Multivariate analysis of UV-spectral data for solute spectral tracking in HPLC

MULTIVARIATE ANALYSIS OF UV-SPECTRAL DATA

, FOR SOLUTE TRACKING IN HPLC

MULTIVARIATE ANALYSIS OF UV-SPECTRAL DATA

FOR SOLUTE TRACKING IN HPLC

PROEFSCHRIFT

ter verkrijging van de graad van doctor aan de Technische Universiteit Delft,

op gezag van de Rector Magnificus, prof. drs. P.A. Schenck, in het openbaar te verdedigen ten overstaan van een commissie aangewezen door het College van Dekanen

op donderdag 6 april 1989 te 16.00 uur door Joost Karel Strasters

geboren te Gouda, scheikundig ingenieur

r

Dit proefschrift is goedgekeurd door de promotor Prof. Dr. L. de Galan

Published and distributed by Delft University Press Stevinweg 1

2628 CN Delft, the Netherlands Tel. (0)15 783254

CIP-DATA Koninklijke Bibliotheek, the Hague, the Netherlands ISBN 90-6275-535-6

Copyright © 1989 by J.Strasters

No part of this book may be reproduced in any form by print; photoprint, microfilm of any other means, without written permission form Delft University Press.

Voorwoord

Het werk dat in dit proefschrift beschreven wordt, heeft plaats kunnen vinden door de inzet en de interesse van een groot aantal mensen. Langs deze weg wil ik allen hiervoor danken.

In de eerste plaats betreft dit mijn promotor, prof. dr. Leo de Galan, die dank zij zijn heldere kijk op het onderwerp en zijn nuttige en kritische suggesties het onderzoek gestuurd heeft. Met name zijn grote bereidheid om, ondanks een verandering van werkkring, altijd voldoende tijd vrij te maken om het werk te bespreken wordt bijzonder gewaardeerd. Ook de steun van de overige leden van de vakgroep analytische scheikunde aan de TU-Delft, zowel tijdens de maandelijkse werkbesprekingen als daarbuiten, heeft bijgedragen tot een goede en stimulerende werksfeer. Met name de praktische adviezen van ing. Hugo Bill iet waren van onschatbare waarde om tot daadwerkelijke resultaten te komen. Verder heeft dr. ir. Anton Drouen een belangrijke bijdrage geleverd bij het opstarten van het onderzoek.

Bij het onderzoek naar en de toepassing van de verschillende algoritmes is veel steun ondervonden van de vakgroep Analytische scheikunde van de Katholieke Universiteit van Nijmegen. Vooral de belangstelling en kritische kanttekeningen van dr. ir. Bernard Vandeginste zijn van grote invloed geweest op het uiteindelijke resultaat.

The discussions with dr. Dave Herman, dr. Gary Low, dr. Akos Bartha and dr. ir. Peter Schoenmakers have contributed to a critical view on analytical chemistry in general and specifically on my own research. Especially the boundless energy and enthousiasm of Akos were responsible for additional research on topics not discussed in this thesis. Furthermore he provided a major contribution to the contents of chapter 5.

Ten slotte had dit onderzoek niet gedaan kunnen worden als niet de volgende stagieres een groot deel van de experimenten hadden uitgevoerd: Jaco Guyt, Joost Möhlman, Eric de Korver, Kurt Boey en Frank Coolsaet. Mede door de praktische problemen die zij aandroegen, heeft de strategie

Contents

Chapter 1

Optimization and Peak-Tracking in Liquid Chromatography

Chapter 2 15 An Evaluation of Peak Recognition Techniques in Liquid

Chromatography with Photodiode Array Detection

Chapter 3 45 The Reliability of Iterative Target Transformation - Factor

Analysis when using Multiwavelength Detection for Peak-Tracking in Liquid Chromatographic Separations

Chapter 4 71 A Strategy for Peak-Tracking in Liquid Chromatography on the

basis of a Multivariate Analysis of Spectral Data

Chapter 5 111 Peak-Tracking and Subsequent Choice of Optimization Parameters

for the HPLC-Separation of a Mixture of Local Anaesthetics

Summary 139

Chapter 1

Optimization and Peak-Tracking in Liquid Chromatography

1.1 Mobile Phase Optimization

During recent years, different optimization procedures for reversed-phase high performance liquid chromatography (RP-HPLC) have been developed (1,2). The purpose of the optimization is to derive an optimal separation by means of the chromatographic process, where the definition of 'optimal' depends on the actual goal of the analyst, for instance: realise a complete separation of all components of interest in the shortest possible analysis time. One of the main parameters used to direct the separation is the mobile phase composition, since this parameter is easy to vary and often has a large influence on the retention behaviour of the individual solutes. In general the overall retention is largely influenced by changing the ratio of a strong and a weak eluting solvent, such as water. The specificity of the mobile phase is determined by the type of organic modifier used as the stronger eluting solvent. By mixing different types of modifiers, such as methanol (MeOH), tetrahydrofurane (THF) and acetonitrile (ACN), the specific interactions of the solutes with the mobile phase can be fine-tuned to derive an optimal separation. It is also possible to enlarge the dimensionality of the parameter space and to involve other factors such as the type of stationary phase, the temperature, the pH of the mobile phase, etc.

The definition of an optimization criterion is a separate problem addressed elsewhere (1): the criterion defines the quality of a

chromatogram (separation) and should express the goal of the optimization. Here we are concerned with the determination of the exact coordinates of the optimum in the vector space described by the parameters. An important point which should be taken into consideration is the total amount of information already available on the sample. For instance, the reasoning involved in the optimization is greatly facilitated when the number of solutes in the sample is known. Another important issue is the number of experiments one is willing to perform in order to locate the optimum.

The optimization strategies currently in use can be divided into two classes. On the one hand we can distinguish the "non-interpretive"-methods. Different chromatograms of a sample are considered individually and the criterion-value is the only important value used to represent a chromatogram. A typical method belonging to this group is the "brute force"-technique where a great number of predetermined grid points are measured and the one with the highest criterion value is selected (3). This method is a typical example of a simultaneous optimization technique. Another approach is the simplex-optimization strategy, which again operates without any model as far as the retention behaviour is concerned and which uses the results of chromatograms measured earlier to derive the parameters for the next run (4). The simplex approach is an example of a sequential optimization strategy, where one tries to approach the location of the optimum on the basis of criterion values observed earlier.

