Anal. Chem. 1998, 70, 1726-1734
Evaluation Techniques for Two-Way Data from in Situ Fourier Transform Mid-Infrared Reaction Monitoring in Aqueous Solution Erik Furusjo 1 ,† L.-G. Danielsson,*,† Erik Ko 1 nberg,‡ Maria Rentsch-Jonas,‡ and Bert Skagerberg‡
Department of Analytical Chemistry, Royal Institute of Technology, S-100 44 Stockholm, Sweden, and Chemical Process Development Laboratory, Astra Production Chemicals, S-151 85 So¨ derta¨ lje, Sweden
A model chemical reaction was monitored with in situ Fourier transform mid-infrared spectroscopy using an attenuated total reflectance probe. The evaluation of the IR spectra is complicated by the fact that the reaction runs in nonisothermal aqueous solution with large variations in pH. Despite this, it was possible to extract large amounts of useful information on the reaction after suitable pretreatment of the spectra. Alternating leastsquares (ALS) multivariate curve resolution is shown to be a useful technique for obtaining pure component spectra and concentrations if suitable spectral regions are analyzed. Rank mapping methods are used as the basis for this sectioning into smaller regions. Techniques for finding and analyzing selective spectral regions are also shown to be applicable to this type of data. Partial leastsquares (PLS) regression models based on spectral data were used to verify the results where possible. The correlation between the concentrations predicted from PLS and ALS is excellent. In situ mid-IR monitoring can provide large amounts of information concerning a chemical reaction. This information can be used for both fundamental mechanistic and kinetic investigations of reactions and in process control. The information provided by in situ measurements is unique in the sense that no sampling, quenching, or workup is needed that may alter the composition of the reaction mixture. This is of special importance when unstable reaction intermediates are present and in fast reactions. In addition, problems with obtaining representative samples from heterogeneous solutions are well-known by analytical chemists. Virtually all organic functional groups exhibit fundamental absorptions in mid-IR that can be used to obtain information on molecular structure.1 Further, the narrow absorption bands reduce spectral overlap. The mid-IR range is thus advantageous for reaction monitoring in many respects, as compared to the more commonly used near-infrared (NIR) and UV-visible ranges. However, mid-IR absorptions are also known to change in * Corresponding author: (e-mail)
[email protected]; (fax) +46-8-108425. † Royal Institute of Technology. ‡ Astra Production Chemicals. (1) Colthup, N. B.; Daly, L. H.; Wiberly, S. E. Introduction to Infrared and Raman Spectroscopy; Academic Press: London, 1990.
1726 Analytical Chemistry, Vol. 70, No. 9, May 1, 1998
frequency and band shape, due to intermolecular forces, e.g., hydrogen bonding and temperature.1 These effects complicate the evaluation of mid-IR data. Mid-IR light can be interfaced to the reaction mixture using an attenuated total reflectance (ATR) probe comprising a thin diamond disk fitted in a corrosionresistant steel mount. This setup makes measurements possible in very aggressive environments and at high temperatures. Further, only a thin film (∼10 µm) close to the cell surface constitutes the actual analytical sample. Thus, spectra from a slurry are in general only affected by the properties of the liquid phase. The theory for ATR measurements has been thoroughly described by Harrick2 and Mirabella and Harrick.3 For mid-IR monitoring of some less complicated reactions, calibration using a single frequency or the ratio of two frequencies has proven adequate to obtain concentration profiles.4,5 For reactions that are more complex, the spectral selectivity obtained might not be enough to allow this simple approach. Partial leastsquares regression (PLS) has been used to overcome this difficulty.6 PLS calibration is not possible if samples cannot be analyzed with a reference method. This is the case when a reaction is largely unknown or external analysis is not possible, e.g., due to the sampling problems described above. In addition, development of reference analysis methods is time-consuming and it is advantageous if this work can be avoided. Self-modeling curve resolution, introduced by Lawton and Sylvestre,7 aims at resolving two-way spectral data into concentration profiles and pure absorption spectra of the constituents without a priori knowledge about the system. These techniques allow determination of concentration profiles from two-way spectral data without calibration samples. Examples are iterative target transformation factor analysis (ITTFA),8 evolving factor analysis (EFA),9-11 simple-to(2) Harrick, N. J. Internal Reflection Spectroscopy; John Wiley & Sons: New York, 1967. (3) Mirabella, F. M.; Harrick, N. J. Internal Reflection Spectroscopy: Review and Supplement; Harrick Scientific: Ossining, NY, 1985. (4) Doyle, W. M.; Jennings, N. A. Spectrosc. Int. 1990, 2, 48-52. (5) Moser, W. R.; Berard, J. R.; Melling, P. J.; Burger, R. J. Appl. Spectrosc. 1992, 46, 1105-1112. (6) MacLaurin, P.; Crabb, N. C. Anal. Chem. 1996, 68, 1116-1123. (7) Lawton, W. H.; Sylvestre, E. A. Technometrics 1971, 13, 617-633. (8) Vandeginste, B. G. M.; Derks, W.; Kateman, G. Anal. Chim. Acta 1985, 173, 253-264. (9) Maeder, M. Anal. Chem. 1987, 59, 527-530. (10) Maeder, M.; Zillian, A. Chemom. Intell. Lab. Syst. 1988, 3, 205-213. S0003-2700(97)01140-2 CCC: $15.00
© 1998 American Chemical Society Published on Web 03/21/1998
Figure 1. (a) Hydrolysis of phosphonoformic acid triethyl ester 1. (b) Side reaction resulting from initial attack on the carbonyl carbon of 1.
