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Final Parameter Selections and Data Reduction

[This is Part III, the last of our three-part series on FTIR analytical systems. Part I appeared in the November/December 2008 issue of Gases & Instrumentation and focused on theory and the associated parameters that need to be considered for real life applications. Part II, published in the January/February 2009 issue, discussed experimental design. Part III discusses regression analysis and obtaining reliable data, choosing the proper parameters, e.g. temperature, pressure, flow rate, and how these impact the final result.]

Introduction
FTIR gas analytical systems are one of the most powerful tools in the arsenal of the gas analyst; however methodology must be consistent with requirements. In the specialty gas industry, FTIR is typically used for the production of "interference-free" EPA protocol standards, however, the usefulness of this technique far exceeds a single application.

In this three-part series of articles dedicated to the exploration of FTIR gas analytical systems, we explored in Part I [1], the theoretical background of infrared absorption and the impact of a number of physical variables on results. These parameters include pressure, temperature, flow, molar absorptivity, and path length. In Part 2 [2] we discussed the actual design considerations and constraints of an FTIR analytical system and proposed some specific parameters for use. In the current discussion we will focus on the impact of two specific variables affecting the data; selection of appropriate quantitation regions, and methods and results of data reduction.

Let us assume that a system has been built that effectively meets all the criteria set forth in Part 2 of this series. We have set the parameters to operate the system in the dynamic sampling mode with a constant flow rate of 3 liters per minute, operational temperature of 100°F, a constant pressure of 5 psig, and utilizing a 10 meter gas cell for sampling purposes.

Matrix and Temperature Effects on Spectral Data
In Part 1 of this series we discussed infrared absorption in terms of rotational-vibrational excitation of bonds within a molecule from ground state to excited state, and showed the resulting absorption spectra along with references to the P, Q, and R branches. As shown in Figure 1, typical gas phase absorbances for a transition occur over a specific range of energy and result in a typical pattern. If we extrapolate a smooth curve that connects the peak maxima for all the absorbance peaks it will describe a "spectral envelope". The shape of this spectral envelope is highly dependent on two parameters—the temperature of the sample and the matrix gas of the sample (in other words, the major component that contains the minor component in the sample). The shape of this envelope may change depending on the temperature or matrix of the sample. The reason for this change lies in the initial distribution of energy among sub-levels in the ground state. If the entire region of the absorption envelope is used for quantitation, these effects will be averaged out and should have a minimal, if any, effect on the final quantitation results. If, however, a specific absorbance peak within the envelope is used for quantitation, there may be significant changes in values based on changes in temperature or matrix gas.

Figure 2 shows high resolution FTIR data for the R branch of the absorbance envelope for methane in nitrogen overlaid at two different temperatures (70°F and 200°F). The overall envelope is flatter at the higher temperature, showing a more homogeneous distribution of energy in the molecular ground state. The result of this distribution means that determining the methane concentration of a gas sample using one or several adjacent absorbance peaks will be different if the calibration were to be performed at one temperature and the measurement at another. For example, in Figure 2, the absorbance peak at ~3158 wave numbers is almost 2 times as large at 200°F as at 70°F. Conversely, the absorbance peak located at ~3095 wave numbers is approximately 1.5 times larger at 75°F than at 200°F.

Figure 3 shows high resolution FTIR data for the R branch of hydrogen chloride at a concentration of 500 ppm in both nitrogen and hydrogen matrices. Similar energy distribution patterns to those seen at different temperatures are exhibited. For example, the absorbance peak at ~3058 is almost 1.5 times larger in a hydrogen matrix than in nitrogen. Conversely, the absorbance peak at ~2905 is almost 1.5 times larger in a nitrogen matrix than in hydrogen. While this effect is slightly less intuitive, it can be attributed to collisional effects in the gas phase. The more important issue associated with the effect is in understanding its existence and allowing for differences in quantitation methodology.

The Effect of Band Selection on Spectral Data
The quality of quantitation data generated by the FTIR gas analytical system is highly dependent on a number of factors. Among these variables are absorbance peak selection, choice of peak height or peak area for quantitation, and the measurement resolution.

Peak height and peak area are both used for FTIR quantitation measurements. Generally speaking, peak area determinations tend to be more repeatable and precise than peak height measurements, especially at higher resolution settings (i.e. 0.125 wave numbers). The reason for this discrepancy lies partially in the discrete measurements made by the FTIR system when the analog signal generated by the detector is digitized into discrete points. Given the sharp characteristics of IR gas absorption, the absolute maximum point of an absorbance band will likely not coincide with a discrete more exacting measurements are derived from peak areas.

