- Hamish Adam

PRESENTED AT: L'Analyse Idustrielle, Paris, France

Keywords

Ultraviolet, Photometers, Absorption, Process Control

Abstract

Many different analytical techniques have made the transition from the laboratory to online process monitoring. UV photometry has made this transition more easily than most because it possesses some inherent advantages. Simple, robust optics and absence of interference from water vapor and carbon dioxide are two of the main benefits of UV photometry. A mathematical model has been developed to enable an objective analysis of resolution effects in UV photometers. Results from this model indicate that UV process photometers using a dual-beam configuration and hollow cathode lamp sources enable superior performance. This design enables better linearity, baseline stability, minimal cross-interference and excellent analyte specificity. The design of a practical process photometer based on this configuration is presented. Applications of this photometer to online process and emissions monitoring are described and data from actual applications are presented.

Introduction

Ultraviolet absorption spectrophotometry is commonly used in gas phase process control and emissions applications, especially for the measurement of sulfur species. One of its distinct advantages over infrared techniques is the lack of interference from carbon dioxide and water vapor, which are often present at much higher concentrations than the analytes of interest. However, a factor which often limits the accuracy of a gas phase ultraviolet absorption photometer is the linearity of response to the species of interest. This is of particular importance if multicomponent analysis is to be performed, since any deviations from linearity complicate the data analysis procedure and can lead to cross-interference between analytes. Absorbance non­linearity is frequently caused by the lack of resolution in the photometer [I]. Linearity of response is most difficult to achieve for analyte species which possess highly structured absorption spectra in the ultraviolet. Sulfur dioxide possesses such a spectrum and is also the species most commonly measured by ultraviolet absorption photometry. The molar extinction coefficients, as measured on a particular spectrometer, are strongly dependent on the spectrometer resolution. Using the ultra-high resolution absorption spectrum of sulfur dioxide as its primary example, a model has been developed which describes the effect of wavelength resolution on the linearity of response of an ultraviolet (UV) absorption photometer. Empirical results have also been obtained which support the findings of the model.

FIGURE 1 – THE MOLAR EXTINCTION COEFFICIENTS OF SULFUR DIOXIDE AT TWO
DIFFERENT SPECTRAL RESOLUTIONS

RESOLUTION EFFECTS ON ABSORBANCE LINEARITY (THEORETICAL)

The Absorption Process

In simple terms, optical absorption photometers typically consist of a light source which produces a beam of photons that pass through a sample cell containing the analyte gas and impinge on a photodetector which converts the number of incident photons to an output voltage. In most cases, the output voltage is first measured using a "clean" sample (ie. the concentration of the analyte gas in the sample cell is zero). This provides a reference voltage, Vzero• to which samples of the analyte gas are compared. When subsequent samples of the analyte are introduced into the cell, the sample voltage from the detector is measured, V sample· The ratio of the reference voltage to the sample voltage may be used to determine the analyte concentration in the cell through the use of the Beer-Lambert law. This requires that the molar absorptivity of the analyte species be precisely known at the wavelength(s) at which the measurement is taking place.

In equation 1, the extinction coefficient is typically expressed in liters mo1e-1 cm·1, the concentration in mole liter-1, and the path length in centimeters. In most gas phase applications, the concentration of the analyte is on the order of tens to thousands of parts per million by mole, and these are the units in which the measured concentration is to be expressed. The absorbance signal is related to the density of the gas, which is temperature and pressure-dependent, it is more convenient to express equation 1 as:

Using equations 1 and 2, the concentration of the analyte species could be determined from the measured detector voltages (zero and sample) provided that the cell length, temperature, pressure, and molar extinction coefficient were known accurately. To account for any inaccuracies in these parameters, a span factor is often introduced when the concentration calculations are performed. This span factor is determined from the observed absorbance signal of the analyzer when a sample of analyte gas of precisely known concentration is introduced in the cell. The concentration is then calculated by combining equations 1 and 2 and introducing a span factor, SF, ie:

Equation 3 may be used to determine the concentration of the analyte gas (in ppm by mole) from the measured zero and sample voltages. To determine how the measured concentration is affected by the resolution of the spectrometer, a model which describes the relationship between these measured voltages and both the spectral distribution of the light source and the wavelength dependant molar absorptivity of the species of interest must be developed.

