From Detector to Decision, Part III: Fundamentals of Calibration in Gas Chromatography

Gas chromatography is a premier technique for quantitative analysis. As gas chromatographs have become simpler to use and data systems more powerful, much of the data processing involved in delivering quantitative results now happens in the background and is seemingly invisible to the user. In this installment, we will review the calibration techniques used with gas chromatography. We will compare calibration methods and the assumptions that underlie them. We will explore common mistakes and challenges in developing quantitative methods and conclude with recommendations for appropriate calibration methods for quantitative problems.

In two previous installments relating to detection and data analysis, we examined how detectors generate signals and how instruments can be operated remotely (1,2). We saw that, in today’s gas chromatographs, there are many operations that happen in the background that can impact data analysis. In this installment, we examine another operation that often happens in the background: calibration and techniques for generating quantitative data.

For quantitative data analysis in gas chromatography, there are five commonly used techniques, summarized in Table I. Area percent normalization and area percent normalization with response factors are both simple and use, only the area percent report generated along with the chromatogram is needed. External and internal standard quantitation both involve the generation of a calibration curve. Finally, standard addition, as the name implies, involves addition of standardized quantities of the analyte of interest to samples. Each of these methods has advantages and limitations, which we will discuss below.

Table I: Summary of calibration methods for gas chromatography

A typical integration report, which provides the retention time, peak height and area, peak width, area percent, and, if this information has been included in the method, an identification of each peak in a chromatogram, is shown in Table II. Classically, when the data system was a strip chart recorder, peak height was often used for quantitation, as this was much more easily measured by hand than peak area. With today’s digital systems easily integrating the peaks, peak area is now almost exclusively used for quantitation, although the height is often still included in the default report on most data systems. In our next installment, we will discuss the principles of peak integration.

Table II: A typical area percent integration report

Area Percent Normalization

The most classical and simplest quantitation method is to simply equate the reported area percent of each peak to the mass or concentration percent in the sample. Although this is very simple, it involves several assumptions that can easily lead to inaccurate results. Most importantly, it assumes that the detected peaks are the only components present in the injected sample. There is no accounting for undetected analytes. It also assumes that all of the peaks are pure, and, finally, it assumes that the detector provides the same response for all analytes.

While area percent normalization is no longer widely used for direct quantitation of analytes, the basic principle is still used in many industries in which impurities or contaminants in finished products, such as pharmaceuticals, must be investigated if detected. Detection protocols for impurities are often based on a percentage of the peak area of the compound of interest. For example, such a protocol might require investigation of any unknown or impurity peak with a peak area greater than 1% of the compound of interest.

Area Percent Normalization with Response Factors

Area percent normalization can be used with detector response factors to mitigate errors due to variable detector response. Response factors, which correct the detector response based on comparison of the analyte of interest to a standard analyte, such as hexane, are used to correct for detector response variability. Table III shows an area percent normalization with response factor calculation for the same mixture seen in Table II. Corrected peak areas are generated by multiplying the raw peak areas by the response factor. Corrected area percent values for each peak are then calculated from the corrected peak areas. As seen in Table III, response factors for flame ionization detection (FID), which most analysts think of as counting carbon atoms, indicate a much more complex mechanism for generating signals. The corrected area percent values seen in Table III differ considerably from the raw area percent values shown in Table II.

Table III: Area percent normalization with response factor calculation

In this case, the raw peak areas are corrected using the response factors to generate a far different quantitative view of the sample than seen by just using the original peak areas. While this method presents a more accurate analysis, it still suffers from the assumption that the peak areas determined by the data system represent all components in the sample. It is also still subject to variability in analyte recovery in the sample preparation and injection processes.

