Methods to improve quantitative and qualitative analysis of spectroscopic measurements. academisch proefschrift

Transcription

1 Methods to improve quantitative and qualitative analysis of spectroscopic measurements academisch proefschrift ter verkrijging van de graad van doctor aan de Universiteit van Amsterdam op gezag van de Rector Magnificus, prof. mr. P.F. van der Heijden ten overstaan van een door het college voor promoties ingestelde commissie, in het openbaar te verdedigen in de Aula der Universiteit op vrijdag 29 april 25, te 1: uur door Hans Ferdinand Michaël Boelens geboren te Olst

2 Promotiecommissie: Promotor: Overige leden: prof. dr. A.K. Smilde prof. Dr. C. Gooijer prof. Dr. Th. Hankemeier prof. Dr. ir. J.G.M. Janssen Dr. P.H.C. Eilers Dr. W.Th. Kok Dr. G. Rothenberg Faculteit der Natuurwetenschappen, Wiskunde en Informatica 2

3 Contents Introduction 9 Data Processing and the Analytical Method Spectroscopic Data Processing Contents of the Thesis Fast on-line Analysis of Process Alkane Gas Mixtures by NIR Spectroscopy Abstract Introduction Theory Calibration Procedure Figures of Merit Experimental Apparatus and Procedures Experimental Design Data Processing Results and Discussion Exploratory Analysis Calibration Model Determination of the Critical Level Analysis Time vs. Critical Level Conclusions Performance Optimization of Spectroscopic Process Analyzers Abstract Introduction Theory The nas Vector The nas View on Multivariate Calibration Description of Spectral Disturbances

4 2.3.4 Signal-to-Noise Ratio of nas Experimental Results and Discussion Outline Spectra and Unwanted Spectral Variation Option A, Including Unwanted Variation as Interferents Option B, pre-processing of Spectra Comparison with pls Models Conclusions Tracking Chemical Kinetics in High-Throughput Systems Abstract Introduction Theory Concept and Assumptions Single- and Multiple Sampling of First-order Reactions A General Sampling Strategy for High-Throughput Experimentation Experimental Results and Discussion An Experimental Example Multiple Sampling in High-Throughput Systems Conclusion New Method for Background Correction in Hyphenated Chromatography Abstract Introduction Theory Notation Used The ebs Method Asymmetric Least Squares Requirements of the Method Comparing the Estimated and the true Analyte Spectra Reference Method Experimental lc-raman lc-dad Simulations Results and Discussion Simulations

5 4.5.2 Application 1: Extracting Analyte Spectrum in lc-raman Application 2: Background Correction in lc-dad Conclusions Tools to detect differences between complex spectral data sets Abstract Introduction Theory Basic Approach Signal Model Ordinary Least Squares (ols) Asymmetric Least Squares (als) Determination of the φ-value in als Overview of the als and the ols Procedure Experimental Chemicals Chromatographic Set-up Acquisition and Initial Processing of the Spectral Data Simulations Results and Discussion Comparison of ols and als for synthetic spectra SEC-IR of a two-polymer mixture SEC-IR of a more complicated polymer mixtures Conclusions A Derivation of the Optimal Design Criterion 115 A.1 The Best Point in Time to Perform a Measurement A.2 Evaluation of Specific Sampling Strategies in Time B Asymmetrical Least Squares Properties 118 B.1 The als Goal Function is convex for each Value of φ B.2 The als Algorithm Summary 122 Samenvatting 129 Acknowledgements 134 CV and Publication List 136 References 141 5

6 List of Figures 1 Components of an analytical method Total experimental design Measured absorbance spectrum of pseudo-component Normalized absorbance plot of the alkanes present in the calibration design mixtures Principal component scores plot rmsecv as a function of the number of LV s in the pls model Spectral error Predicted mole fraction of normal alkanes based on offset corrected nir spectra and best pls model The critical level of the mole fraction of normal alkanes versus the analysis time Illustration of nas vector and correspondence between vector space and spectral domain Summary of nas view on a multivariate calibration Situation in the space orthogonal to the interferent space nir absorbance spectrum of P S compounds and blanks nas vector of P S 5, orthogonal projections on various spaces nas vector of P S 5, space I nas vector of P S 5, space I Candidate selection in high throughput approach Common high-throughput experimental set-up Examples of various sampling strategies Some first-order reaction profiles Plot of f 2 for first-order reaction: A B Reaction scheme Estimated values of k for 31 experiments Standard deviation of k

7 3.9 First order reactant concentration and f 2 curve Comparison of sampling strategies Results of simulation 1: Analyte and background species Elution profile simulation Result of simulation 2: Analyte and two eluent species, changing eluent composition Results of simulation 3: Three co-eluting analytes and two eluent species Results of simulation 4: Spectral baseline and noise added Comparison between reconstructed and true analyte spectra Raman spectrum of solvent (eluent) UV-detector signal of AMP Results for ref method Estimated analyte spectra during elution ref method and ebs method Comparison correlation coefficient between true and estimated AMP spectrum, comparison mse Chromatograms blank and sample runs (total spectral intensity) Comparison UV-spectra of polystyrene Corrected chromatograms Explanation of the concept of the orthogonal vector for ols method Comparison ols and als two component situation Comparison ols and als, three component situation Retrieval of PMMA from PMMA/PC mixture Dependency of the median reconstructed data (Med a ) on the φ sec-ir elution profiles of PMMA Retrieving the PMMA from PMMA/PBMA mixtures Retrieving the spectra of PMMA from a synthetic PC/PMMA/PBMA mixture B.1 Flow scheme of als the algorithm

8 List of Tables 1.1 Composition of pseudo-components Wavenumber ranges used for building pls models Results of error analysis for best pls model Prediction results for test set of the best pls model nas approach and various pls models Gain of (S/N) nas with respect to raw measured spectra Composition of calibration and test set of various pls models Overview of simulations Results simulation 1 ; spectral noise added Results of hplc-dad measurements

9 Introduction This thesis deals with some chemometric methods to improve the quantitative and qualitative analysis of spectroscopic measurements. Mainly applications in vibrational spectroscopy are discussed, but also uv-vis spectroscopy is used. Both fields: vibrational spectroscopy and chemometrics are large. In its rather short history (since 197 s) chemometrics has developed and made available a large number of techniques and procedures to extract information from analytical measurements [1, 2]. One of the application areas in which chemometrics is very successful is the processing of direct spectroscopic measurements on objects or mixtures. Spectroscopic techniques and especially the vibrational spectroscopies, such as ir, mir, raman and nir are generally regarded as attractive tools to perform analyses in all kinds of fields. A method based on analytical spectroscopy is fast, it is non-destructive (important in life sciences), it allows the measurement of samples mostly without much sample pre-processing and as an instrumental technique, spectroscopy is stable and has a high signal-to-noise ratio. From an analytical point of view, the major disadvantage of a spectroscopic measurement is that the whole composition of the sample is reflected in the same measured spectrum. Depending on the spectroscopic technique, some processing of the measured spectra is therefore needed to extract information about the components of interest. Chemometrics contributes to this processing of the spectra by delivering algorithms to find differences between spectra (pattern recognition, classification), to link spectra to concentrations of compounds or to physical or other properties (calibration [3, 4]) and to optimize the effort spent on doing measurements (experimental design). The best example of the success of combining spectroscopy with smart spectral processing is the widespread use of near infrared technology. Without multivariate calibration software it would be 9

10 hard to arrive at a sensible application of nir at all, because of its lack of selectivity. Applications of vibrational spectroscopy and chemometrics are found in various fields. They are found in life sciences [5 12], pharmaceutics [13], process industry [14 18], food and agricultural industry [19]. In process, food and agricultural industry the use of vibrational spectroscopy is mainly quantitative, in life sciences also qualitative use of spectroscopy is made. Data Processing and the Analytical Method Analytical methods are designed to get the best information about the amount of an analyte in a sample. Several properties of an analytical method guide this design. Analytical methods should be selective and they should be sensitive. The ideal analytical method is fully selective when it delivers an analytical signal that depends only on the analyte of interest and not on the other chemical compounds in the sample. The method is highly sensitive when a small concentration change of the analyte causes an large change of the magnitude of the analytical signal. Related figures of merit of the analytical method are the precision and the robustness of the method. The precision of the method is directly related to its sensitivity. When the instrumental noise level stays the same for a method with high sensitivity the precision of the estimated quantity (e.g. concentration) will be better. Also, a method is in general more robust when its selectivity increases. In case an analytical signal that is fully selective for the analyte is found, the analytical method will be very robust. For example, when for all kinds of samples with different matrices an analytical spectroscopic band is not disturbed, a method that uses this band for quantification is considered a robust method. Another important criterion to judge an analytical method is the time needed to do an analysis and the time needed to set-up a calibration. Real world instrumental methods, however, are neither fully selective nor infinitely sensitive and data processing is either needed to get a distinctive analyte signal at all (increase selectivity), or can be helpful to improve the poor quality of the available instrumental analytical signal (increase sensitivity). The border between what is achieved by the instrumental part of the analytical method and what is contributed by data processing is flexible. 1

11 To take an example: in order to reduce analysis time in routine applications in chromatography one could rely more on peak deconvolution and spent less effort on the full optimization of the separation. Sample preprocessing & presentation Instrumental technique Extraction & Processing of analytical signals Figure 1: Components of an analytical method Processing of the raw measured analytical signal, eg. a detector signal in chromatography or a spectroscopic measurement, is therefore considered here to be part of the analytical method itself. Especially the processing of the (vibrational) spectroscopic data in a multivariate setting is an integral and essential part of an analytical method not only an addendum to an existing instrumental method. Spectroscopic Data Processing In the quantitative use of spectroscopy the purpose is to find the composition of a chemical mixture. Strictly speaking, the term quantitative should be reserved here for the case that some knowledge exists about the spectral active compounds in the sample that is analyzed. This knowledge consists of the number of interfering compounds and approximate concentration ranges in which the interferents vary. In such a case it is possible to set up a reliable quantification. It is not necessary, however, to explicitly know the spectra of the interferent compounds. In inverse least squares models the spectral properties of the interferents are modeled implicitly [3]. When nothing is known either explicitly or implicitly about the spectral features of one or more compounds of the mixture, analyte quantification might fail. So, first information about the spectra of unknown compounds should be extracted either explicitly or implicitly and subsequently quantification can be tried again. In the most simple quantitative approach, a channel (wavelength or 11

12 wavenumber) is selected that can be assigned solely to the analyte (full selectivity). The intensity at this wavelength is linked to the amount (the concentration) of that compound. For quantification a univariate calibration problem must be solved. Much is known about univariate calibration [1, 2]. The exact standardization of figures of merit connected to this calibration still receives attention in literature [21, 22] and there are new developments, see e.g. Liao [23]. The spectroscopic technique that is actually used, determines whether or not such selective analytical channels are available. For example in raman spectroscopy, analyte bands are narrow and often selective channels can be found. On the opposite, in near-infrared spectroscopy selective channels can not be found. The broad indistinct spectral shapes that are usually found in nir and the impossibility to find isolated analytical band were initially precisely the reason to discard it as a spectroscopic technique [24].When no selective channels are available, the intensity of each channel is caused by a number of compounds in the sample. A multivariate calibration allows one to extract the information related to one or a number of compounds and link it to various other properties. For these types of quantitative applications, standardization and validation of calibration models are topics. For this reason, techniques and methods that promote the faster development of robust calibration models that can easily be understood and analyzed is an important research subject. One of the advances made the last years in better understanding multivariate calibration is the development of the Net Analyte Signal [25 27]. It not only relates the multivariate calibration situation better to the well understood univariate case [28, 29], but it also offers insight at the spectral level of multivariate calibration. Moreover, it gives the opportunities to faster scan a calibration situation to decide whether it is viable attempt to solve a certain analytical problem, to do wavelength selection [3, 31] or to optimize preprocessing of spectra [32 37]. It may also supply some guidance with respect to the calibrations samples that should be measured. Contents of the Thesis In this thesis methods are discussed to improve the extraction of quantitative and qualitative information from spectra. Chapters 1 to 3 focus on 12

13 several aspects of the quantitative processing of spectra. In Chapters 1 and 2 spectral processing for multivariate calibration is discussed for near infrared spectroscopy. In Chapter 3 a way to compare several sampling strategies to track first order kinetics is presented. Although the presented results are general, they are best suited for on-line spectroscopic measurements. In Chapters 4 and 5 attention is paid to qualitative spectroscopic processing (raman and ir spectroscopy). 13

14 14

15 Chapter 1 Fast on-line Analysis of Process Alkane Gas Mixtures by NIR Spectroscopy. 1.1 Abstract Proper operation of a molecular sieve process for the separation of iso- and cyclo-alkanes from normal alkanes requires the fast on-line detection of normal alkanes breaking through the column. The feasibility of using nearinfrared (nir) spectroscopy for this application was investigated. Alkane mixtures were prepared according to an experimental design. These mixtures, containing small amounts of normal alkanes (C5-C7) and varying amounts of iso- and cyclo-alkanes (seven compounds), were analyzed simultaneously at 16 C using nir spectroscopy and gas chromatography as a reference method. With an analysis time of 9 seconds, a critical level of.4% [mole/mole] of normal alkanes could be achieved. If a faster response is required, the analysis time can be reduced to 4 seconds, at the cost, however, of an increase in the critical level to about 1% [mole/mole]. Published as: Fast on-line Analysis of Process Alkane Gas Mixtures by NIR Spectroscopy, H.F.M. Boelens, W.Th. Kok, O.E. de Noord, A.K. Smilde in: Applied Spectroscopy 54 (2), c 2 Society for Applied Spectroscopy 15

16 1.2 Introduction In the work described in this chapter, the feasibility of near-infrared (nir) spectroscopy and multivariate data processing techniques for fast on-line analysis of alkane gas mixtures was studied. Currently the use of nir spectroscopy in process industry is increasing [38 43]. This trend may be attributed to developments in instrumentation, such as the availability of fiber optics and increased ruggedness and reliability of instruments [44]. Growing experience with multivariate techniques for data processing [3] also promotes the use of nir spectroscopy for quantitative purposes. The purpose of this study was to develop a method to monitor a gasphase process in which normal alkanes are separated from iso- and cycloalkanes. This separation process is based on the selective retention of normal alkanes on a zeolite molecular sieve [45]. When the mixture, containing normal, iso- and cyclo-alkanes with carbon numbers from 5 to 8, is purged through a column containing the molecular sieve, the iso- and cyclo-alkanes are eluted first. When the column becomes saturated and normal alkanes start to break through, the process should be switched to desorb the alkanes by back flushing with a purge gas. Since the efficiency of the separation process strongly depends on the exact timing of switching, an on-line method to monitor the break-through of normal alkanes would be of major value. Since the cycle time of the process is less than one minute, such a method should have an analysis time on the order of seconds. An experimental set-up is described that enables the simultaneous analysis of the alkane vapor mixtures by gas chromatography (gc) and nir spectroscopy. The simultaneous gc measurement prevents errors due to evaporation of the volatile compounds during sample preparation and handling. With this set-up, a number of partial least squares (pls) models are built that enable quantification of the mole fraction of normal alkanes in the vapor mixtures using a measured nir spectrum. Evaluation of the pls models is performed by calculation of some common multivariate figures of merit and by determination of the critical level for the mole fraction of normal alkanes. This critical level is determined using available knowledge about the spectral noise of the nir spectra. The analyzed alkane mixtures contain small amounts of three normal alkanes: pentane, hexane and heptane and a varying background of iso- and cyclo-alkanes that is representative for the 16