use interactive self-modeling mixture analysis (SIMPLISMA),12 orthogonal projections approach (OPA),13,14 and heuristic evolving latent projections (HELP).15-17 Most of these techniques have been developed and used for rank determination and resolution of data from HPLC with diodearray detection in the UV-visible range (HPLC-DAD), and some are not well suited for data from reaction monitoring. HELP, for example, relies on selective time regions in the data that are usually present in chromatographic data. This is almost never the case in data from reaction monitoring. The self-modeling curve resolution methods have a built-in capability for determining the rank of the spectral matrix. In addition, there are methods for mapping the local rank in parts of a spectral matrix, as a primary step prior to resolution, e.g., eigenstructure tracking analysis (ETA)18,19 and fixed-size window evolving factor analysis (FSW-EFA).20 Latent projective graphs (LPG)15 is used for finding selective regions in the data as a part of the HELP approach. Recently an investigation concerning the applicability of some different curve resolution techniques on data from LC hyphenated with FT-IR was published.14 The authors succeeded in resolving overlapping peaks from the chromatographic separation of a reaction product mixture and made suggestions on the identity of the constituents based on the resolved pure analyte spectra and chemical knowledge. This demonstrates the benefit of applying curve resolution to mid-IR data, as in the present work. SIMPLISMA has been used for resolution of Raman spectral data from reaction monitoring,12,21 and an application of curve resolution to IR data collected during an industrial reaction has been published.22 The chemical reaction used as a model system in this work (Figure 1) is the hydrolysis of triethyl phosphonoformate (1) in (11) Keller, H. R.; Massart, D. L. Chemom. Intell. Lab. Syst. 1992, 12, 209-224. (12) Windig, W.; Guilment, J. Anal. Chem. 1991, 63, 1425-1432. (13) Cuesta Sa´nchez, F.; Toft, J.; van den Bogaert, B.; Massart, D. L. Anal. Chem. 1996, 68, 79-85. (14) Cuesta Sa´nchez, F.; Vandeginste, B. G. M.; Hancewicz, T. M.; Massart, D. L. Anal. Chem. 1997, 69, 1477-1484. (15) Kvalheim, O. M.; Liang, Y.-Z. Anal. Chem. 1992, 64, 936-946. (16) Kvalheim, O. M.; Liang, Y.-Z. Anal. Chem. 1992, 64, 946-953. (17) Liang, Y.-Z.; Kvalheim, O. M. Chemom. Intell. Lab. Syst. 1993, 20, 115125. (18) Toft, J.; Kvalheim, O. M. Chemom. Intell. Lab. Syst. 1993, 19, 65-73. (19) Cuesta Sanchez, F.; Toft, J.; Kvalheim, O. M.; Massart, D. L. Anal. Chim. Acta 1995, 314, 131-139. (20) Keller, H. R.; Massart, D. L. Anal. Chim. Acta 1991, 246, 379-390. (21) Vacque, V.; Dupuy, N.; Sombret, B.; Huvenne, J. P.; Legrand, P. Appl. Spectrosc. 1997, 51, 407-415. (22) Tauler, R.; Kowalski, B.; Fleming, S. Anal. Chem. 1993, 65, 2040-2047.