When determining absorbance areas to use for quantitation, it is important to decide whether or not to use a baseline correction routine. If such a routine is used, it is equally important to decide where to create the baseline used for the area calculation. In the instance shown in Figure 1, the absorbance peaks return to baseline prior to the next absorbance beginning. In this case, if only one or a few peaks are used for calculation instead of the entire absorbance envelope, the method should still work well. If the absorbance envelope looks more like Figure 5, the determination of area becomes significantly more difficult (if the entire envelope is not used).

The linearity of FTIR detectors is normally best between 0 and 1 absorbance units, and the better analytical methods use well-defined absorbance peaks within this range. Figure 6 shows two different spectral scans for carbon monoxide. The upper spectra was taken using a 5000 ppm standard and the lower spectra was taken using a 50 ppm standard. The choice of quantitation absorbance areas in this case is determined by the intensity of the absorbance. For the accurate detection of percent levels of carbon monoxide, smaller absorbance peaks near the edges of the spectral envelope are best for the quantitation area selection since large absorbances may exceed 1 absorbance unit and extend the calibration curve into the non-linear response range of the detector. For low detection limits, the choice of the stronger peaks in the envelope would be appropriate. The one caveat with these selections was mentioned earlier in this article—these particular areas of the spectral bands are highly susceptible to changes in temperature or matrix gas changes. The selection of appropriate absorbance peaks for an FTIR quantitation method must necessarily take into account a number of factors including spectral shape, intensity, and potential interferences from other components in the mixture.

Quantitative Data Reduction
Once a quantitation method has been defined and the data taken with the appropriate standards over the concentration ranges of interest, it must be reduced to a useable form by selecting a mathematical function that best fits the data. There are any number of software packages available today that provide this capability. Most statistical data packages are more than capable of generating fitting functions (from first order, i.e. linear, to higher order polynomials); however, these programs can be somewhat cumbersome to learn. A number of relatively simple (and quite inexpensive) add-on programs are available to give additional capabilities to Microsoft Excel, and render excellent data fitting results with adjustable parameters important to establishing a good fit, and therefore a good method. There are also full program packages designed specifically to develop and maintain calibration data for FTIR systems. These packages are available with varying levels of capabilities from both FTIR manufacturers and third party software companies.

FTIR quantitative data should normally show a best fit with a first to 3rd order polynomial. In rare cases, the fit must be increased to 4th or 5th order, although higher order fits are unusual and must be used with caution. Fitting functions must also have a statistically significant amount of data for the fit to be meaningful. In other words, a perfect fit for a five point data curve of any shape (good or bad) can be obtained using a 5th order polynomial. This would be called "overfitting" the data and gives meaningless results. This could also be a case of "fitting the noise" which is essentially a meaningless calibration function. A good rule of thumb is to use a minimum of 3 times the order of the fit as the number of different calibration concentrations obtained. In other words, to qualify a 3rd order fit a minimum of 9 data points should be obtained. To qualify a 5th order fit a minimum of 15 data points should be obtained.

Once the data is gathered and the best fit determined, the fit equation should be tested by inserting the original data back into the formula to determine predicted concentrations. The predicted concentration should then be compared to the actual concentration to determine the "goodness of fit" with an error assigned to each value (see Table 1). Another parameter used in determining the "goodness of fit" is the R-value of the regression analysis. The maximum value for R is 1; therefore, regression analyses that approach an R value of 1 are considered "good fits". In other words, a regression analysis with an R value equal to 0.99999 would be a candidate for a "good fit" scenario. A typical pitfall of regression analysis is using this value as the only criterion for accepting a regression fit function. The R value does not tell the complete story and must be used with caution and only in conjunction with the above procedures and appropriate validation (or check) standards that were not used for the generation of the calibration curve. The case study we will discuss in the next section demonstrates some of these methods.

Following the generation of an appropriate appropriate data curve, it must be validated using different standards than those used to generate the calibration curve. Ultimately this is the true test of the validity of the calibration. Many users of instrumentation will perform validation functions much more frequently than full calibrations and, in some instances, a bad validation test will trigger a full calibration requirement. "Good" and "bad" are relative terms that must be defined by a specific user for a specific requirement.

A final caveat for the use of regression data curves—or really for the use of any calibration curves whatsoever—is determining what the valid sections of the fit really are. Some companies restrict calibration curves to the use of the middle 80% of the curve. In other words, the top 10% and the bottom 10% tend to be more susceptible to error in the function than the middle 80%. In general, this assumption is true; however if validation standards are used to validate the curve from one end of the range to the other, this should not become an issue to the typical user.