17 mole sieve process. 1.3 Theory Calibration Procedure To relate the nir absorbance spectrum of a process sample to the amount of normal alkanes in that sample, a first order calibration model [46] is needed. The quantity of interest is the mole fraction of normal alkanes in the alkane mixture. An inverse least squares model (ils) for the quantification of this mole fraction of normal alkanes is used. In ils the concentrations of the iso- and the cyclo-alkanes in the calibration mixtures need not to be known. This is an advantage when applying the method to the actual process. The only requirement is that the concentrations of all these compounds vary within the set of calibration samples measured. The ils model is made by modeling the (n samples 1) column vector y GC, containing the mole fractions normal alkanes in the n samples calibration mixtures as determined by the gc reference method, using the nir spectra: y GC = R b + e (1.1) In Eq. (1.1) the (n samples n chan ) matrix R contains the measured absorbances at n chan wavenumbers for the n samples calibration mixtures. The (n samples 1) vector e contains the errors and the (n chan 1) vector b is a vector with the regression coefficients. These coefficients are estimated by partial least squares (pls) [3]. Once the vector b is determined, the mole fraction of normal alkanes in unknown alkane mixtures can be estimated by: ŷ NIR = r T un b (1.2) In this equation the (n chan 1) vector r un is the nir spectrum of the unknown mixture to be analyzed, and the scalar ŷ NIR is the predicted mole fraction of normal alkanes in the mixture Figures of Merit Because the break-through of the normal alkanes in the process under consideration is of major interest, the critical level [47] (L C ) for the mole fraction of normal alkanes is taken as performance measure. For a univariate 17

18 calibration this limit would be calculated in the mole fraction domain as: L C = t.95,n 1 s (1.3) In this equation n is the number of measurements on which the standard deviation (s ) of the predicted mole fraction of normal alkanes of a blank mixture (containing no normal alkanes) is based and t.95,n 1 is Student s t- value for a.95 probability and n 1 degrees of freedom. For the multivariate case, no consensus has yet been reached about the most reliable procedure to calculate this critical level [48]. The exact way in which the critical level is determined here will be explained. Other used performance measures are the root mean square error of prediction (rmsep) of the mole fraction of normal alkanes calculated by using the test set and the rmsecv by leave-one-out cross-validation using the set of calibration samples: rmsep = 1 M (ŷ NIR,i y GC,i ) M 2 (1.4) i=1 rmsecv = 1 n samples n samples i=1 (ŷ NIR,i y GC,i ) 2 (1.5) In Eq. (1.4) the index i is running over the M test mixtures. The scalar ŷ NIR,i is the predicted mole fraction of normal alkanes for the i th test mixture and the scalar y GC,i is the mole fraction of normal alkanes according to the reference method (gc). The rmsecv is similarly defined. The index i in Eq. (1.5) is running over the n samples calibration mixtures. The predicted mole fraction of normal alkanes for the i th calibration mixture, ŷ NIR,i, is based on a calibration model that is built with the use of the remaining calibration samples. 1.4 Experimental Apparatus and Procedures Figure 1.1 shows a scheme of the experimental set-up. A home made evaporation vessel with a volume of 1 liter consisting of a glass cylinder and two stainless steel lids is used. All tubing and the inlet for the injection needle (septum) 18

19 NIR-spectrometer N 2 Waste Gas flowcell Waste Inj. Port Cal. gas Evp. Vessel SV1 SV2 GC Figure 1.1: Experimental set-up. Cal. gas = calibration gas; Evp. Vessel = evaporation vessel; GC = gas chromatograph; Inj. port = injection port; N 2 = purge gas; SV1, SV2 = switching valve. The area within the dotted line is kept at 16 C. pass through these steel lids. The vessel is situated in an oven (16 C). Valve SV1 (VALCO, 6CWE), enables the switching between a methane/argon calibration gas (5:95 (m/m)) and the vaporized alkane mixture to be analyzed. Valve SV2 (VALCO, 6UWE) is used to inject the alkane mixture on the gc (sample loop volume: 5 µl). The gas chromatograph (Hewlett Packard, HP589) is used in the constant pressure mode. Nitrogen is used as a carrier gas. The detector zone of the FID detector is kept at a temperature of 25 C. The capillary column (J&W Scientific, DB-Petro1) is directly connected to the injection valve (SV2). The near-infrared spectrometer (BOMEM, MB155) contains a InAs detector module. A spectral resolution of 4 cm 1 is selected. The time needed to acquire an absorption spectrum at this spectral resolution is 45 seconds (3 scans), 9 seconds (5 scans), or 5 seconds (1 scan). The home-made gas flow cell has a volume of 1 ml and a light path length of 2 cm. Two round quartz windows, having a diameter of 2.5 cm (Hellma Benelux), pressed on the body of the cell allow the nir light to pass through the cell. This connection is made gas tight with chemically inert KALREZ O-rings (Du Pont). The cell is heated with an heating coil and the temperature (16 C) is controlled by a proportional integrating and differentiating (PID) controller. 19

20 The measurements are set-up in such a way that the composition of the vaporized alkane mixture is determined almost simultaneously by gas chromatography, which is used as the reference method, and nir spectroscopy. For each measurement approximately 4 ml of liquid sample was injected in the evaporation vessel. After evaporation of the alkane mixture and the flushing of the flow cell with the alkane vapor, several interferograms with different numbers of scans (viz. 1, 5 and 3) were recorded. Immediately thereafter the injection on the gc was performed. Before each measurement the whole experimental set-up was thoroughly purged with nitrogen gas Experimental Design The alkane mixtures were prepared from the pure compounds (purity more than 98%) according to a mixture design. These compounds are known to be present in the molecular sieve separation process under consideration. Instead of using pure compounds for the corners of this design, mixtures of alkanes, so called pseudo-components, were used. This has been done for two reasons. First, the use of pseudo-components increases the flexibility that is needed to cover the desired range of alkane mixtures and, second, the resulting calibration mixtures will be more representative for the mixtures of the process to be analyzed, because the number of pure compounds in the prepared mixtures will be higher than is the case when only pure compounds are used as the corners of the design for the same number of samples. The composition of these pseudo-components (Table 1.1) has been chosen No Compound P S 1 P S 2 P S 3 P S 4 P S 5 1 Pentane Hexane Heptane methyl-pentane methyl-pentane ,2,4-trimethyl-pentane Cyclopentane Methyl-cyclopentane Cyclohexane Methyl-cyclohexane Table 1.1: Composition of pseudo-components in %[mole/mole] that are used in the experimental design. in such a way that several requirements are satisfied. First, alkane mixtures must be present that have an iso- and cyclo-alkane fraction that closely resembles the iso- 2

21 and cyclo-alkane composition of the output of the process. Second, a considerable variety of mixtures of normal, iso- and cyclo-alkanes should be covered by the design. Finally, some mixtures must be present for which the nir spectra of the iso- and cyclo-alkane fraction of such a mixture have a large overlap with the nir spectrum of the normal alkanes. Pseudo-component 1 (P S 1 ) contains only iso-alkanes and cyclo-alkanes, and its composition approximately matches the composition of the alkane mixture flowing out of the reactor. Pseudo-component 5 (P S 5 ) contains only the normal alkanes pentane, hexane and heptane. Three levels are selected for this pseudo-component, viz., mole fractions of 1%, 2% and 5%. For each level 21 design mixtures are measured with varying amounts of the other four pseudo-components. Each of these design mixtures is measured only once. The pseudo-component mixtures are all measured in triplicate. PS3 1% PS5 1% A B 5% 2% 1% % % PS1 PS2 PS1 PS2 Figure 1.2: Total experimental design. A) The contribution of the pseudo-components 1, 2 and 3 to the iso- and cyclo-alkane fraction of those design mixtures that do not contain pseudo-component 4, is shown. B) The composition of design mixtures not containing pseudo-components 3 and 4 is shown. Figure 1.2 illustrates cross-sections of the total experimental design. Figure 1.2A shows the fractions of the first three pseudo-components of the design mixtures, and in Figure 1.2B the fractions of the pseudo-components 1, 2 and 5 in some design mixtures are shown. The design for pseudo-component 4 can easily be 21

22 extrapolated from these plots Data Processing The peak areas and retention times of the recorded chromatograms are determined by a chromatographic integration package (Hewlett Packard; gc ChemStation Software 5895A; version 4., 1988) running on an HP 9/3 system. The interferograms of the reference (N 2 ) and alkane samples are recorded with the software package WINBE Easy (BOMEM, version 3.1c, 1994). The same software converts interferograms into absorbance spectra (wavenumber range: 35-1 cm 1 ; resolution: 4 cm 1 ). The absorbance spectra and the gc results are imported into Matlab (MathWorks, Version 5.2, 1997), in which all further data processing is performed. For building the pls models, the pls Matlab toolbox (Eigenvector Technologies Research, Version 2., 1998) is used. 1.5 Results and Discussion Exploratory Analysis An example of a measured nir absorbance spectrum is shown in Figure 1.3. Several wavenumber regions are considered for building the calibration models (Table 1.2). Part of the combination band region ( cm 1 ) is used. Also a part of the first overtone region ( cm 1 ) is used. The wavenumber range above 66 cm 1 and between 4652 cm 1 and 5556 cm 1 is discarded, because hardly any absorbance is measured. Moreover, the wavenumber range between 51 cm 1 and 5556 cm 1 is known to be disturbed by water vapor bands [49]. Finally, the second overtone region is also considered. Each wavenumber region is offset corrected. The wavenumber ranges used for offset correction are listed in Table 1.2. In Figure 1.4 the nir absorbance spectra of pure alkanes are shown. These spectra are normalized by the number of moles of substance as determined by gc. It may be observed that the differences between spectra of the normal alkanes and the cyclo- alkanes (Figure 1.4A and 1.4C) are larger than the differences between the normal and the iso-alkanes (Figure 1.4A and 1.4B). Furthermore, it can be seen that the spectra of the normal alkanes are similar apart from a difference in intensity. 22

23 .1 Absorbance / A.U Wavenumber / cm 1 Figure 1.3: Measured absorbance spectrum of P S 1. The full wavenumber range is shown. The realization of the experimental design is checked by a principal component analysis. The principal components of the normalized absorbance spectra of the pure alkanes (listed in Table 1.1) are determined, and the scores of the various pseudo-compounds and mixtures of these compounds (containing 5% normal alkanes) are calculated. In Figure 1.5 the score plot is shown of the first two principal components, which account for 87.4% of the total variance. It can be seen that the space between pseudo-compound 5, Name wavenumber range wavenumber range used for offset correction C st nd Table 1.2: Wavenumber ranges used for building pls models, wavenumbers in cm 1. 23

24 6 4 A 15 1 A 2 5 Normalised Absorption / arbitrary units B C B C Wavenumber / cm Wavenumber / cm 1 Figure 1.4: Normalized absorbance plot of the alkanes present in the calibration design mixtures. Offset corrected spectra (3 scans) are shown. A) normals: = 1 ; = 2 ; = 3 B) iso s: = 4 ; = 5 ; = 6 C) cyclo s: = 7 ; = 8 ; = 9; = 1. Numbers refer to Table 1.1. a mixture of normal alkanes, and pseudo-compound 1, a mixture of iso- and cyclo-alkanes resembling the actual process mixture, is well covered. Furthermore, the scores of the individual normal alkanes are on a straight line through the origin, indicating that their spectra mainly differ in intensity Calibration Model Inverse calibration models are built using a pls algorithm. The offset corrected, mean centered nir spectra of the alkane mixtures of the experimental design are used as the R matrix, and the mean centered mole fractions of the normal alkanes in the mixtures as determined by gc are used as the 24

25 2 1 PS4 9 Principal Component PS3 4 3 PS5 2 5 PS2 1 PS Principal Component 1 Figure 1.5: Principal component scores plot. = Pure compounds, numbers correspond to Table 1.1 ; = Design mixtures; = Pseudo-components, numbers correspond to Table 1.1. vector y GC. The calibration set consists of 33 design mixtures containing various amounts of normal alkanes. The test set consists of the other 3 mixtures prepared according to the experimental design and the triplicate measurements of the pseudo-component mixtures 1 to 4, which did not contain normal alkanes (Table 1.1). Several alternative ways of splitting the total set of measurements into a calibration and a test set were tried, all giving similar results. The rmsecv values for this alternative calibration sets do not significantly deviate from the results for the original split according to the randomization test of van der Voet [5]. A leave-one-out cross-validation procedure was used to determine the number of latent variables (LV s). Each subset created in this crossvalidation procedure is mean centered. Also, pls models are built that use various other wavenumber ranges of the recorded nir spectra. Figure 1.6 shows the rmsecv (for spectra based on 3 scans only) for some of 25

26 RMSECV Number of LV s Figure 1.6: rmsecv as a function of the number of LV s in the pls model. The pls models are built using different wavenumber ranges (see: Table 1.2): = region C ; = (region C + region 1 st ) ; = (region C + region 1 st + region 2 nd ) ; = region 1 st ; = full spectrum is used. these wavenumber ranges as functions of the number of LV s used in the pls model. With the use of these results, the following observations can be made. The shape of the rmsecv curve is roughly the same for all wavenumber ranges. First the curve rises and subsequently it sharply decreases when five or more LV s are used in the pls model. The increase of the rmsecv for the third (and higher) LV s indicates that these factors are mainly used to describe variation in the spectral data (matrix R) at the cost of describing variation in the mole fraction (y GC ). When only the combination band range is used, the lowest rmsecv values are found. For this wavenumber region the pls model based on five factors is the best. It has the lowest rmsecv for the lowest number of factors. The randomization test showed that the pls based on five factors does differ significantly from a six factor model. This observation is further confirmed by inspecting the loading vector of the pls model. The loading vectors of the first five LV s reflected spectral information, and the loadings of the sixth factor resembled pure noise. Note 26

27 that when the Beer-Lambert law is assumed to hold, it is to be expected that exactly five LV s are needed in the pls model, because the calibration mixtures were prepared by varying the amounts of five pseudo-components in the calibration mixture. The use of the randomization test to compare the pls models based on the combination band region (C) with the models based on either the combination band region and the first overtone region (C + 1 st ), or only the first overtone region (1 st ), shows that the pls models based on the C region are significantly better. The best models based on wavenumber ranges (C + 1 st ) or (1 st ) need at least seven latent vectors. This indicates that, although the signal-to-noise ratio in the first overtone region is rather high, for the quantification of the mole fraction of normal alkanes, the wavenumbers in the first overtone region do not carry any additional information. Figure 1.6 also shows that addition of more wavenumbers (e.g., adding the second overtone region or using even the full wavenumber range) causes deterioration of the predictive capability of the calibration models even further. Again, at least seven factors are needed in pls models using these wavenumber ranges. No significant improvement in rmsecv could be reached by preprocessing the measured spectra any further. It is concluded that a five LV calibration model based on the combination band region (C in Table 1.2) of the spectra yields the best results Determination of the Critical Level The critical level (L C ) for the best pls model is determined by performing an error analysis of the predicted mole fraction of normal alkanes for the blank mixtures of the experimental design. The triplicate measurements of the four pseudo-component mixtures (Table 1.1) that do not contain normal alkanes are used as blanks. The composition of pseudo-component 1 resembles the iso- and cyclo-alkane composition of the mole sieve process, so the L C value determined for this blank mixture will be a good indication of the L C when this analysis procedure will be implemented. In general, three error sources will contribute to the total error in the predicted mole fraction of normal alkanes: 1) The error in the mole fraction of normal alkanes as determined by the 27