Alternatively, one can make use of all the available knowledge on the chromatographic behaviour of the solutes, by applying so called "interpretive"- methods. These methods are based on a retention model that can be derived from a limited number of experiments. The retention behaviour of the solutes in the sample is important rather than the criterion-value. On the basis of the expected retention behaviour, chromatograms can be calculated for different mobile phase conditions within the examined parameter space and the separation quality can be predicted. Again, two mainstreams can be considered: one can try to predict the "real" retention behaviour with sufficient accuracy from a quadratic model fitted to a number of experiments that is sufficiently large (a simultaneous approach (5)), or one can start from a few initial

experiments and use a simple linear model which is updated after each new experiment. The position of the initially calculated optimum is then continuously adjusted on the basis of the new data (a hybrid technique combining simultaneous and sequential elements (6)).

An example of this iterative approach is given in figure 1.1. The lower part of the figure represents the predicted retention behaviour from chromatograms 1 and 2 (the chromatograms on the left and right of the figure). The upper part of the figure shows the quality of chromatograms calculated over the whole range of mobile phase compositions assuming linear retention behaviour (in this case the applied criterion is the resolution of the least separated peak pair, Rsmin). It should be clear that in order to calculate the criterion-value over the parameter space,

O 0.2 0.4 mobile fraction mobi pbose 1 chromatogram 1 0.6 0.8 9 phase 2 mobile phase 2

7

Fid. 1.1: The first step in the iterative optimization procedure. Based on the chromatograms 1 and 2, capacity factors k are estimated for all components (1-5) in thé mixture of mobile phases 1 and 2. Thé location of the optimum is determined after evaluation of the predicted chromatograms on the basis of a criterion.

the identity of the peaks in the two chromatograms must be matched. This means that the numbering of the peaks as given in chromatogram 1 should also be known for chromatogram 2, i.e. it is necessary that we are able to determine which peaks in the two chromatograms correspond to the same compound as indicated by the numbering in Fig.1.1.

This chapter will concentrate on different peak recognition techniques. We intentionally use the term "peak recognition" instead of "peak identification" because, primarily, we are not so much interested in the identity of the solutes but in first instance in their retention behaviour. This process is also known as "peak-tracking".

1.2 Methods currently available for Peak-Tracking

When the composition of the sample is completely known, the retention behaviour of the individual solutes can be determined by separate injections, a rather time-consuming procedure. If we are faced with an unknown sample (not necessarely completely unknown) or, for time-saving reasons, want to inject the sample as it is, then it is necessary to use some form of peak-tracking. Peak-tracking must be done by means of specific detection methods as illustrated in figure 1.2.

The simplest form of peak recognition is applied in one-dimensional detection systems using a single wavelength or refractive index detection and considering peak area as being specific for the different solutes (fig. 1.2A). This method can be applied when changes in experimental conditions (mobile phase influences on absorption characteristics) do not influence the^^e^e^ticLn_char-acter-istics-(peak area) too . Apart from the fact that within one chromatogram several peaks can have almost the same area, and that the experimental conditions do have an influence on the spectral properties, peak overlap will cause severe problems, since the individual peak-areas will be more difficult to determine. A possible solution can be found in using curve-fitting procedures with a predetermined peak model (7) or evaluating different combinations of individual peak areas observed in other chromatograms (8). However, both these methods depend heavily on the

assumed number of components: when severe overlap i s observed i n a l l chromatograms of a given sample, more elaborate procedures are required. Problems related to the inherent uncertainty i n the observed peak areas, caused by peak overlap or influence of the experimental c o n d i t i o n s , have been approached by application of the " f u z z y - s e t " - t h e o r y ( 9 ) .

rel. area:

A

I A J ^

B

J Ü U

JLnJ

c

■Ü31Ü sUJsM

Fio. 1.2: Three examples of peak-recognition by means of specific detection: a) based on peak area, b) based on the ratio of the absorbances at 254 and 280 nm, c) based on the spectra recorded during the elution. Peaks marked with '*' are matched in both chromatograms. When the overlap is too severe to determine the characteristic value for a particular component, this is indicated by a question mark (?).

It is possible to increase the specificity of the detection considerably by using more wavelengths and/or different detectors. The most extreme example is the use of a variable wavelength detector at a certain wavelength which is specific for one solute and does not detect the others. Such a detection is unambiguous. The use of two detectors at different wavelengths will increase the specificity considerably. The absorbance ratio over a peak consisting of a pure solute is a constant value independent of the concentration and only dependent on the molar absorptivities at the wavelengths of interest:

Ai b . c . «i ex

Ratio = - — = - {1.1}

A2 b . c . e2 c2

Ai and A2 are the observed absorbances at wavelength 1 and 2

respectively, b is the cell-constant, c the concentration and e the

molar absorptivity (extinction coefficient) at the specified wavelength, according to Beer's Law. The so-called ratio method (see fig. 1.2B) can be used as peak recognition technique because the value of the ratio is a unique quantity only related to the extinction coefficients. However, this method also suffers from some serious drawbacks (10). For instance, it is difficult to estimate the ratio-value in the case of severe peak overlap or in the case of a baseline with a different drift at both wavelengths. One obtains an indication on the complexity of the sample, but the exact number of components can not always be determined. Furthermore, small changes in the spectral characteristics of the components due to different experimental conditions (for instance a change in organic modifier) can strongly influence the ratio-value, causing addititional confusion in the tracking procedure.

An obvious extension of this method is to use a multiwavelength detector like the linear photo diode array detector (LPDA) (11) which records complete UV-spectra of the eluens in a very short time (figure 1.3). For fully separated peaks the characteristic spectra can be determined easily and compared with the spectra recorded in other chromatograms (figure 1.2C). If the spectra of the solutes in the sample differ enough, a visual comparison can be sufficient to recognize the peaks. A

number of methods exist to perform this comparison in an objective manner: usually the correlation coefficient is applied (12) which is equivalent with a sum of squared differences of normalised and averaged spectra. However, alternative methods based on absolute differences (13), root of the mean squared difference (14) and fuzzy set theory (15) have been described. All methods imply or require some form of normalisation to eliminate concentration effects.

As with the other techniques, peak-tracking based on the comparison of observed spectra runs into problems with severe peak overlap, since mixture spectra are generated during coelution of different solutes. Occasionally, spectra taken at the front and tail of the peak can be used to represent "pure" spectra for the first eluting and last eluting

Fig. 1.3: A three-dimensional representation of the information obtained by means of a photo diode array detector: the observed absorbance A is a function of the wavelength \ and the time t.

solutes in the peak cluster (16), but only in the case of modest overlap. Solutes eluting somewhere in the middle of such an overlapping system can never generate pure component spectra unless the resolution from the neighbouring solutes is sufficiently large. Only for large differences in spectral characteristics visual interpretation may be performed as has been shown in the past (17). By plotting normalised spectra in overlay, taken at different places over the elution profile and watching characteristic changes in those spectra, full or partial recognition is sometimes possible. However, so-called 'intelligent' systems are not as capable of detecting small specific similarities as the human eye and further treatment of the data is required for automated peak-tracking.