External Standard Calibration

External standard is the classical calibration method that we all learned as undergraduates. To generate a calibration curve, the signal, in our case peak area, is plotted as the dependent (y) variable against the concentration or mass of analyte injected as the independent (x) variable on a two-dimensional plot. Nearly all chromatographic detectors provide a linear response versus concentration or mass over a specified range. While detector linear range and response are not discussed in detail here, the are discussed in previous installments, on ChromAcademy, LCGC International’s online training platform and in numerous textbooks (3–5). A typical external standard and calibration curve is shown in Figure 1.

Figure 1: External standard calibration curve. Peak area is plotted against mass or concentration of injected analyte standard.

In contrast with the two area percent normalization techniques, an external standard calibration requires that several standards, in addition to the analyte samples, be run to determine the calibration curve. In Figure 1, each data point represents a standard that was analyzed in addition to any analyte samples. Due to differences in response factors, if there is more than one analyte of interest in the sample, separate calibration curves would be needed for each analyte.

While external standard calibration mitigates the need to consider response factors and does not assume that the components of interest are the only components in the mixture, it does suffer from experimental uncertainty that may arise from sample preparation and injection. Most sample preparation and extraction techniques that are more complicated than “dilute and shoot” may introduce unacceptable variation, often on the order of 10% or more, relative, on the amount of analyte extracted. This translates into a similar uncertainty in the calibration curve. Furthermore, classical injection techniques, such as split or splitless, may also introduce several percent additional relative experimental uncertainty. In short, external standard calibration curves in gas chromatography are often very noisy, and may not meet statistical linearity requirements for regulated laboratories. Today’s inlets and autosamplers generally provide much better reproducibility than in the past, somewhat mitigating this problem.

Internal Standard Calibrations

When external standard calibration is subject to experimental errors due to variability in analyte extraction during sample preparation and injection, internal standard calibration can mitigate these problems. Before discussing internal standard calibration, we should note that the uncertainties and errors that exist in the external standard method still exist in the internal standard method, except that the internal standard method corrects for them by dividing the variability out in the calculation.

An internal standard is a known mass or concentration aliquot of a compound that does not, and cannot, appear in any of the samples (that is, added to all samples and standards) prior to sample preparation or extraction. Since it is added to all samples and standards, the internal standard is then subjected to the same extraction and injection process as the samples and standards. When a calibration curve is generated, the peak areas for the compound of interest are ratioed with the peak area of the internal standard, prior to plotting on the curve. A typical internal standard calibration curve is shown in Figure 2. The peak area ratio of analyte to internal standard is plotted against the known mass or concentration of the analyte in the standards. For analyte samples, the peak area ratio is calculated and the mass or concentration of the analyte is read from the calibration curve or calculated using the equation for the line.

Figure 2: Internal standard calibration curve. Peak area ratio of analyte to internal standard is plotted against mass or concentration of injected standard.

Internal standard calibration mitigates variations in analyte extraction recovery and injected quantity from sample-to-sample by dividing the peak areas obtained for the analyte be the peak area for the internal standard. It is assumed that the internal standard and analyte will behave the same through the extraction and injection processes. If there is low recovery of analyte, there should be the same low recovery of the internal standard. Likewise, the internal standard must behave similarly in the chromatographic column as the analyte, but not co-elute.

These ideas lead to several requirements for the internal standard that often make internal standard selection challenging.

• The internal standard cannot be a possible analyte, contaminant, or interference in the samples. If this happens, the peak area for the internal standard will be artificially large, leading to an artificially low calculated analyte concentration.
• The internal standard must undergo similar behavior and recovery in the extraction process. Internal standards with similar structural features as the analytes of interest are often chosen.
• The internal standard must undergo similar behavior and recovery through the injection process. It should be chosen to have similar inlet discrimination to the analytes.
• The internal standard peak must not overlap with any peaks in the standards or samples. The chromatography of the internal standard must be checked to ensure no peak overlap.
• The internal standard must be available at high and reproducible purity. If it is impure or of low quality, it may generate interfering peaks or have inconsistent peak area.