28 reference method (gc). This mole fraction error is estimated to be smaller than.2% [mole/mole]. The estimation of this mole fraction error is based on repeated measurements of the calibration gas. 2) The spectral error of the measured spectra of the mixtures that are used in the calibration set. Several factors contribute to this spectral error, such as the detector noise of the spectrometer and the drift of the spectrometer over time. 3) The spectral error of the measured spectra of the blank mixtures. In order to give an impression of this spectral error, Figure 1.7 is provided..1.5 Absorbance Wavenumber / cm 1 Figure 1.7: Spectral error. One curve (the absorption spectrum ) in this figure is the ratio of two N 2 single beam spectra measured with a time interval of an hour. From these curves the instrumental repeatability for the current experimental setup can be estimated. The figure clearly shows that, apart from spectral noise, a significant spectral drift is present for the whole wavenumber range. Furthermore, two water vapor bands regions, one around 53 cm 1 and one around 715 cm 1, can be distinguished. To determine the effect of the three mentioned error sources (1 to 3) on the final error (s total ) in the predicted mole fraction for the blank mixtures, 28

29 three types of simulations are set up that correspond to the three error sources. The measured spectra and the measured mole fraction of normal alkanes (with gc) for the calibration mixtures are used as the starting value for these simulations. These measured spectra and measured mole fractions are referred to here as the nominal mole fractions and the nominal spectra: 1) The impact of the mole fraction error of the reference method is established by generating 1 perturbed sets of mole fractions. A perturbed mole fraction is drawn from a normal distribution with the nominal mole fraction as a mean and the value.2 as a standard deviation. For each perturbed set of mole fractions a new calibration model (Eq. 1.1) is built using pls. Each calibration model uses the mean centered nominal spectra in the R matrix. The standard deviations calculated over the 1 predicted mole fractions of the blanks for spectra based on 3 scans are collected in the first row, labeled s MF, of Table 1.3. Type of error P C 1 P C 2 P C 3 P C 4 s MF s cal s blanks s total L c Table 1.3: Results of error analysis for best pls model (5 LV s ; wavenumber region C). 2) The impact of the spectral measurement error of the calibration mixtures is evaluated by generating 1 perturbed sets of calibration spectra. Each perturbed set is generated by adding an error spectrum to the nominal spectra of the calibration mixture. An error spectrum consists of a spectral drift part and a spectral noise part. The spectral drift part is generated by a stochastic slope and a stochastic offset. The standard deviation of the spectral noise is, therefore, wavenumber dependent. For each set of perturbed calibration spectra a new calibration model is built (pls). Each time the vector y GC (Eq. 1.1) is set to the mean centered nominal mole fractions. The standard deviations calculated over the 1 predicted mole fractions are collected in the second row, labeled s cal, of Table ) To evaluate the impact of the spectral measurement error on the 29

30 spectra of the blanks, one generates 1 perturbed sets of blank spectra (are generated using the same procedure as described under point 2). For each set the predicted mole fraction of normal alkanes is calculated by using the calibration model based on the mean centered nominal calibration spectra and the mean centered nominal mole fractions. The results are collected in the third row, labeled s blanks, of Table 1.3. The three prediction errors in the mole fraction of normal alkanes that arise from these three separate errors are assumed to be independent. This assumption is reasonable, because in these simulations as well as in reality the spectral errors on a calibration spectrum are statistically independent of the spectral errors on the spectra of the blanks or the unknown alkane mixtures. Furthermore, because of the completely different method of analysis, the mole fraction error is also statistically independent of the spectral error. The probability density functions of the predicted mole fractions of these simulations are confirmed to be normal distributions by the Anderson- Darling test [51]. The total error (s total ) in the predicted mole fraction for the blank mixtures can thus be determined by: s total = s 2 MF + s2 cal + s2 blanks (1.6) This value is listed in the fourth row in Table 1.3. From these values for s total the L C value is determined by the next formula: L C = 1.65 s total (1.7) The value 1.65 (95% confidence limit) is based on n = 1 in Eq. (1.3). Inspection of the results in Table 1.3 shows that the contribution of error in the reference method (s MF ) to the total prediction error in the mole fraction of blanks (s total ) is very small. Furthermore, the errors s blanks and s cal are of the same magnitude, and the differences between the calculated L C values for the four types of blank mixtures are small. Except the blanks of pseudocomponent 3 that have a slightly larger value. As already mentioned the L C value for pseudo-component 1 is indicative for the L C value when the method will actually be implemented for the mole sieve process. It may be concluded from the other results that this value does not depend much on changes in the iso- and cyclo-alkane composition of the mixture. 3

31 1.5.4 Analysis Time vs. Critical Level Both an increase in the number of scans used for recording the interferograms and a higher spectral resolution will result in a longer analysis time. The time scale of the mole sieve process is on the order of a minute and, therefore, the analysis time must be much shorter than a minute. The measurements according to the experimental design were performed at a fixed spectral resolution of 4 cm 1 and for a varying number of scans. This approach offers the opportunity to asses the impact of the number of scans and thus the analysis time on the quantitation of the mole fraction of normal alkanes. In the current experimental set-up, the time needed to analyze an alkane mixture is 5 seconds (1 scan), 9 seconds (5 scans) and 45 seconds (3 scans). Calibration models are built for these numbers of scans. For each calibration model the combination band wavenumber region (C ) was used for quantification and five factors were selected. Figure 1.8 and Number of scans rmsep L c Table 1.4: Prediction results for test set of the best pls model (5 LV s, wavenumber region C). Table 1.4 show the results. Both the rmsep value and the L C value increase for a decreasing number of scans. For the rmsep the increase from 3 to 5 scans is less than the increase from 5 scans to 1 scan. This is also visible in Figure 1.8. The spread in the points of Figure 1.8A and Figure 1.8B is almost the same, while in Figure 1.8C the spread has increased. In general, a decrease in the spectral resolution will also result in a faster analysis, at the cost of an increasing L C. To get an impression of the impact of the decrease of the spectral resolution on performance of the pls model, the resolution of the measured nir spectra was artificially lowered by leaving out wavenumbers. The validity of this procedure was tested by recording some nir spectra at different wavenumber resolutions of the same sample. Starting with the whole set of measured spectra that are recorded at a spectral resolution of 4 cm 1, new sets of spectra are generated by 31

32 6 A 4 2 Predicted mole fraction normal alkanes NIR B C Mole fraction normal alkanes GC Figure 1.8: Predicted mole fraction of normal alkanes based on offset corrected nir spectra and best pls model ( 5 LV s ;wavenumber region C ) vs. the mole fraction determined with gc. A: Number of scans is 3. B: Number of scans 5. C: Number of scans 1. = test set mixture ; = calibration set mixture. leaving out wavenumbers. Sets for 8, 16, 32 and 64 cm 1 are generated. For each new set of nir spectra, the L C was calculated for the three selected values for the number of scans. In Figure 1.9 the determined L C values are plotted against the analysis time. It can be seen that for spectra based on 3 scans a decrease in the spectral resolution only gives rise to a slight increase of the critical level. For spectra based on a lower number of scans (5 and 1), this increase is more 32

33 3. L c normal alkanes / % mole/mole Analysis Time / s 8 4 Figure 1.9: The critical level of the mole fraction of normal alkanes vs. the analysis time: = 3 scans; = 5 scans; = 1 scan. Numbers in the plot refer to the wavenumber resolution used. pronounced. The figure also shows that using spectra based on 5 scans and a resolution of 4 cm 1 results in a L C of approximately.4% and an analysis time that is approximately 9 seconds. Apparently, almost the same L C could be reached by measuring spectra based on 3 scans at a resolution of 64, 32 or 16 cm 1. The disadvantage, however, is the increase in analysis time to seconds. The plot also shows that when a critical level of 1% is acceptable, the analysis time may be decreased to 4 seconds. This is achieved by using low resolution (64 cm 1 ) spectra based on 5 scans. 1.6 Conclusions This study shows that it is feasible to perform fast and accurate analysis of n-alkanes in gaseous alkane mixtures with the use of nir spectroscopy. The information about the mole fraction of normal alkanes is extracted from the combination band region of the nir spectrum. No additional information about the mole fraction could be gained from other spectral regions of the 33

34 nir spectrum. The critical level (L C ) that may be reached using an analysis time of 1 seconds, is about.4%. The relation between analysis time and L C for the mole fraction of normal alkanes was established. The analysis time may be reduced to 4 seconds if an L C of 1% is allowed. Slightly faster analyses are feasible at low wavenumber resolution and a low number of scans, but at the cost of a largely increased analysis error. 34

35 Chapter 3 Tracking Chemical Kinetics in High-Throughput Systems 3.1 Abstract Combinatorial chemistry and high-throughput experimentation (hte) have revolutionized the pharmaceutical industry - but can this success by repeated in the fields of catalysis and materials science? It is proposed to bridge the traditional discovery and optimization stages in hte by enabling the parallel kinetic analysis of an array of chemical reactions. The theoretical basis to extract concentration profiles from reaction arrays and to derive the optimal criteria to follow (pseudo)first-order reactions in time in parallel systems is presented here. The information vector f is used and the information gain ratio, χ r is introduced to quantify the amount of useful information that can be obtained by measuring the extent of a specified reaction r in the array at any given time. This method is general and independent of the analysis technique, but it is more effective if the analysis is performed on-line e.g. by spectroscopy. The feasibility of this new approach is demonstrated in the fast kinetic analysis of the carbon-sulfur coupling Published as: Tracking Chemical Kinetics in High-Throughput Systems, H.F.M. Boelens, D. Iron, J.A. Westerhuis, G. Rothenberg in: Chemistry, a European Journal 9 (23) c 23 Wiley-VCH Vela GmbH & Co KGaA, Weinheim 54

36 between 3-chlorophenylhydrazonopropane dinitrile and β-mercaptoethanol. The theory agrees well with the results obtained from 31 repeated C S coupling experiments. 3.2 Introduction The discovery of new catalysts and the synthesis of new materials have been advanced in the last decade by the introduction of combinatorial and other high-throughput techniques originating from the pharmaceutical industry [61 67]. Still the chemical industry s high expectations have not been fulfilled yet, as new catalyst libraries have not yielded dozens of exciting new pathways to produce base chemicals and intermediates [68, 69]. One reason for this is that a host of properties and process conditions must Discovery Optimisation discovery test Yield accept reject t 1 Time t 2 Figure 3.1: Graphic showing candidate selection according to the traditional two-stage high-throughput approach (top) and the reaction profiles for three candidates (bottom). Good candidates may be mistakenly discarded (and vice versa) if the discovery test is performed at the wrong time. be fine-tuned in order to yield a catalyst that is active, selective and stable. 55

37 The new high-throughput experimentation (hte) techniques are invariably based on a two-step approach comprised of primary screening of a large number of candidates (discovery stage) followed by optimization of a small number of leads. In the discovery stage, thousands or even tens of thousands of catalysts may be tested, but often only one binary parameter is scanned (for example, the product yield may be measured only once for each reaction vessel) [7 73]. Thus, good catalysts may be overlooked and not pass into the optimization stage if they score low, for any reason, in the initial discovery tests, and vice versa. Figure 3.1 illustrates this candidate selection process according to the traditional two-stage high-throughput approach. In this example, a single measurement (the discovery test) is performed for three different catalysts at t 2, giving the results shown by the bold dots. Looking at the reaction profiles (broken lines) it would have been better to perform the test at t 1, because then the low initial activity of the red candidate would be observed. Thus, it is crucial to perform the discovery measurement at the correct time, yet this correct time is found only when one already knows the kinetic profiles - a time-resolved chicken-and-egg problem. A possible solution to this problem would be to merge the discovery and the optimization stages by adapting time-resolved analysis to high-throughput environments. Unfortunately, parallel hte set-ups are ill-suited to quantitative time-resolved analysis: most robotic systems consist of many small and inexpensive reactors and one (expensive) analyzer (Figure 3.2). On-line analysis time, Reactor array Single analyser Figure 3.2: Most common high-throughput experimental set-up used in optimization studies, in which one expensive analyzer is used to monitor an array of reactors sequentially. 56

38 becomes the limiting factor simply because time does not wait for parallel experimentation. Even in cases when numerous samples can be stored for later off-line analysis, it is essential to determine which samples should be analyzed. To reach these goals and bridge the gap between the discovery and the optimization stages, new concepts in analysis must be realized to complement the hte robots [74 76]. Previously some approaches to array analysis based on the results of computer simulations were given [77]. Now the theoretical basis that is required to perform efficient kinetic studies in parallel reaction systems is presented. This approach is demonstrated for the fast analysis of 31 repeats of a carbon-sulfur coupling reaction. 3.3 Theory Concept and Assumptions Consider an array of reactors that are all interfaced to one analysis instrument similar to the set-up depicted in Figure 3.2. Suppose that these reactors are running simultaneously the (pseudo) first-order process A B, where the initial concentration of A is a, the initial concentration of B is, the reaction rate constant is k and the concentration of A at time t, a t, is measured from t to t (where t is defined as the time when conversion > 99.5%). It is assumed that all of the reactions follow a first-order rate law. Thus, for each reaction in this array, Eq.3.1 describes the true concentration profile of A: a t = a e kt (3.1) Regardless of the analytical technique, the measurement of the extent of a chemical reaction over time always yields a rate constant k that is only an estimate of the true rate constant k, and has an error k which is comprised of systematic (bias) and random parts [1]. Assume that the reaction is monitored by spectroscopy. In this case, k depends both on the experimental set-up and on the way the spectra are processed. This means that k is influenced by both the spectroscopic measurement itself and the calibration Spectra can be measured either with dispersive or with Fourier transform spectrometers. In both cases the spectrum is based on a window comprised of a number of scans 57

39 window size (scans) S1 non-sampling time a t a t number of windows Time Time S2 S3 1/3 a t a t 1/ /3 Time Time Figure 3.3: Examples of various sampling strategies with system parameters shown on top left. Strategy S 1 - equidistant sampling along the time axis. Strategy S 2 - packing the samples at the start. Strategy S 3 - even distribution of samples along the concentration axis (example shown with three equidistant samples, the concentration curve is shifted for clarity). model used. The concentration estimate ã t obtained at time t has an error ã t. When an adequate calibration model is used, the systematic part of the concentration error will be negligible compared with the random part. It is assumed that this random concentration error is additive and that it is averaged over time. This time averaging increases the signal-to-noise (S/N) ratio. However, the disadvantage of increasing the number of scans per window is that the total time needed to collect one spectrum also increases and meanwhile the reaction continues and concentrations change. A calibration model must be applied to the measured spectrum to estimate concentrations. The error of these estimates depends on the model because any calibration model is based on spectroscopic and reference measurements pertaining to a finite number of calibration samples [3, 4]. 58

