Identification and quantification of overlapped peaks in liquid chromatography with UV diode array detection using an adaptive Kalman filter

ANALYTICA

CHIMICA ACTA

ELSEVIER Analytica

Chimica Acta 335 (1996) I-10

Identification and quantification of overlapped peaks in liquid chromatography with UV diode array detection using an adaptive Kalman filter Jinchang Chen, Sarah C. Rutan” Department

of Chemistry, Virginia Commonwealth Received

13

University, Box 842006, Richmond, VA 23284-2006.

USA

February 1996; revised 6 June 1996; accepted 13 June 1996

Abstract A method for the identification and quantification of overlapped peaks in liquid chromatography with UV diode array detection is reported. The adaptive Kalman filter, which is optimized using simplex optimization, can detect low levels of isomeric impurities. The filter optimization is based on the maximum information yield from the filtering procedure, and is capable of compensating the model errors. This approach is combined with the commercially available software to result in a complete method for chromatographic peak analysis. A mixture of two isomers, chrysene and benz(a)anthracene, has been evaluated. This method can detect as low as 1 pM benz(a)anthracene in a 121 pM chrysene solution, and 1 pM chrysene in a 106pM benz(a)anthracene solution. Both, identification and quantification of the major and minor components have been achieved. For the overall method, the prediction errors are within 2% for the major components and within 10% for the minor components. If the reference spectrum of the minor component is unavailable, this filter can also predict the concentration of the major component within an error of 7%. The reliability of this method has been tested by the second isomeric system, a mixture of benzo(k)fluoranthene and be.nzo(b)fluoranthene. This method is valid for highly overlapped peaks even when the chromatographic resolution is zero, but an overlap-free region is required in the spectra. Keywords:

Liquid chromatography;

Adaptive Kalman filter; Peak purity analysis;

1. Introduction In chromatographic analysis, one of the most important step is to determine whether a peak is composed of only one component. This process is called peak purity analysis. In biological and environmental samples especially, a variety of

* Corresponding cabell.vcu.edu.

author. Fax: (804)-828-8599;

e-mail: srutan @

0003-2670/96/$15.00 0 1996 Elsevier Science B.V. All rights reserved PII SOOO3-2670(96)00304-2

Polycyclic

aromatic hydrocarbons

isomers and degradation products interfere with the chromatographic analysis. In spite of the high separation efficiency of liquid chromatography, the occurrence of overlapped peaks is still unavoidable [l]. If one of the compounds is at a very low concentration, even data from a diode array detector may not be able to provide evidence of impurities in the sample. In such circumstances, developing data processing methods for peak analysis is really necessary.

2

J. Chen, S.C. RutardAnalytica

The general procedure of peak analysis consists of the following five steps: (1) Identification of the major component in a chromatographic peak. (2) Detection of the presence of impurities (peak purity analysis). (3) Quantification of the major component. (4) Identification of the impurities in the mixture. (5) Quantification of the impurities in the mixture. Peak purity analysis is only one step in this procedure. The method proposed in this paper is able to perform all the five steps in peak analysis if adequate a priori information is available In the literature, many techniques have been proposed only for peak purity analysis. For some techniques, several wavelengths are selected to evaluate the peak purity. For example, the ratiogram method uses the ratio of tbe absorbances measured at two different wavelengths to characterize the peaks [2]. The multiple absorbance ratio correction (MARC) uses six wavelengths to determine the correlation coefficient between the apex spectrum with each spectrum in the peak [3]. In addition, the most widely used techniques include the absorbance index technique [4], spectral suppression [5], derivative spectra [6,7] and other parameter calculation methods [8,9]. These methods are simple and easy to use. Some of them have been implemented in instrumental software. However, these methods are not able to detect low concentration impurities and/or give good quantitative results for spectrally similar compounds. Moreover, experimental conditions have a significant influence on the performance of these methods. If the impurity content in a mixture is greater than lo%, it is not too difficult to detect with any of the approaches described above. When impurities in a mixture are at lower levels, however, the observed chromatographic peaks and the UV spectra may be very similar to those of the major components. In such a case, it may not be possible to recognize the impurities present in a chromatographic peak by using several wavelengths only. Therefore, more sophisticated and powerful techniques that use all the wavelengths to calculate the peak purity have been developed, and many are based on certain aspects of self-modeling curve resolution techniques (SMCR) such as, evolving factor analysis (EFA)