Case Study: Low Level Nitrogen Dioxide Calibration
All analyses for this study were performed using a ThermoNicolet Magna 750 FTIR spectrometer, with a liquid nitrogen cooled MCT detector, fitted with an 8.4 meter folded path gas cell supplied by Gemini Optics. The resolution of the spectrometer was set to 0.5 cm-1 and 128 scans were accumulated. The sample introduction and control (pressure = 1000 torr, flow = 3 liters per minute, and temperature = 25°C) was achieved by a delivery system designed and built in our facility to reproducibly sample gas streams for FTIR analysis. Dilution calibration curves were generated by a computer-controlled dilution system designed and implemented by Custom Gas Solutions. The nitrogen dioxide concentration was monitored by IR absorbance in the spectral region of 1660 — 1550 cm-1. There were no interferences in the absorbance assigned in this region. The limit of detection of the nitrogen dioxide is approximately 5 —10 ppb.

The FTIR system was calibrated for nitrogen dioxide with a ten point calibration curve from 3.33 ppm to 0.35 ppm and the results were fit with a 1st order (linear) regression function to a high degree of accuracy as demonstrated in Table 1. Figure 7 shows the FTIR spectral data for the nitrogen dioxide component in a multicomponent mixture shown as an overlay. The actual overlay of the fitting function with the data is shown in Figure 8 and the residuals, or rather error points, is shown in Figure 9. In this case study, we used the entire spectral band (or envelope) and integrated across the entire band (1660-1550 wave numbers); the absorbance exhibited a very classic linear behavior.

Linear Versus Non-Linear Calibration Behavior
All gases have non-linear absorbance regions and may or may not have linear regions. An additional complication to this statement is that linearity is dependent upon concentration and/or intensity of absorption. At this point it would be wise to remember that any calibration curve is not just a function of the gas of interest but includes the FTIR operational characteristics of the specific instrument used. Therefore, after any repairs or changes in the FTIR system, the calibration curves must be, at a minimum, validated and usually regenerated in their entirety. In the case study we just reviewed, the nitrogen dioxide data taken over that specific absorbance region, in that specific concentration range, and on that specific instrument, exhibited linear behavior to a high degree of accuracy. Not all gases are this well behaved. Generally speaking, methods using large concentration ranges and gases with sharp spectral features tend to exhibit the worst non-linearity profile.

One of the worst gases for non-linear behavior is carbon monoxide. Figure 10 shows a calibration data curve for carbon monoxide using a 1st order curve fit. Clearly, this is not good technique. Figure 11 demonstrates that a 3rd order fitting function yields a higher degree of accuracy. Figure 12 plots the residual data verifying the "goodness of fit." Table 2 shows the numerical values and the error associated with each data point versus the fitting function. Figures 10, 11, and 12 and Table 2 were generated using TQ Analyst – a total solutions calibration program available from Thermo Fisher for the Nicolet product line of FTIR instrumentation.

Conclusions
In Part 1 of these three articles we defined the theoretical methods and backgrounds for FTIR absorbances and the requirements of an effective FTIR gas analytical system. In Part 2 we defined the physical instrumental and control requirements used to design and implement a fully functional FTIR gas analytical system. In Part 3 we have shown the nuances and understanding required for an accurate reduction of data and the validation of results. (See sidebar for the protocol considerations for generation and validation of an effective calibration method.) G&I

Acknowledgements:
We appreciate the assistance of the following companies and/or persons who contributed graphics, data, or information to this current article:

Thermo Fisher Scientific, 5225 Verona Road, Madison, WI, 53711. Contact: Ken Gowin at ken.gowin@thermofisher.com.

1. S.O. Vaughan, W.K.Vaughan. "FTIR Gas Analytical Systems Design and Utilization Considerations," Gases & Instrumentation, Vol. 2, Issue 6, (November/December 2008) pp. 14-17.

2. S.O. Vaughan, W.K.Vaughan. "FTIR Gas Analytical Systems Design and Utilization Considerations," Gases & Instrumentation, Vol. 3, Issue 1, (January/February 2009) pp. 16-22.

Dr. Stephen Vaughan is the Founder and President and COO of Custom Gas Solutions, LLC, 1750 East Club Boulevard, Durham, NC 27704. Dr. Vaughan is a leading authority in the Fourier Transform Infrared Spectroscopic (FTIR) analysis of gases and in the development and implementation of gas mixing and delivery systems for both process and analytical use. Dr. Vaughan holds a B.S. degree in Chemistry from the University of North Carolina, Chapel Hill, North Carolina, and an M.A. and Ph.D. in Physical Chemistry from the Johns Hopkins University, Baltimore, Maryland. He can be reached at 919-220-2570 or steve@customgas.com

Kip Vaughan is currently in his senior year at Durham Academy in Durham, North Carolina. He has worked for his father at Custom Gas Solutions as a summer intern for three years and plans to pursue a career in the sciences. He assisted with research and graphics.

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