40 independently, identically normally distributed (i.i.d.). If it is not possible to monitor all of the vessels at a given time, a protocol to allocate the analyzer time is needed (this is called a sampling strategy). This can be simple and straightforward (for example, sample each vessel in turn, one after the other) or more complicated (for example, feed back concentration information and sample more frequently those reactions that are changing more rapidly). Figure 3.3 shows three examples of such sampling strategies Single- and Multiple Sampling of First-order Reactions In theory, since a is known, one measurement should suffice to estimate k for each reaction. It is clear a priori that the accuracy of this k would 1.8 a t / [M] Time / min Figure 3.4: Plot of 1 theoretical first-order reaction profiles, each estimated by taking only one measurement at t = 1 s (indicated by a ). The estimated profiles all start from the same a and the differences are due only to the error of this one measurement. Note that large differences are observed even though the measurement error is only ±.5% of a. depend on when this measurement is performed. For example, when the measurement is taken immediately after the start of the reaction, k can The random error, ã t, at each point in time is assumed to be N(, σ) distributed. Furthermore, errors at subsequent points in the time are assumed to be statistically independent. And finally, the measured concentration ã t is taken to be equal to ã t + ã t. So, the concentration error is additive and independent of the concentration level. 59

41 be large. This is true even when the error in measuring the concentration is small (c.f. the ten concentration profiles shown in Figure 3.4, that are based on 1 k values with an error in the concentration measurement at t = 1s of only ±.5%). This problem is solved by deriving a method to find the optimal time point for a single sample (see Appendix A). For a first-order 1 f 2.5 t = 1/k t obs s k / min t = 1/k Time / min Figure 3.5: Plot of f 2 for the first-order reaction A B as a function of time (top) and the change in the standard deviation of k for the same reaction (bottom). The broken lines indicate the optimal sampling time at t = 1/k. The shaded area on the right is proportional to the improvement in the accuracy of k if one would dedicate all measuring time from t obs onwards to the current reaction. reaction, given that k is an initial guess for k, the best time to measure is at t = 1/k. This is the same value obtained first by Carr [78] and by Holler et al. [79], in their elegant analysis of random and systematic fluctuations in first-order rate constants. The purpose is, however, different: as little information as possible should be lost from the reaction array. The key quantity here is the information value f (Eq. A.8 in Appendix A). Figure 3.5, top, shows the change in f 2 as a function of the sampling time. For each measurement time t, the height of the curve indicates the accuracy in k. The optimal time to measure corresponds to the maximum of the curve (t = 1/k ). The information value f is inversely proportional to the square root of the variance in k (Eq. A.7 in Appendix A). This is shown in Figure 6

42 3.5. In practice, however, several measurements are performed for every reaction, and so several sampling strategies are possible (Figure 3.3). Deciding which sampling strategy would yield quick yet accurate k values from a large reaction array is far from trivial. For this a general and fast method to evaluate k is introduced here. This method also enables easy visual comparison between different sampling strategies. In high-throughput systems analysis times must be kept short and sample numbers should be confined to a minimum. Again, the curve shown in Figure 3.5, top, is useful, as the sum of the curve s intensities at the given sampling times is proportional to the success of the measurement. For example, if only two samples are taken per reaction, one can see that taking both at the start or at the end of the reaction is not very sensible. The best k values are obtained when both measurements are done at the maximum of the curve, and sampling at time points close to the maximum gives near-optimal results A General Sampling Strategy for High-Throughput Experimentation The above examples are now extended to an overall approach for performing kinetic studies in high-throughput systems, where a large number of experiments is performed simultaneously. A good hte sampling strategy must be able to decide to what reaction the next analyzer time slice should be allocated. Such a strategy should also indicate when the monitoring of a particular reaction is no longer sensible (for example when conversion is >99%). For the moment, assume that (1) the running reactions are (pseudo) first-order; (2) that some measurements were already performed for each reaction; and (3) that the results of those previously performed measurements are accessible. At time t obs the system must decide which reaction vessel should be analyzed. Number the reaction vessels with an index r = 1..R, and assume that for each reaction N r measurements are already performed. These N r measurements yield an estimated rate constant k r. Based on this estimate When multiple samples are taken the information vector f replaces f. The sampling strategy that yields the highest value for f 2 gives the best k (see Appendix A). 61

43 one can easily quantify the amount of information when the measurement at t obs is actually assigned to reaction r. This is done by taking the ratio of the f 2 value at t obs to the sum of the f 2 values at previous measuring times. This ratio is called the information gain ratio, χ r. For each reaction r the value χ r can be easily calculated using Eq. 3.2, in which f r,before 2 is the sum of the f 2 values at earlier points in time for reaction vessel r (Eq. A.9 in Appendix A). Thus the best investment of analyzer time would be to sample the reaction that has the highest χ r value. χ r = t2 obs e 2 k rt obs 1% (3.2) f r,before 2 The point in time when it is no longer useful to monitor a given reaction can be determined in several ways. One way is to estimate k error analysis of the non-linear regression (or any other method) used to determine k from the measurement. It can then be checked when k drops below a preset limit. Alternatively, one can check whether the remaining area below the error curve (the shaded area in Figure 3.5) is smaller than a userdefined percentage of the current value of k. The shaded area represents the improvement that could be obtained when all available measuring time would be spent on the reaction r only. The advantage of this method is that one can actually look ahead in time. 3.4 Experimental All chemicals were commercially available (99% pure) and were used without further purification. KH 2 P O 4 buffers were purchased from Acros (pro analysis.2m). UV-vis spectra were recorded using a Hewlett-Packard 8453 spectrometer (quartz cuvettes, 1. cm path length). Data processing was performed using Matlab 6.1 (The MathWorks, Inc., Natick, USA, 21). A detailed description of the sample preparation methods and the experimental apparatus has been published [8, 81]. A total of 32 identical experiments were performed and monitored using UV-vis. A stock solution of 3-chlorophenylhydrazonopropane dinitrile A (1.34 M in.1 N NaOH) was prepared. For each experiment, part of this stock solution was then diluted to µm, buffered to ph 5.4 with KH 2 P O 4, and mixed in the quartz cuvette with an excess (276:1 mol:mol) of β-mercaptoethanol solution (2.5 µl β-mercaptoethanol in 7.5 µl KH 2 P O 4 buffer solution). UV-vis spectra of the 62

44 reaction mixtures were recorded every 1 s at a wavelength range from 3 to 5 nm. 3.5 Results and Discussion An Experimental Example The carbon-sulfur coupling of 3-chlorophenylhydrazonopropane dinitrile A with β-mercaptoethanol to give the adduct B (Figure 3.6) was examined as a model reaction [8,81]. An excess of β-mercaptoethanol was used to realize pseudo first-order conditions for A B. The reaction was followed using UV-vis spectroscopy. 32 repetitions of this experiment were performed, the first of which was used to estimate the spectra of A and B. 271 UV-vis spectra were recorded for each experiment, and using these spectra a set of 31 concentration profiles was obtained. These repeated experiments are NC H CN N N HS + ph = 5.4, 25 ºC, 45 min H 2 O/Phosphate buffer NC HN H N SCH 2 CH 2 OH CN Cl OH Cl A B Figure 3.6: Reaction scheme. used to corroborate the theoretical derivations. From the data 31 k values are estimated and their average and standard deviation are calculated. As shown below, it is indeed found that the standard deviation depends strongly on the sampling time and that lowest standard deviation (i.e., the best estimate of k) is obtained at the optimal sampling time. The mean of the 31 concentrations of A at t = was used as the best estimate of a. The kinetic model of Eq. 3.1 was fitted to each measured concentration profile using non-linear regression. The value of a was kept fixed and k was the only parameter. The 31 resulting k values are plotted in Figure 3.7. These k values are random as no outlying values are found; this 63

45 .25 k / min k nlin Experiment number Figure 3.7: Calculated k values for each of the 31 experiments, determined by non-linear regression. The mean is indicated by the dotted line and designated as k nlin. confirms that the reactions are well performed. The mean kinetic constant (designated k nlin ) equals.23 min 1. Normalized concentration profiles of A are used to validate the results derived in Appendix A. The profiles were normalized by dividing each a t at by the initial concentration (a ). The resulting r th concentration profile is designated a r (t i ), and for each profile r and each point in time t i the minimization of the non-linear function in k (Eq. 3.3) is performed: min k a r (t i ) e kt i (3.3) This yields a matrix of k values (note that each of these is based on only one measurement). For each point in time the standard deviation of k is then calculated over the 31 concentration profiles. Figure 3.8 shows these standard deviations a function of time. The theoretical model fits to the experimental results (cf. Figure 3.8 and Figure 3.5). The lowest standard deviation is found at t = 5 min 55 s. This is close to 1/k nlin (4 min 18 s) considering the flatness of the optimum and the 95% confidence regions. The optimal k is indeed found by sampling at t 1/k. 64

46 3.5.2 Multiple Sampling in High-Throughput Systems It would be nice to obtain accurate rate constants that are based on a large number of measurements. However, the size of current reactor arrays and their centralized structure with respect to analysis dictate that no more than, say, four or five measurements should be allowed per reaction. This makes the curve of f 2 a useful visual tool to compare and evaluate different sampling strategies as a function of the number of samples. As an example, consider the case for three measurements. The concentration profile for k =.23 min 1 and the points in time when the measurements are taken are plotted in Figure 3.9A. The f 2 -curve is plotted in Figure 3.9B, together with the points that correspond to these measurements. Clearly, strategy S 3 (see Figure 3.3) is superior to S 1 and S 2 (because overall the points are high on f 2 curve) and S 2 in this case is the worst (points on the curve are close to zero). Examining the performance of the different sampling strategies with respect to the best possible strategy as a function of the number of samples gives even more information. In the ideal case all measurements would be done at t = 1/k. Figure 3.1 shows that sampling strategy S 3 is closest to the best strategy given a low number of samples. The performance of S 1 (equidistant sampling along the time axis) improves as the number of 3 1/k nlin s k / min Time / min Figure 3.8: Standard deviation of k (shown as ) based on the experimental data (each dot is based on 31 k values). The vertical line is drawn at t = 1/k nlin and the arrow indicates the lowest value of s k. The 95% confidence intervals are shown as dashed lines. 65

47 a t 1.5 A f S 1 S 3 S Time / min B Figure 3.9: First-order reactant concentration profile (A) and f 2 curve (B), used to compare the sampling strategies shown in Figure 3.3 (example with three measurements). 1 Relative Performance / % S 1 S 3 S Number of Measurements Figure 3.1: Relative performance of the sampling strategies S 1, S 2 and S 3. The ideal sampling strategy (i.e., taking all measurements at 1/k) is taken as 1%. The sampling window size is 1 s. 66

48 samples is increases while the performance of S 3 deteriorates. 3.6 Conclusion New approaches in analysis must be taken in order to realize the goal of high-throughput kinetic studies. In the parallel reactor set-up (the most common to date) it is crucial to find the optimal allocation of the analyzer time. This is even more important in the case of slow analytical methods such as gc and hplc. It is shown how the information vector can be applied in various ways. It can be used to quickly assess the performance of different sampling strategies, and to decide which reaction in the array can best be monitored at any given time, and to halt the monitoring of a reaction at the right moment. The information vector can this be used as part of automatic procedure in high throughput studies that decides about the most interesting reaction to monitor. To quantify this, it is proposed to the use the information gain ratio (χ r ). The shown examples depict first-order kinetics. The real experimental world, however, is unfortunately seldomly first-order. The above framework is currently extended to include more complex systems (secondorder reactions, cascade reactions, catalyst deactivation, pre-equilibria and Michaelis-Menten kinetics). In the future, the same approach could be used for monitoring biochemical kinetics, determination of NMR relaxation rates [82] and high-throughput screening of biological functions. 67

49 Chapter 4 New Method for Background Correction in Hyphenated Chromatography 4.1 Abstract A new method to eliminate the background spectrum (ebs) during analyte elution in column liquid chromatography (lc) coupled to spectroscopic techniques is proposed. This method takes into account the shape and also intensity differences of the background eluent spectrum. This allows the ebs method to make a better estimation of the background eluent spectrum during analyte elution. This is an advantage for quantification as well as for identification of analytes. The ebs method uses a two-step procedure. First, the baseline spectra are modeled using a limited number of principal components (PCs). Subsequently, an asymmetric least squares regression (als) method is applied using these principal components to correct the measured spectra during elution for the background contribution. The asymmetric least squares regression needs one parameter, the asymmetry factor φ. This asymmetry factor determines the relative weight of positive and negative residuals. Published as: New background correction method for LC-DAD, IR and RAMAN spectroscopic detection, H.F.M. Boelens, R.J. Dijkstra, P.H.C. Eilers, F. Fitzpatrick, J.A. Westerhuis in: Journal of Chromatography A, 157, (24), c 24 Elsevier B.V. 68

50 Simulations are performed to test the ebs method in well-defined situations. The effect of spectral noise on the performance and the sensitivity of the ebs method for the value of the asymmetry factor φ is tested. Two applications of the ebs method are discussed. In the first application the goal is to extract the analyte spectrum from an lc-raman analysis. In this case the ebs method facilitates easy identification of unknown analytes using spectral libraries. In a second application, the ebs method is used for baseline correction in lc diode array detection (dad) analysis of polymeric standards during a gradient elution separation. It is shown that the ebs method yields a good baseline correction, without the need to perform a blank chromatographic run. 4.2 Introduction When column liquid chromatography (lc) is coupled to spectroscopic techniques, such as uv-vis diode-array detection (dad), Fourier transform infrared (ft-ir) or Raman, it is often difficult to completely remove the interfering spectrum of the eluent. The spectral response of the eluent is usually much larger than the contribution from the analyte and the composition of the eluent may not be constant. To overcome this problem, it is common practice to select an eluent that has spectral bands outside the spectral range of the analytes. However, this is not always possible. For instance, in the case of on-line lc-raman and on-line lc-ir the spectrum of the solvent always contains distinct bands that overlap or partially overlap with the bands of the analyte. In addition, in lc-dad, an eluent that is suitable from a separation point of view can sometimes be rejected because it has an unacceptable spectroscopic response. Having a background correction method that can remove the spectral contribution of the eluent from the detector response would broaden the eluent choice in lc-dad. One example where a good background correction procedure would increase efficiency is in solvent gradient elution in lc-dad. Normally, the background is removed by subtraction of a blank chromatographic run. If the ebs method could be used to calculate the background spectrum during analyte elution, a blank run would no longer be needed. This would save significant time and effort. Why does simple subtraction of the eluent spectrum just before analyte elution (auto-zeroing) not always give good results? These are two main rea- 69