NaOH(aq). The reaction mechanism and kinetics of this type of reaction in CH3CN/H2O mixtures has been the subject of some investigations.23-25 Two separate reaction pathways are possible, depending on the site of initial nucleophilic attack from the hydroxide ion.23 If the phosphorus atom of 1 is attacked initially, the reaction proceeds according to Figure 1a. The reaction products are the trisodium salt of phosphonoformic acid (4) and 3 equiv of EtOH. The two intermediates in this reaction, 2 and 3, will be denoted the diester and the monoester, respectively, in the remainder of this text. 4 will be denoted the product. If the initial nucleophilic attack occurs on the carbonyl carbon of 1, a side reaction according to Figure 1b is initiated.23 The resulting carboxylate anion decomposes to CO2 and a phosphite diester 6. Hydrolysis of 6 yields a phosphite ion 7 and EtOH. In this reaction pathway, the final products are 7, carbonate, and EtOH (3 equiv). The reaction is performed as a semibatch process. The starting material is added at constant rate to the NaOH solution under isothermal conditions. The solubility of 1 in NaOH(aq) is low, resulting initially in an oil/water two-phase system. When the reaction mixture is heated to drive the reaction to completion, EtOH is distilled off and the formed product precipitates, thus resulting in another two-phase system. In the final phase of the process, the mixture is allowed to cool, leading to further crystallization of product. The model system was chosen because the reaction process involves several potential difficulties in quantitative in situ IR measurements: aqueous solution, large variations in pH, temperature, and concentration of H-bonding species, and multiphase mixtures. One aim of this study was to determine whether these difficulties can be overcome and what limitations they pose to the data evaluation. In the present work, the rank of the spectral data matrix is determined by EFA, FSW-EFA, and LPG. Resolution is accomplished by a constrained alternating least-squares (ALS) procedure, with initial estimates of concentration profiles from EFA. PLS models are also developed for two species. The results from the two techniques are compared with concentrations from external HPLC analysis to validate the results and to determine the applicability of these techniques to mid-IR reaction monitoring data. METHODS Principal component analysis (PCA) and PLS regression are well-established chemometric techniques and are assumed familiar to the reader. Algorithms can be found, for example, in the book by Martens and Naes.26 Instead, this section will deal briefly with the methods used for rank determination and resolution of secondorder data. Matrices are indicated by bold, uppercase letters. Column vectors are indicated by bold lowercase letters and row vectors are written as transposed column vectors. Scalars are denoted by italic letters. (23) Krol, E. S.; Davis, J. M.; Thatcher, G. R. J. J. Chem. Soc., Chem. Commun. 1991, 2, 118-119. (24) Krol, E. S.; Thatcher, G. R. J. J. Chem. Soc., Perkin Trans. 2 1993, 793794. (25) Mitchel, A. G.; Nicholls, D.; Walker, I.; Irwin, W. J.; Freeman, S. J. Chem. Soc., Perkin Trans. 2 1991, 1297-1303. (26) Martens, H.; Naes, T. Multivariate Calibration; John Wiley & Sons: Chichester, U.K., 1989.
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Spectra are collected at regular time intervals during the reaction. The collected spectra are ordered with respect to time in a data matrix X (ns × nf), where ns denotes the number of collected spectra and nf the number of frequencies at which absorbances were measured. Under the assumption of bilinearity, the signal part of the matrix can be decomposed into pure analyte spectra (ai, nf × 1) and concentration profiles (ci, ns × 1) according to
X)
∑ ca
T
i i
) CA
(1)
nc
where nc is the number of chemical components. The matrices C and A are formed by combining the c and aT vectors, respectively. The aim of curve resolution is the decomposition of X into physically meaningful matrices C and A. Chemical Rank Determination and Rank Mapping. For successful resolution of X, it is essential to know the number of absorbing chemical components, i.e., the chemical rank of the matrix. PCA can provide the chemical rank of X in terms of the size of the eigenvalues. When these no longer decrease with increasing number of factors or are smaller than a predetermined level, noise is assumed responsible. If the system is complicated, i.e., contains many absorbing chemical species, it is necessary to divide the spectral matrix into submatrices with lower chemical rank prior to resolution. This can be done in either the spectral or the time direction or both. In the evolving factor analysis9-11 approach, submatrices of X are decomposed by PCA. The procedure starts using only the first spectrum in the submatrix and proceeds, adding one spectrum at a time, until all spectra are decomposed, thus giving eigenvalues from a total of ns submatrices. The same procedure is repeated in the backward direction, yielding ns more sets of eigenvalues. If the eigenvalues from the forward and backward procedures are plotted, a picture showing at what times chemical components appear and disappear is obtained. The chemical rank of the full matrix equals the number of chemical components in the system. The FSW-EFA20 approach, like EFA, relies on the decomposition of submatrices of X. The eigenvalues of m consecutive spectra are calculated. The m spectra window is moved over all rows of X, yielding ns - m + 1 sets of eigenvalues that are plotted as a function of window number. The number of eigenvalues above noise level for each time window indicates the local chemical rank of that window, i.e., the number of independently changing concentrations of absorbing chemical species. No measure of the total chemical rank of X is obtained with this method. FSW-EFA can be implemented in the spectral direction of X in a similar manner, moving a window over the columns of X instead of the rows. Using this procedure, the number of absorbing species in each spectral region is indicated by the eigenvalues. Latent projective graphs15 is a technique for finding selective regions in the spectral or time direction of the data matrix. The principle behind LPG is that a selective region will map as a straight line through the origin in a graphic representation of the matrix. Selective spectral regions will map as straight lines in the row space of X, and selective regions in the time direction will map as straight lines in the column space of X. A straight 1728 Analytical Chemistry, Vol. 70, No. 9, May 1, 1998
