Geometric Approach to Factor Analysis for the Estimation of Orthogonality and Practical Peak Capacity in Comprehensive Two-Dimensional Separations

Abstract

Procedures were developed for the estimation of orthogonality in two-dimensional (2D) separations. The parameters evaluated include peak spreading angle, retention correlation, and practical peak capacity. Solute retention parameters, such as retention times and capacity factors on both dimensions, were used to establish a correlation matrix, from which a peak spreading angle matrix was calculated using a geometric approach to factor analysis. The orthogonality is defined by the correlation matrix with correlation coefficients that vary from 0 (orthogonal) to 1 (perfect correlation). Equations were derived for the calculation of practical peak capacity in 2D separations. The calculations are based on the peak capacities obtained on each dimension and the peak spreading angle in an orthogonal, 2D retention space. The equations and the procedures can be used to evaluate the performance of a comprehensive 2D separation. Using experimental data from a 2D GC separation, it is demonstrated that the equations are very useful for the comparison, evaluation, and optimization of 2D separations.