51 sons for this. The first one is the change in spectral intensity of the eluent spectrum during a chromatographic run. For instance, the intensity of the eluent spectrum during analyte elution is smaller than the intensity of the spectrum before elution. Straightforward subtraction will, therefore, lead to overcorrecting. The second reason is that small spectral shape changes of the eluent spectrum might occur. These changes may have several causes, such as wavelength shift, spectral drift and/or offset. In addition, in solvent gradient elution the solvent composition is deliberately changed, which causes both shape and intensity changes in the eluent spectrum. Here a new correction method, called Elimination of Background Spectrum (ebs), is described, that can take into account these shape and intensity differences of the eluent spectra. Some simulations are discussed that show the advantage of this method with respect to straightforward subtraction of the eluent spectrum. Subsequently, the ebs method is evaluated for two test cases. In the first application, an lc-raman separation is evaluated. In this case, the analyte spectrum is completely overwhelmed by the strong spectrum of the eluent. A companion publication discusses the application of the ebs method to these lc-raman data in more detail [83]. In the second application, a gradient lc-dad is evaluated. Compared to the first application, the analyte spectrum is more intense. It is shown that the ebs method removes the baseline well, without requiring a blank chromatographic run. Several multivariate approaches to background correction in hyphenated chromatography are known [84 9]. The ebs method has some differences and advantages compared to these methods. Second order calibration methods can be used to estimate concentrations and uncover the spectra of unknown compounds when measurement of reference mixtures is feasible [84 87]. In case the chromatographic run is used to find what analytes are present in the sample such an approach would be begging the question. This is because the analytes for which the calibration should be done are not yet known. Even if such a second order approach is feasible, the disadvantage is that some second order methods require the retention times of the additional chromatographic run to be well reproducible. The ebs method only needs data of a single chromatographic run and does not presuppose knowledge of the analyte spectra. Additional measurements on standards are not needed and therefore retention time stability is no longer crucial. Another method based on (adaptive) Kalman filters and derivative spec- 7

52 troscopy is used by Gerow and Rutan [88]. This method requires knowledge about the spectral response of the individual analytes. Although this knowledge does not need to be fully accurate, it is not always available. The method proposed by Liang et al. [89] does only use the measurements from one chromatographic run. Major principal components (PCs) are extracted from spectra measured in zero component regions before and after analyte elution. Essentially, their correction procedure assumes that the eluent contribution during analyte elution is constant. Gemperline et all. [9] relieve this assumption and automate the whole procedure. They allow the scores of major principal components (and thereby in fact the concentration of the eluent compounds) to change according to a cubic polynomial model. In contrast with this type of approach, the ebs method corrects each spectrum measured during elution separately and does not assume a predefined model for the concentrations of the eluent compounds in time. Another drawback of an interpolation approach is that it cannot account for the decrease of the spectral contribution of the eluent during analyte elution caused by the presence of the analyte. The ebs method is able to do this. Additionally, the ebs method only needs some representative background spectra to work. All of these spectra could very well be collected during the same chromatographic run before (or after) analyte elution. These features make the ebs method a more versatile tool for the user. 4.3 Theory Notation Used Bold-face capital letters represent matrices, bold-face lowercase characters represent vectors, and italic, lower case letters represent scalars values. Some subscripts are used: b indicates quantities at retention times when only a chromatographic baseline is present (eluent), ab indicates quantities at retention times at which also some analyte is present. And finally a indicates that quantities only refer to the analyte The EBS Method The measured data is collected in a data matrix X (n chan n) having n columns. Each column contains a spectrum measured at a number of chan- 71

53 nels (n chan ). These channels may be wavelengths or wavenumbers. Also, assume that the matrix X can be split into two parts. One part is the matrix X b (n chan n b ), where only the eluent is present, the other part is X ab (n chan n ab ), where eluent and analyte are present. In practical use the matrix, X b, will often contain spectra before and after elution of the analyte. The ebs method accounts for intensity and shape differences between the eluent spectra and the spectroscopic contribution of the eluent to the spectra measured during elution. The ebs method is a two step procedure: first, all variation of the eluent spectra at baseline level is modeled in a background spectral subspace (B-space) constructed by principal component analysis [3, 91]. Second, the spectra measured during analyte elution are corrected by performing an asymmetric least squares regression (als) with respect to the B-space found. Step i): The matrix X b is modeled with a limited number n pc of its principal components: X b = P K b + E b (4.1) The columns of the (n chan n pc ) matrix P form an orthonormal basis that allows a faithful description of the changes in shape and size of the eluent spectrum. The spectral space spanned by this orthonormal basis is called the B-space. The columns of the (n pc n b ) matrix K b contain the coordinates of all eluent spectra in this B-space. The (n chan n b ) matrix E b describes all spectral variation of the eluent spectra that is not modeled in the B- space. Ideally, this matrix E b contains only spectral noise. There are many methods and algorithms to determine the number of principal components that span the B-space. An overview and comparison of these methods can be found in literature [92 94]. Here the ind [95] algorithm is used. Step ii): Assume that this orthonormal basis (i.e. P ) is also valid for the eluent spectrum that is present during elution of the analyte. Each spectrum (vector x ab ) measured during elution of the analyte, can now be written as: x ab = P q ab + s a (4.2) The first part, namely P q ab, gives the contribution of the eluent to the measured spectrum and s a represents the spectrum of the analyte. The 72

54 n pc 1 coefficient vector q ab is still unknown. Exactly, this vector allows to describe shape and intensity changes of the eluent spectrum during analyte elution. A (too) simple approach to estimate the vector q ab would be by using ordinary linear regression. Such a regression yields positive and negative deviations around the fitted model (viz. P q ab ). It is known, however, that all elements of the analyte spectrum are positive. A solution to this problem is to use asymmetric least squares [96 99] for the estimation of the coefficients q ab Asymmetric Least Squares In asymmetric least squares (als) positive residuals and negative residuals do not receive the same weights. The (n pc 1) residual vector r is introduced as: r = x ab P q ab (4.3) als now minimizes the quantity f by changing q ab : f = n chan i=1 w i r 2 i (4.4) The weight w i in this equation depends on the sign of the corresponding residuals r i. For a residual larger than zero the weight is set to φ, while for a residual smaller than or equal to zero the weight is set to 1-φ. This φ is called the asymmetry factor ( < φ < 1). It is clear that if φ is near zero, the positive residuals get much less weight than the negative ones; hence the coefficients q ab will be such that the vast majority of residuals are positive. Once the n chan weights in w are given it is easy to estimate q ab by a weighted linear regression [1]. And once the coefficients q ab are known, it is trivial to set the weights w. This suggests an iterative algorithm, starting with all weights equal and set to 1. One can show that this iterative algorithm is gradient-following [96]. The goal function is convex and convergence must follow [99]. Practice shows that convergence is nearly always obtained in about 1 iterations Requirements of the Method Some requirements of the ebs method can be stated in advance. The spectra that are used to calculate the B-space should be representative of the 73

55 spectral variation that is caused by the eluent and the instrument. If not, the ebs method will fail. As an example, consider a case where the eluent consists of two spectroscopic active species (B 1 and B 2 ). If only one of these species, say B 1, is captured in the B-space, the ebs method will yield an estimated analyte spectrum that is a combination of the real analyte spectrum and the spectrum of B 2. This is clearly undesirable. In most cases, however, enough baseline spectra are available to model the spectral variation of the eluent. Moreover, the selection of the spectra to be used is not critical. Another limitation is posed by the amount of spectral overlap of analyte and eluent spectrum. If the shape of the eluent spectrum and the analyte spectrum are very similar, then the amount of specific analyte information in the measured spectrum is only limited. This will hamper the method and results in errors. Finally, in deriving the method the spectral noise was disregarded. If the φ value is set closer to, the negative residuals are more and more punished. In the end all residuals will thus forced to be zero or positive. In the presence of spectral noise on the measured spectra this may lead to an (small) offset in the reconstructed analyte spectrum (s a ). However, it is easy to correct for this type of offset. On the other hand for values of φ close to.5 the positive and negative residuals will receive nearly equal weights. The asymmetric least square solution then will approach the ordinary least squares solution. The reconstructed analyte spectra (s a ), will contain negative phases, which is obviously wrong Comparing the Estimated and the true Analyte Spectra To evaluate the ebs method, it is necessary to compare the background corrected spectrum with the true analyte spectrum. Two indicators are used for this purpose: the correlation coefficient (ρ) which is a measure of the similarity in shape between the estimated (ŝ a ) and true analyte spectrum (s a ). Also the amount of remaining spectral variation is calculated. This is expressed by the mean square error (mse) of the spectral residuals. The spectral residuals (e) are calculated by modeling the estimated an- 74

56 alyte spectrum as: ŝ a = c 1 s a + c 2 + e (4.5) in which c 1 and c 2 are constants determined by a linear regression. residuals are: The e = ŝ a c 1 s a c 2 (4.6) The mse is defined as: mse = 1 n chan 2 e 2 (4.7) A correlation coefficient that is close to unity and a low value for mse are indicators for a good similarity between the extracted and the real analyte spectrum. The lowest value that the mse can take is the variance of the instrumental spectral noise. A good estimate of the analyte spectrum will have mse s close to this variance Reference Method A straightforward subtraction of the background spectrum using a measurement just before (x before ) and just after elution (x after ) of the analyte is used as a reference method (ref). The analyte spectrum (ŝ a ) during elution at time t is calculated using the following equation: ŝ a = x ab x before t t before t after t before (x after x before ) (4.8) Note that this reference method is an advanced version of an auto-zero approach in which only the eluent spectrum measured just before elution of the analyte is subtracted. 4.4 Experimental LC-RAMAN The Raman spectra were recorded using a lc system coupled to a Raman spectrometer via a liquid-core waveguide (LCW). The eluent composition was an aqueous 1 mm HCl solution with 5% (v/v) methanol. The flow was set to.4 ml/min. After 75

57 passing through an on-line UV absorbance detector, the effluent was led into the LCW. The UV absorbance signal was used to determine the start and end times of the analyte elution. The spectroscopic resolution of the Raman spectrometer was 2 cm 1 (FWHM). Adenosine 5 -monophosphate disodiumsalt (AMP; Fluka, Buchs, Switzerland) was used as a model compound. The 4 ml of an aqueous solution of 2 mg/ml AMP was injected into the lc system. Other chemicals were of analyticalgrade quality. The standard deviation of the instrumental noise is estimated to be 35 counts. The spectrum of an aqueous solution of AMP was measured separately. This spectrum was corrected for water contribution. A spectral baseline correction was also performed. The resulting spectrum is the AMP reference spectrum. More details can be found in Dijkstra et al. [11, 12] LC-DAD Experiments were carried out on a Waters 269 lc system. Gradient control, data acquisition and analysis were controlled by Waters Millennium 3.2 software. The stationary phase was Supelco Discovery C 18, particle size 5 µm, pore diameter 18 Å, column dimensions were 15 mm x 2.1 mm i.d. and column temperature was maintained at 25 C. The solvents were THF (Biosolve, Valkenswaard, The Netherlands) and acetonitrile (Rathburn Chemicals, Walkerburn, UK), both were HPLC grade. The flow rate was.2 ml/min. Samples consisted of lowdispersity polystyrene standards (Polymer Laboratories, Church Stretton, UK, Pressure Chemical, Pittsburgh, PA and Polymer Standards Service, Mainz, Germany). The sample-injection volume was 1 µl and sample concentrations were 1.5 mg/ml each. uv-vis spectra (resolution 1.2 nm) were collected each second. Details can be found in Fitzpatrick et al. [13]. uv-vis spectra of polystyrene standards in THF were recorded separately in a cuvette on a Hewlett-Packard 8453 spectrometer (path length: 2 mm, spectral resolution 1 nm). Two full repeats were measured of each polystyrene standard. The mean spectrum was used for comparison Simulations The simulations and all processing of the measured spectra were performed in Matlab (MathWorks, Natick USA, version 6.1, 21). The Matlab code to perform correction with the ebs method is available from the author. 76

58 4.5 Results and Discussion Simulations Simulations were performed to illustrate the ebs method. An overview of these simulations is supplied in Table 4.1. Simul. Number of eluent species Baseline drift Spectral noise ρ REF ρ EBS mse REF a mse EBS a 1 1 No No.899 > No No No No.65 > > > Yes Yes a ( 1 6 ) Table 4.1: Overview of simulations. ρ EBS : correlation coefficient between estimated and true analyte spectrum for the ebs method at peak apex. ρ REF : same for the ref method. The mse values are calculated according to Eq In the first set of simulations it is assumed that apart from the analyte, only one eluent species is present. The noiseless spectra are shown in Figure 4.1A. It is assumed that the concentration of the analyte at elution maximum is about 3% (v/v) of the flow through the detection cell. The ref method clearly overcorrects for the presence of the eluent spectrum (Figure 4.1C), because the intensity of the eluent spectrum at peak-start (and peak-stop) is higher than during peak elution. Too much background signal is subtracted by the ref method. The ebs method on the other hand, yields a near perfect estimate of the analyte spectrum (Figure 4.1D). The correlation between the estimated and the true analyte spectrum is larger than.999 (Table 4.1). The difference between the ref and ebs method is also reflected in the mse values. Because this simulation is noiseless, it is expected that the mse value is equal to zero. This means that the estimated analyte spectrum in such a simple case should be identical to the true analyte spectrum. The mse for the ebs method is indeed close to zero, but for the ref method, this is clearly not the case. To investigate the sensitivity of the method the noise level is varied. At each noise level 5 runs are performed. In each run a different noise realization is used. Normally distributed white noise was 77

59 used in these runs. Table 4.2 shows that the mse value for the ebs and the (S/N) tot (S/N) a ρ REF ρ EBS mse REF mse EBS > > > Table 4.2: Results simulation 1 ; spectral noise added. (S/N) tot is the S/N ratio calculated as the maximum total spectral intensity measured during the run (.5) divided by the standard deviation of the white noise added. (S/N) a is the S/N ratio for the analyte signal, calculated as the maximum spectral intensity of the analyte measured during a run divided by the same standard deviation of the noise. Explanation of other symbols is supplied in Table 4.1. Spectral Intensity 1 A B Spectral Intensity.3.2 C 5 1 Channel Number.3 D Channel Number Figure 4.1: Results of simulation 1. A: Spectrum of analyte (solid) and background species (dashed). B: Spectra during elution of analyte. C: Reconstructed analyte spectra using the ref method. D: Same for the ebs method. 78

60 ref method increases with a decreasing signal-to-noise (S/N) level as may be expected. For both methods the correlation between the true analyte spectrum and the estimated analyte spectrum at peak apex decreases. At a S/N level of 6 with respect to the maximum level of the analyte spectrum (.3) both methods break down. For this S/N level the analyte spectrum is getting totally blurred by spectral noise and both methods are failing. For higher S/N levels the ebs method outperforms the ref method. The difference between the methods becomes smaller for decreasing S/N ratio s. In the second simulation, another eluent species is added. Figure 4.2 Intensity / [arb. units] Percentage of eluent A B Elution time / [arb. units] Figure 4.2: Simulation 2. A: Elution profile of analyte. B: Change in eluent composition: first eluent species (solid), second eluent species (dotted). shows that the eluent composition changes slightly during the chromatographic run, as it is the case for gradient elution. The concentration of the second eluent species increases from 5% to about 18% during elution. Figure 4.3C shows that the ref method has severe difficulties in returning a correct estimate of the analyte spectrum. The estimated spectra contain large spurious bands that do not originate from the analyte. The intensity of the analyte spectrum (at the correct band position) is also incorrect. In this case, the ebs method (Figure 4.3D) is not perfect, - a small positive band shows up at about 35 nm -, but the overall picture remains rather satisfactory. The correlation between the estimated and the true analyte 79