line is projected as a straight line in any new coordinate system that is nonorthogonal to the line. Thus, linear regions in bivariate loading or score plots from PCA indicate selectivity in the spectral or time directions, respectively. The loading vectors, having a norm of 1, are multiplied by the norm of their corresponding score vector, before plotting. This makes the influence of each component in the graph related to its degree of explanation of the data. Initial Estimates of the Concentration Profiles. The sets of eigenvalues produced by EFA can be used to obtain initial estimates of the concentration profiles during the reaction. Assuming that the compound that enters the system first also leaves first, one can simply combine the eigenvalues from the forward and backward analysis to give concentration profiles. This is accomplished by comparing the first significant eigenvalue from the forward analysis with the last significant value from the backward analysis. The smaller of these two at each time constitutes the first concentration profile. In the same manner, the other eigenvalues are combined until all significant eigenvalues have been used. The assumption of first in-first out is usually valid in chromatography, but this is not the case in reaction monitoring. Still, the estimated profiles are often good enough to be used as initial estimates in the subsequent resolution process. Resolution into Analyte Spectra and Concentration Profiles. Resolution of X into concentration profiles and pure analyte spectra is accomplished using a constrained alternating leastsquares procedure, according to
A ) (CTC)-1CTX
(2)
C ) XAT(AAT)-1
(3)
The relative intensity of each concentration profile and the corresponding absorbance spectra is mathematically indeterminate if no extra information on extinction coefficients or component concentrations is provided. The usual approach is to normalize the rows of A to unit length. C will then contain profiles that are not mutually comparable but showing the change in concentration of each individual compound during the reaction. After each calculation with eq 2, the rows of A are therefore normalized to unit length. After each calculation with eq 3, the concentration profiles are constrained to be nonnegative by setting all negative elements in C to zero. Normally, the absorbance spectra are also constrained to be nonnegative, but in this work, the second-derivative spectra were used for resolution, precluding this approach. The calculations are continued using eqs 2 and 3 until convergence is reached. An average change at each wavelength smaller than 0.01% of the maximum value in the data set between successive iterations has been used to indicate convergence. Resolution of one reaction at a time can be unreliable because of the rank deficiency of the spectral matrix27 and the rotational ambiguities present in the solution,28,29 which may only be partly (27) Amrhein, M.; Srinivasan, B.; Bonvin, D.; Schumacher, M. M. Chemom. Intell. Lab. Syst. 1996, 33, 17-33. (28) Tauler, R.; Smilde, A.; Kowalski, B. J. Chemom. 1995, 9, 31-58. (29) Manne, R. Chemom. Intell. Lab. Syst. 1995, 27, 89-94.
overcome by the use of constraints in the resolution process. If the same chemical species are present in several reactions, however, they can be analyzed simultaneously, reducing the rotational ambiguities. The spectral matrices from the individual reactions are combined in the time direction to one matrix, yielding a (ns1 + ns2 + ...) × nf X matrix, where ns1, ns2, and so on are the number of spectra collected during the individual reactions. This restricts the absorption spectra of the chemical species obtained in A to be identical in the different reactions. C will contain concentration profiles from all reactions treated. Despite this approach, there is no guarantee that the correct solution is reached, i.e., that the extracted components correspond to real chemical components.28 EXPERIMENTAL SECTION Procedure. All reactions were carried out in a 1000-mL reaction vessel equipped with reflux condenser and distillation equipment. Water and concentrated NaOH(aq) were mixed in different proportions to a total volume of 450 mL and cooled to the addition temperature. A 112-g portion of triethyl phosphonoformic acid (Hoechst) was added at constant rate during 54 min. The reaction mixture was kept at constant temperature during the addition and for 20 min thereafter. The mixture was then heated, and EtOH was distilled off. When no more EtOH could be seen in the condenser, the mixture was kept at 85 °C for another hour and was then allowed to cool to 25 °C. The total time for a reaction is 5-6 h. Seven reactions were run under different conditions. Six of them comprised a factorial 22 design with duplicated center point. The addition temperature was 0, 10, or 20 °C and the amount of NaOH was 4, 5, or 6 equiv with respect to 1. The theoretical NaOH consumption is 3 equiv of for total conversion. To investigate the effect of peak shifts caused by temperature variations, a reaction was also run under isothermal conditions at 23 °C. Instrumentation. The spectra were obtained using an ASI ReactIR 1000 Fourier transform infrared spectrometer (Applied Systems, Millersville, MD) equipped with a DiComp probe for in situ measurements and a liquid nitrogen-cooled MCT detector. Spectra in the wavelength range 650-4400 cm-1 at ∼4-cm-1 resolution, giving 1944 data points per spectrum, were collected in absorbance mode at 2-min intervals during the reactions. Each spectrum is an average of 256 scans. The region 1900-2300 cm-1 is not useful due to poor light throughput. All spectra were baseline corrected by subtracting the mean of the absorbances at the 50 highest wavenumbers, to reduce the effect that changing refractive index in the solution has on ATR spectra. Data processing was performed in Matlab v4.2c (Mathworks Inc., Natick, MA) on an IBM-compatible personal computer. During two of the reactions in the factorial design, samples were taken for HPLC analysis of the monoester, the diester, and the product. The analyses were performed using a C-18 column (Chrompack) with a 10:90 MeOH/H2O mobile phase containing 0.55 mM tetrahexylammonium hydrogen sulfate and buffered with acetate to pH 4.40. UV detection at 230 nm was used. Samples were filtered using a 0.5-µm Teflon membrane filter preheated to the solution temperature and diluted approximately 0.35:100 w/w with mobile phase to before injection.
Figure 2. Sample spectrum (solid, left y-axis) from a reaction and its second derivative (dashed, right y-axis).