Chimica Acta 335 (1996) I-10

[ 10,111, iterative target transformation factor analysis (ITTFA) [ 12,131, fixed size window evolving factor analysis (FSWEFA) [14], heuristic evolving latent projections (HELP) [15,16], and SIMPLISMA [ 17,181. Recently, other techniques such as GramSchmidt orthogonalization [ 19,201 and orthogonal projection analysis [21] have also been reported for peak purity analysis. These methods are very useful when reference spectra are not available. Comparisons of these techniques have appeared in the literature [22-251. However, these techniques are not frequently used to obtain quantitative results. Multicomponent analysis (MCA), based on the information available from reference spectra can provide good quantitative results once the above techniques have been implemented [26]. The application of a Kalman filter to overlapped peak resolution has been reported in [27,28], and some applications using principal component analysis based on Kalman filter networks have also been reported [29,30]. The latter approach is actually similar to many of the SMCR related techniques, which are described above. Here, we use an adaptive Kalman filter, which can compensate for the presence of model errors [31]. Therefore, errors caused by the presence of an unrecognized interference are significantly reduced while using this filter. The adaptive Kalman filter has been successfully used to resolve overlapped UV spectra in characterizing stationary phases used in liquid chromatography [32]. In this paper, an adaptive Kalman filter based on the information theory is used to evaluate overlapped peaks for isomeric polycyclic aromatic hydrocarbons (PAHs). Simplex optimization is used to maximize the information yield from this filter, and to provide accurate predictions. This adaptive Kalman filter can automatically find the appropriate wavelengths to quantify the component instead of depending on the user’s choice. Thus, the identification and the quantification of the components in a mixture are more efficient. The research work in this paper is aimed at detecting low levels of impurities in the isomeric mixtures but assumes that some spectral information about the potential components is available. Two mixtures, benz(a)anthrancene-chrysene and benzo(k)fluorantbene-benzo(b)fluoranthene, have been evaluated in this work. The identification for both, the major component and the minor component,

3

J. Chen, XC. RutadAnalytica Chimica Acta 33.5 (1996) l-10

is based on the PAH library created in the HewlettPackard ChemStation software. The total approach provides a method for peak analysis that does not require the determination of the individual elution profiles.

adaptive Kalman filter, the measurement variance, r-,&k), is adjusted to compensate for model errors, and is employed in the algorithm when ever r,&(k) is greater than rconst(k). rvk(k)

. V(k

-j)]

-

hT(k)

. P(k)

. h(k)

(3)

The details of the theory of the informationoptimized and adaptive Kalman filter have been described in other papers [31,33]. The Kalman filter is a recursive least-squares filtering algorithm, where data points are processed sequentially. The measurement model for the Kalman filter is described as:

(1)

where z(k) is the measurement such as UV absorbance. The vector h(k) is the measurement function containing the spectral information for each compound (i.e., the molar absorptivity). x(k) is a vector, which is composed of the parameters to be estimated in the filter. In this paper, it represents the vector of concentration of the components. v(k) is the contribution of the noise to the measurement, which has a variance of r(k); and k is an wavelength index. Eq. (2) is used to estimate the parameters, which is: n(k) = x(k - 1) + g(k) ’ [z(k) - IIT

-j)

j=l

2. Theory

z(k) = hT(k) .x(k) + v(k)

= e[v(k

. n(k - l)] (2)

The Kalman gain g(k), that is inversely proportional to the variance of the measurement noise r(k), is a calculated weighting factor for each data point. Therefore data with a larger signal/noise level (large weight factor) will make more contibution to the parameter estimates, while data with a smaller signal/ noise level (small weight factor) will be given less weightage. In Eq. (2), x(k- 1) is the previous estimate of the concentration. At the beginning, any initial guess of this concentration can be made, but this filter successfully approaches the true value after processing several data points. For the regular Kalman filter, the measurement variance, r,,,,,(k), is determined before curve fitting, and should represent the variance of the noise in the spectral measurement. For the

