Here we’ll be looking at some of the basic calculations used in HPLC, with an emphasis on their practical utility for evaluating separations, developing methods and isolating problems. The first in line is the retention factor, k, often called the capacity factor, k’. The retention factor is a measure of the distribution of the sample between the mobile phase and the stationary phase – somewhat analogous to a partition coefficient for a solute between two liquids.
The calculation is a simple one, as shown in Figure 1. t R is the retention time and t 0 is the column dead-time. Retention is measured from the time the sample is injected to the highest point on the peak. Measurement of the column dead-time is most easily measured as the first disturbance in the chromatogram (the “solvent front”) – we’ll consider t 0 more next week. As both t R and t 0 are in the same units (min, sec, furlongs or fortnights), the units cancel out and k is a dimensionless quantity.
The calculation of k is a simple one, but it still requires a calculator, and this activation-energy barrier is too much for many of us (where is that calculator…?), so we don’t bother. But for many purposes, we don’t need to know k to much better than half a unit, which means that an estimate is quite adequate.
The retention factor is estimated simply as follows. Note that the numerator of the equation (t R – t 0) tells us to subtract t 0 from the retention time. Or simply throw away everything before t 0 and start measuring from t 0. The denominator (t 0) says to use t 0 as our unit of measure, instead of time or distance. So we just mark off the baseline in units of t 0, starting at t 0, as shown at the bottom of Figure 1. When we do this, you can see that for the three peaks, k ≈ 1, ≈2 and ≈3, respectively.
As we’ll cover in a later discussion, we get the “best” chromatography if 2 < k < 10, and usually
1 < k < 20 is acceptable for isocratic separations. If the retention range is wider than this, it is likely that a gradient will be required. And if k < 1, we tend to have more problems – less stable separations and a higher chance of chromatographic interferences at the beginning of the chromatogram.
This blog article series is produced in collaboration with John Dolan, best known as one of the world’s foremost HPLC troubleshooting authorities. He is also known for his research with Lloyd Snyder, which resulted in more than 100 technical publications and three books. If you have any questions about this article send them to TechTips@sepscience.com