61 Spectral Intensity 1.5 A B Spectral Intensity.3.2 C 5 1 Channel Number.3 D Channel Number Figure 4.3: Results of simulation 2: Analyte and two eluent species, eluent composition is changing (see: Figure 4.2). A: Spectrum of analyte (solid), first background species (dashed) and second background species (dotted). B: Spectra during elution of analyte C: Reconstructed analyte spectra using the ref method. D: Same for the ebs method. spectrum is still high (.995, Table 4.1). A more difficult situation is considered in simulation 3. Instead of only one analyte as in simulation 2, three co-eluting analytes with overlapping spectra are used. The spectra of the compounds (three analytes and two background species) are shown in Figure 4.4A, the separate chromatographic profiles of the analytes are shown in Figure 4.4B. Figures 4.4C and 4.4D show some of the estimated analyte spectra recovered with the ref and the ebs method. It can be seen that the true spectral profiles at elution maximum of analytes can be recovered very well with the ebs method, but not with the ref method. For the ebs method only slight deviations of the true spectra occur at channel numbers between 3 and 5. This is also reflected in Table 4.1 (3 rd - 5 th entry) in which the figures of merit are collected. Correlation of estimated spectra with true spectra is high for the ebs method (>.999) and low (.5-.6) for the ref method. The mse values are very low for the ebs method (target value is zero) indicating no residual spectral variation. The mse values are higher for the ref method. 8

62 Spectral Intensity 1.5 A 5 1 Channel Number.6.3 B 1 2 Time /A.U. Spectral Intensity.3.3 C.3 D 5 1 Channel Number 5 1 Channel Number Figure 4.4: Results of simulation 3: Three co-eluting analytes and two eluent species. A: Spectra of the three analytes (1: dashed, 2: dash-dotted, 3: dotted) and of both background species (solid). B: Elution profiles of the three analytes separately (1: dashed, 2: dash-dotted, 3: dotted) and of the overall elution profile (solid bold line). C: The spectra (solid) at the three times of maximum elution (indicated by dots in B) reconstructed with the ref method. True spectra at the same points in time (dotted). Note that each true spectrum shown is the sum of the three analyte spectra because of co-elution of the analytes. D: Same as figure C, but for the ebs method. Finally, in the fourth simulation, a varying spectral baseline and spectral noise is added to the data generated in the simulation 2. The varying spectral baseline and noise are shown in Figure 4.5A. The generated spectral noise is white normal distributed noise (σ = 1 4 ). Figure 4.5B shows the reconstructed analyte spectra using the ref method. The disturbing spectral baselines have the shape of a second order polynomial. Figures 4.5C and 4.5D show that the overall results for the ebs method are still very similar to simulation 2. Adding noise and a varying baseline does not hamper the ebs method. In fact, the ebs method seems to be able to suppress spectral baseline fluctuations. The correlation between the estimated and the true analyte spectrum is only slightly lower (.976) than in simulation 2 (Table 4.1). When the reconstructed analyte spectrum would perfectly 81

63 Spectral Intensity B A Spectral Intensity.3.3 C 5 1 Channel Number.3 D Channel Number Figure 4.5: Results of simulation 4. A: Spectral baseline and spectral noise added. B: Reconstructed analyte spectra using the ref method. C: Same for the ebs method. D: True analyte spectrum (dotted), estimated analyte spectrum with the ebs method (solid) and the ref method (dashed) at maximum elution. match the true analyte spectrum the presence of spectral noise determines the lowest mse value. In that case the limiting mse would be 1 8 (=σ 2 ). It can be seen that both methods have an mse larger than this lowest possible value. The ref method, however, has a much higher mse value than the ebs method. To establish the effect of a different choice of the φ-value, the correlation between true and reconstructed analyte(s) spectral contribution is calculated as a function of the φ-value. The φ-value is varied between 1 1 and 1 5. Figure 4.6 shows the results for simulations 1 to 3 that have a different amount of spectral overlap between analyte and eluent spectra. It can be seen that for φ-values smaller than 1 2 the correlation is high (>.999) and slightly varying. Taking the φ-value larger than 1 2 decreases the correlation. Overall the correlation is not very sensitive to the φ-value (φ < 1 2 ). 82

64 1.999 correlation φ value Figure 4.6: Correlation between reconstructed and true spectral contribution of analyte(s) as a function of the φ- value of the ebs method. Data of simulation 1 (dotted), simulation 2 (dash-dot), simulation 3 (dash-dash) and data of simulation 1 disturbed by noise, S/N= 1 (solid) Application 1: Extracting Analyte Spectrum in LC- RAMAN In lc-raman both the analyte and the solvent (eluent) contribute to the Raman spectrum. Figure 4.7A shows the Raman spectrum of the eluent. The bands at 125, 112, 1171 an 1471 cm 1 are from methanol (dotted vertical lines) and the band at 1647 cm 1 (vertical dashed) is from water. Figure 4.7B shows the reference spectrum of AMP that was measured separately. The figure also shows the spectra that are recorded during analyte elution (Figure 4.7C). The inset shows the wavenumber range where strong analyte bands are present. No distinct analyte information can be found. Obviously, the eluent spectrum overwhelms the smaller analyte bands. The ebs method uses all spectra measured at baseline level to determine the B-space. The points in time that are used to determine this space are shown in Figure 4.8 (solid fat line showing the UV detector trace of the separation). The ind method finds four principal components. The asymmetry factor (φ) of the ebs method was set to.1. Figure 4.9 shows the estimated analyte spectra at maximum elution for both methods. Figure 4.9C shows the analyte spectrum and Figure 4.9A the residual spectral variation for the ref method. Figure 4.9B and 4.9D show 83

65 5 x 15 Intensity / cnts A 5 x 16 4 B Intensity / cnts 5 x C wavenumber / cm 1 Figure 4.7: A: Raman spectrum of solvent (eluent). Major bands of methanol (dotted vertical lines) and of water (dashed vertical line) are shown. B: Raman spectrum of analyte (AMP). C: Raman spectra measured during elution of AMP. Inset magnifies wavenumber range that should contain large analyte bands. 1.2 Absorbance / A.U Time / min Figure 4.8: UV-detector signal of AMP: (solid fat) points in time considered to be part of baseline. Spectra measured at these time points are used to determine the B-space. 84

66 REF EBS Intensity / cnts 5 A 5 B C D Intensity / cnts wavenumber / cm wavenumber / cm 1 Figure 4.9: Results for ref method (A and C). A: Residuals calculated using Eq C: Estimated AMP spectrum (solid) at elution maximum and true analyte spectrum (grayed solid). Results of the ebs method (B and D). The vertical dotted lines are drawn at strong bands of the eluent (1124 and 1468 cm 1 ). the results for the ebs method. The residual spectral variation is calculated using Eq It can be seen that the ref method fails in two ways. In the first place, two spurious bands can be seen in the estimated spectrum. These bands are located at approximately 1124 cm 1 and 1468 cm 1 (dotted vertical lines). At these positions strong bands are present in the spectrum of the eluent (Figure 4.7). These bands can be assigned to methanol. It appears that the concentration of methanol during AMP elution was not completely constant. Second, the analyte spectrum (the ref method) is more disturbed by baseline drift. This can be seen more clearly in Figure 4.1, where six estimated analyte spectra during AMP elution are overlaid. The spectral baseline drift is much smaller for the ebs method, although it has not been fully removed. In Figure 4.11A, the correlation coefficient of the estimated AMP spectrum and the known spectrum of AMP is plotted as a function of elution time. The ebs method has a fairly high correlation 85

67 Intensity / cnts] 75 5 A Intensity / cnts 75 5 B wavenumber / cm 1 Figure 4.1: A: Estimated analyte spectra during elution (the ref method). The gray solid line indicates a slow drift-like estimation artifact. B: Same for the ebs method. (>.9) at the elution maximum and has near zero correlations at the peakstart and the peak-stop times. On the other hand, for the ref method, the maximum correlation is smaller (.6) and at the peak-start and peakstop a small correlation (.2) still exists. The small correlations at peak start and peak stop can be traced back to the combination of the broad band-like features (see the gray line in Figure 4.1A) and the spurious bands at 1124 cm 1 and 1468 cm 1 in the estimated analyte spectra. When both effects are removed from the estimated analyte spectra, the correlation curve for the ref method starts and ends at approximately zero correlation (Figure 4.9A, dash-dotted curve), but also the maximum correlation drops to a lower value (<.5). Figure 4.9B shows that the variance of spectral residuals for the ebs method is close to the variance of the spectral noise. It is two orders of magnitude smaller than for the ref method. It was also checked whether the number of spectra used for estimating the B-space is critical. To a certain degree, changing the number of spectra does not affect 86

68 Correlation A Intensity / 1 6 cnts B 1 12 Elution Time / min 1 12 Elution Time / min Figure 4.11: A: Correlation coefficient between true AMP spectrum and estimated AMP spectrum as a function of elution time: the ebs method (solid line), the ref method (dashed line) and curve (dashdotted) of corrected (see text) analyte spectra (also the ref method). B: mse (Eq. 4.7) between the residuals of estimated AMP spectrum as a function of elution time: the ebs method (solid) and the ref method (dashed). The dotted horizontal line ( 5 x 1 4 ) is at instrumental noise level. the shape of the estimated analyte spectrum. Of course always more spectra should be used than the number of independent phenomena hidden in the baseline spectra (matrix X b ). Using more spectra improves the estimate of the B-space and stabilizes the estimated analyte spectrum Application 2: Background Correction in LC-DAD To further illustrate the feasibility of the ebs method, two (different) lcdad separations were performed. A mixture of four polystyrene standards was injected in each sample run. Immediately, after that, a blank run was recorded. Figure 4.12 shows the total spectral intensity in the uv-vis spectrum in the wavelength range from 2 to 3 nm for the sample and the blank runs. The settings for the ebs method were as follows. The spectra used to determine the B-space are indicated by dots. The asymmetry factor (φ) was.1. Similar results were obtained for φ-values between 1 5 and 1 1. No dependency on the value of φ could be detected. For the ref method, the 87

69 Total intensity 2 3 nm / A.U. 5 RUN RUN Time / min Figure 4.12: Total spectral intensity between 2 and 3 nm as a function of elution time. Dotted line is blank chromatographic run. RUN 1: Sample is mixture of four polystyrene standards (M p = 1.9, 17.6, 3., 39.2) in THF / Acetonitril. RUN 2: Sample is mixture of four polystyrene standards (Mp=1.9, 17.6, 39.2, 76.6) also in THF/Acetonitril; gradient is different. spectra just before and just after elution of the polystyrenes were selected (circles in Figure 4.12). For both lc-dad runs the adequate number of PC s was 3. The B-space thus has dimension 3. Two eluent species change in relative concentration during the chromatographic run. Therefore, it is expected to find at least a two dimensional B-space. The third dimension is apparently required to describe small disturbances in the eluent spectra during the run. Table 4.3 shows the results when the reconstructed analyte at peak maxima are compared with off-line measured uv-vis spectra of the standards. The correlation for the ebs method is somewhat higher than for the ref method, mse of the ebs method are lower. In Figure 4.13 for run 2 the reconstructed (the ref and the ebs method) spectra at the apex of the last peak are shown together with the off-line measured spectrum of the 39.2 standard. It can be seen that the ref method yields 88

70 a too high intensity of the estimated spectrum at low wavelengths (near 2 nm). This artifact is located at the position of strong THF band (2-21 nm). Thus, the change in the relative concentration of THF during the run will, for the ref method, still affect the overall spectral intensity of the estimated polystyrene spectrum. This explains the somewhat lower correlation coefficients and higher mse values for the ref method (Table 4.3). In order to show that the ebs method is more flexible in use than the Absorbance / A.U Wavelength / nm Figure 4.13: Mean spectrum of polystyrene standard 39.2 (solid line) measured off-line on HP8453 diode array spectrometer. For RUN 2 the reconstructed polystyrene spectra for the apex of the corresponding peak is shown: the ref method (dotted line) and the ebs method (dashed line). Run M p ρ REF ρ EBS mse a REF mse a EBS a ( 1 6 ) Table 4.3: Results of hplc-dad measurements. Comparison of off-line measured spectra of the standards with the reconstructed spectra using the ebs and the ref method for RUN 1 and RUN 2. Legend see Table

71 ref method the next processing was performed on the collected data. Only the spectra measured before elution of the polystyrene peak cluster (Figure 4.12), are used for correcting the contribution of the background signal (establishing the B-space). In effect, this means that the ref method now truly is an auto-zero method. Results in Figure 4.14 shows that the ebs method succeeds in nearly fully correcting the baseline of the runs, while the auto-zero method cannot fully correct for the baseline and some additional baseline correction procedure is needed. For both the ref and the ebs method the peak area ratios are the same as for the blank corrected chromatographic signal. Total intensity 2 3 nm / A.U. 5 RUN RUN Time / min Figure 4.14: Total spectral intensity between 2 and 3 nm is plotted as a function of elution time. Sample run signal corrected for blank run signal (solid line); signal corrected using auto-zero method method (dotted line), signal corrected using the ebs method (dashed line). Only the background spectra (shown in Figure 4.12) before elution of standards are used for correction. 9

72 4.6 Conclusions A new method (ebs) based on asymmetric least squares is proposed to eliminate the spectral contribution from the eluent in the hyphenated chromatography. Simulations and first tests of this background correction method on lc-raman and lc-dad data show its feasibility. Advantage of the method are that it only needs the data of one single chromatographic run and that each spectrum during analyte elution can be analyzed separately, without using relation to other spectra during elution. From simulations it can be concluded that the new method performs better than a straightforward spectral subtraction method (ref). This is also true in the presence of spectral noise. Furthermore, setting the value of the only parameter of the method (asymmetry factor) is easy and turned out not to be critical. The practical significance of the method is shown for an lc-raman and an lc-dad application. In lc-raman the ebs method can extract the analyte spectrum much better the ref method. A more extensive comparison between the methods is made in a companion publication [83]. In the lc-dad examples the performance advantage of the ebs method is smaller than for lc-raman. However, the flexibility of the ebs method allows one the correct for spectral background using only some spectra measured on one side of the eluting peak cluster. 91

73 Appendix A Derivation of the Optimal Design Criterion Eq. 3.1 is expanded in a Taylor series around a given initial value k of the kinetic constant (Eq. A.1), wherein R 1 indicates the Lagrangian remainder after a one term Taylor expansion. a t a e k t = t(k k )a e k t + R 1 (A.1) Then the time axis is made discrete. The interval along this discrete axis is determined by the time needed by the spectrometer to do one measurement. In general the time axis will therefore be equidistant because the settings of the spectrometer will not be changed during an experiment. However, no such assumption is needed in the derivation below. So, assume that measurements are done at N time points t i and define the (N 1) vector t to be [t 1, t 2, t 3,..., t N ]. Also take the vector a to contain the measured concentrations at these points in time: a = [a(t 1 ), a(t 2 ), a(t 3 ),..., a(t N )]. Substituting both vectors into Eq. A.1 and dropping the term R 1 leads to: a a e k t = a (k k ) t e k t (A.2) in which is the Hadamard product (element-by-element multiplication) of the two vectors. This vector equation can be written in the form: a a (k t + 1) e k t = a t e k t k (A.3) or, more simply, y = f k (A.4) 115