The Measurement of Light

Consider first a source of photons, whose spectral distribution may be approximated as a Gaussian or normal distribution. Other distributions could be used to model the light source but would provide no additional insight into the study of resolution effects on linearity of response. Furthermore, the normal distribution is a reasonable approximation to the bandpass of an optical filter, the resolving power of an individual pixel in a photodiode array, and the band shape of an emission line from a hollow cathode lamp. The intensity or brightness of the light source as a function of wavelength may thus be described as:

The parameter cr is of particular importance in that it defines the resolution at which the spectrometer is operating. In the subsequent analysis, a range of values for the spectrometer resolution were employed to determine the effects of resolution on the absorbance linearity. Typical values for cr are presented in Table I along with the photometer design which they represent.

Table 1 – SPECTRAL RESOLUTIONS AND PHOTOMETER DESIGNS

The amount of light which reaches the detector will be determined by both the output of the light source, and by the absorbance of the sample gas. In the case where there is a "clean" sample in the cell (analyte concentration is zero), the intensity of the light impinging on the detector is assumed to be given by equation 4 (i.e. there is no light loss in the measurement system). This is rarely true in practice since some of the light is lost during transmission through lenses or reflection off mirrored surfaces. However, this light loss affects both the zero and sample measurement, cancels out in the absorption calculations, and thus does not affect the subsequent analysis. In the case where there is a non-zero concentration of analyte gas in the cell, the light reaching the detector is attenuated by the wavelength dependant absorbance of the sample gas. In the sample case, the light flux reaching the detector is:

Electro-optic detectors, such as photodiodes or photomultiplier tubes, provide an output signal which is linearly proportional to the sum of all of the photons incident on the detector during the measurement period. In simpler terms, such detectors provide a signal proportional to the amount of light they see. While the conversion efficiency of such devices is typically wavelength-dependent, the efficiency will be assumed to be equal for all wavelengths for the purpose of these discussions. Furthermore, the efficiency of the detectors cancels out when the ratio of the zero and sample signals is taken, as in equation 3. The wavelength dependency of the detectors does not play a significant role in determining the linearity of response of the system. In mathematical terms, the output voltage from the detector may be expressed as:

Equations 6 and 7 may be used to calculate the measured voltages for both zero and sample gas, for any concentration of the analyte species, provided that the molar extinction coefficients at the wavelengths of interest are known.

Figure 2 – THE MOLAR EXTINCTION COEFFICIENTS OF S02 vs. WAVELENGTH

Molar Extinction Coefficients

In evaluating the results of the model, sulfur dioxide is a particularly interesting species to consider. This is true both from the perspective that the measurement of sulfur dioxide is important to a multitude of industrial applications, and that sulfur dioxide has a highly structured absorption spectrum. The molar extinction coefficients have previously been measured at extremely high resolution, and are presented in Figure 2. While most UV photometric analyzers measure sulfur dioxide at approximately 280 nanometers, the region around 228 nanometers has been chosen for analysis in this paper. This wavelength region is of particular importance in applications where other sulfur species must be measured, such as in Claus Tail Gas analysis or stack gas analysis of reduced sulfur compounds in a high background of sulfur dioxide. In order to perform such analyses reliably, a linear response to the SO2 concentration in the 228 nanometer region is required. The digitized molar extinction coefficients[3], presented in Figure 2, were used in evaluating the integral in equation 7.

Model Results

To evaluate the effects of spectral resolution on the linearity of the measured absorbance signals, the following series of steps were performed:

1. Values for the temperature, pressure and cell length were chosen
2. A value for cr was chosen to represent a particular spectrometer design (refer to Table 1)
3. Using these parameters, the zero gas voltage, V_zero• was determined (equation 6)
4. A range of concentrations was used as input to equation 7
5. For each of these concentrations, the related sample voltage, V_sample, was determined (equation 7)
6. A span factor, SF, was determined using one of the test concentrations and solving equation 3 for the span factor
7. For each test concentration, the measured concentration was determined from equation 3
8. The linearity of response was determined through analysis of the input versus the calculated concentration.

Note that the results are dependent on the ratio LPCff, and not solely determined by the concentrations used. Parameters used in the analysis are summarized in Table II. These parameters were chosen to match the experimental conditions in place in our laboratory (see EXPERIMENTAL RESULTS).