Safety Considerations. The dissolution of NaOH in H2O is a highly exothermic process. The resulting solutions are corrosive and should be handled with caution. Triethyl phosphonoformic acid can cause allergic reactions on contact. RESULTS AND DISCUSSION Pretreatment of Spectra. Water is known to have a strong IR absorption that changes with the conditions in the solution. IR spectroscopy has even been used to study the structure of liquid water at different temperatures.30,31 During the course of the reaction, not only temperature but also pH changes drastically as the NaOH is consumed. This results in even larger changes in the spectrum. Initial experiments aimed at developing a method for predicting IR spectra of the solvent, NaOH(aq), at different concentrations and temperatures. These spectra would then be subtracted from the spectra collected during a reaction. PLS prediction of solvent spectra from NaOH concentration and temperature was not a problem. However, it turned out that the solvation of the species participating in the chemical reaction affected the solvent spectrum too much for this to be a useful approach. In the spectral region with wavenumbers lower than the water bending vibration at ∼1640 cm-1, the organic molecules have relatively sharp absorptions compared to the solvent (cf. the solid line in Figure 2). Locally, the changes in the solvent spectrum in this region can be approximated by straight lines changing slope and offset. This means that the second-derivative spectra will be largely free of the effects of the changing solvent absorption. To further suppress the solvent signal, a solvent spectrum was subtracted from each spectrum before differentiation. The spectrum used for this purpose was the first collected spectrum during each reaction, i.e., the spectrum acquired before addition of starting material was initiated. Although this spectrum is not a very good approximation of the solvent spectrum during the course of the reaction, it still reduces the influence of the solvent on the calculated second-derivative spectra significantly. Savitzky-Golay differentiation32,33 using a fourth-degree polynomial (30) Libnau, F. O.; Toft, J.; Christy, A. A.; Kvalheim, O. M. J. Am. Chem. Soc. 1994, 116, 8311-8316. (31) Libnau, F. O.; Kvalheim, O. M.; Toft, J.; Christy, A. A. Vib. Spectrosc. 1994, 7, 243-254. (32) Savitzky, A.; Golay, M. J. E. Anal. Chem. 1964, 36, 1627-1639. (33) Steinier, J.; Termonia, Y.; Deltour, J. Anal. Chem. 1972, 44, 1906-1909.
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Table 1. Characteristics of PLS Models for the Monoester and the Product spectral range cm-1
species
pretreatment
4400-650 monoester centering 1604-830 monoester centering 1604-830 monoester 2nd derivative + centering 4400-650 product centering 1604-830 product centering 1604-830 product 2nd derivative + centering
PLS components
ra
SEPb
4 3 2
0.994 0.0055 0.990 0.0072 0.992 0.0065
5c 5c 5
0.926 0.0026 0.951 0.0021 0.983 0.0012
a Correlation between measured and predicted concentrations. Standard error of performance in weight fraction determined by crossvalidation. Calculated as standard deviation of the residuals. c More than five components needed for best fit. Model with five components shown for comparison with second-derivative model.
b
containing 17 data points was found to preserve the analyte signals best, while still removing most of the solvent signal and reducing the amplification of noise. The differentiation approach to removal of the solvent signal is only applicable in the spectral range 1604830 cm-1, denoted the narrow spectral range below. This range from a spectrum, collected during a reaction, and its second derivative are shown in Figure 2. PLS Calibration for the Monoester and the Product. The HPLC method is able to determine the concentrations of the diester 2, the monoester 3, and the product 4. However, the samples taken out during the reactions showed no signs of the diester. There can be two reasons for this. The first is obvious; the reaction mixture does not contain significant amounts of the diester, due to immediate hydrolysis to the monoester upon formation. It is also possible that the diester is consumed during sampling and workup, prior to injection. This would lead to erroneously high concentrations of the hydrolysis product, the monoester, in the injected sample and thus problems during the PLS calibration for this substance. The results shown below indicate that the latter is not the case. PLS models were based on 28 samples taken out during two of the reactions in the designed experiment. The concentrations of monoester and product spanned the ranges 0-15.6% (w/w) and 0-2.5% (w/w), respectively. Two samples were removed as outliers when the monoester was modeled, and three samples were removed when the product was modeled. As indicated above, the second-derivative spectra in the narrow spectral range are less influenced by variation in solvent spectrum than the raw spectra. This shows clearly in the characteristics of the three different PLS models developed for each substance. The models are based on full raw spectra, the narrow spectral range chosen above, and the second-derivative spectra in this range (cf. Table 1). The higher number of PLS components needed in the product models is probably due to the much lower concentration of this species. No further effort to improve the second-derivative models was made, since the remaining prediction error was considered mainly due to errors originating in sampling and workup prior to HPLC analysis. This conclusion was drawn from plotting the predicted concentrations from PLS models and measured concentrations as a function of reaction time during the two reactions (not shown). From the plots, it is seen that the 1730 Analytical Chemistry, Vol. 70, No. 9, May 1, 1998