Further expansion of the dimensionality of the data is possible when detection techniques such as fluorescence are used. Since the observed spectra are dependent on the excitation wavelength, there is an additional axis present (the others being time and absorption wavelength). Although the information content of these spectra is much higher than those of UV-VIS spectra, the main drawback is that only few solutes produce a fluorescence signal. Furthermore, in order to exploit the full power of fluorescence usually a stopped-flow technique is used, although one is currently improving the speed of the scanners (18).

1.3 Hultivariate Analysis of Mixture Spectra

In this thesis, we will limit ourselves to the use of the LPDA. Direct comparison of absorption spectra taken from well separated peaks in an automated fashion is no real .pr.ob_leni-(.19.) However,-sinee one-of-the purposes of the optimization is the separation of coeluting components, methods devised for automated peak-tracking must be capable of handling complex peak clusters, containing a number of coeluting solutes. During the elution of such a peak cluster a set of mixture spectra is observed

(figure 1.3).

Another way to visualize these spectra is by using a vector representation (figure 1.4). Taking the spectra as objects, the

absorbances observed at subsequent wavelengths are considered as variables and a hyper-space over nw wavelengths is defined containing the observed spectra. Figure 1.4 i l l u s t r a t e s t h i s f o r two components, represented by spectra 1 and 2, examined at three wavelengths, \i t \2

and X3. The pure component spectra are represented by means of the

vectors s_i and s_2 r e s p e c t i v e l y , normalised to u n i t length (normalised to

the norm). I f only one component is present i n a peak, the observed spectra w i l l a l l be located on the basis o f the corresponding pure component vector: the length of the vectors ( i n d i c a t i v e of the concentration) w i l l d i f f e r but the d i r e c t i o n w i l l be the same f o r a l l of them since the r a t i o of the molar a b s o r p t i v i t i e s w i l l remain constant (eq. 1.1). When two components are present i n a peak c l u s t e r , t h i s no longer holds true and the observed mixture spectra w i l l be l i n e a r combinations of the. pure component spectra. Consequently, the vectors representing the mixture spectra w i l l a l l be located i n the plane

Fia. 1.4: A vectorial representation of the pure component spectra 1 and 2, Si and s2 respectively, in a three dimensional space

defined by the wavelengths Xi, Xz and X3. The shaded area

represents the plane containing mixture spectra of components 1 and 2, indicated by '*'.

defined by the corresponding pure component vectors as indicated by the asterixes in figure 1.4. If more than two components are present, similar reasoning requiring hyperplanes of higher dimensionalities is involved. Inversely, the dimensionality of the hyperplane required to hold all mixture spectra is indicative of the number of components with different spectra present in the cluster.

The observed spectra can be analysed further in a number of ways (fig. 1.5): a multicomponent analysis concentrates on the separate mixture spectra, requiring a set of reference spectra. Other methods start by a definition of the hyperplane containing the mixture spectra by means of a principal component analysis (PCA) (20,21). This enables a test on the presence of individual components by means of a so-called target factor analysis (TFA). Furthermore, a number of methods exist which do not require any information on the individual pure component spectra or elution profiles, but determine both by imposing a number of boundary conditions on the derived solution, for instance the iterative target transformation - factor analysis (ITT-FA). The next chapter will describe the above techniques in more detail.

Obviously, the most important of these techniques are those that can be categorized as a form of 'self-modeling curve resolution' (22): without assumptions on the peak shape both spectra and profiles are derived from the mixture spectra. If these techniques can be applied to every peak cluster no other methods are required and the tracking strategy can be solely based on one method. From the available methods, the ITT-FA was selected because an (in principle) unlimited number of components can be resolved in this way. The method was examined extensively to determine its applicability and limitations, as described in chapter 3. Unfortunately, there are some restrictions_to^a,succesfulJ^appUcatlon, especially with respect to the acceptable minimal resolution.

Since the ITT-FA can not be used in every situation, other methods such as the TFA are required to resolve those clusters which have a limited resolution. A systematic combination of these techniques to produce a complete strategy for peak-tracking is described in chapter 4. This procedure is further extended in chapter 5 for cases where components with identical spectra coelute.

mixture spectrum

reference spectra

mixture spectrum multi—component _analysis

elution profiles reference spectrum mixture spectra reference spectrum reference spectrum t r a n s f o r m a t i o n ^ ^ elution profiles not present

mixture spectra iterative

torqet transformation!

elution profiles

pure spectra

Fig. 1.5: An overview of three methods which can be applied for deconvolution of overlapping peak profiles using multiwavelength detection.

Literature

1. Schoenmakers, P.J., Optimization of Chromatographic Selectivity, a guide to method development, Elsevier, Amsterdam, 1986.

2. Berridge, J.C., Techniques for the Automated Optimization of HPLC Separations, John Wiley and Sons, Chichester, 1985.

3. PESOS: Perkin-Elmer Solvent Optimisation System. 4. Berridge, J.C.; Trends Anal. Chem. 1984, 3, 5.

5. Weyland, J.W.; Bruins, C.H.P.; Doornbos, D.A.; J. of Chrom. Science 1984, 2£, 31.

6. Drouen, A.C.J.H., Bill iet, H.A.H., Schoenmakers, P.J. and de Galan, L.; Chromatographia, 1982, 16, 48.

7. Roberts, S.M., Wilkinson, D.H. and Walker, L.R.; Anal. Chem. 1970, 42, 886.

8. Issaq, H.J.; McNitt, K.; J. of Liquid Chrom. 1982, 5, 1771.

9. Otto, M., Wegscheider, W. and Lankmayr, E.; Anal. Chem. 1988, 60, 517.

10. Drouen, A.C.J.H., Bill iet, H.A.H, and de Galan, L.; Anal. Chem. 1984, 56, 971.

11. Jones, D.G.; Anal. Chem. 1985, 5_Z, 1057A.

12. Reid, J.C.; Wong, E.C.; Applied Spectroscopy 1966, 5, 1966. 13. Hill, D.W.; Kelley, T.R.; Langner, J.; Anal. Chem. 1987, 59, 350. 14. Fell, A.F.; Clark, B.J.; Scott, H.P.; J. of Chrom. 1984, 316, 423. 15. Otto, M.; Bandemer, H.; Anal. Chim. Acta 1986, 191. 193.

16. Debets, H.J.G.; The automatic optimization of reversed-phase HPLC-separations; Mobile phase composition; thesis 1986, 128.

17. Drouen, A.C.J.H., Billiet, H.A.H. and de Galan, L.; Anal. Chem.

1985^57^962^-1985-18. Skoropinski, D.B.; Callis, J.B.; Danielson, J.D.S.; Christian, G.D.; Anal. Chem. 1986, 58» 2831.

