## Basics of 2D-LC

### When it Gets Really Complex

- Fig. 1: Graphical representation of the peak capacity based on the signals separated with a constant resolution of R = 1, which are included in the elution time window from t0 (void time) to te (end of the gradient). The blue dashed line represents the solvent gradient. For the given example, the obtained peak capacity is 10.
- Fig. 2: Experimental peak capacity (nc) as a function of the gradient time (tG) for a 50 × 0.3 mm column packed with 3.0 μm fully-porous particles.
- Fig. 3: a) Principle of Heart-Cut 2D-(LC - LC); b) Principle of comprehensive 2D-(LC x LC).
- Fig. 4: Representation of the dependence of the interaction mechanisms for the case of a) low orthogonality and b) high orthogonality between the first and second separation dimension. The blue dots represent the peak maxima of the separated substances in the first and second dimension.

**The requirements for the analysis of complex samples are becoming ever greater. This is mainly due to the fact that with ever more sensitive detectors, extremely low concentrations can be determined. Furthermore, powerful chromatographic methods have been established which allow the separation of complex mixtures.**

A measure of the performance of a chromatographic separation system is the peak capacity, which indicates how many peaks with a constant chromatographic resolution R fit into an elution time window. This issue is depicted graphically in Figure 1 for one-dimensional separation processes.

The concept of peak capacity is based on the early work of Grushka [1]. In this publication, he defined a resolution of 1 for the calculation of peak capacity. Almost all the values published in the literature refer to this definition. As a rule, the elution time window extends from the time of a non-retained compound that exhibits no interaction with the stationary phase (void time t_{0}) to the retention time of the last eluting compound. Alternatively, the end point of the gradient can be selected to calculate the theoretical peak capacity. While for isocratic separations the peak width depends on the analysis time, for gradient elution it is often assumed that the peak width of all components eluting within the gradient window is constant. The reason for this is the band-compression which does not increase the peak width during the gradient [2]. The peak capacity for the gradient mode can thus be calculated using the following equation:

Here n_{c} is the theoretical peak capacity of the system, t_{G} the gradient time, and w̅ the average peak width.

The question now arises, which peak capacity can be achieved with one-dimensional chromatographic methods. When a column with a length of 5 cm, an inner diameter of 300 μm and particles with a diameter of 3.0 μm is considered, the peak capacity is between 50 and 200 for a gradient time of 1.6 and 34 min, as can be seen from the plot in Figure 2 [3, 4].

In this case, the maximum gradient time is 34 minutes.

It should be noted that an increase of the gradient time by a factor of 2 from 15 to 30 min does not lead to an increase of the peak capacity by the same factor (n_{c} = 146 at t_{G} = 15 min, n_{c} = 185 at t_{G} = 30 min). The resulting curve is nonlinear and approaches asymptotically a limit value with increasing gradient time. If different systems are to be compared, it is useful to introduce a normalized parameter. This parameter, which is the peak capacity production rate, will be obtained by dividing the absolute peak capacity by the gradient time. For the example given above, a peak capacity production rate of 197/34 min = 5.8 min^{-1} is obtained.

An often cited major advantage of two-dimensional separation methods compared to one-dimensional separation systems is the significantly higher peak capacity > 1000 [5]. This statement is based on the concept of comprehensive two-dimensional liquid chromatography (LC x LC) and the assumption that an orthogonal separation system exists. In the case of comprehensive 2D LC, the complete chromatogram of the first separation dimension is transferred in defined fractions to a second separation column. This process is characterized by the adjective “comprehensive”. In this case, the sign for the multiplication “x” is to be used. The chromatogram section in Figure 3b illustrates this issue.

In this context, orthogonality means that the separation mechanisms of both dimensions are completely independent from each other. As an example, in the first dimension a separation is achieved by hydrophobicity and in the second dimension by size. Ideally, the analytes present in the sample are evenly distributed across the two-dimensional chromatographic area. This case corresponds to the scenario shown in Figure 4b. The blue dots represent the peak maxima of the separated substances in the first and second dimension. In contrast, the blue dots shown in Figure 4a are arranged along the bisecting line. Thus, only a very small part of the available area is used which means that the separation mechanisms of both dimensions are not very different.

For practical applications, orthogonal separation systems are very difficult to find. An exception is polymer analysis, in which the interaction mechanisms specified above are independent in many cases [6]. In contrast, a combination of ion exchange chromatography and reversed-phase chromatography has proven to be particularly advantageous in the field of proteomics [7]. If orthogonality is assumed, the peak capacities of both separation dimensions can be multiplied and the total peak capacity can then be calculated according to equation 2:

n_{total} = n_{1} x n_{2}

For practical applications, a number of factors must be taken into account, which might lead to a significant reduction in the effective peak capacity. A detailed discussion is out of the scope of this article, but the reader should be aware that the values for the peak capacity of two-dimensional systems given in many publications are to be taken with extreme caution [8]. From a practical point of view, the user is more interested in the question of whether a two-dimensional approach can actually separate and detect more components in a given mixture. This question cannot be answered generally. In order to decide whether a one-dimensional or two-dimensional separation system is more suitable to solve a specific analytical problem, the experiments have to be carried out on both systems and the results have to be compared [9, 10].