samples that were removed as outliers in modeling the monoester were taken during the initial period of the reaction, when the starting material is continuously added and the reaction is fast. This makes it probable that the sampling and workup were not fast enough to stop the sampled compounds from continuing to react. Likewise, the samples that were considered outliers when the product was modeled were taken from the period with high temperature when the product is formed, and crystallizes, at high rate. During this period, the solution is most probably oversaturated, which makes sampling and filtering without disturbing the phase distribution very difficult. These errors are probably also present, albeit smaller, in the samples that the model is built from, thus limiting the precision in the predicted concentrations. The developed PLS models based on second-derivative spectra were used to predict the concentrations of monoester and product in the six reactions constituting the designed experiment. From the X-block residuals, it can be concluded that the calibration model for the monoester is applicable for prediction in all six reactions. The product calibration does not perform well on the three reactions with addition temperature and NaOH concentration different from those in the reactions used for calibration (one of the reactions used in the calibration is one of the two identical center point reactions). In these cases, the predicted concentrations must be considered unreliable. No results from the predictions are shown in this section, since they are compared with results from curve resolution below and shown there. Multivariate Curve Resolution of Mid-IR Data. The reaction system under study is complicated. The reaction mixture contains a maximum of 11 chemical substances to different extents, if the reaction mechanisms described above are valid. The 11 substances are the ones shown in Figure 1 plus EtOH and ethyl phosphite. This is a far too high number to make resolution of the complete spectral matrix possible. The matrix has to be analyzed in sections; sectioning in the spectral direction has been used in this work because this approach yields concentration profiles for the whole reaction, which is generally desirable in the study of a reaction. During the reaction under study, the temperature varies between 0 and 85 °C, and the hydroxide concentration in the solution between 3.2 and ∼1 M. As noted above, peak shifts and band broadening are common in mid-IR spectra obtained under such conditions. This leads to deviations from bilinearity that complicate chemical rank determination and resolution. It is obvious from analysis of the spectra that effects of this type are present in the experimental data. Resolution must thus aim at the main chemical components, having absorptions significantly larger than these nonlinear effects in the analyzed region. There is no way to distinguish between weak absorptions from chemical species at low concentrations or with small extinction coefficients and the nonlinear effects. Analysis of Selective Spectral Regions. The analysis was started by using LPG to find selective spectral regions. Only the narrow spectral range 1604-830 cm-1 of the second-derivative spectra has been used, due to the difficulty in removing the effects from the water absorption in other spectral regions. One of the center point reactions was treated initially, and the selective regions found were then verified by analysis of the remaining six reactions. A large number of principal components were needed
Figure 3. Loadings (a) and scores (b) from PCA of the region 1220-1170 cm-1 in spectra from one of the reactions. The first and second principal components are shown as solid and dashed lines, respectively.
to describe the full matrix, consisting of 173 spectra with absorbances at 401 discrete frequencies in the narrow spectral range. Due to this, it is not possible to find selective regions by looking at bivariate graphs from PCA decomposition of the full matrix. Instead, the matrix is divided in the spectral direction into a small number of equally sized submatrices, and these are analyzed separately by LPG. Approximately five submatrices, formed with a small spectral overlap between individual submatrices, were found suitable. PCA on matrices formed by each selective wavelength region, as indicated by LPG, and all spectra in the reaction were used to verify the detected selectivity. For a selective region, all significant chemical information should be explained by the first principal component. In this way, it was possible to conclude that only one main component absorbs in each of the regions 1329-1295 and 899-861 cm-1. Closer visual inspection of the spectra reveals that the region 1229-1142 cm-1 is probably also selective for one chemical substance. The selectivity is not detected by LPG due to a shift in the absorption frequency of ∼5 cm-1. Results from PCA of the region, given in Figure 3, show that the shift correlates well with the changing properties of the solution. This type of result is typical for a shifting absorption peak. The first principal component models the mean absorption and the second principal component the frequency shift. Initially, the peak is shifted to lower frequency due to consumption of hydroxide as seen in the scores plot. When the temperature is raised, the peak shifts quickly to higher frequency and the scores for both components then approach zero as the substance is consumed at the high temperature. The first and second components describe 96-98% and 2-3%, respectively, of the sum of squares (ssq) in the data from the six reactions in the factorial design. For the reaction