In gas chromatography-mass spectrometry (GC–MS), these problems are often solved by using a deuterated analog of the parent compound of interest. For example, in cannabis analysis, the main active component, Δ9-tetrahydrocannabinol can be analyzed alongside a d-3 analogue, which has the same shape and structure as the parent compound, except a 3 Da higher atomic mass, due to the replacement of three hydrogen atoms with deuterium. Deuterated analogs extract and traverse the column nearly identically with the parent compounds, with a slight difference in retention time. The peak overlap is solved in GC–MS using extracted ion chromatograms or selected ion monitoring to generate separate peaks for the parent compound and analogue. In non-GC–MS analyses, candidate internal standards must be analyzed until one that meets all the requirements is found.

Since the calculations are very similar and the data for external standard calibration is also collected when performing internal standard calibration, I often perform both during method development or troubleshooting. Ideally, the internal and external standard methods should give the same quantitative result and the same uncertainty. Differences in the quantitative results or uncertainty indicate potential hidden problems with the extraction or injection processes.

Standard Additions

Standard addition calibration can be used when the sample matrix is too complex to allow ready addition of an internal standard or when the baseline or other peaks may be interfering with the peak of interest. It can be used with either peak height or peak area and is one of the few instances in gas chromatography where peak height is often superior to peak area. A typical standard addition calibration curve is shown in Figure 3. First, the samples are run, and the peak(s) of interest are identified. A known mass or concentration aliquot of each analyte of interest is added to each sample and the sample is re-run. This procedure is repeated with successive additional known aliquots added to each sample.

Figure 3: Standard addition calibration. Peak area of samples with added aliquot of standard is plotted against added aliquot of standard.

Once enough aliquots to generate a line have been added, a separate plot of peak area versus amount of standard added is generated for each sample. The mass or concentration of analyte in the sample is then determined by extrapolating the line to the x-axis. In Figure 3, this extrapolation is seen in the data point to the left of the y-axis, showing negative values for the concentration. The actual concentration of the sample would be read as about 10 ppm.

Conclusions and Summary

Referring to Table I, the main calibration techniques for quantitative analysis by gas chromatography are, in order from simplest to most complex, area percent normalization, area percent normalization with response factors, external standard calibration, and internal standard calibration. Standard addition is used in situations where samples are too complex for the other techniques. Each method has built-in assumptions, advantages, and disadvantages. While the simple area percent methods are useful for estimations, due to their assumptions, they are not generally effective for accurate quantitative analysis. Internal standard calibration is usually more precise than external standard calibration, but can hide uncertainty and variability in the sample preparation and injection processes. An understanding of the fundamentals of calibration is critical in the detection to decision process.

References

(1) Snow, N. H. From Detector to Decision: How Does the GC Instrument Generate Your Data? LCGC N. Am. 2020, 38 (9), 496–500.

(2) Snow, N. H. How Can We Run a Gas Chromatograph from Anywhere? LCGC N. Am. 2020, 38 (11), 601–605.

(3) Snow, N. H. Basic Care and Feeding of Your Detector. LCGC N. Am. 2023, 41 (7), 256–258. DOI: 10.56530/lcgc.na.zd5789d1

(4) ChromAcademy, https://www.chromacademy.com/ (accessed December 2023).

(5) Poole, C. F. “Conventional Detectors for Gas Chromatography” in Gas Chromatography, 2nd Ed., Poole, C. F., Ed. Elsevier 2021, 343-370.

About the Author

Nicholas H. Snow is the Founding Endowed Professor in the Department of Chemistry and Biochemistry at Seton Hall University, and an Adjunct Professor of Medical Science. During his 30 years as a chromatographer, he has published more than 70 refereed articles and book chapters and has given more than 200 presentations and short courses. He is interested in the fundamentals and applications of separation science, especially gas chromatography, sampling, and sample preparation for chemical analysis. His research group is very active, with ongoing projects using GC, GC–MS, two-dimensional GC, and extraction methods including headspace, liquid–liquid extraction, and solid-phase microextraction. Direct correspondence to: LCGCedit@mmhgroup.com