquid chromatography—ultraviolet detection data is demonstrated with simulated and real analyses of polynuclear aromatic hydrocarbons.