Anal. Chem. 1990, 62, 1597-1603
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Ratio of Sequential Chromatograms for Quantitative Analysis and Peak Deconvolution: Application to Standard Addition Method and Process Monitoring Robert E. Synovec,* Edward L. Johnson,' Timothy J. Bahowick, and Andrew W. Sulya
Center for Process Analytical Chemistry, Department of Chemistry, BG-IO, University of Washington, Seattle, Washington 98195
this paper descrlbes a new technlque for data anaiysls in chromatography, based on taking the point-by-point ratio of sequential chromatograms that have been base ilne corrected. This ratio chromatogram provldes a robust means for the klentlfkatkn and the quantkation of analytes. I n addltion, the appearance of an lnterferent Is made highly vlslble, even when it coelutes with desired anaiytes. For quantltatlve analyds, the region of the ratlo chromatogram corresponding to the pure elution of an analyte is Identified and is used to calculate a ratlo value equal to the ratio of concentratlons of the analyte in sequential injectlons. For the ratlo value calculation, a variance-welghted average is used, which compensates for the varyhg slgnal-to-ndse ratlo. This ratlo value, or equivalently the percent change In concentration, is the basis of a chromatographlc standard addltlon method and an aigorlthm to monltor anaiyte concentration In a process stream. I n the case of overlapped peaks, a splking procedure is used to calculate both the orlginai concentratlon of an analyte and Its signal contribution to the orlglnal chromatogram. Thus, quantltatlon and curve resolution may be performed shultaneoudy, without peak modeling or curve flttlng. These concepts are demonstrated by uslng data from Ion chromatography, but the technlque should be applicable to all chromatographlc technlques. I n a preiknlnary evaiuatlon for overlapped peaks (resolution = 0.87), the mean percent change for 10 replicates was accurate to wlthin 1%of the true change: thus, the technlque Is not blased. The wtthln-run standard devlatlon was conservatively a 4 % concentration change. A rlmulatlon of reduced resolutlon suggested that concentratlon changes could be estimated for a resolution as low as 0.1.
INTRODUCTION Chromatography is a powerful quantitative analytical technique because the detector response for an analyte can be related to the analyte concentration. In the case where a chromatographic peak is fully resolved, the maximum peak height is usually measured and made quantitative via a calibration curve of peak heights that has been created from known standards (1). However, such use of a single point on the peak wastes much of the "peak" information. Statistically improved quantitative information and an improved limit of detection can be provided by integrating the peak (2). In the case where analyte calibration is not straightforward, the method of solute-independent calibration (SICAL) was developed (3, 4). In many circumstances, unresolved chromatographic peaks occur and indeed may be desirable. For example, in process Present address: Alpkem Corporation, Box 1260, Clackamas, OR
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chromatography, the analysis time may be conserved by removing the requirement of base-line resolution. However, the quantitation of unresolved peaks by traditional methods is difficult and often results in large errors. Recently, much work has been devoted to the development of better methods of extracting quantitative information from overlapped peaks. Ideally, such methods should be applicable to peaks over a broad range of concentrations and should have the ability to detect possible contaminants. The ideal method should function with all degrees of overlap, e.g., coeluting peaks. If possible, a model should be avoided since a model may not represent all peak shapes. Quantitation should be accomplished without knowing the number and the identity of the analytes in the sample, since there are many analytical situations where the sample composition is unknown. Finally, the method should produce simple and accurate quantitative data without introducing error, degrading the signal-to-noise ratio ( S I N ) ,or excessively lengthening the analysis time. A review of the quantitation methods for unresolved peaks is useful to put into context those efforts geared toward providing the ideal method. The quantitation methods for unresolved peaks that depend upon drawing boundaries of integration between two overlapping peaks are perpendicular drop, triangulation, tangent skimming, and democratic distribution (5,6). Though simple, these methods choose models that often do not accurately represent the true contributions of each peak. Lin and Lu have improved the perpendicular drop method by calculating correction factors that are based on an exponentially modified Gaussian model (7). In general, these methods require a valley between the peaks. Curve-fitting algorithms that more accurately reflect the true shape of a chromatographic response have been developed (6,8-11). These methods require a peak model to fit the chromatographic profile. This is undesirable since the shape of a peak varies with the type of chromatographic instrument used. However, Olive et al. have