19. Demorest, D.M., Fetzer, J.C., Lurie, I.S., Carr, S.M. and Chatson, K.B.; LC-GC 1987, 5, 128.

20. Malinowski, E.R.; Howery, D.G.;.Factor Analysis in Chemistry; Wiley, New York 1980.

21. Meuzelaar, H.L.C.; Isenhour, T.L. Eds.; Modern Analytical Chemistry: Computer Enhanced Analytical Spectroscopy; Plenum Press, New York 1987.

Chapter 2

An Evaluation of Peak-Recognition Techniques

in Liquid Chromatography with Photodiode Array Detection

Abstract

Four methods connected with peak recognition in liquid chromatography by means of photodiode array detection are evaluated with respect to the application in the iterative regression design optimization of the mobile phase. These methods are the multi component analysis, the multi component analysis with a non-negativity constraint, target factor analysis and iterative target transformation analysis. The influence of two important factors is investigated, i.e. the chromatographic resolution and the change in the UV-spectra caused by a variation of the eluent composition. What method should be applied depends on the information already available and the chromatographic conditions encountered.

2.1 Introduction

The optimization of a liquid chromatographic separation can be performed by a systematic variation of the composition of the eluent. When the optimization is performed by an iterative regression design (1,2) with the advantage of a limited number of chromatograms, it is essential that the retention times of all solutes in each chromatogram are known. This can be achieved by separate injection of all solutes, provided they are known and available. However a more efficient method can be developed when corresponding solutes can be recognized directly in consecutive chromatograms of the sample. Such recognition is prerequisite when we are dealing with an unknown sample.

A one dimensional detection system, such as single-wavelength UV- or RI-detection, does not provide enough information to be used in a recognition procedure. The limitations of dual-wavelength detection, i.e. the ratio-method, have been reported (3). An extension towards detection systems with a higher dimensionality, such as the multi-wavelength linear photodiode array detector, is indicated (4,5).

In a previous publication (6) an approach has been described based on visual evaluation and comparison of spectra collected during elution of a mixture using mobile phases with different compositions. As a first step towards further automation of the optimization scheme, we will now attempt to evaluate the observed chromatograms by means of mathematical techniques.

The ensuing problems can be divided into two categories. First, in the case of a complete separation, we have a direct comparison of spectra of puce components, _either_mutual-l-y-or-with-reference-spectra.-Contrar-y-to library searches with reduced (coded) IR- or mass-spectra, a more extensive comparison between the spectra is needed due to a lack of specificity of UV-spectra. Since we are dealing with libraries of limited size, the time required for the comparisons is not an important factor. Previously, direct correlation has been used to compare UV-spectra. Wegener et.al. (7) have used several statistical techniques and direct correlation for the identification of cosmetic dyes. Fell (8)

proposed the use of higher order derivatives to emphasize small differences between the spectra.

Second, when optimizing a chromatographic system, complete separation of all components is unlikely in the first chromatograms recorded. Hence, poorly resolved components must be recognized either by matching mixed spectra with those from a library, or by extracting pure component spectra from the measured mixture spectra. When the peaks of the chromatogram under consideration are represented by sets of spectra one can perform an analysis of variance, thus avoiding strict assumptions on peak-shape. Again two situations arise: either all contributing solutes (in a peak or in the sample) and their spectra are known or for one or more components no spectrum is available in the set of reference spectra. In the latter case there is a possibility that the unknown spectra can be derived form another chromatogram of the same sample, or one can use one of the deconvolution techniques currently available (9,14,15).

Here we are concerned with the performance of certain well known techniques, such as multi-component analysis (10,11) and target factor analysis (12,13), both utilizing spectra from a library, and the iterative target transformation analysis (14), which can be used when no preliminary information is available. Special emphasis is given to the two major problems encountered, i.e. the influence of the chromatographic resolution and the change in the spectral characteristics of the solutes due to a change in the mobile phase composition.

A separate problem is the determination of the actual number of components involved in each peak cluster. The answer to this question is usually derived by performing an analysis of variance i.e. principal component analysis (PCA) or factor analysis (FA) coupled with a discrimination criterion (12). The best results in this respect are achieved by using the technique of cross-validation (16). A residual error function is generally adequate when the experimental error is well known and normally distributed.

2.2 Theory

In this section we will briefly discuss some well known mathematical and statistical techniques with special emphasis on the problems mentioned in the introduction.

2.2.1 Direct Comparison of UV-spectra

When we want to recognize more or less completely separated component peaks in different chromatograms the problem is reduced to a direct comparison of UV-spectra. Since the recorded spectra are in digital form and show little fine structure a comparison of all corresponding absorbances expressed in a correlation coefficient will yield the best results (17,18). For systems with a relatively small number of components the required calculation time is of less importance. The correlation-coefficient p can be expressed as follows:

(Zx.y. - 2x.2y./n)

— L 1 (2.1)

J m^V-^VM . (Z^J'-Gy^Vn)'

where xi and yi represent the absorbances of the spectra x and y

measured at wavelength i. Introduction of the denominator into equation (2.1) normalizes the spectra in such a way, that the sum of squared absorbances for each spectrum equals 1. The correlation coefficient thus compares spectra for their shape, but not for their magnitude. Other statistical tests employed (7) are closely related to the correlation coefficient. For instance the sum of squares, SS, of the differences between two normalized and averaged spectra can be expressed as:

The following sections are concerned with chromatographic peaks observed for two or more poorly resolved components, thus requiring a more extensive pretreatment of the data, known as spectral deconvolution.

2.2.2 Hulticomponent Analysis (MCA)

When we have a spectral description of all possible components contributing to the observed spectra, the application of a multi-component analysis is straightforward. After a general description with regard to spectral analysis by Blackburn (10), it was extensively used for different applications in the last decades (11). Using a matrix notation the general problem can be described by:

[S] . [ C ]T = [D] (2.3)

where [S] is a (nw x nr) matrix with nr columns of reference spectra defined for nw wavelengths and [D] is a (nw x ns) matrix with ns columns representing mixture spectra recorded during the elution of a chromatographic peak. These two matrices are coupled through the

(ns x nr) matrix [C] containing the contributions of the individual reference spectra needed for a reproduction of the measured spectra after summation. In an ideal situation the nr columns of matrix [C] will either contain zeroes, indicating the absence of a component, or follow a more or less Gaussian elution profile, since the measured spectra are ordered with respect to time.

MCA is straightforward when the number and nature of the reference spectra agree with the actual components present in the elution profile. In the more realistic situation that the number of candidate reference spectra exceeds the number of components, we ask from MCA that it uses (and hence selects) out of that larger number only those solutes actually present in the profile.

