Comprehensive Study on the Optimization of Online Two-Dimensional Liquid Chromatographic Systems Considering Losses in Theoretical Peak Capacity in First- and Second-Dimensions: A Pareto-Optimality Approach

Abstract

A method to optimize different objectives (total analysis time, total peak capacity, and total dilution) has been applied to comprehensive two-dimensional liquid chromatography. The approach is based on Pareto-optimality, and it yields optimal parameters (column particle sizes, column diameters, and modulation times). Losses in the peak capacities in the first dimension (due to undersampling) and in the second dimension (due to high injection volumes) have been taken into account. The first effect (detection band broadening) reduces the original peak capacity by about a half, the second effect can reduce the total peak capacity by an additional half. Thus, the total loss in peak capacity may be 75% of its theoretical value. Analytical expressions to calculate these effects under gradient and isocratic conditions are derived. Of particular interest is the study of the optimal modulation times, which corresponded to between 2 and 3 two-dimensional runs per one-dimensional peak. The effects of using gradient or isocratic elution, conventional (40 MPa) or "ultra-high" (100 MPa) pressures, and focusing between the first and second dimensions were also studied. A trade-off between total peak capacity, total analysis time, and total dilution can be established.

Fourier transform assisted deconvolution of skewed peaks in complex multi-dimensional chromatograms

“…This can be achieved by increasing the efficiency of the used columns and reduction of extra-column effects, but most effectively by increasing the number of orthogonal separation dimensions [17]. The principles for the interpretation of these multi-dimensional chromatograms remain the same.…”

Theoretical and practical interest in UHPLC technology for 2D-LC

“…Vivo-Truyols et al [18] showed that, under certain circumstances, the loss in peak capacity may reach 75%. It is therefore of crucial importance to find a way to evaluate these correction factors correctly in calculating the effective peak capacity and optimizing LC x LC parameters.…”

“…2 σv, col is the peak standard deviation in volume units resulting from peak band broadening in the second column, 2 σv, total is the total peak standard deviation in 2 D and CF is the compression factor [30]. CF is related to the two solute retention factors in 2 D, the first one with the 1 D mobile phase and the second one at elution with the 2 D mobile phase [18,30,31]. The compression factor is high if the injection solvent in the transferred fraction is weak.…”

“…The compromise between peak capacity and analysis time was established by means of an attractive pareto-optimality approach [18]. In this study, the calculations were made easier by:…”

Recent advances on multidimensional liquid chromatography–mass spectrometry for proteomics: From qualitative to quantitative analysis—A review

“…× P cn . Unfortunately, it is difficult to reach the theoretical limits for currently available MDLC systems due to the intrinsic imperfection in orthogonality and some practical limitations such as the unavoidable band broadening caused by dead volumes [3,[12][13][14]. Up to now, various combinations of MDLC have been reported, such as strong cation exchange chromatography -reversed phase liquid chromatography (SCX-RPLC) [15][16][17][18], size exclusion chromatography (SEC) -RPLC [19][20][21], RPLC-RPLC [22][23][24][25], and hydrophilic interaction chromatography (HILIC) -RPLC [26][27][28][29], in either online or offline formats for different proteomics applications.…”