run under isothermal conditions, however, practically 100% of the ssq is described by the first component, consistent with a much smaller shift in the absence of temperature differences. The same pattern can be seen in plots from EFA and FSW-EFA applied in the time direction (not shown). For these methods, the apparent number of chemical species absorbing during the temperature raise is two, due to the peak shift. This shows the effect of peak shifts on rank determination and that rank mapping of mid-IR data must be done with caution, taking measurement conditions into consideration. Determinations of concentration profiles from selective regions are done using PCA scores, rather than the absorption at a single wavelength. The use of many variables reduces both noise and disturbances from peak shifts. As noted above, the first component tends to model a mean absorption and the second the shift. The concentration profile obtained from the 899-861-cm-1 range is consistent with what could be expected for EtOH in the reaction. It rises quickly during the addition period and is then approximately constant until the temperature is raised. During the temperature increase, the EtOH concentration reaches a peak for the reactions with 5 and 6 equiv of NaOH before it decreases due to distillation. This is not the case for the reactions with 4 equiv of NaOH. The explanation is that the lower NaOH concentration reduces the reaction rate, making the production of EtOH slower than the removal by distillation. It was also found that the absorption, centered at 878 cm-1, exactly matched an absorption frequency of EtOH in a NaOH/H2O mixture, verifying the assignment. The absorption centered at 1187 cm-1 matches the PdO stretching absorption band of the monoester in the solvent. The concentration profile obtained from this region shows a good correlation with the concentrations of this substance determined by HPLC. Due to the disturbances of peak shift and possibly also minor absorbing compounds, the correlation is not quite as good as for the concentrations predicted by the PLS model for the substance. No available reference spectra matched the absorption frequency at 1310 cm-1. The concentration profiles obtained show a linear increase during the addition and a rapid consumption when the reaction mixture is heated. Since the absorption spectra of the starting material and the diester are known not to match the absorption, the band is assigned to either the mono- or the diester of phosphite, formed in the side reaction. Rank Mapping Prior to Curve Resolution. The aim of the rank mapping is to find regions of moderate rank that are suitable for further analysis by curve resolution. As in the detection of selective spectral regions, only the narrow spectral range of the second derivative spectra has been used and one of the center point reactions was analyzed initially with verification of the result on the remaining reactions. Application of FSW-EFA in the spectral direction of the data does not yield a firm basis for determining the rank of the different spectral regions, due to varying noise levels and nonlinear effects. The results can be used, however, as starting point for further analysis. FSW-EFA and EFA in the time direction of submatrices formed by spectral regions for which the analysis in the spectral direction indicated a low chemical rank is a better base for rank assessment. As an example, the results from FSW-EFA and EFA Analytical Chemistry, Vol. 70, No. 9, May 1, 1998
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Figure 4. Rank analysis of the region 1604-1493 cm-1 from one of the reactions. The four largest eigenvalues are shown: (a) EFA. Forward evolving eigenvalues are solid lines. Backward values are dashed. (b) FSW-EFA, using a window of six spectra. Table 2. Spectral Regions with Moderate Rank spectral region
(cm-1)
1604-1493 1329-1295 1229-1142 982-909 899-861 a
rank 2 1 1a 3 1
Rank 2 indicated by EFA and FSW-EFA; see text.
of the region 1604-1493 cm-1 are shown in Figure 4. Both methods indicate a rank of 2 for the region. The two spectral regions determined by FSW-EFA and EFA to be suitable for resolution are shown in Table 2 together with the detected selective regions. The remaining regions have a rank higher than 3. No resolution was attempted for these. Resolution. Resolution was first performed for the 16041493-cm-1 region with chemical rank 2. The matrices from monitoring the reactions in the designed experiment were grouped two and two in three groups with respect to equal initial NaOH concentration. The two matrices in each group were then combined, as described previously, prior to ALS resolution. Initial estimates of the concentration profiles were taken from EFA on each individual matrix. These were then combined accordingly. Combining the matrices in groups of two yields a higher degree of explanation of the data matrix than when all six reactions where analyzed simultaneously. The reason for this is small shifts in absorption frequencies between the reactions due to the different NaOH concentrations. The resulting pure absorbance spectra from the analysis of the three groups are very similar, with only very small differences 1732 Analytical Chemistry, Vol. 70, No. 9, May 1, 1998
Figure 5. Concentration profiles for the monoester (a) and the product (b) during a reaction, determined by PLS (solid), curve resolution (dashed), and HPLC (squares). For the monoester, the profile from a selective region is also shown (dotted).
