“PRISMA” Model for Computer-Aided HPLC Mobile Phase Optimization Based on an Automatic Peak Identification Approach

Abstract

The tripartite “PRISMA” optimization model, as part of the “PRISMA” system, includes all possible solvent combinations between 1–4 solvents, with a possible fifth one as modifier. The solvent composition is characterized by the solvent strength (S_T) and the selectivity points (P_S).

At a constant S_T the correlation between the P_S and the retention data (horizontal function) can be described by a quadratic function. For constant P_S the solvent strengths and retention data correlate (vertical function) with a logarithmic function. These correlations are used to formulate a mathematical model for the dependence of retention times (capacity factor) on the mobile phase composition. Unknown compounds are estimated in the mathematical model from a sequence of standard chromatograms after having identified individual peaks by an automatic procedure. Only retention times, relative peak areas, and information about the mobile phase compositions are required as input for the identification approach. The approach involves a combination of statistical methods which exploit both the basic properties of retention data and the mathematical relation between retention data, selectivity points, and solvent strength as derived from the “PRISMA” model. Diagnostic information for checking the identification is generated as a by-product. The mathematical model completed by the estimated constants predicts the expected retention times for each possible mobile phase combination. Peak start and peak end times are predicted in a way similar to the retention times, once the identification has been performed. The most important aspects of a chromatogram can thus be predicted for arbitrary mobile phases.

The separation quality of predicted chromatograms is assessed by the chromatographic response function (CRF). The optimal mobile phase combination is that which theoretically generates the chromatogram with the maximal CRF value. This optimal composition is found by a simple mathematical procedure, which maximises the CRF in dependence upon the mobile phase combination. The optimum found is a local one if the starting set of chromatograms contains no variation of the solvent strength, and a global one if, in the set of starting chromatograms, the solvent strength is varied in a suitable way. Recommendations for the starting position are given.

Twelve measurements are necessary for a local optimum, and 15 for the global one. To increase the accuracy, six measurements at three different solvent strength levels are proposed. Generally the highest and the lowest solvent strength level differ by ±(5)% from the middle level.

This strategy is also relevant when modifiers are used in constant amounts. The chromatographic behavior of substances to be separated can be predicted with 1% accuracy from correlations of k' values and selectivity points. Based on these relationships, an automatical mobile phase optimization strategy for isocratic separations is suggested with the “PRISMA” model.