In Eq. (3), P(k), the covariance matrix, is used to describe the errors in the parameter estimation process and m is the number of points corresponding to a smoothening window. If there is another component making a contribution to the measurement, the on-line residual v(k), which is the difference between the measurement and the prediction, will result in a large measurement variance according to Eq. (3). Therefore the resulting small weight factor can turn off the filter if the on-line residual is too large, and that data point will not be used to estimate the parameters. The adaptive Kalman filter used in resolving an unexpected impurity contribution is based on the assumption that some part of the spectral response is due solely to contributions from the model spectrum [31]. Therefore, an overlap-free region in the mixture spectrum is required. Otherwise, the filter is unable to give reliable fit results. In this paper, the performance of the adaptive Kalman filter is evaluated by the use of information theory. The simplex optimization method provides the optimal information as a function of the initial guess for the concentrations. The fit results are more accurate when the information is maximized as shown by Eq. (4) [33], where det represents the determinant of the matrix. log (det ~~!r [h(k) . r(k)-‘hT(k)]

In(tota1) =

+

1)

21og2 (4)

The programs based on this approach have been tested using a set of simulated data [33]. In this paper, the UV spectral data obtained from chromatographic experiments are employed to evaluate these programs for the applications of peak identification and quantification, especially in the case of the presence of an impurity at a low concentration.

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J. Chen, S.C. RutadAnalytica Chimica Acta 335 (1996) l-10

3. Experimental

3.1. Apparatus and chemicals The HPLC used in this experiment is a HewlettPackard 1090 series II HPLC system. A diode array detector system (DAD) is used to record the UV spectra. The built-in HPLC 3D ChemStation software can be used to create the library, to integrate chromatographic peaks, and to identify the components. The separation is performed on a Sigma (St. Louis, MO, USA) Spherisorb ODS II column (100x4.6 mm id.), containing 3 pm octadecyl silica particles. The mobile phase consists of 90% methanol and 10% water at 0.4 ml min-’ except when indicated otherwise. Both, methanol-water and acetonitrilewater have been employed as mobile phases in the initial studies. 20 yl injections were used. UV spectra used for the determinations are recorded from 200 nm to 400 nm, and the library spectra are in the range of 190 nm to 600 nm, at 2 nm intervals. A PAH library has been created in the ChemStation software and used for identifying the components in the mixtures. In creating the library, each compound has been analyzed in two or three repeated runs and yielded reproducible spectra. The apex spectrum of each peak is selected as the library spectrum, and the library search is based on the comparison of the peak apex spectrum or average peak spectrum for the sample with the library spectrum. Both, methanol and acetonitrile are of HPLC grade, purchased from EM Science (Gibbstown, NJ, USA). All the PAHs used in this experiment are from Sigma Chemical Co. Stock solutions of chrysene (CHR), benz(a)anthracene (BAN), benzo(b)fluoranthene (BBF) and benzo(k)fluoranthene (BKF) were prepared in acetonitrile at concentrations of 123, 107, 16 and 16 uM, respectively. 3.2. Programs and procedures The programs for the simplex-optimized and adaptive Kalman filter were written in the MATLAB (Mathwork, Natick, MA, USA) programming environment by Agbodjan and Rutan [33]. One mixture spectrum, one or two reference spectra, and one blank spectrum are required to run these programs. In this experiment, when benz(a)anthracene is used as a

reference to evaluate a mixture of chrysene and benz(a)anthracene, the experiment is called a BAN fit. When chrysene is used as a reference to evaluate a mixture of benz(a)anthracene and chrysene, the experiment is called a CHR fit. When the Kalman filter programs are run with the reference spectra from both the major component and impurity to quantitatively determine how much of each component is present in the mixture, the approach is called the double fit approach. In the double fit approach, the filter can be used either as a regular Kalman filter (identical to ordinary regression) or as an adaptive Kalman filter. The double fit uses more spectral information than the individual fits (BAN fit or CHR fit) and thus, the fit results should be better than either of the individual fits. In order to correct a nonzero background, an offset is added to the model spectrum vector h(k). The final results will provide estimates for the offset and the component concentration(s). The unknown component spectrum is obtained by subtracting the fit result and offset from the mixture spectrum. The blank spectrum is obtained from the same chromatogram as the mixture spectrum, and is used to calculate the measurement variance (rconst); estimates are obtained from the variance of consecutive measurements in the baseline region. It is assumed that the noise is homoscedastic. The number of components, the measurement variance (rconst), the number of points in the filter window (m), the fit direction (forward/reverse), and the data range are all parameters which are to be provided by the operator. The number of points in window (m) has been studied in previous work [33], and the minimum window size (one) was used in these adaptive Kalman filter fits. The effect of the fit direction and the data range have been evaluated in this work. For our system, the reverse fit, in which the fit starts from the high-wavelength end, yielded much better results than the forward fit, in which the fit starts from the low-wavelength end, since chrysene and benz(a)anthracene have an overlap-free region in the high wavelength range. In the reverse fit mode, the algorithm will evaluate the overlap-free region and result in a model containing the correct information. It has been observed that omitting some data in the high-wavelength end will reduce the model accuracy in the individual fit since, the