An alternative approach to comprehensive two-dimensional LC x LC is the heart-cut technique (LC - LC). As shown in Figure 3a, only one or a few fractions are transferred from the chromatogram of the first separation dimension to a second column. This approach is suitable whenever a peak purity analysis of a single compound has to be performed [11]. In this case, the total peak capacity of the two-dimensional separation system is less important than the intelligent combination of separation columns and mobile phases, which differ significantly in their selectivity. A combination of a reversed phase with a normal phase or HILIC phase should be very suitable if the sample contains both very polar and non-polar compounds [12]. However, in practice it is frequently observed that a HILIC separation is not appropriate if the compounds contained in the sample are sufficiently retained on a reversed phase [13]. Therefore, it may be useful to combine two RP systems and to obtain the necessary difference in selectivity by varying the pH, temperature, organic co-solvent, and gradient slope [14].

**Conclusion and outlook**

Comprehensive two-dimensional chromatography will presumably be established in all areas where extremely complex samples need to be analyzed. This applies to environmental analysis, food analysis and in particular bioanalysis [15]. Since quantification of individual compounds from an LC x LC analysis run is very difficult, this variant of two-dimensional chromatography is suitable for screening analysis. If a quantification of individual target compounds is required, the heart-cut approach or one-dimensional methods are most applicable. In order to be able to evaluate the actual performance of two-dimensional separation processes on the basis of real applications, a comparison between one-dimensional and two-dimensional separation methods would be absolutely necessary by means of a broad-scale round robin test. In addition to the optimization of the peak capacity, the selection of the separation systems in both dimensions, which should have a great selectivity difference or a high orthogonality, also plays a decisive role.

**Authors**

Thorsten Teutenberg^{1}, Terence Hetzel^{2}, Juri Leonhardt^{1}

**Affiliations**

^{1}Institute for Energy and Environmental Technology e. V., IUTA, Duisburg, Germany

^{2}Bayer AG, Wuppertal, Germany

**Contact
Dr. Thorsten Teutenberg**

Department Head Research Analysis

& Miniaturization

Institute for Energy and Environmental

Technology e. V. (IUTA)

Duisburg, Germany

adlichrom@iuta.de

References:

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[2] Schellinger, A. P., Carr, P. W., Isocratic and gradient elution chromatography: A comparison in terms of speed, retention reproducibility and quantitation. Journal of Chromatography A, 2006, 1109, 253-266; DOI:10.1016/j.chroma.2006.01.047

[3] Neue, U., Theory of peak capacity in gradient elution. Journal of Chromatography A, 2005, 1079 (1-2), 153-161

[4] Hetzel, T., Blaesing, C., Jaeger, M., Teutenberg, T., Schmidt, T.C., Characterization of peak capacity of microbore liquid chromatography columns using gradient kinetic plots, Journal of Chromatography A, 2017, 1485, 62-69; DOI:10.1016/j.chroma.2005.03.008

[5] Stoll, D. R., Wang, X., Carr P. W., Comparison of the Practical Resolving Power of One- and Two-Dimensional High-Performance Liquid Chromatography Analysis of Metabolomic Samples. Analytical Chemistry, 2008, 80 (1), 268-278

[6] Kilz, P., Radke, W., Application of two-dimensional chromatography to the characterization of macromolecules and biomacromolecules. Analytical & Bioanalytical Chemitsry, 2015, 407, 193-21; DOI:10.1007/s00216-014-8266-x

[7] Donato, P., Cacciola, F., Mondello, L., Dugo, P., Comprehensive chromatographic separations in proteomics. Journal of Chromatography A, 2011, 1218 (49), 8777-8790

[8] Li, X., Stoll, D. R., Carr, P. W., A Simple and Accurate Equation for Peak Capacity Estimation in Two Dimensional Liquid Chromatography. Analytical Chemistry, 2009, 81 (2), 845-850; DOI:10.1016/j.chroma.2011.05.070

[9] Teutenberg, T., Leonhardt, J. Peak versus Peak capacity – The role of comprehensive two-dimensional liquid chromatography. GIT separation 2/2014, 20 – 21, WILEY-VCH Verlag GmbH & Co. KGaA, GIT VERLAG, Weinheim

[10] Leonhardt, J., Teutenberg, T., Türk, J., Schlüsener, M. P., Ternes, T. A., Schmidt, T. C., A comparison of one-dimensional and microscale two-dimensional liquid chromatographic approaches coupled to high resolution mass spectrometry for the analysis of complex samples. Analytical Methods, 2015, 7 (18), 7697-7706; DOI:10.1039/C5AY01143D

[11] Lee, C., Zang, J., Cuff, J., McGachy, N., Natishan, T. K., Welch, C. J., Helmy, R., Bernardoni, F., Application of Heart-Cutting 2D-LC for the Determination of Peak Purity for a Chiral Pharmaceutical Compound by HPLC. Chromatographia, 2013, 76 (1), 5-11; DOI:10.1007/s10337-012-2367-5

[12] Francois, I., Sandra, K., Sandra, P., Comprehensive liquid chromatography: Fundamental aspects and practical considerations - A review. Analytica Chimica Acta, 2009, 641(1-2), 14-31; DOI:10.1016/j.aca.2009.03.041

[13] Leonhardt, J., Teutenberg, T., Buschmann, G., Gassner, O., Schmidt T. C., A new method for the determination of peak distribution across a two-dimensional separation space for the identification of optimal column combinations. Analytical and Bioanalytical Chemistry, 2016, 408 (28), 8079-8088; DOI:10.1007/s00216-016-9911-3

[14] Pursch, M., Lewer, P., Buckenmaier, S., Resolving Co-Elution Problems of Components in Complex Mixtures by Multiple Heart-Cutting 2D-LC. Chromatographia, 2017, 80 (1), 31-38; DOI:10.1007/s10337-016-3214-x

[15] Fumes, B. H., Andrade, M. A., Franco, M. S., Lancas, F. M., On-line approaches for the determination of residues and contaminants in complex samples. Journal of Separation Science, 2017, 40(1), 183-202