The least squares solution for equation 3 can be expressed as the pseudo-inverse:

[ C ]T = ([S]T.[S])_ 1. [ S ]T. [D] (2.4)

Various alternatives to determine matrix [C], based on different transformations of the data, have been proposed (20).

Experimental conditions can introduce deviations in the measured spectra, which will produce errors in the estimated contributions of all library spectra used. In general, random errors will be small and will influence the calculated concentrations of all components more or less equally. Systematic errors such as a shift will tend to influence only the estimated concentrations of certain components, thus suggesting the presence or partial absence of certain components.

Burns (19) improved the accuracy of MCA by imposing a certain peak-shape, something we prefer to avoid. He also applied an algorithm of Hanson and Lawson (20) to prevent the occurence of negative concentrations. Since these negative concentrations are often introduced in connection with erroneous positive amounts of other components, aplication of this nonnegative least squares solution will improve the overall results.

2.2.3 Target Factor Analysis (TFA)

Because MCA_consjders_every-itiixture spectrum-recorded-during-e-Tut-ion-in turn, all pure component spectra must be available collectively. In contrast, we may test for the presence of individual components sequentially by an evalution of the variation in subsequent mixture spectra. This technique, an application of factor analysis, is described by Malinowski (among others), both in general (12) and for HPLC-UV (13).

Again, we use the general description (eq. 2.3) as derived by the application of the linearity principles of the Lambert-Beer law. By eliminating those components not present in the set of spectra under consideration we reduce the matrices to [S'], a (nw x nc)-matrix consisting of the spectra of the nc components actually present, and [ C ] , a (ns x nc)-matrix containing the elution profiles of those nc components:

[D] = [S'] . [ C ' ]T (2.5)

In this way we can describe all observations (the absorptions of matrix [D]) with only a limited number of elements (the spectra and elution profiles in the matrices [S'] and [ C ] ) .

When we regard the spectra as ris points in a nw-dimensional space, with the absorptions observed at different wavelengths represented on the respective axes, only a limited part of the total space can be occupied by spectra resulting from mixtures of a limited number of components, due to the relations between the observed absorbances at different wavelengths for the same component. When only one component is present all points are situated on a straight line through the origin, since only the concentration varies, but not the relative absorptions. Similarly two components will define a two-dimensional surface and nc components a nc-dimensional hyperspace.

Through mathematical techniques (principal component analysis, factor analysis) we can derive a description of the nw-dimensional hyperspace connected with a set of observations. This abstract description has the same structure as equation 5 (and is therefore a form of data-reduction) and can be transformed to the true component spectra or elution profiles:

[R] is a (nc x nw)-matrix, giving a general description of all spectra present in the mixture: every spectrum of the original set can be derived from a linear combination of the rows of [R]. This holds also true for the pure component spectra, hence an appropriate transformation of [R] through the (nc x nc)-matrix [T] will result in the calculation of [S']. The same applies for the (ns x nc)-matrix [V] containing the abstract description of the elution profiles (as columns).

The actual target test determines whether a given pure component spectrum can be expected to be situated in the hyperspace described by [R]. This can be achieved by projecting a known spectrum onto the hyperspace and comparing the projection and the original spectrum. If they resemble each other closely enough the component is thought to be present. From a chromatographers point of view, the problem is that all components must be identified before the corresponding elution-profiles can be found from the inverse transformation [T]"1, since the

calculation of every row of [T]"1 depends on all columns of T. The

individual calculation of these columns t is performed by:

i = ([R]T.[R])"1.[R]T. s (2.7)

where s represents a spectrum from the collection of reference spectra. Mark the similarity between equations 4 and 7, indicating that MCA is nothing but a projection of the unknown spectrum in the hyperspace defined by the reference spectra.

2.2.4 Iterative Target Transformation (ITT)

The methods described thus far have as major limitation that all pure component spectra connected with a chromatographic peak should be available before the individual elution-profiles can be determined. More often than not the chromatographer is only partly aware of what is present in a mixture. By using the general description of equation (2.6) and imposing a number of boundary conditions (non-negative concentrations and individual absorptions) one can approximate the

original spectra by means of an extrapolation of the observed variation, either in the abstract description of the spectra or the elution-profiles. Applications of this socalled self modelling curve resolution have been described for two and three component profiles (15).

Recently, a more general approach for the HPLC-UV combination was described by Vandeginste et al. (14), the socalled iterative target transformation - factor analysis. The method is applicable to clusters of more than three components and does not require any spectral knowledge with regard to the pure component spectra. The only assumptions made are connected with the shape of the elution-profile: it should be non-negative at all times and exhibit an unimodal distribution (only one maximum).

The method may be briefly described as follows. After a rotation of the abstract description of the elution-profile (Varimax) a first approximation of the contributing solute-profiles is derived. This approximation determines the first target to use in a target test, equivalent to equation (2.7) but using the matrix [V] instead of [R]:

t = ([V]T.[V])"1.[V]T. £ l (2.8a)

c{= [V] . t (2.8b)

Where Ci represents the first target and c{ its projection. The resulting projection is refined according to the demands formulated above and again subjected to a target test. This process is repeated until no further refinement is possible or no further iteration is observed. In this way the elution-profiles of all components present in the peak are determined. Having thus found [C] and [T] , we can use the inverse transformation (eq. 2.6) to determine the corresponding pure component spectra.

2.3 Experimental

2.3.1 Instrumentation

The chromatographic experiments were performed using a NOVAPAK C18 column (15 cm, 5 /im particles) and a M6000A pump, both from Milipore Waters (Milford MA, USA). The detector was the HP-1040A fast scanning LDA detector (Hewlett-Packard, Waldbronn, Germany) connected to an HP-85 desktop computer, equipped with input/output, plotter/printer, mass storage and advance programming ROMs, 16 kByte additional memory, HP-IB IEEE-488 interface and RS-232C serial interface. The data were temporarily stored on 5 1/4 inch flexible disks using a HP82910M disk-drive.

The collection of recorded spectra were transfered from the HP-85 to a PDP11/03 system (Datacare, Zeist, The Netherlands) by means of the serial interfaces on both computers. All calculations were performed on the PDP11/03, which was equipped with two 8 inch disk-drives, a RD51 hard disk unit, 4006-1 Computer Display Terminal (Tektronix Inc., Oregon, USA) and HP7470A graphics plotter with serial interface.