determined that the log-normal function gives the most accurate fit to peaks from a variety of chromatographic systems (11). In general, curve fitting is more successful when the number of analytes is known and there are no coeluting peaks. These methods do not give definitive information about the presence of contaminants in a peak. Because curve fitting can require lengthy computations, faster algorithms are being developed. For example, the algorithm of Caruana et al. fits an ill-resolved chromatogram of 15 components in about 10 min (8). In cases where the peaks have no valley or noticeable shoulder, derivative methods give excellent qualitative identification of the overlap (12-19). Quantitative methods are being tested; e.g., Jen et al. created a nonlinear calibration curve by integrating the peak satellite of a derivative signal produced by a first-derivativeconductivity detector for ion chromatography (14). Numerical deconvolution methods are very accurate at the expense of lengthy computation time. Rayborn et al. described an improved Fourier transform deconvolution method that is less hampered by S I N degradation problems @ 1990 American Chemical Society
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ANALYTICAL CHEMISTRY, VOL. 62, NO. 15, AUGUST 1, 1990
(20). Crilly has applied Jansson's method to deconvolution to achieve 0.5-4% accuracy in quantitation (21). The Kalman filter resolves overlapped peaks in real time although it requires an initial peak shape model. The Kalman filter is difficult to apply to samples with unknown composition (5, 22). Correlation chromatography, an excellent technique for trace analysis, requires that the sample concentration remains constant over the duration of the injection sequence (23-26). If a multichannel detector is available, e.g., a UV-vis photodiode array or a mass spectrometer, multivariate factor methods can quantitate peaks that have extreme overlap if the component spectra are sufficiently different. Osten and Kowalski reported a method to determine three components that coelute in a fused peak (27). This method requires spectra of the pure components. Lacey has reported an improved factor method that does not require pure component spectra (28). Both methods seek a trade-off between the precision and the computation time. The aforementioned deconvolution methods strive to reconstruct homogeneous peaks in order to quantitate by traditional measurements either the peak height or the peak area. This paper introduces a standard addition method for chromatography that performs quantitation without peak height or peak area measurements and without base-line-resolved peaks. We will demonstrate that by taking the ratio of two sequential chromatograms, unresolved analytes can be identified and the relative change in concentration of the analytes can be measured. Once identified, the peaks may be deconvolved without fitting a model. This technique minimally requires single-channel data to provide a quantitative parameter that also implies qualitative information; e.g., the emergence of an interfering component can be readily identified from the ratio signal. Our approach contrasts with the absorbance ratio (29-31) and absorbance index techniques (32) that minimally require dual-channel data from a single chromatogram to provide a qualitative parameter that is often used in peak purity assessment. If chromatography is being used to monitor a time-varying chemical process, the ratio of sequential chromatograms can quantitate the relative concentration change of the analytes. In this paper, we will also demonstrate a potential process monitoring application that employs an ion chromatography (IC) system. IC has been applied to process analysis because of its ability to analyze aqueous samples like those found in power generation, semiconductor manufacture, metal finishing, wastewater, and fermentation (33). Another process application advantage of IC is that the low back pressure allows a high flow rate and, consequently, a short analysis time. Our ratio quantitation technique may be exploited with data from other chromatographic systems, e.g., gas chromatography (GC) and liquid chromatography (LC). THEORY A pure-component chromatographic peak can be represented, for example, as Si(t) (not necessarily of a Gaussian form) for component i as a function of time, t , with a retention time, tr,i. Fowlis and Scott (34)have represented the response of an almost linear detector as Si(t) = A(Ci(t))" (1) where C is the detected concentration, A is the apparent sensitivity at unit concentration, and x is the response factor. In the linear case, x = 1, and linearity may be assumed for x between 0.98 and 1.02. A two-component chromatogram will be used as an example, although the approach may be extended to additional components. For two analytes, i and j, adjacent and ill-resolved, with tr,i< trj, the equation for the elution profile, S ( t ) ,is given by S ( t ) = S J t ) + Sj(t) (2)
2
1
3
TIME (min)
0
1
2
TIME (min) Flgure 1. (A) Ion chromatograms of known solutions. The concentrations were 12.0 ppm sulfate and 8.8 ppm oxalate for S ( t )and 10.0 ppm sulfate and 12.3 ppm oxalate for U ( t ) . (B) Ratio chromatogram calculated by using chromatograms in A.