74 where 1 is an (N 1) vector of ones, and y and f are as defined in Eq. A.5. y = a a (k t + 1) e k t f = a t e k t (A.5) Solving Eq. A.3 is easy when is it viewed as a linear regression problem (see Eq. A.4), in which y contains the measured values, f contains the errorless ordinate and the scalar k is the parameter to be estimated. The solution [1] to this problem is given by Eq. A.6, in which T is the transpose operator. k 1 = (f T f) 1 f T y = f T y f 2 (A.6) Given the initial estimate k, Eq. A.6 supplies the update, k 1, of the reaction rate constant that has the lowest error. Using the assumption about the errors in the measured concentration (see above) and realizing that the time values in the vector t are error-free, the error structure of y is identical to the error structure of a. The error in the estimate k 1 is given by Eq. A.7, in which var(a) is variance of the concentration error and var(k 1 ) is the variance of the estimate of the rate constant. var(k 1 ) = f T f f 2 f 2 var(a) = 1 f 2 var(a) (A.7) Note that var(a) is a given value that depends on the instrumentation and the calibration model, and that the error in the estimated rate constant is minimized by maximizing the value of f 2. This result is known as a D-optimal design [121]. From Eq. A.5 one sees that the value of f 2 is determined by the time points (vector t) at which the samples are taken. A.1 The Best Point in Time to Perform a Measurement Suppose that it is possible to do only one concentration measurement during a reaction. At what point in time should that measurement be performed? In this specific problem the vectors t and f turn into scalars (t and f) and Eq. A.5 simplifies to: f = t a e k t (A.8) 116

75 Maximizing f 2 is now equivalent to finding the maximum of f 2. A simple calculation shows that there is one maximum, at t = 1/k. A.2 Evaluation of Specific Sampling Strategies in Time When multiple measurements can be performed on the same reaction, the above approach can be used to evaluate different sampling strategies. Assume, for example, that two strategies S x and S y should be compared, starting with the same initial estimate k. Strategy S x uses samples at the time points t x (an N x 1 vector) and strategy S y consists of measurements at points in time t y (N y 1). A simply comparison of the quantities f x 2 and f y 2 can be made. The sampling strategy that yields a higher value is better. When the ratio of the highest value with respect to the lowest is taken, it is even possible to state how much better a specific sampling strategy is. Writing out the expression for f 2 gives: N f 2 = f T f = a 2 t 2 i e 2 k t i i=1 (A.9) The constant a is irrelevant in deciding which strategy is better. The effectiveness of a given sampling strategy may be visualized simply by plotting the sampling times for this sampling strategy on the curve t 2 e 2 k t as is shown in Figure

76 Summary In this thesis methods are discussed to improve the extraction of quantitative and qualitative information from spectra. Mainly applications with vibrational spectroscopy are discussed: Raman, Infrared (ir) and near infrared (nir) spectroscopy, also some examples with uv-vis spectroscopy are supplied. In Chapter 1 and 2 the focus is on quantitative spectral processing of online nir spectra. In Chapter 3 a way to compare several sampling strategies to track first order kinetics is presented. Although the presented results are general, they are best suited for on-line spectroscopic measurements. In Chapters 4 and 5 the focus is on qualitative spectroscopic processing. The aim of qualitative processing is to detect the presence of new compounds and preferably also to identify them. The spectra of these new compounds are not known. So, the challenge of qualitative spectroscopic processing is to come up with a good estimate of the shape of the new compound spectra or new spectral features. Depending on the spectroscopic technique and the availability of spectral libraries identification of new compounds is then possible. In Chapter 1 [59] a feasibility study is performed, concerning the application of near-infrared spectroscopy (nir) in process industry. The purpose is to investigate whether it is possible to monitor the output gas stream of a mole-sieve process with nir. Mole-sieve processes have economic importance especially in petroleum industry. They are used to separate normal alkanes from branched chain hydrocarbons. Such a separation is needed, because new specifications of gasoline demand a lower aromatic content in the end product. Moreover, a high content of branched hydrocarbons is preferred 122

77 because this increases the octane number. Monitoring a mole-sieve process with nir offers the opportunity for further optimization and fine-tuning of the process settings (e.g. timing of valve switching). This is possible because nir is a fast technique (measuring time in the order of several seconds) that will give almost real time information about the composition of the output gas stream of the mole sieve process. Additionally, nir has a rather simple process interface, because optical fibers and a gas flow cell can be used. The conventional gas chromatographic (gc) technique on the other hand has a more cumbersome and vulnerable process interface and the measurement typically takes more time (at least several minutes). In the chapter an experimental set-up, a nir calibration model and a numerical analysis of that model is presented. It is shown that monitoring the mole-sieve process with nir spectroscopy is well feasible. An experimental set-up has been built that allows the analysis of the same gas sample by gas chromatography (reference method) and by nir. The set of gas samples that is analyzed is made according to a mixture design and the samples resemble the expected alkane composition at the outlet of the mole-sieve process. All these samples contain small amounts of low C normal alkanes and a varying composition of several important iso-alkanes and cyclo-alkanes. A pls calibration model is developed that extracts accurate information about the mole fraction normal alkanes in the gas mixture from the combination band region of the nir spectrum. With the help of this calibration model the critical level is determined. Above this level it is unlikely that no normal alkanes are present in the outlet stream. For a spectral measurement taking 1 seconds at a spectral resolution of 4 cm 1 the critical level found is.4% mole/mole. A numerical error analysis of this calibration model makes it possible to assess the relative contributions of several error sources to the overall modeling error. These contributions are (a) the error of the reference method (gc), (b) the spectral error of the spectra of the calibration samples and (c) the spectral error of the blank spectra that were used for determination of the critical level. It turned out that the overall error and therefore also the critical level is mainly determined by the spectral error in the blank measurements and to a lesser degree by the spectral error of the calibration 123

78 samples. Spectral noise and other instrument factors that cause spectral variation are thus dominating and the error of the reference method has only a relatively small contribution. Lowering of the critical level (L c ) is only possible by using a better instrument, or by increasing the measurement time (more time averaging). An alternative is proposed. It is possible to decrease the needed measuring time for a scan by selecting a lower spectral resolution. At such lower resolution in a fixed time interval more spectral scans can be averaged and this leads to a lower spectral noise. The disadvantage of selecting a lower resolution is that more band overlap will occur. This will make quantification more difficult. Several options to trade off the spectral resolution against a lower spectral noise in this case are discussed. During the development of this calibration model and other spectroscopic applications [ ] it turned out that spectral variation that is not related to the property of interest (eg. concentration of compounds) affects the performance a multivariate calibration model considerably. Using for example the raw measured nir spectra of the gas samples without any spectral pre-processing would not yield a useful critical level (L c > 1%). In Chapter 2 [37] this type of spectral variation and the impact on multivariate calibration models is investigated more in detail. The effect on quantification is analyzed with the help of the Net Analyte Signal (nas) concept. The nas concept allows for an elegant and clear description of a multivariate calibration situation. There are two different ways to deal with this non-related spectral variation. Pre-processing of the measured spectra before construction of the calibration model is a way to suppress spectral disturbances and to amplify the analytical spectra variation. Another option is to incorporate the systematic part of the spectral disturbances as instrumental interferents in the calibration model. Both options and combinations thereof are discussed in the chapter. When spectra are preprocessed often unwillingly the part of the relevant analytical spectral variation needed for quantification of the chemical composition of the sample is removed or distorted. In general this will deteriorate the detection limit of the analytical method. Therefore, the fine tuning of the specific combination of spectral pre-processing methods is crucial. To find a better or a near-optimal combination of pre-processing methods 124

79 a nas based criterion is derived and used in the chapter. The criterion is the empirically determined signal-to-noise ratio of the nas. A nice feature of this criterion is that almost no input from a reference method is needed. The selection of the best pre-processing method can thus be done (nearly) completely in the spectral domain. The major advantage is accordingly that optimization of pre-processing can still be done when the error of the reference method is relatively large. Additionally, a diagnostic plot is introduced that supplies insight at the spectral level how disturbances influence the final quantification. Such a plot might indicate which pre-processing methods to select. These ideas are later refined and applied to calibration models for nir reflectance measurements of pharmaceutical powders and transmission spectra of tablets [129]. Chapter 3 [13] deals with finding the optimal sampling strategy in the field of high throughput experimentation (hte). The characteristic of hte is that performing an experiment is very cheap and that the analyzer time becomes scarce. Therefore, doing an analysis, -even a spectroscopic analysis-, is relatively expensive. The problem is thus how to distribute the available (spectroscopic) analyzer time efficiently over a set of running reactions. In several publications sampling strategies are proposed and compared that contribute to the solution of this problem [13 134]. In the chapter the focus is on the optimal sampling of (pseudo) first order reactions. The general theory for optimal experimental design is applied to first order reactions. This leads to the use of an information vector. An entry in this information vector indicates for a point in time how much information about the reaction constant can be retrieved by a concentration measurement at that particular point in time. It is shown that such an information vector can be used very well to evaluate a proposed sampling strategy. It can thus equally well be used as part of an automatic procedure for hte that decides about the most interesting reaction to monitor at a given point in time. To quantify this the use of an information gain ratio is proposed. For each running reaction this ratio quantifies the amount of information that is gained when the measurement is actually assigned to a specific reaction. For the evaluation of potential sampling strategies of first order reactions a simple diagnostic plot based on the square of the information value is 125

80 introduced. The relevance of the study is shown by processing the uv-vis spectra measured during the 32 repeated pseudo first order reactions of a carbon-sulphur coupling of 3-chlorophenylhydrazonopropane dinitrile and β-mercaptoethoanol [81]. In Chapter 4 [135] a new method for background correction in hyphenated chromatography is introduced. Spectroscopy is not only used for direct analysis of samples, but can also be used as a detection technique after the sample has been subjected to a separation methods like liquid or gas chromatography. The advantage of such an indirect analysis is that spectra of the mixture passing the detector are considerably less complex than the spectra taken directly of the sample. For an optimized separation the mixture passing the detector (hopefully) contains one single analyte and the mobile phase. This mobile phase may still consist of more than one chemical species. Normally, the presence of a spectroscopic active species in the mobile phase is considered a disadvantage, because it may overload the detector or it may interfere with the spectral contribution of the analyte. Another reason is that the amount of analyte is usually very small and therefore the spectral contribution of the mobile phase compounds in such cases may completely blur the analyte contribution. In case of spectral active mobile phase components the challenge is to extract the unknown spectrum of the analyte. It is assumed that information about the spectral contribution of the mobile phase compounds can be collected. Analyzing the spectra measured during chromatographic baseline will yield this information. Moreover, it will supply knowledge about instrumental spectral variation. A pca model is used to capture all the systematic spectral variation. Now the spectrum measured during analyte elution can be partially modeled. For most spectroscopic techniques the true analyte spectrum is essentially positive. This property can be used as restriction on the partial data model. Such a restriction can be exploited by an asymmetrical least squares algorithm. Using this algorithm the intensity and shape difference of total spectral contribution of the mobile phase can be estimated for each spectrum measured during analyte elution. In this way better estimates of the analyte spectrum can be achieved, compared to conventional methods. The new method is applied to lc-raman data and lc-dad data. For the 126

81 lc-raman data it is shown that the method is able to extract the raman spectrum of the analyte better. For the lc-dad data the method proved to be slightly better and more flexible in use. Dijkstra et al. [83] performed an elaborate evaluation of the background correction method for lc-raman spectra. In Chapter 5 two methods to detect differences between two or more spectral data sets are compared. When two sets of samples (reference and test samples) are compared that only differ slightly in their properties, it is interesting to know whether one set of samples contains new chemical components or functional groups. The problem thus is to find the real new spectral features of the spectrum of a test sample. Depending on the type of spectroscopy used the new spectral features can traced back to new functional groups or new compounds that are present in the test sample. The next problem, however, will occur. Assuming that the spectra of the reference samples are linear combinations of the spectra of chemical components of the reference samples, it is possible that the spectrum of the test sample has a contribution of these reference components that is different from that in any reference sample. This spectral change is non-relevant for detection new components or function groups in the test samples, but such a spectral change may prevent the easy detection of new spectral features. Essentially the same framework is used as in the previous chapter. Now the set of reference spectra is modeled by a pca model that captures all systematic spectral variation. Subsequently, this pca model is used as partial model for the spectra of the other the test set. Residuals with respect to this model are calculated in two ways. Conventionally, the residuals are calculated as what remains after ordinary least squares modeling (ols). Here it is proposed to use an asymmetrical least squares to calculate the residuals (als). In this application of als the positive residuals receive less weight than the negative residuals. This approach is justified because after pre-processing many spectroscopic techniques yield essentially positive quantities. The simulations in the chapter indicate that interpretability and detection of new spectral features is considerably better for the als than for the ols method. As a test several sec-ir measurements on polymer mixtures are analyzed. It is shown that the als based procedure yields the best recovery of these new spectral features in this case. Band positions and band 127

82 shapes of new spectral features are better retrieved with the als method. The fact that als leaves the band shapes of the new features largely intact means that the signal produced by als can be interpreted as an regular ir spectrum. Additionally, the retrieved band intensity is higher for als. The als method thus has better detection properties and is a more sensitive technique to find new spectral features. Finally, for als the band intensities are closer to their true intensity. This offers the opportunity to use the als method semi-quantitatively in the application. Kok [136] used the ols technique described here in a study to trace the chemical changes during aging of polymers with sec-ir. 128

83 Samenvatting In dit proefschrift worden methoden besproken om kwantitatieve en kwalitatieve informatie te halen uit spectroscopische metingen. Het gaat daarbij met name om vibrationele spectroscopie: Raman, Infrarood (ir) en Nabij Infrarood (nir) spectroscopie, en verder om uv-vis spectroscopie. In hoofdstuk 1 en 2 staat de kwantatieve verwerking van on-line nir metingen centraal. In hoofdstuk 3 wordt een methode gepresenteerd om de verschillende bemonsteringsstrategieen voor het volgen van eerste orde kinetiek te vergelijken. De resultaten in dit hoofdstuk zijn algemeen toepasbaar. Ze zijn echter het meest relevant voor spectroscopische metingen. In hoofdstuk 4 en 5 staat qualitatieve spectroscopische data verwerking centraal. Het doel daarvan is de aanwezigheid van nieuwe componenten te detecteren en deze vervolgens zo mogelijk ook te identificeren. De eerste stap bestaat erin om een zo goed mogelijk schatting te krijgen van de nieuwe spectral banden die aanwezig zijn. In hoofdstuk 1 [59] wordt de haalbaarheid van on-line NIR spectroscopie onderzocht voor het monitoren van de gasstroom aan de uitgang van een molekulair zeef proces. Het gaat om een proces dat vaak in de petrochemische industrie wordt gebruikt om normaal alkanen te scheiden van iso- and cyclo-alkanen (gasfase). Het volgen van het proces met nir biedt de mogelijkheid om de proces instellingen verder te optimaliseren en aan te passen. Dit is mogelijk omdat nir een snelle analyse methode is (de meettijd is slechts enkele seconden) die vrijwel real time compositie informatie kan geven over van het uitstromende gas. Ook is de interface die nodig is voor de bemonstering van de gasstroom, voor online NIR relatief simpel (doorstroomcel en optische fibers). Met conventionele gas chromatografische methode is de bemonstering van de gasstroom moeizamer. Verder kost een GC meting meer tijd (in de orde van minuten). In het hoofdstuk worden de volgende onderwerpen besproken: (1) een experimentele laboratorium opstelling en een experimenteel ontwerp om de vergelijking tussen de twee methoden (NIR versus GC) mogelijk te maken. (2) de ontwikkeling van een multivariaat calibration model om de fractie normaal alkanen in de gasstroom aan de uitgang van het proces te bepalen op basis van een on- 129