J. Chen, XC. RutadAnalytica

overlap-free region is in the high-wavelength range. This indicates the importance of the overlap-free region for a successful use of this filter. For the BAN and CHR studies, both the mixture spectra and the reference spectra are collected at the peak apex. The peak apex corresponds to the maximum concentration, eluted in the standard samples. In the mixture, if the concentration profiles of both components are the same, that is, the resolution is zero, the double fit predictions will be accurate for both the major and minor components. If the components are partially resolved, this peak apex spectrum will be closer to the peak apex spectrum of the major component than that of the impurity. Thus, the double fit can accurately predict the concentration of the major component, but relatively large errors may result in predicting the concentration of the impurity. In order to obtain better results for the impurity, chromatographic area data are used to calculate the impurity concentrations. Peak area calibration curves are made for BAN and CHR standard samples at 254nm. Based on these calibration curves, the major component concentration produced from the double fit can be converted to peak area, and the peak area contributed by the impurity is obtained by subtracting the major component peak area from the mixture area. The impurity concentration is then calculated from the corresponding calibration curve.

5

Chimica Acta 335 (1996) I-10

the 230-400nm spectral range results in better match qualities than use of the 190-600nm spectral range. Since most PAHs have no significant absorbance between 400 and 600nm, this difference is attributed to the absorbance between 190 and 230 nm. All these PAH compounds have an obvious absorbance in this area, and reproducibility is poor between 190 and 230nm. Therefore, library search match quality is reduced if this range of data is included. Experiments with a BAN sample indicate that the library search results are insensitive to the changes in the experimental conditions. The library search match qualities are above 99.00 when the methanol contents in the mobile phase are 90%, 80%, and 70%, respectively. Chrysene and benz(a)anthracene were chosen as the isomeric pair for peak analysis based on the following considerations. First, chrysene and benz(a)anthracene is one of the isomeric pair of PAHs most difficult to separate [34]. This difficulty may lead to problems in detecting low levels of impurities in peak purity analysis. Second, the spectral similarity of the mixtures at different elution times (because the resolution is almost zero) makes some peak purity methods invalid while the adaptive Kalman filter has an advantage in such a situation. Finally the spectra of the two compounds are different and there is an overlap-free region for benz(a)anthracene. The latter is a requirement of the adaptive Kalman filter. The spectra of pure chrysene and pure benz(a)anthracene are shown in Fig. 1.

4. Results and discussion

4.1. Creating the library ,200 ABSORBANCE(mAU)

The major component and the unknown spectrum are identified by a user-built library created by using the Hewlett Packard software. There are, in all, 32 spectral entries created for 12 PAH compounds in the PAH library, obtained under different experimental conditions. For each of these compounds, library spectra have been obtained by using both methanol/ water and acetonitrile/water as the mobile phases. For most of the PAHs, there are no significant differences between the spectra obtained with acetonitrilelwater vs. methanol/water. However, the UV spectral range was found to be an important factor affecting the library searching match quality. In general, use of

1000

n

CHR

800 600 400 200 0 -200 1 190

240

290

340

390

WAVELENGTH (nm) Fig. 1. UV spectra of pure benz(a)anthracene

and pure chrysene.