The model predictions for the three resolutions of interest are presented in Figure 3 and 4. The model results indicate that a photometer which employs hollow cathode lamps as the light source will be able to achieve a nearly linear response (+/-1 %) to sulfur dioxide in the 228 nanometer region of the spectrum. Spectrometers which used broadband sources, whether with interference filters or a grating and photodiode array, will display significant non-linearities in their SO2 response at 228 nanometers. In fact, the non-linear response of a photodiode array-based spectrometer will not be significantly different from that of an interference filter-based analyzer. The response of a low-resolution analyzer may, of course, be linearized through the use of polynomial correction terms. However, such linearization becomes extremely sensitive to the wavelength precision of the device.

Table 2 – PARAMETERS USED IN MODEL STUDIES

Figure 3 – MEASURED vs ACTUAL CONCENTRATION FOR VARIO US SPECTROMETER RESOLUTIONS

Figure 4 – DEVIATIONS FROM LINEARITY vs CONCENTRATION FOR VARIOUS SPECTROMETER RESOLUTIONS

To demonstrate this effect, the model results for a device with 0.5 nanometer resolution were calculated assuming first that the center band was located at 228.0 nanometers, and then again with the center band located at 228.1 nanometers. Since an individual pixel in a photodiode array is typically 25 microns wide, a shift of 0.1 nanometers on a 0.5 nanometer resolution device would physically correspond to displacing the spectrum by only five microns on the measuring element. This displacement could result from minor changes in orientation of an optical element (for example, when a sample cell is cleaned), or from any irreproducibility in the placement of a light source when it is replaced. Spectral shifts of this type will change the model required to linearize the data. If multi-component analysis is being performed, these types of spectral shifts often lead to cross-talk between species.

To evaluate the effects of spectral shifts, we have assumed first that the analyzer response is linear to S02 at 280 nanometers, which is the typical measurement region for S02 and where there is less fine structure in the spectrum (and thus a linear response is expected). In operation, the absorbance at 280 nanometers would be measured, and the concentration of S02 thus determined. The absorbance at 228 nanometers due to S02 would then be estimated from the S02 concentration. By subtracting this absorbance from that measured at 228 nanometers, the residual absorbance due to the presence of another species (such as H2S or COS) would be determined. In the example data presented in Table III, the apparent COS concentration is calculated based on the residual absorbance occurring after a 0.1 nanometer spectral shift.

Table 3 – THE CROSS-TALK OF SO2 ONTO COS RESULTING FROM A 0.1 nm SPECTRAL SHIFT ON A 0.5 NANOMETER RESOLUTION SPECTROMETER.

Spectral shifts do not occur on devices which employ hollow cathode lamps as the light source. The wavelength of the emission line(s) are known precisely and accurately. The emission lines uniquely determine the wavelength at which the absorbance measurement is occurring. The wavelength of the emission line is determined solely by the material used in the cathode of the lamp and is not affected by any environmental changes. Provided that there are no nearby emission lines to the primary measurement lines, large changes ( on the order of one to two nanometers) in the bandpass wavelength of the interference filter may also be tolerated without affecting the linearity of response.

Experimental Results

The model predicted that there would be relatively large ( ~ 10 % ) deviations from linearity on a spectrometer with 0.5 nanometer resolution. These predictions were unexpected, in that this is better resolution than is typically available on commercial photodiode array devices (1 to 2 run) used in process and emissions monitoring, and no mention of these non-linearities is typically made for such devices. An experimental program was initiated to determine if such deviations actually occur.

The absorbance of sulfur dioxide was measured using a EG&G OMA II laboratory photodiode array (PDA) spectrometer. The device used a 2400 groove/nm holographic grating, a thermo-electrically cooled I 024 element photodiode array, and a 25 micron entrance slit width. A broadband 30 watt deuterium lamp was used as the light source, focussed through a 32.7 cm optical path length. Experiments were perfonned under the conditions presented in Table II. For comparison, a hollow cathode lamp spectrometer was operated with a 40 cm cell, but otherwise identical conditions to those in Table IL