84 line gemeten spectrum. (3) een numerieke analyse om de kritische grens voor deze on-line NIR analyse te bepalen. Het bleek dat bij een meettijd van 9 seconden de kritische grens (L c ) voor de hoeveelheid normaal alkanen in de gasstroom.4% mol/mol is. Verder kon worden vastgesteld dat de spectrale ruis van de calibratie monsters en de blanko s voor de waarde van deze kritische grens doorslaggevend is. Verdere verlaging van de kritische grens is dus alleen mogelijk wanneer de spectrale ruis wordt verlaagd door bijvoorbeeld een betere instrument te gebruiken, of door de meettijd te verhogen. Een andere optie is om de spectra te meten bij een lagere spectrale resolutie. Gebruik van een lagere resolutie maakt het mogelijk om meer spectra te meten in hetzelfde tijdsinterval. Dit betekent dat meer spectra kunnen worden gemiddeld. De signaal-ruis verhouding van het uiteindelijke spectrum is daardoor beter. Een nadeel van het gebruik van een lagere spectral resolutie is dat meer spectrale overlap plaatsvindt. Dit maakt kwantificatie moeilijker. In het hoofdstuk wordt de relatie tussen meettijd, kritische grens en spectral resolutie besproken. In hoofdstuk 2 [37] wordt de invloed van de spectrale variatie die niet gerelateerd is aan de chemische compositie van een monster nader bekeken. Met hehulp van de zogenaamde net analyte signal benadering wordt deze invloed geanalyseerd. Er zijn twee manieren om de genoemde spectral variatie, de niet- relevante spectrale variatie, te behandelen. De eerste mogelijkheid is om de gemeten spectra te bewerken voordat een calibratie model wordt gemaakt. Deze bewerking heeft als doel de ongewenste niet-relevante spectrale variatie zoveel mogelijk te onderdrukken. Een andere optie is om het systematische deel van de niet-relevante spectrale variatie expliciet te gebruiken bij het maken van het calibratie model. Deze spectral variatie wordt zo behandeld als een instrumentele interferent. Beide mogelijkheden en combinaties daarvan worden in het hoofdstuk besproken. Bij het voorbewerken van spectra wordt vaak ook ongewild een deel van de relevante spectrale variatie verwijderd of vervormd. In het algemeen verslechtert daardoor de detectiegrens van de analyse. Het correct instellen van de combinatie van voorbewerkingsmethoden is dus van belang. Om de beste instelling van de voorbewerking van de spectra te vinden wordt de empirisch bepaalde signal-ruis verhouding van de nas geintroduceerd. Het voordeel is dat zo goed als geen informatie van een referentie analyse methode nodig is. De selectie van de juiste voorbewerkingstechniek kan dus vrijwel geheel plaats vinden in het spectrale domein. Dit betekent dat selectie ook nog mogelijk is wanneer er sprake is van een relatief grote meetfout in de referentie analyse. In het hoofdstuk wordt verder een diagnostische plot geintroduceerd. Dit plot geeft op spectraal niveau inzicht hoe verstoringen de uiteindelijke kwantificatie beinvloeden. Zo n plot kan ook een aanwijzing geven over andere geschikte voorbewerkingsmethoden. 13

85 De aanpak beschreven in dit hoofdstuk is later gebruikt en verder uitgebreid voor verbetering calibratie modellen voor nir reflectie metingen aan farmaceutische poeders en de nir transmissie metingen aan tabletten [129]. Het hoofdstuk 3 [13] handelt over het vinden van een goede bemonsteringsstrategie een voor een bepaald type high throughput experimenten (HTE). Karakteristiek voor HTE is dat het uitvoeren van een reactie goedkoop is. Daardoor wordt het uitvoeren van een analyse, zelfs van een spectroscopische analyse, relatief duur. Het probleem is dus hoe de beschikbare analyse tijd het best verdeeld kan worden over de actieve, nog lopende reacties. In een aantal publicaties worden diverse bemonsterings strategieen besproken en vergeleken [13 134]. In dit hoofdstuk staat de beste strategie voor het bemonsteren van (pseudo) eerste orde reacties centraal. Daartoe wordt de algemene experimental design theorie toegepast op eerste orde reacties. Dit leidt tot het gebruik van de informatie vector. Een getal in de informatie vector geeft voor het corresponderend tijdstip aan hoeveel informatie over de reactie constante van de eerste orde reactie kan worden verkregen door op precies dat tijdstip een (concentratie) meting te doen. Het ligt voor de hand deze informatie vector te gebruiken om bemonsteringsstrategieen te evalueren. Bovendien kan de informatie vector toegepast worden in een automatische procedure waarin beslist wordt aan welke lopende reactie op dat tijdstip het best gemeten kan worden. Ten behoeve hiervan wordt de information gain ratio geintroduceerd. Voor elke lopende reactie geeft deze factor aan hoeveel informatie winst voor een specifiek reactie gehaald wordt, indien de meting aan die reactie wordt uitgevoerd. In het hoofdstuk wordt verder een plot geintroduceerd om de potentiele bemonsteringsstrategieen voor een eerste orde reactie op eenvoudige wijze visueel te evalueren. De aanpak wordt geillustreerd en getest door een analyse van de uv-vis spectra die gemeten zijn aan 32 herhaalde pseudo eerste orde reacties van 3 chlorophenylhydrazonopropane en β mercaptoethanol. In hoofdstuk 4 [135] wordt een nieuw methode voor achtergrond correctie in hyphenated chromatografie geintroduceerd. Spectroscopie wordt niet alleen gebruikt om direct de chemisch samenstelling van een monster te analyseren, maar kan ook worden gebruikt als een detectie methode na een scheiding van het oorspronkelijk monster bijvoorbeeld in vloeistofof gaschromatografie. Vanuit dataverwerkingsoogpunt is het voordeel van een dergelijke indirecte spectroscopische analyse dat de mengsels die uiteindelijk spectroscopische worden geanalyseerd minder componenten bevatten en de gemeten spectra dus eenvoudiger zijn. Voor een geoptimaliseerde scheiding bevat het mengsel dat de detector passeert alleen analiet en mobiele fase. Die mobiele fase kan echter meer dan een component bevatten. De aanwezigheid van een spectroscopische actieve mobiele fase component wordt vaak gezien als een nadeel. 131

86 Dit komt omdat de spectrale activiteit van de mobiele fase componenten aanleiding kan geven tot het optreden van verzadiging van de detector. Verder kan interferentie optreden met het analiet spectrum. Een andere reden is dat de hoeveelheid analyte erg klein is en dat daarom de spectrale bijdrage van de mobiele fase componenten de spectrale bijdrage van de analiet volledig overheerst. Het doel is hier om het onbekende analiet spectrum zo goed mogelijk te reconstrueren. Daarbij wordt aangenomen dat er informatie over de spectrale bijdrage van de mobiele fase componenten kan worden verkregen. De analyse van de spectra die worden gemeten gedurende basislijn elutie, levert deze informatie. Bovendien wordt kennis over de instrumentele spectrale variatie verkregen. Een pca model wordt gebruikt om al die systematische spectrale variatie te beschrijven. Dit pca model is een partieel model voor de spectra gemeten gedurende analiet elutie. In de meeste spectroscopische technieken is het analiet spectrum een positieve grootheid. Deze eigenschap kan worden gebruikt als een restrictie op het partiele data model. Een asymmetrische kleinste kwadraten (als) methode kan dit type restrictie op een handige manier gebruiken. Met de als methode kunnen de intensiteits en de vorm verschillen van de bijdrage van de mobile fase componenten voor elk spectrum worden geschat. Op deze wijze kan een betere schatting van het analiet spectrum worden verkregen dan met een conventionele achtergrond correctie methoden. De nieuwe methode is toegepast op lc-raman en lc-dad data. Voor de lcraman data blijkt de methode in staat te zijn om het analiet spectra beter te reconstrueren. Voor de lc-dad data is de methode iets beter en flexibeler in gebruik. Dijkstra et al. [83] geven een uitgebreide evaluatie van deze achtergrond correctie methode voor lc-raman spectra. In hoofdstuk 5 worden twee methoden vergeleken om verschillen tussen verzamelingen van spectra te detecteren. Wanneer twee groepen van monsters (referentie en test samples), die maar weinig verschillen, worden vergeleken, is het interessant om te weten of de ene groep van monsters nieuwe componenten of nieuwe functionele groepen bevat. Het gaat er dus om welke echt nieuwe spectrale kenmerken het spectrum van een test sample heeft. Afhankelijk van het type spectroscopie is het soms mogelijk de gevonden spectrale kenmerken terug te voeren op nieuwe functionele groepen of op nieuwe componenten die aanwezig zijn in het test monster. Bij het zoeken naar die nieuwe spectrale kenmerken treedt het volgende probleem op. Neem aan dat de spectra van de referentie samples lineair combinaties zijn van de spectra van de chemische componenten van de referentie samples. Dan is het mogelijk dat de bijdrage van die referentie componenten in een test sample anders is dan in de verzameling van referentie samples. Deze verandering in het spectrum is echter niet relevant voor het vinden van nieuwe functionele groepen of 132

87 nieuwe componenten in het test sample, maar ze kan wel de detectie van nieuwe spectrale kenmerken hinderen. Hier wordt dezelfde aanpak gekozen als in het voorafgaande hoofdstuk. Van de verzameling van refentie spectra wordt alle systematische spectrale variatie zo goed mogelijk beschreven in een pca model. Dit pca model wordt vervolgens gebruikt als een partieel model voor het gemeten test spectrum. De residuen van het test spectrum ten opzichte van dit partiele model worden berekend op twee manieren. Het is gebruikelijk die residuen te bepalen na toepassen van een gewone kleinste kwadraten methode (ols). Hier wordt voorgesteld om een asymmetrische kleinste kwadraten methode (als) te gebruiken om de residuen te bepalen. In de gekozen vorm van als krijgen de positieve residuen beduidend minder gewicht dan de negatieve residuen. Deze weging kan worden gerechtvaardigd omdat veel spectroscopische technieken spectra opleveren die positieve grootheden zijn. De simulaties in het hoofdstuk laten zien dat met de als methode de detectie en de interpretatie van nieuwe spectrale verschijnselen beduidend beter gaat dan met de ols methode. Als test zijn er verschillende data sets van sec-ir metingen aan polymeer mengsels geanalyseerd. Het blijkt dat als beter in staat is om nieuwe spectrale kenmerken te vinden. De positie en de vorm van een nieuwe band kan beter worden teruggevonden met de als methode. In feite kan het residuele signaal van de als methode geinterpreteerd worden als een regulier ir spectrum. Verder is de intensiteit van de gevonden band groter met als. De als methode heeft dus betere detectie eigenschappen en is een gevoeliger techniek om nieuwe spectrale kenmerken te vinden. Tenslotte ligt voor de als methode de intensiteit van de gevonden band dichtbij die van de werkelijke band. Dit biedt de mogelijkheid om de als methode in dit geval (semi)kwantatief te gebruiken. Kok [136] heeft de ols aanpak gebruikt in zijn studie naar het vinden van chemische verandering tijdens de veroudering van polymeren. 133

88 Acknowledgements Many people have been around me during the work that is presented here. First of all I like to thank Age for giving me large and open spaces to move in and, -at essential points in time-, for presenting people, problems and interesting research fields to me. Age s clear and systematic way of stripping a problem to its essentials is a joy to watch. His rational and quiet approach of any kind of problem is an example for me. Wim was bringing analytical common sense to the things I was doing and is in that respect still a kind of yardstick. His sense of humor makes him a very agreeable person. I am further indebted to Onno that helped me to set the first steps in the unknown Near Infrared territory (Chapters 1 and 2). I thank Gadi, Johan and David for the very stimulating period of time, more than a year ago in which we were publishing like hell (among which the text of chapter 3 of the thesis). Gadi showed me another way to approach scientific work and another way to write introductions to publications; quicker and more optimistic. Johan always delivers loads of careful criticism on anything you give him to read, for which I thank him. Especially, the chapter 4 in this thesis benefited from his criticism. Paul was a kind of advisor in the background. Several years ago we were starting on a (still pending) project of spectral baseline estimation using asymmetrical least squares (als). It took me some time to realize that als can be used very fruitfully to solve other problems too. The results are Chapter 4 and 5 of the thesis. Paul has a sharp mind and the rare ability to distinguish between senseless and more targeted data-processing techniques. He is not very fond of a detailed comparison of techniques: short and simple is his approach. So, he probably thinks there is still too much fuss in the last two chapters of this thesis. Thanks Paul! 134

89 Chapter 4 in fact is also a spin-off of a baseline correction problem that Reyer encountered in LC-Raman. We worked for some time together on this and other spectral data processing; thanks for that time, Reyer! Fiona is thanked for supplying me with some of her LC-DAD data on polymers. Thomas was helping me a lot in the SEC-IR project (Chapter 5) that was triggered by a seemingly simple question of one of his PhD students Sander Kok. Sander was interested to characterize the aging of polymers and helping him gave me the idea for the last chapter of the thesis. Thomas arranged some new and clean measurements at TNO (thanks to Erwin of TNO). Thanks, Thomas for all your kindly presented remarks that helped to improve work and text! Funny, that some strange cosmic, event seems to synchronize our lives since: we married, moved and we will be nearly simultaneously fathers in the very near future. I thank all former members (Ad, Steve, Sabina, Renger, Florian, Frans) and current members (Age, Johan, Huub, Jeroen, Olja, Eric, Susana, Maikel, Suzanne, Robert, Henk-Jan, Jos, Rimmy, Coen, Alexandra) of our group and of the polymer analysis group (Peter, Petra, Monique, Simona, Fiona, Aschwin, Inger Lill (and Morten), Mauro, Filipo, Wim, Bas, Gabriel) for making live and work enjoyable. Some of them were indirectly contributing to this. Explaining, for example the net analyte signal approach to Susana in her first year helped me to write Chapter 2 of the thesis more clearly and Huub sharpened my mind in the time we were cooperating on Frans thesis (thanks). Some were more directly involved with the thesis. Jeroen, I much enjoyed the balcony sessions that preceded the conception of my thesis. The TIPb ers are thanked for giving one more reason to finish a PhD. Wim was always available to answer all kinds of software questions. Maikel, thanks for kicking me off with the TEX typesetting, Jos for advices when I was stuck in TEX again, and my gentle roommate Suzanne for bearing my puffing when struggling to convert already published text into a thesis. The members of the commission I thank for their time spent on reading the thesis and their effort to come up with questions. Most of all I am grateful to Olja. She gave me the reason to start this and she surrounds me with so much love that it makes a thesis look very small. And that helps a lot to finish it. My parents, finally, are at the basis of this all. Their love and support also generated this in the end. It took some time to grow, but here it is

90 CV and Publication List I got my Bachelor s and Master s degree in Electrical Engineering at University of Twente. My specialization at that time was bio-informatics. Since then, I am working as a research analist at the Universiteit van Amsterdam. For some 8 years now I am a member of the Process Analysis and Chemometrics group of prof. Age Smilde. This group changed its name lately into Biosystems Data Analysis group and moved into the field of systems biology. Next to my regular job I am for 1 year a consultant for a spin-off company of the University (TIPb). My main expertise is in the field of regression modeling, time series analysis and multivariate calibration. Most of my publications concern (new) methods for improved processing and analysis of chromatographic and spectroscopic data. Contact me: tel: fax: hans.boelens@science.uva.nl Web: hboelens 136