The object of chromatography is to separate a sample into a series of chromatographic peaks, within a reasonable time, each representing a single component of the sample. The resolution (R) between two peaks (Fig. 1) is given by equation 1:
R = (tR2 – tR1) / [(w2 + w1)/2] = 2 Δt / (w2 + w1) (1)
Where, tR2 και tR1 are the retention times of the retained components 1 και 2 measured from injection to peak maximum and w2and w1 are peak widths in units of time measured at the base of the peaks 1 and 2.
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| Fig 1: Peak resolution in chromatography. Where, tR2 και tR1 are the retention times of the retained components 1 και 2 measured from injection to peak maximum and w2 and w1 are peak widths in units of time measured at the base of the peaks 1 and 2. |
For two peaks that are close w2 = w1 and equation (1) gives:
R = Δt / w1 (2)
Resolution depends upon two factors:
Narrowness of the peaks (zone width)
The distance between the peak maxima (zone separation)
Equations 1 and 2 show that as Δt increases the resolution R between the two peaks improves. We can increase Δt by enhancing the interaction of the solutes with the column or by increasing the column’s selectivity for one of the solutes.
The resolution R also improves as w the peak widths become narrower. Peak width is a kinetic effect and has to do with the partitioning of the solute between the mobile (carrier liquid) and stationary phase (column). The column efficiency determines the peak width (zone spreading).
In general, the value obtained for the resolution R of two peaks gives us a measure of the separation’s success. As R increases the separation between the 2 compounds also improves.
Poor resolution results when components elute close to the unretained component. The relationship between resolution, efficiency and selectivity are shown in Fig. 2
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| Fig 2: A) Good resolution due to column efficiency B) Poor resolution. The compounds elute almost at the same time C) Good resolution due to column selectivity |
Column efficiency is expressed quantitatively by the number of theoretical plates , N (Fig. 3).
N = (tR / σ)2 = 16 (tR / w)2 (3)
Where σ is the peak standard deviation, tR is the retention time of the peak and w = 4σ
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| Fig 3: Column efficiency is expressed quantitatively by the number of theoretical plates N. The column efficiency determines the peak width (zone spreading). |
In reality, what happens when the solute is injected into the column can be described as follows: In the beginning it occupies a narrow band of finite width. As it travels in the column the width of its band continually increases in a process called band broadening. Therefore, column efficiency is concerned with the broadening of an initially compact band of a solute as it passes through the column. The broadening is a result of the following:
- Column design
- Column operating conditions
Basically, equation (3) (the number of theoretical plates N) compares the width of the peak w to the length of time tR the solute (analyte) has been in the column. Thus, an efficient column keeps bands from spreading (keeps narrow peaks).
The number of plates is proportional to the column length. The height equivalent to a theoretical plate H is the most informative measure of column efficiency because it allows comparison between columns of different lengths. It is related to the number of theoretical plates N as follows:
H = L/N (4)
where L is the length of the column usually expressed in millimeters (mm).
High performance columns have plate heights 0,3 or less.
References
1) D. Harvey, “Modern Analytical Chemistry”, McGraw-Hill Companies Inc., 2000
2) L.R. Snyder, J.J. Kirkland, “Introduction to Modern Liquid Chromatography”, 2nd Edition, John Wiley & Sons, 1979
3) Nina Hadden et al., “Basic Liquid Chromatography”, Varian Aerograph, 1971
4) C. F. Simpson, “Techniques in Liquid Chromatography” Wiley-Hayden: Chichester, England, 1982
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