.J. Chen, XC. RutadAnalytica

6

Chimica Acta 335 (19%) l-10

4.2. Fit results for mixtures of BAN and CHR

As shown in Fig. 2, a five-step peak analysis approach has been developed. In order to check peak for purity in the chromatogram, the peak apex spectrum is extracted from the UV diode array detector data. A library search of this spectrum will identify the major component. By applying the adaptive Kalman filter to this spectrum by using reference spectrum of the major component, the first estimate for the major component concentration and a residual spectrum are obtained. If no other components arc found (the residual spectrum is at the noise level), the average spectrum over the whole elution range is evaluated by the adaptive Kalman filter again to, make sure that there is no second component anywhere in the chromatographic peak. If there is another component in the peak, a library search of the residual spectrum may be able to identify the minor

, Rwidulatthenoisclevel

I

1

t

I

1

Noref..

spectrum found

Fig. 2. Scheme for five-step peak analysis procedure

210

260

310

360

WAVELENGTH (nm) Fig. 3. Fit results of adaptive Kalman filter mixture spectrum and BAN standard spectrum.

with

BAN-CHR

component. An example of the fit results with the major component spectrum (BAN) and the mixture spectrum is given in Fig. 3 (BAN fit). The impurity spectrum is extracted after fitting the major component (BAN) reference spectrum to the mixture spectrum by using the adaptive Kalman filter. By applying reference spectra of both, the major and the minor component, the adaptive Kalman filter (the double fit approach) can give an improved concentration estimate for the major component and the concentration estimate of the minor component. The peak area data are used to calculate the final concentration estimate for the minor component, as described in the experimental section. A data set consisting of four mixtures with BAN as the major component and four mixtures with CHR as the major component has been examined using the procedure outlined in Fig. 2. In all these mixtures, the impurity contents are below 20%. The double fit predicts the concentrations of the major components within 2% error. The minor component concentration is predicted by the peak area data (Figs. 4 and 5). In practical applications, however, sometimes a reference spectrum for the impurity is not available; the individual fit must be used in such cases and can also predict well for the concentrations of the major components. Table 1 gives the CHR fit and BAN fit results, which are based only on the fit to the reference spectrum of the major component. These fit results have larger errors than those for the double fit. From Fig. 1, one can see that chrysene spectrum is overlapped more by benz(a)anthracene, while benz(a)anthracene has an overlap-free region at high

.I. Chen, SC. RutadAnalytica Chimicu Acta 335 (1996) l-10 1

Y $j

0.6

3 I-

0.6

2 a 0 F 0 P

8 9

I= 4

0.0

06

04

E P

0.4

0.2

F 0 E

0.2

I 0 0

I).2

0.4

08

0.6

Fig. 4. The BAN concentrations predicted standard concentrations, peak area. (area).

0.4

0.2

0

1

0.6

1

0.8

CHR RELATIVECONC.

BAN RELATIVE CONC. by the double fit and + double fit, n peak

Fig. 5. The CHR concentrations predicted peak area. (standard concentrations, area).

by the double fit and + double fit, n peak

Table 1 CHR and BAN fit results for CHR and BAN mixtures Mixture

Cal. CHR cont. a

CHR cont. ’

Error %

Mixture

Cal. BAN cont. a

BAN cont. a

Error 8

1

0.850 0.878 0.943 0.968

0.800 0.857 0.900 0.950

6.25 2.45 4.78 1.89

5 6 7 8

0.835 0.879 0.914 0.973

0.800 0.857 0.900 0.950

4.38 2.20 1.56 2.42

in mixture/concentration

of the stock solution.

2 3 4

a Relative concentration:

Table 2 The predictions

calculated

concentration

of model component

for the blind studv from the double fit and ueak area data

Mixture

Cal. CHR cont. ’

CHR cont. ’

Error 8

Cal. BAN cont. ’

BAN cont. a

Error %

1 2 3 4

0.937 0.923 0.052 b 0.089 b

0.938 0.917 0.056 0.095

-0.11 0.65 -7.14 -6.32

0.066 b 0.077 b 0.931 0.892

0.063 0.083 0.944 0.905

4.76 -7.23 -1.38 -1.44

‘Relative concentration: calculated concentration b Concentration calculated using chromatographic

of model component peak area data.

wavelength range; and thus, the BAN fit is better than the CHR fit. If the impurity spectrum is entirely overlapped by the known component spectrum, this error may be significant since an overlap-free region is required by the adaptive Kalman filter. Another set of mixture samples was evaluated by the peak analysis method in a blind study (samples prepared by Z. Li). These fit results are given in Table 2. The errors in the predicted concentrations of the major component are less than 2% and those of the minor components (impurities) are around 7%. Due to the successful predictions of the unknown samples, it is believed that this method, based on the adaptive

in mixture/concentration

of the stock solution.

