Likelihood of total resolution in liquid chromatography: evaluation of one-dimensional, comprehensive...

Computer simulations of three methods of liquid chromatography (LC) are developed to understand better the conditions under which each method is superior to the others. The methods are one-dimensional LC (1D-LC), comprehensive two-dimensional LC (LC×LC), and selective comprehensive two-dimensional LC (sLC×LC). The criterion by which superiority is measured in this case is the probability that all peaks in a given sample are separated by a resolution equaling or exceeding unity. A point-process model is developed for the simulation of sLC×LC to complement existing models for 1D-LC and LC×LC. In the sLC×LC model, first-dimension singlet peaks remain in that dimension, and first-dimension multiplets, or clusters of overlapping peaks, are transferred to the second dimension for further separation during the interval of time between successive multiplets. Criteria are developed for the success or failure of multiplet transfer. The three LC methods are simulated for peak numbers ranging from 2 to 50 and analysis times ranging from 10 to 1200s, using peak capacities that reflect the performance of modern instrumentation. The probability computations predict the experimental finding that LC×LC is superior to 1D-LC at long times (over 210 or so seconds) but is inferior at shorter times due to the broadening of first-dimension peaks by sampling. In general, sLC×LC is predicted to be superior to LC×LC for samples with less than 40 peaks separated using three samples or less per multiplet. Conversely, LC×LC is predicted to be superior to sLC×LC for samples containing more than 40 peaks and when sLC×LC separations are carried out with six samples per multiplet. We find that the analysis time required to attain a 50% probability of total resolution is always predicted to be shorter for sLC×LC than for 1D-LC, and 30-75% shorter than for LC×LC when 20 or so peaks are separated. Finally, in light of the substantial predicted time savings for sLC×LC analyses the computations are interpreted relative to practical concerns, e.g., retention-time shifts, to establish good working conditions (e.g., the number of samples per multiplet) for future experimental studies of sLC×LC.