2.3.2 Chromatographic Data

For the calculations to be described in the next section we used spectra and chromatograms obtained for eight chlorinated phenols. The identities, applied concentrations and some retention times are listed in Table 2.1. Throughout the following discussion the components will be refered to by their_number_Jn_this-table.~With-the-basic optimization method in mind, we collected spectra in seven mobile phases of approximately isoelutropic composition, by separately injecting all components and storing the recorded spectra on the upslope, apex and downslope of the detected peaks. Although the spectra were recorded between 190 and 400 nm, only the interval between 230 and 400 nm was used, due to excessive noise at lower wavelengths caused by the absorption of the mobile phase. The spectra in a 35% ACN/65% H20-mixture

Table 2.1: The identities of the chlorinated phenols. Listed are the concentration C used in the experiments and the retention times observed in acetonitrile-water (35:65) (tr^) and tetrahydrofuran-water (35:65) (tr2). The water was acidified

with phosphoric acid (0.001 H).

no. 1 2 3 4 5 6 7 8 Component p-chloor-o-cresol 2,5-dichloor-phenol p-chloor-m-cresol 2,3-dichloor-phenol 3,5-dichloor-phenol 2,4-dichloor-5-me-pheno1 p-chloor-phenol o-chloor-phenol C mg/ml 0.49 0.25 0.25 0.25 0.50 0.50 0.26 0.25 t r i min 5.87 5.84 4.92 5.21 7.96 9.35 3.50 3.10 t r2 mm 7.70 9.46 6.48 6.48 13.33 11.40 5.32 4.33 230 Xlnm) W>0 230 Mnm) W0

Fia. 2.1: The UV spectra of eight chlorinated phenols, listed in table 2.1. The components were dissolved in acetonitrile-water

are presented in figure 2.1.

In addition, mixture spectra were recorded during the elution of chromatograms of varying resolution of components 5 and 6. The corresponding mobile phase compositions are listed in table 2.II. The elution profiles recorded at 230 nm are displayed in figure 2.2. For a mathematical treatment of the data we selected 45 evenly spaced mixture spectra across every profile.

2.3.3 Software

The software used in the analysis of the spectrum-clusters and for the comparison of spectra was written in Fortran IV. The applied algorithm for the multicomponent analysis was directly derived from the pseudo-inverse (eq. 2.3). The algorithm for the non-negative version of the HCA is described by Lawson and Hanson (20). The software for the application of the target test was developed using the description by Howery and Malinowsky (12) and was extended to the iterative target test according to Vandeginste et.al. (14).

As far as internal memory allowed, the matrix-calculations were used from the Scientific Subroutine Package from DEC (Marlboro, Massachusetts, USA) as was the Varimax subroutine. In all other cases the calculations were performed by simple algorithms, if necessary with intermediate storage on disk. The eigenvalues and eigenvectors of the covariance-matrix of the data-matrix were determined by the HQRII algorithm (21).

All calculated elution profiles were expressed as quantities of pure component spectra, normalized such that the sum of all squared absorptions of a pure component spectrum equals 1. This means that the vectors connected with these pure component spectra have unit length. In the case of the iterative target transformation we transformed the calculated spectra and elution profiles in such a way, that they complied to this condition as well.

7afe7e 2.II: The mixing ratios $ and corresponding mobile phase compositions, used to elute the mixture of components 5 and 6 and record the spectra of all chlorinated phenols listed

in table 1. The water was acidified with phosphoric acid (0.001 H).

0

Eia.

2.4 Results and Discussion

In order to evaluate the above techniques with respect to spectral recognition and determination of retention-times, there are three major influences to be considered: first, the dependence of the spectral characteristics on the mobile phase composition; second, the amount of chromatographic resolution; and third, the spectral similarity of the components involved (spectral resolution). The first two factors can be studied and varied systematically. The spectral similarity is inherent in the group of components under examination (fig. 2.1). Except for solute number 8, the correlation coefficient between pure component spectra varies from 0.85 to 0.998. The influence of chromatographic resolution was investigated for the two-component system containing the chlorinated phenols 5 and 6 (table 2.II, figure 2.2), which cross-over when going from a 35% ACN binary to a 35% THF binary. Unavoidably, the variation in chromatographic resolution thus achieved is accompanied by a variation in spectral characteristics as a result of the changing mobile phase.

To avoid differences in injection volumes, sampling times and chromatographic reproducibility, reference elution profiles for components 5 and 6 were not derived from separate injections of the solutes. Instead, we used the theoretically most reliable profiles, to be found from spectral deconvolution: the profiles resulting after a multicomponent analysis using only the spectra of components 5 and 6 recorded in the same mobile phase used to elute the mixture. An example is presented in figure 2.3. Consecutive elution profiles resulting from the application of the different spectral deconvolutions were compared with the reference profiles in the following way: the sum of squared differences was calculated after normaljizing_both_profiles--to-the norm of the reference profile. In this way not only the shape but also the observed deviations in the amount of absorbance was involved in the evaluation.

Fid. 2.3: The recorded chromatogram, T, of a mixture of components 5 and 6, and the individual component profiles calculated by means of MCA, using only the correct pure component spectra of 5 and 6. Mobile phase: acetonitrile-tetrahydrofuran-water

(17.5:17.5:65) (</> = 0.5).

2.4.1 The Influence of the Mobile Phase Composition

First, we investigated the performance of a multicomponent analysis using an extended set of pure component spectra, a situation which would occur when we know which components are present in the mixture, but when we do not know where they are situated in the chromatogram. This method, however, is very susceptible to experimental and systematic errors, especially in the case of large sets of reference spectra.

Fairly good results are obtained when we perform the MCA with the reference spectra of all chlorinated phenols, recorded in the same mobile phase used to elute the mixture. The results for the mixture containing 17% ACN/ 18% THF (0 = 0.5) are displayed in fig. 2.4A. As we can see, there is only a minor disturbance from components not present in the mixture, caused by experimental errors in the measured spectra and mathematical round-off. Attention is drawn to the reverse profiles of components 1 and 3: the spectra are so much alike that a combination of a positive and negative contribution is used to describe the observed experimental error.

f/o. 2.4: The true profiles (dashed Tines) of component 5 and 6 as determined for 0 = 0.5 and the, individual component profiles

(straight lines) calculated by means of MCA, using the spectra of all eight chlorophenols. (A) Profiles calculated using the correct spectra, recorded in the same solvent used to elute the mixture. (B) profiles calculated using approximate spectra, recorded in a different solvent (<f> = 0).

0.6 5 '/ \ 1/ \ X Intn) 400 230 Xlnml

0.05-Fip. 2.5: The pure component spectra of components 5 and 6, recorded in acetom'tril e-water (35:65) (dashed line) and in tetrahydro-furan-water (35:65) (solid line), respectively, as well as the difference spectra.

A systematic error can be introduced by a difference in composition between the mobile phase used to elute the mixture, and the solvent used for the determination of the pure component spectra. Fig. 2.5 shows the difference between the spectra of components 5 and 6 in a 35% ACN/ 65% H20 and a 35% THF/ 65% H20 mixture, respectively. A small shift of

1 to 2 nm can be observed.