Kalman filter is viable for detecting small amount of impurities and yielding good quantitative results. The identification is performed by using the HP ChemStation software. Because of the overwhelming amount of the major component in the mixture, it is easy to identify this by using the user-built library with HP ChemStation library search software. The library search results and the peak purity factors provided by the HP software are given in Table 3. The peak purity factors are generated by collecting nine spectra at different elution times in one overlapped peak and by comparing how well they match. Ideally, this factor is supposed to be 100 for a pure peak.

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J. Chen, XC. RutarvAnalytica Chimica Acta 335 (1996) l-10

Table 3 Library search results and peak purity factors BAN as the major component Sample

Concentration

1 2 3 4 5

with

Library search results

Match quality

Peak purity factor

1.OO BAN 0.00 CHR

BAN

99.99

99.99

0.95 0.05 0.90 0.10 0.86 0.14 0.80 0.20

BAN

99.75

99.84

BAN

98.90

98.49

BAN

97.76

98.05

BAN

96.05

97.29

‘Concentrations

a

for mixtures

BAN CHR BAN CHR BAN CHR BAN CHR

are relative to the stock solutions.

Compared to those methods that use several wavelengths described in Section 1, this method uses more wavelengths, and it is believed to be fairly reliable. However, for low impurity content in the mixture (below lo%), the difference in this factor between the pure sample and mixture is too small to determine the presence of an impurity in the peak. When the peaks are highly overlapped, the spectra are very similar throughout the entire elution range. In these cases, the library search results and the peak purity factors can not provide reliable information about the presence of the impurities. Moreover, the main disadvantage of the purity factor is that it is unable to identify the impurity and give quantitative results without additional calculations. However, the small difference between the library spectrum and mixture spectrum caused by an impurity in the mixture can be extracted by using the adaptive Kalman filter. This difference provides important information on the spectral properties of the impurity, and a library search of this residual spectrum can identify this minor component. 4.3. Limits

of

identijkation

for

CHR

and

BAN

mixtures

We define the limit of identification as the lowest concentration that can give reliable library search results. Generally, if the match quality between the experimental spectrum and the library spectrum is above 70%, the library search results are believed to

be reliable. The limit of identification (LOI) data given in this section are different from that of the limit of detection (LOD). The LO1 is the lowest concentration of the component that can be identi$ed with the instrument and the software whereas the LOD indicate the lowest concentration of components which can be detected. LO1 depends both on the instrument and the method which is used to calculate match quality, whereas the LOD depends only on the instrument characteristics (signal to noise ratio). In general, the LO1 value is higher than the LOD value for a certain analyte under the same experimental conditions. The LO1 value for pure benz(a)anthracene is 0.08 PM. For pure chrysene, the LO1 value is 0.12 PM. If there is another component in the solution, the LO1 will significantly increase because of the interference. For example, the LO1 value of benz(a)anthracene is 1.07 uM in a 122 uM chrysene solution. The LO1 value of chrysene is 1.23 uM in a 106 uM benz(a)anthracene solution. Below these LO1 values, the impurity spectra produced by the adaptive Kalman filter fit are at the noise level, and thus the PAH library search is unable to identify the impurities with match quality above 70%. LO1 is a parameter that depends on the instrument, the calculation of the match quality, and the nature and concentration of the major component. In order to compare the different LO1 values with different instruments and different analytes, it is suggested that a specific calculation method for match quality and concentration of the major component (for example 100 PM) be specified as a reference. 4.4. Fit results for BKF and BBF mixtures Benzo(k)fluoranthene and benzo(b)fluoranthene is another pair of isomers that are difficult to separate. Fig. 6 shows the UV spectra of pure benzo(k)fluoranthene and pure benzo(b)fluoranthene. Compared to the CHR and BAN sample, the BKF and BBF pair has more similar UV spectra but are less overlapped in their chromatograms. The peak apex spectrum basically consists of the major component. Again, the approach outlined in Fig. 2 is used for the peak analysis. If only the peak apex spectrum is used for peak purity analysis, it is possible to miss the presence of the impurity. Thus, for the BKF/BBF

