There seem to be a disproportionate number of problems encountered in the concentration region near the limit of detection
(LOD) and lower limit of quantification with calibration curves used for liquid chromatography (LC) methods. Some of these
problems relate to improperly selecting the model used for calibration. The choice of the LOD and quantification is an important
decision that can be confusing. This month's instalment of "LC Troubleshooting" is the first of a series about calibration
curves. This month we will discuss some different calibration models, how to decide if a calibration curve goes through zero
and some problems that can occur if the wrong choices are made. In future columns, we will look at how to determine the lower
limits of a method as well as standardization techniques: internal standardization, external standardization and the method
of standard additions. We also will look in more detail at normal errors as they relate to signal-to-noise (S/N) ratio in
trace analysis.
Calibration
Most LC methods are used for quantitative analysis — that is, the methods that answer the "how much is there?" question. Nearly
all of these methods rely on comparison of the peak area (or less often, peak height) of a sample with that of a reference
standard. To do this, we use a calibration curve (also referred to as a standard curve or sometimes "line"). The two most
popular methods of calibration are external and internal standardization. In external standardization, the calibration is
based upon comparing the response of the reference standard with its concentration. For internal standardization, a constant
concentration of an internal standard is added to each sample and the ratio of the response of the analyte to that of the
internal standard is compared with the concentration. The external-standard method is simpler and will be used for all the
examples discussed here; the details of these two methods will be discussed in a future article.
There are several different ways to use a calibration curve to quantify samples. Because UV detection is used for most LC
methods and the UV detector response versus peak area is linear over five or more orders of magnitude, we can assume linear
response is possible when using a method calibration that covers a wide range of concentrations. Some other detection methods,
for example, mass spectrometry (MS) or evaporative light scattering detection (ELSD), have narrower linear ranges, so a linear
calibration might not be appropriate. If a UV detector is used, we assume that the well-behaved calibration curve will be
linear. Linearity is defined as
where y is the response (area), x is the concentration, m is the slope of the curve and b is the y-intercept. (Even though the relationship is linear, we still call it a curve.) When the curve goes through the origin (x = 0, y = 0), b = 0 and the curve can be expressed as