Calibration Curves, Part I: To b or Not to b? - - Chromatography Online
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Calibration Curves, Part I: To b or Not to b?


LCGC North America



John W. Dolan
There seem to be a disproportionate number of problems encountered in the concentration region near the limit of detection 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 limits of detection and quantification is an important decision that can be confusing. This month's installment 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 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 vs. 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





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