J. Chen, XC. Rutan/Analytica 7. ABSORBANCE(mAU)

I

I

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Chimica Acta 335 (1996) l-10

5. Conclusions

60 50

40 30 20 10 0 -10

1

190

240

290

340

390

440

WAVELENGTH (nm) Fig. 6. UV spectra benzo(b)fluoranthene.

of

pure

benzo(k)fluoranthene

and

pure

pair, the average spectrum over the whole elution time is taken to check for the presence of the impurities. Identification and quantification of the major component can be achieved by using the peak apex spectrum. Identification is performed using the PAH library, and quantification is achieved by using the adaptive Kalman filter in the individual fit mode. The concentration determination of the impurity contents in the mixtures can be achieved by using the peak area data as described in Section 3. The predicted concentrations for ten samples of the mixture are given in Table 4. Both BKF and BBF have been quantitatively determined, no matter which one is the major component. Again, the percentage of error for the major component prediction is about 2%, while that of the minor component is within 10%.

The successful analyses of the overlapped peaks for both the isomeric samples indicate that the method developed in this paper is a general technique and applicable to different isomeric PAH systems. For samples with a low level impurity or highly overlapped chromatographic peaks, the adaptive Kalman filter has advantages over other techniques, in spite of the limitations of the highly similar spectra. In this work, only two-component mixtures are used in the adaptive Kalman filter approach, but this technique should be able to deal with threecomponent mixtures, although the probability of observing an overlapped free region will become less. A synthetic three-component data set has successfully been evaluated using these programs [33]. One disadvantage of this technique is that it is unable to determine the number of components in the mixture directly. If the modelled and unmodelled component spectra are completely overlapped, there will be a significant error in the model, and the adaptive Kalman filter will fail due to the requirement of an overlap-free region in the mixture spectra. Finally, this is a model-based technique, thus the method can not be used if reference spectra are not available. Self-modelling curve resolution techniques are advantageous in such cases for peak purity analysis. The proposed method in this paper has demonstrated the advantages of the adaptive Kalman filter for peak identification and quantification, First, this

Table 4 The predicted

concentrations

Mixture

Cal. BBF cont. a

BBF cont. a

Error %

Cal. BKF cont. a

BKF cont. =

1 2 3 4 5 6 I 8 9 10

0.947 0.886 0.847 0.796 0.741 0.249 0.206 0.151 0.090 0.045

0.950 0.900 0.857 0.800 0.750 0.250 0.200 0.143 0.100 0.050

-0.30 -1.56 -1.16 -0.50 -0.90 -0.40 3.00 5.59 10.0 10.0

0.054 b 0.103 b 0.143 b 0.202 b 0.275’ 0.764 0.813 0.868 0.913 0.961

0.05 0 0.100 0.143 0.200 0.250 0.750 0.800 0.857 0.900 0.950

b b b b h

for the BKF and BBF mixtures

a Relative concentration: calculated concentration b Calculated concentrations from chromatographic

of model component peak area data.

in mixture/concentration

of the stock solution.

Error % 8.00 3.00 0.00 1.oo 10.0 I .87 1.63 1.28 1.44 1.16

10

J. Chen, SC. RutadAnalytica

method can automatically find the selective wavelengths and thus gives accurate quantitative results. For the adaptive Kalman filter, the pure component regions need not be determined by the user, which is the case for many of the methods, described in Section 1. Second, the fit results are independent of peak shape and other experimental conditions since, chromatographic data are not used in the calculations as long as peak shapes are reproducible. The method is useful even for highly overlapped chromatographic peaks. Finally, both identification and quantification can be performed in this method. Most techniques in overlapped peak analysis either check the peak purity or quantify the components in the mixtures. The approach described in this paper can determine the concentration of the components in the mixtures, as well as provide reliable identification of unexpected impurities.

Chimica Acta 335 (1996) I-IO

[sl 191 UOI 1111 [Ql 1131 u41 [I51 1161 v71 WI 1191 PO1 WI

Acknowledgements Pa

The authors would like to acknowledge support from the US Department of Energy, Grant No. DEFG-05-88ER 13833, and appreciate the preparation of unknown samples by Zengbiao Li in the blind study. Ed Scharnhorst participated in the work for HP software data transfer. We also thank EC. Sanchez for reading this manuscript and for providing good suggestions.

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