Figure 5 – OBSERVED DEVIATIONS FROM LINEARITY AT 228 AND 285 nm USING HOLLOW CATHODE LAMPS

Figure 6 – OBSERVED DEVIATIONS FROM LINEARITY AT 228 AND 280 nm USING PDA AND DEUTERIUM LAMP

The observed linearity from the hollow cathode lamp spectrometer and the photodiode array spectrometer are shown in figures 5 and 6 respectively. The maximum deviation from linearity for the hollow cathode lamp based spectrometer at 228 nm was approximately 1.5 %, which is in good agreement with the model predictions. The maximum deviation from linearity was approximately 10 % for the photodiode array spectrometer, and, at least qualitatively, the results are in good agreement with the model predictions. Some of the disparity between the analytical results and the model predictions may be explained by the variation in molar absorptivity with temperature. In the model , the high resolution extinction coefficients used were measured at 223 K. At lower temperatures, the fine structure of the spectrum is somewhat enhanced since the statistical distribution of the eigenstates is shifted towards the ground state. This results in slightly larger molar extinction coefficients than those observed at 298 K. Since the model is dependent on the total molar absorption (determined from the product of the concentration and the molar extinction coefficients), the use of larger extinction coefficients results in the non-linearities being accentuated in the model as compared to the experimental data.

Figure 7 – OBSERVED MOLAR EXTINCTION COEFFICIENTS IN 228 nm REGION USING PDA AND DEUTERIUM LAMP

Figure 8 – OBSERVED MOLAR EXTINCTION COEFFICIENTS IN 285 nm REGION USING PDA AND DEUTERIUM LAMP

The observed molar extinction coefficients for S02 in the 228 and 285 nanometer region of the spectrum, as measured on the photodiode array spectrometer, are presented in figures 7 and 8 respectively. The non­linearities in the 228 nanometer region appear as a concentration dependent variation in the measured molar extinction coefficients. In the 285 nanometer region, the observed variations are significantly smaller. The critical parameter which determines whether a spectrometer will display a linear response to the species of interest is the total variation of the molar extinction coefficients over the bandpass of the spectrometer, relative to the average molar extinction coefficient of the species in the same bandpass. When the resolution of the spectrometer is increased, a narrower wavelength band is viewed by the detector, which typically leads to less variation in the molar extinction coefficients across the bandpass of the analyzer. This results in improved linearity.

Conclusions

A model has been developed which describes the fundamental processes occurring in an optical absorption spectrophotometer. Using the resolution of the spectrometer and the high resolution molar extinction coefficients of the species of interest, the model can be used to predict the linearity of response of the photometer and the sensitivity of the spectrometer to wavelength shifts. Sulfur dioxide was used as the test species for the model, since it is of significant interest to both process and emissions monitoring. Three spectrometer resolutions were tested, chosen to correspond with those attainable on a broadband, interference filter based spectrometer, a diode array spectrometer, and a hollow cathode lamp based spectrometer. The 228 nanometer region of the spectrum was chosen for use in the analysis since this area of the spectrum is extremely important when multicomponent analysis for sulfur dioxide and reduced sulfur species is being performed.

The model results indicate that diode array spectrometers may exhibit deviations from linearity on the order of 10 % in this region of the spectrum, and that the results using a PDA may not be significantly different from those using a broadband, interference filter based spectrometer. The non-linear behaviour predicted by the model was also observed in the experimental results, and there was excellent qualitative agreement between the model results and the experimental data These results are not inconsistent with the predictions of the Beer Lambert Law, which only states that the absorbance will vary linearly with concentration for monochromatic light[4]

The extremely narrow spectral bandwidth of atomic emission lines, such as those from hollow cathode lamps, are an excellent approximation to monochromatic radiation. Thus, when these light sources are used in an optical absorption spectrometer, the requirements for the Beer Lambert law are met, and the observed absorbance varies linearly with concentration. Furthermore, since the spectral distribution is determined by the light source, and not by the alignment of the spectrometer, there is no possibility for spectral shifts. The linear response of the analyzer, precise measurement wavelengths, and absence of wavelength drift, ensure that analyzers optimized to use hollow cathode lamps can provide accurate and robust analysis of multicomponent process streams.

References

[1] J.E. Steward, Ultraviolet and Visible Spectrophotometry, Pye Unicam Ltd, 1979.
(2] The natural line width is on the order of 104 angstroms. J. C. Van Loon, Analytical Atomic Absorption Spectroscopy, Academic Press, NY, 1980. Collisional broadening with the fill gas (Lorentz broadening)occurs, resulting in an achieved line width on the order of 0.15 angstroms
(3] D. E. Freeman et al, High Resolution Absorption Cross Section Measurements of SO2 at 213 Kin the Wavelength Region 172 - 240 run, Planetary Space Science, 32(9), pp.1125-1134, 1984.
[4] J.C. Van Loon, Analytical Atomic Absorption Spectroscopy, Academic Press,NY, 1980.