Because of this influence, quite a different picture emerges when we perform the same calculations on the profile recorded for <p = 0.5 with

the spectra recorded in 35% THF (0 = 0.0) (fig. 2.4B). The small shift in the spectra causes large errors in the estimated concentrations, both positive and negative, because the procedure tries to eliminate the differences between measured spectra and linear combinations of reference spectra with additional contributions of the other components. As a consequence we can no longer determine which or even how many components are present in this cluster.

Some improvement can be obtained with the non negative MCA, as is shown in fig. 2.6A. Again we used the reference spectra in 35% THF but by eliminating the negative contributions of component 3, the compensating contributions of component 1 are automatically reduced. Still the

results are far from satisfactory. Component 6 is correctly identified, but component 5 is at best uncertain and there seem to be more than two components present. Fig. 2.6B demonstrates an even more dramatic example for the same solutes at lower resolution. Here, component 5 has completely disappeared and has been replaced by a combination of the components 4 and 7. Apparently, multicomponent analysis only performs well when the exact spectra in the mobile phase used are available.

t

t

Fia. 2.6: The true profiles (dashed lines) of components 5 and 6 and the individual component profiles (solid lines) calculated by means of MCA and applying a non-negativity criterion, using

approximate spectra of all eight chlorophenols recorded at

0 = 0 . The elution profiles were recorded at (A) $ = 0.5 and

(B) * = O.6.

*6 5 \

Far better results are observed when we perform a preselection of appropriate spectra (components) by means of a target test. As was described in the theoretical section, we project our targets on the description derived from the mixture spectra. As the first step we conclude from a principal component analysis, that there are two components present in this cluster, hence we reduce our abstract description to two vectors: every observed spectrum can be reconstructed as a linear combination of these two vectors. Similarly, the true solute spectra can also be reconstructed as a linear combination of the two vectors. After performing a target test with all eight reference spectra from our reference file the two most likely candidates are determined. The corresponding transformation matrix is inverted and used to determine the corresponding elution profiles. As an example fig. 2.7 displays the elution-profiles derived from profile recorded for <f> = 0.5,

after a target test with the spectra of all eight components in 35% THF and selecting 5 and 6 as the true components, since these components display the highest correlation when used as targets.

Fig. 2.7: The true profiles (dashed lines) of components 5 and 6 and the individual component profiles (solid lines) calculated by means of TFA, after selecting approximate spectra of components 5 and 6 recorded at $ = 0.

Obviously target factor analysis provides a much better estimate of the true elution profiles than MCA or nonnegative MCA. The main reason is that the disturbances caused by the other components in the reference file are removed beforehand. In principle we can perform a MCA with the selected targets, but, as is shown by eq. 2.6, when we have determined the necessary transformations for the spectra we might as well determine the corresponding elution-profiles by means of the inverse transformation. In fact we are investigating all measured spectra in one calculation, thus compensating partly for the time required for the principal component analysis.

As before, the remaining difference in fig. 2.7 between the estimated and the true elution profiles is due to mobile phase effects on the solute spectra. When these deviations are expressed as the sum of squared absorbance differences (SS), their value increases with increasing difference in mobile phase composition used for recording the reference spectra and the sample spectra, respectively. This is illustrated in fig. 2.8, where the curves refer to the observed deviations in the profiles of components 5 and 6 for $ = 0.5, presented

o.i

0.05

ss

o

0 0.2 0.4 0.6 0.8 1

Fia. 2.8: The observed difference between true profiles and profiles calculated by means of TFA of components 5 and 6 at <f> = 0.5, when using reference spectra recorded in various solvents, indicated by the mixung ratio 4>(ref). The difference is expressed as the sum of squared differences, SS, between true and calculated profile.

in fig. 2.7, after target factor analysis was performed with reference spectra recorded in different solvents {</> ranging from 0.0 to 1.0). It

is important to note, however, that for this set o f components TFA invariably selects the correct solutes 5 and 6 from the total set of eight chlorinated phenols tested. Consequently, although elution profiles and, hence, quantitative analysis is hampered by a poor knowledge of the exact spectra, the correct identification is not. Obviously, for the present purpose of optimization, the latter observation is extremely important.

When investigating the iterative target transformation we are dealing with the reversed approach. Now we start with the determination of the elution profiles and use these to derive the pure component spectra. Again two points are important with regard to peak recognition for chromatographic optimization: first, the identity of the component as indicated by its spectral characteristics; and second, the corresponding retention time, or more general the quality of the elution profile.

0.95 4 0.9 -^ ■ • • t -0.86 I 4-— i 1 1 1 1 r 4-— 4-— i 4-— 02 0A 0.6 0.8 »rtf —

Fig. 2.9: The correlation coefficient p between a spectrum obtained by ITT from the elution profile recorded at $ = 0.7 (R =0.4), and reference spectra of six chlorinated phenols recorded in various solvents indicated by Href). Displayed are the correlation coefficients resulting from comparisons with spectra of the components 1 (d), 2 (O), 3 (0), 4 (A), 5 (9) and 6 CyJ. Component 5 is selected as the most probable solute in all cases.

Because of the nature of the technique, the simultaneous contemplation of a collection of mixture spectra, these two characteristics are closely related: when the calculated elution profile deviates from the true profile the calculated component spectrum will be in error as well.

When the components are reasonably well separated and consequently the elution profiles are fairly well defined, the major differences between the calculated spectra and the corresponding spectra in the reference set are mostly caused by the difference in the respective mobile phase compositions. As was to be expected from fig. 2.5, this deviation is not dramatic. This is further illustrated in fig. 2.9, which shows correlation coefficients between the calculated spectrum of component 5 for 0 = 0.714 (R = 0.41) after application of ITT, and reference spectra of 6 solutes recorded in various mobile phases defined by the mixing ratio </>. The performance in the total recognition procedure will be

mainly determined by the spectral similarities between the components in the reference set. In this example the component 5 is always identified correctly, independent of the mobile phase used to record the reference spectra; the same result was found for the other component in the cluster, i.e. component 6.

2.4.2 The Influence of the Chromatographic Resolution

The second major influence on the performance of the spectral deconvolution techniques is the extent of chromatographic separation between the components. Because of the asymmetric peakshape of the chlorinated phenols we express the chromatographic resolution by means of the first and second moments of the reference profiles instead of retention times and.peak widths:

R = |M16 - M1 5| / 2.(yM25 + / M2 6) (2.9)

where Mi5 and Mi6 are the first (central) moments of components 5 and 6,

and M2 5 and M2 6 are the second moments of these components,

It follows from theoretical considerations that the performance of MCA and MCAO is independent of the chromatographic resolution. Since every measured spectrum is evaluated apart from the others, there is an independent determination of the concentrations in every mixture spectrum. It is for this reason that only MCA can be applied to unresolved solutes (as in UV-spectrometry), although it only performs well when the reference spectra correspond exactly in number and in nature with those of the components in the mixture.

