This blog is part of our separation science primer series which provides an easy-to-understand overview of key topics in solid-phase extraction and chromatography.
This blog focuses on Resolution Selectivity and Efficiency in liquid chromatography (LC)
Liquid chromatography separations are based on movement differences the various analytes in a mixture take as they are pumped through a porous media bed. For example, some mixture of analyte A and analyte B may be separated into its constituent parts if A moves through the porous media (stationary phase) at a different rate than B. In this way, the mixture is “spread out”, and each component may be detected and collected separately. By forcing a mixture through a porous bed, you are making each component of that mixture interact with the media. Some of the analytes of the mixture will “like” the media more than others and have a tendency to move through it more slowly. Other analytes will not want to associate with the media at all and speed straight through.
The individual interactions each analyte has with a porous media are defined by the physical and chemical properties of both media and analyte. More specifically, since each analyte is suspended in a liquid (mobile phase) moving through the stationary phase, for each unique analyte there is a set of competitive forces that either attracts or repels it to these phases. The net total of these forces define how an analyte will behave in the liquid chromatography system.
A primary goal of liquid chromatography is to provide clear separations between sequentially eluting analytes. In a chromatogram, we would like to see a discernable gap at the baseline between peaks that are next to one another.
Figure 1: The effect LC parameters efficiency and selectivity have on the resolution of sequentially eluting peaks. Selectivity defines the “distance” between peaks. Efficiency defines the “width” of each peak.
Resolution (R) is the term used in chromatography to define the quality of the separation between two adjacent peaks. Both the distance between peaks and the width of each individual peak contribute to this separation.
Selectivity (α) is used to define the ratio of retention times of two sequentially eluting analytes and is a descriptor for the distance between them.
Efficiency (N) is used to define the width of each peak and is primarily determined by particle size, quality of the pack and morphology of packing material.
These ideas have been related mathematically as follows:
(Equation 1)
Figure 1 offers a visual representation of the relationship between selectivity and efficiency as they relate to resolving two sequentially eluting analytes.
In Figure 1(1)we see a chromatogram produced with a column of High Efficiency and High Selectivity for the analytes, indicating that narrow sharp peaks appear far apart. This combination leads to the highest resolution offering a clear and unambiguous separation.
In Figure 1(2) we have the combination of High Efficiency and Low Selectivity. Narrow sharp peaks are grouped close together. This may be acceptable, given that we have baseline separation, however this method may not be “rugged”.
Figure 1(3) illustrates the combination of Low Efficiency and High Selectivity, showing broad peaks spaced far apart. Again, this method appears to produce an acceptable chromatogram, however quantitation reproducibility could be low.
In Figure 1.4 we have the combination of Low Efficiency and Low Selectivity. Here, broad peaks appearing close together do not show acceptable separation.1
Resolution can be improved by altering any of the three factors k, a, or N, however, improving separation selectivity (values of a) is by far the most powerful option (ref.2).
Figure 2: Plotting Resolution against Selectivity (a), Efficiency (N) and Retention Factor (k’).
Adapted from ref. 3
When resolution is plotted vs. the three parameters that define it (as shown in Figure 2), it becomes apparent that selectivity has the greatest effect. Equation 1 shows that resolution increases with the square root of efficiency. This term grows very slowly as depicted, so it has a small return on investment. Selectivity on the other hand increases resolution with a linear term. This means that a very small increase in selectivity will produce a large impact on resolution.
Resolution of 1.5 is typically regarded as sufficient for baseline separation. Table 1 summarizes changes required in efficiency and selectivity to improve resolution from 1 to 1.5. If we assume that a standard HPLC column produces separations with efficiency N = 10,000, with a small increase in selectivity from 1.04 to 1.06, resolution increases from 1 to 1.5. If, however, we keep selectivity fixed, then the column efficiency would need to more than double to 22,500 in order to realize the same resolution.
Table 1: Variations in Efficiency and Selectivity Required to increase Resolution from 1.5(ref.1)
Selectivity is defined by the surface chemistry of the stationary phase material and how it interacts with the analytes. To best way to change selectivity is to change the column. Finding alternative stationary phase materials will lead you down the path of investigation differences in selectivity. The market is continually producing new stationary phases that offer novel selectivity for challenging applications. I like to remain open to new ideas and see what strategy works best in our lab.
In a future post here, we will continue to investigate selectivity and take a deep dive into the surface chemistry of carbon and how it contributes to retention differences observed in LC.
References
1 Kazakevich, Y. & Lobrutto, R. 445 - 447 (2006).
2 L. R. Snyder, J. J. K., J. W. Dolan. Introduction to Modern Liquid Chromatography. 3rd edn, (John Wiley & Sons, 2010).
3 Mao, Y. Selectivity optimization in liquid chromatography using the thermally tuned tandem column T (3) C concept. (University of Minnesota, 2001).
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