## Chromatography Basics

### Selectivity versus Efficiency

- Fig. 1: The resulting chromatographic resolution R depending on the selectivity α, the number of theoretical plates N and the retention factor k. For the calculation of the relevant parameters, the following values were taken: α = 1.03, N = 5,000 und k = 3.
- Fig. 2: Dependency between inner diameter of the column and the linear velocity (left y-axis) and the absolute flow rate (right y-axis).
- Fig. 3: The resulting van-Deemter curves for 50 x 0.3 mm columns packed with 1.9 µm and 3.0 µm fully porous and 2.7 µm core-shell particles at 30 °C. The monolithic column exhibited a dimension of 150 x 0.2 mm. By courtesy of John Wiley & Sons, Inc.

^{1}, Terence Hetzel

^{1}, Denise Loeker

^{1}, Juri Leonhardt

^{1}

**There are several strategies that can be used when we’re looking for a solution to a chromatographic separation problem. The Purnell-equation, often called the “Master Equation” of chromatography, specifies the parameters for the targeted optimization of the chromatographic resolution [1, 2].**

*R*. These are the increase in selectivity

*α*, the efficiency with respect to the number of theoretical plates

*N*and the retention using the retention factor

*k*. The aim is usually a minimum resolution of 1.5, so that a baseline separation can be obtained. Figure 1 shows the resolution plotted against the three variables

*α*,

*k*and

*N*.

**Retention Factor**

However, retention factors of > 5 do not lead to a significant increase in the resolution. With this in mind, the elution strenght of the mobile phase should be adjusted to achieve a retention factor between 2 and 10. Retention factors of > 10 only lead to an increase in the analysis time and no significant impact on the resolution can be observed. The following theoretical example shows that the retention factor as a dimensionless quantity says nothing about the actual analysis time and that short analysis times are possible despite higher retention factors. If the column void time (t_{0}) is one minute and the retention factor is 10, this equals a retention time (t_{R}) of the component of

**Flow Rate and Linear Velocity**

_{0}) of the mobile phase – this can be calculated using the following equation:

^{-1}, very high linear velocities can be achieved. The inner diameter of the column is plotted against the linear velocity (left y-axis) using the given flow rate or rather against the absolute flow rate (right y-axis) using the given linear velocity. Using the plotted data, it can be seen that at a constant absolute flow rate of 40 μL min

^{-1}, the linear velocity increases from 0.058 mm s

^{-1}to 13.6 mm s

^{-1}if the inner diameter is reduced from 4.6 mm to 300 μm. Based on a constant linear velocity of 13.6 mm s

^{-1}, the absolute flow rate increases from

^{-1 }up to 9.4 mL min

^{-1}when the column inner diameter is increased from 300 μm to 4.6 mm. So when using the conventional column formats the absolute flow rate has to be drastically increased to achieve analysis times comparable to Micro-LC. This inevitably leads to a very high consumption of expensive and toxic solvents.

*H*is plotted against the linear velocity

*u*for different stationary phases.

_{0}*N*. Therefore, sub 2 µm particles should be used for fast analysis. Using the Master Equation for the resolution it is clear that the increase in the number of theoretical plates also leads to an improvement in the resolution, although the resolution only increases in proportion to the square root of

*N*. Therefore, doubling the number of plates only results in a factor of 1.4. This means that for the targeted optimization of the resolution for a single peak pair, the selectivity of the phase system can be accepted as the key parameter. Relatively small changes in the

*α*-values lead to considerable changes in the resolution, as shown in figure 1.

**Selectivity**

*k*-value of 2 and the second component at a

_{1}*k*-value of 12, the resulting

_{2}*α*-value is 6. If the

*k*-value is 50 and the

_{2}*k*-value 40, the same difference in the

_{1}*k*-value only leads to an

*α*-value of 1.25. On the basis of this example it becomes impressively apparent that high

*k*-values are not advantageous when the goal is to increase the selectivity and therefore the resolution of a single critical peak pair.

*co*-elution is unavoidable. The fact that a complete baseline separation of “only” 50 compounds in a chromatographic run represents a significant challenge is clear in the following example calculation that dates back to Calvin C. Giddings’ reflections in 1983 [3].

*N*the number of plates for isocratic separation, one has to consider

*n*, the peak capacity for gradient separations. In the next article we will therefore be describing the strategy for maximizing the peak capacity on the basis of one and two-dimensional separations.

_{c}**Do you have questions regarding the application and technology in the field of Micro-LC and 2D-LC? Ask the experts at IUTA under:**adlichrom@iuta.de

**Affiliation:**

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

**Contact**

**Dr. Thorsten Teutenberg**

**Project “Advanced Liquid**

**Chromatography”:**http://www.laboratory-journal.com/advanced-liquid-chromatography

**More on Chromatography:**http://www.laboratory-journal.com/search/gitsearch/Chromatography%20type:topstories

**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