In contrast, such an exact match is not needed for TFA and ITT, but conversely some chromatographic resolution is essential and results become better with increasing resolution. Indeed, when two solutes approach each other more closely in the chromatogram, the mixture spectra recorded across the elution profile display less variations, thus increasing the difficulties in the determination of the correct number of components. In the preliminary principal component analysis the first component is emphasized and the second one diminishes and becomes more subject to experimental error. Because the second principal component discriminates between the spectra of different components, these errors can cause distortions in the calculated elution profiles even when the solutes are correctly identified in TFA. In ITT the distorted profiles produce equally distorted spectra making solute recognition much more difficult.

In order to seperate the influence of the mobile phase composition from the influence of the resolution on the results of TFA, different degrees of chromatographic resolution were simulated by summing the individual profiles of the components 5 and 6 with varying relative positions. A target test was performed with reference spectra recorded in different mobile phases. The resulting deviations in the calculated elution profiles are shown as the sum of squared differences in fig. 2.10. When the reference spectra agree exactly with those in the solvent used in eluting the mixture, which is the case at <t> = 1, the elution profiles

are reconstructed with remarkable precision down to a resolution as low as 0.006 (the smallest value tested). When the reference spectra do not match exactly, the reconstructed profiles deviate as shown by the larger values of SS at high resolution. Also, the deviations increase somewhat more at very low resolution (R < 0.1).

SS

Fio. 2.10: The observed difference between true profiles and profiles calculated by means of TFA of component 5, resulting after simulation of an elution profileof a mixture of components 5 and 6 at <f> = 1. The profiles display a variation in chromatographic resolution R. The difference is expressed as the sum of squared differences, SS, between true and calculated profile. The reference spectra of component 5 and 6 were recorded in solvents corresponding to </> = 1 (T3), <j> = 0.6 (()), <t> = 0.3 (•;, and <f> = 0 (^).

Fia. 2.11: The observed difference between true profiles and profiles calculated by means of ITT of components 5 (\J) and 6 (%). The investigated profiles display a variation in chromatographic resolution R. The difference is expressed as the sum of squared differences, SS, between true and calculated profile.

A

B

12: The results of the ITT performed on a profile of components 5 and 6, showing severe overlap (R = 0.1). The mixture was eluted at <t> = 0.6. (A) The true (dashed lines)

and calculated (solid lines) elution profiles. (B) The true (dashed line) and calculated (solid line) spectrum corresponding to component 5. (C) As B for component 6.

It might be argued that these distortions are not important for qualitative investigations (e.g. the optimization strategy) as long as the components are identified correctly and the retention times do not deviate too much. When two (or more) components overlap severely they have almost identical retention times, hence the application in the optimization strategy should pose no problem. The major problem in cases of extreme overlap remains the correct determination of the number of components by principal component analysis.

When iterative target transformation is applied, the correct calculation of the elution profiles is much more important because of the earlier mentioned connection between calculated profiles and the derived spectra. Unfortunately ITT is more sensitive to the degree of overlap than TFA. In comparison to fig. 2.10, the SS values in fig. 2.11 are higher and rapidly increase further when the resolution decreases below 0.2. As an example fig. 2.12A shows the reconstructed profiles in

F/o. 2.13: The correlation coefficient p, resulting from a comparison of a spectrum, calculated by means of ITT from the profile recorded at 0 = 0.6 (R = 0.1), and reference spectra of six chlorinated phenols recorded in various solvents indicated by <p(ref). Displayed are the correlation coefficients resulting from comparisons with spectra of components 1 (\3)> 2 (O), 3 (§)> 4 (A), 5. (+) and 6 (\J). Instead of component 5, which was actually present, component 2 is selected as the most probable solute in all cases.

the case of a severe degree of overlap (R = 0.09). Not only is the shape of the profiles distorted (evidenced by the absence of one peak-tail), there is also a shift in the location of the maxima. As expected, the distortions in the profiles lead to deviating spectra (fig. 2.12B and 2.12C). As a result, fig. 2.13 shows that a correct identification of component 5 is no longer possible, since component 2 shows a greater similarity with the calculated spectrum, independent of the solvent used to record the reference spectra.

2.5 Conclusions

From the analysis of various mathematical techniques for the deconvolution of a two component elution profile the following conclusions can be drawn.

Although the application of a multicomponent analysis is independent of the chromatographic resolution, it has some major disadvantages when used with larger reference sets. It is highly sensitive to a difference between the actual spectra and the reference spectra caused by a change in the mobile phase composition. This leads to large deviations of the estimated profiles and more serious, impairs the correct identification of the two solutes present in the profile. Although we observed some improvements when applying a non-negativity criterium, the results are still inadequate for an unambiguous recognition. Finally, MCA can only be applied when the set of reference spectra includes at least those of the components actually present in the peakcluster.

In the case of target factor analysis the influence of the change in the spectral characteristics is much less pronounced, mainly because the preliminary principal component analysis limits the reconstruction to the number of components actually present, even though their identity remains to be ascertained. Furthermore we can test for the presence of a component without knowing the spectra of the other components involved. Because we do need all spectra for a reconstruction of the elution profiles, however, this is only a minor advantage with respect to the chromatographic optimization strategy, which needs retention times as

well as identities. As the examples have indicated the method becomes somewhat less accurate in cases of extreme overlap, although within the investigated group of eight chlorophenols positive recognition is still possible down to R = 0.006. Consequently retention times can be determined with high accuracy, which is important for optimization purposes. The ultimate value of TFA will rely on the ability of PCA to determine the number of components correctly.

Obviously, the main advantage of iterative target testing is the potential to determine elution profiles and spectra without any previous knowledge. When the solutes are reasonably well separated the influence of the mobile phase composition is again minor. The major limitation of the method is connected with the sensitivity to the required resolution. When resolution drops below a minimum value, dependent on the spectral characteristics of the components involved, the method still yields approximate elution profiles, but the derived spectra are too inaccurate for reliable solute recognition.

A summary of the above observations: if there is adequate resolution we can apply iterative target testing, which requires the least knowledge of the sample. When this fails, and unfortunately this is not always apparent, we have to use previously collected pure component spectra, e.g. from another chromatogram with more resolution. The method of choice is then TFA, where distortions caused by minor differences in the spectra can usually be ignored. When there is hardly any resolution (i.e. when we cannot determine the correct number of components) the only possibility is the application of a multicomponent analysis, preferably with boundary conditions (nonnegativity criterion). The results, however, cannot be trusted if there is a large difference between the reference and_the_exp_erjmental—spectra as a result of the mobile phase effects.