Small changes in retention time of a liquid chromatography (LC) method are normal. At what point is a problem suggested? Retention
time shifts can be frustrating when you can't figure out if a shift is something you caused or if there is another reason
It is interesting how problems tend to cluster — in the last few weeks I've received several questions related to retention
time shifts with liquid chromatography (LC) methods. Some of these correspond to the preparation of new batches of mobile
phase, some are from one day to another, some are from within a batch of samples, and some result from a change in instruments.
In this month's "LC Troubleshooting," I will discuss some of the factors that influence small changes in retention.
Most LC methods run on modern instrumentation with a good quality column will have quite stable retention times. I generally
expect to see run-to-run variation in the second decimal place of the retention time, such as ±0.02–0.05 min. However, the
historical behavior of the method should be used to determine what is normal for that method. For example, with large biological
molecules, such as proteins, that use shallow gradients, the variability can be an order of magnitude or more larger.
Mobile-Phase Organic Concentration
One of the most common causes of shifts in retention time in reversed-phase LC separations is a minor change in the concentration
of the organic solvent, usually methanol or acetonitrile. This can happen from a minor error in formulation or a change in
the mobile-phase composition if one solvent evapo rates over time.
Figure 1: Plots of log k versus %B for compounds of 500 Da (red), 5000 Da (blue), and 50 kDa (green). See text for details.
For small molecules (arbitrarily <1000 Da), we can use the "Rule of Three" to estimate the effect of a change in organic solvent,
or %B. This rule states that the retention factor, k, changes approximately threefold for a 10% change in %B. This rule derives from plots, such as that in Figure 1, where k is plotted versus %B on a semi-log plot. The red line in Figure 1 represents the retention behavior for a 500 Da analyte.
Retention changes from ~29 min at 40% B to ~4 min at 60%. For practical purposes, this relationship can be considered linear
and represented in the standard y = mx + b format as
w is the (theoretical) retention in 100% water, S is the slope of the plot, and Φ is the %B as a decimal (0.5 = 50%). Values of S can be determined from two experimental runs using equation 1. Empirical observations indicate that S can be estimated as
where MW is the molecular weight (Da). Thus for a 500 Da analyte, S ≈ 5.6. If we consider S ≈ 5 as an average for sub-1000 Da molecules, we can then estimate how k changes with %B with
where Δk is the change in k value for a Φ change in organic. If S = 5, a 10% change in organic gives Δk ≈ 105×0.1 = 3.16 ≈ 3. This is the basis of the Rule of Three.
As an example, our 500 Da analyte in Figure 1 has k = 5 at 50% B. We can convert this to retention time, t
R, by rearranging the equation for k,
0 is the column dead time (also abbreviated t
M). If we assume a 150 mm × 4.6 mm column operated at 1 mL/min, t
0 ≈ 1.5 min, so t
R = 1.5(1 + 5) = 9.0 min. The Rule of Three would suggest that k ≈ 3 × 5 = 15 for a change to 40% B, which would correspond to t
R ≈ 24 min. In fact, S = 5.16 for our analyte, so k = 18.1 and t
R = 28.7 min — close enough for a rule of thumb.
Mobile-phase formulation errors should not be in the 10% region if you are at all careful, so what happens for smaller changes?
We can use equations 3 and 5 to determine the effect of a 0.1%, 0.5%, and 1% error in formulating our 50% B mobile phase for
our "average" S = 5 small molecule. I'll leave the calculations to you, but the results summarized in Table I show that these correspond
to retention shifts of approximately 0.1, 0.4, and 0.9 min, respectively (I have rounded values for display, so if you try
to repeat my calculations, your results may vary somewhat). So, you can see that it takes only a minor error in mobile-phase
formulation to shift retention times enough to notice the change.
Table I: Effect of small errors in mobile-phase composition on the retention for analytes of different S values
With larger molecules, the problem is magnified, because S increases markedly with an increase in molecular weight. This makes the log k versus %B plots steeper, as is seen for 5000 Da (blue) and 50,000 Da (green) compounds, such as peptides or proteins, respectively.
Steeper plots mean that these compounds are much more sensitive to minor changes in the mobile-phase composition. Our Rule
of Three for <1000 Da samples becomes the Rule of 60 at 5000 Da, and the Rule of 400 at 50,000 Da. This extreme sensitivity
of the retention of large molecules to small changes in %B means that isocratic separation is not practical for most separations
of these analytes.