For a subsequent chromatogram of a similar sample, U ( t )is obtained, and it has a similar form
U ( t ) = Ui(t) + Uj(t)
(3)
where U ( t )is not necessarily equivalent to S(t). Note that S ( t ) and U ( t ) will have equal duration and number of elements. By triggering the data acquisition to begin automatically upon injection, the elements of S ( t )will correspond to those of U(t). Prior to performing subsequent calculations, an objective correction to center the base line at zero (2) is applied to all chromatograms. Typical data for S ( t )and U t ) are shown in Figure 1A. The ratio chromatogram, R ( t ) ,shown in Figure lB, is obtained from element-by-element division of the base-linecorrected chromatograms
(4) The ratio chromatogram, R ( t ) ,possesses three regions: the elution of pure i, the coelution of i and j, and the elution of pure j. If S ( t ) is nonzero and no change in the concentration has occurred between sampling times for U ( t )and S ( t ) ,the three regions will be indistinguishable and centered around unity. Note also, where no analyte is present in S(t),the ratio chromatogram will be arbitrarily set to zero for easy interpretation. If concentration changes have occurred, the pure regions for i and j will show the relative concentration changes. In the pure i region, where Uj(t)= S j ( t )= 0, a time-invariant value, Ri, is expected from eq 4 and eq 1, where a linear detector has been assumed:
Likewise, for elution of pure j, Ui(t) = Si(t)= 0, and a second constant value, Rj, is expected:
PrNALYTICAL CHEMISTRY, VOL. 62, NO. 15, AUGUST 1, 1990
In the overlap region where i and j coelute, R(t) maintains the form of eq 4 and connects the two flat regions represented by eqs 5 and 6. Ri and Rj will be constant, invariant with time, when the chromatographic concentration profiles, C(t), are governed by linear isotherm conditions. This condition is typical when the injected analyte concentration is small. Where the chromatographic signal in either S ( t )or U t )becomes indistinguishable from the base line, the flat regions are terminated and R(t) is arbitrarily set to zero. More specifically, the outer bounds of the flat regions are chosen as the points where either S ( t )or U ( t )falls below a threshold that is a factor, n, of the standard deviation of the base-line noise: threshold = ns (7) An objective method for locating the inner bounds, the two points that distinguish the flat regions from the overlap region, will be discussed in the Experimental Section. The flat regions of the ratio chromatogram can be used to calculate the concentrations of analytes i and j in two analytical problems. First, if the injected concentration of j in chromatogram S ( t )is known, then the injected concentration, C,,mk, in a later chromatogram, U ( t ) ,is easily found from the flat region ratio value:
= RjCj,known For the almost linear detector, x from eq 1 must be determined by calibration (351, and Cj,unk
Cj,unk
= Rjl’xCj,hown
(9)
For brevity, linearity will be assumed in the remaining discussion. Analyte i is similarly determined. Second, if the concentration of analyte j in S(t)is unknown, then a standard addition procedure is followed. A known amount of analyte j, Mj, is added, either as pure j or as a volume, AV, of a solution of j so that Mj = Cj,spikeAV.The ratio chromatogram is calculated from the unspiked, S ( t ) ,and spiked, U ( t ) ,chromatograms. The resulting Rj is related to the concentration, Cj, by
where V, is the sample volume to which the spike is added. By rearranging eq 10, Cj is obtained: ‘j
Mj/ Vu + Rj(AV/Vu)
= (Rj - 1)
(11)
If A V