in the maximum absorption frequencies of the two compounds, consistent with the different NaOH concentrations. From the concentration profiles obtained in the resolution, it is possible to assign the two compounds to the monoester and the product. The concentration of the monoester increases linearly during the addition to a relatively high concentration that is constant until the solution is heated. The concentration then decreases to approximately zero for the reactions with 5 and 6 equiv of NaOH. For the reactions with 4 equiv, the concentration decreases to about half of the maximum concentration, consistent with a lower hydrolysis rate due to the significantly lower hydroxide concentration in this phase when large amounts are already consumed. When the reaction mixture is allowed to cool, the reaction stops and the monoester concentration is approximately constant. The product concentration pattern is similar for all six reactions. The concentration is very low during the addition. When the solution is heated, the concentration increases rapidly and is then approximately constant until the temperature is lowered and the crystallization phase starts. The resulting concentration profiles for one of the reactions with 4 equiv of NaOH is shown in Figure 5. Scaling of the profiles to absolute concentrations was made by calculating extinction coefficients using the HPLC data. In the figure, the HPLC concentrations used in the PLS modeling and the predicted concentrations from the PLS models are also shown for comparison. For the monoester, the concentrations obtained from the selective region are also shown, to point out
the usefulness of this approach. Scaling is done in the same way as for ALS profiles. Note the absence of HPLC concentrations during the high concentration period of the product. As mentioned in the discussion on the PLS models, the solution is oversaturated in this phase and sampling is very difficult. The correlation coefficient between the concentrations calculated with ALS and those predicted using the PLS models are 0.995 for the monoester and 0.997 for the product. When the ALS concentrations are compared with HPLC data, the correlation coefficients obtained are 0.965 and 0.996, respectively. These figures show that the agreement between the results obtained with the different methods is very good. The maximum absorption frequencies obtained for the two compounds are consistent with those from the carboxylate stretchings in the reference spectra of the monoester and the product, confirming the assignments made above. When resolution was attempted for the region 982-909 cm-1 with chemical rank 3, no physically meaningful convergence point was reached in the ALS process. It was, however, possible to see that two of the concentration profiles generated during the process, before convergence, were similar to the ones obtained from the 1604-1493-cm-1 region. It was thus suspected that two of the compounds absorbing in the region were the same as in the previously resolved region. To obtain a physically meaningful convergence point, this region was combined with the previously analyzed region and the profiles obtained from the rank 2 region were used as initial estimates of the concentration profiles for two of the compounds. A constant concentration during the whole reaction was used as the initial estimate for the third (unknown) compound. With this approach, convergence was reached quickly and the results can be given a chemically relevant interpretation. The results are shown in Figure 6 for the same reaction as shown in Figure 5. The profiles for the monoester and the product are very similar to the ones obtained form the rank 2 region alone, although the correlation with the other methods is not quite as good. The third concentration profile is assigned to the byproduct phosphite 7, which is known to be formed during the reaction and has a high solubility in the solution. It can be concluded that phosphite is formed solely during the heat-up phase and, thus, that the phosphite diester and/or the phosphite monoester is not hydrolyzed until the solution is heated. Absorption frequency comparison with reference phosphite spectra confirms the assignment. The negative peak in the rank 2 region is most likely not due to phosphite spectral features but to other effects present in the spectra covarying with the phosphite concentration. The results show that combination of spectral regions and better concentration profile estimates are useful approaches for resolving regions that are more complex. The EFA estimates of the concentration profiles for the rank 3 region were not at all similar to the obtained ones, due to the first in-first out assumption inherent in the EFA method. This is probably the major reason for the unsuccessful resolution using EFA for initial concentration estimates. It is important to note that although reference spectra were available for most of the intermediates and products in the studied system, no such information was included in the resolution process. It was used only to verify the chemical relevance of the results from resolution and assignment to chemical substances.
Figure 6. Concentration profiles (a) and pure absorbance spectra (b) for the monoester (solid), the product (dashed), and a byproduct (dotted) during a reaction determined by resolution combining two regions.
Assignments were possible to make purely from the obtained concentration profiles and chemical knowledge concerning the reaction, as noted above. In both cases of ALS resolution, presented above, the fit of the resolved data to the spectral data is good. Typically, when the concentrations are not very low, the mean deviation for each element in a spectrum is ∼2% of the maximum absolute value. Validation. For PLS and PCR, validation is usually performed by means of cross-validation, as in the PLS models developed in this work, or by using an external test set. These types of validation are in general not applicable in self-modeling curve resolution, since there are no reference data available. Validation must then be accomplished by the use of chemical knowledge or reference spectra. As long as the model explains the data satisfactorily, the main problem is the so-called rotational ambiguities associated with the solutions; i.e., the spectra and concentration profiles obtained from resolution are combinations of the true ones. In this work, HPLC data were available for the monoester and the product and used to validate the results from the curve resolution process for these compounds, as discussed above. For phosphite, no quantitative data for validation existed. The concentration profile obtained is, however, chemically reasonable. It is known that phosphite has a high solubility in the resulting solution even at room temperature. This is in agreement with the concentration profile extracted from spectra. In addition, the separately measured spectrum of pure phosphite in NaOH(aq) is Analytical Chemistry, Vol. 70, No. 9, May 1, 1998
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very similar to the one obtained from the resolution. Therefore, we consider the results for phosphite also validated. CONCLUSIONS In this paper, we have evaluated different chemometric approaches to extraction of information in spectral data obtained from in situ mid-IR reaction monitoring. For the model system studied in this work, self-modeling multivariate curve resolution and analysis of selective regions provided concentration profiles as good as PLS. In addition, concentration profiles of three chemical species were obtained that could not be obtained with PLS, because reference analysis methods are lacking. Thus, we have shown that self-modeling multivariate curve resolution and techniques for location and analysis of selective regions constitute a good alternative to PLS regression (and other regression techniques) when complex data of this type are evaluated. These techniques do not require calibration data, and consequently, no time-consuming external analysis is needed. The main problem with self-modeling curve resolution techniques is the rotational ambiguities associated with the solutions.
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We obtained physically meaningful solutions from the resolution process, although the only constraint used was nonnegativity of the concentration profiles, if the initial estimates of the concentration profiles were good enough. This could be validated using spectral and concentration information. Bilinearity is an inherent assumption in self-modeling curve resolution. As mentioned above, peak shifts and other effects in the spectra disturb bilinearity. The system used in the present work must be considered a “worst-case scenario” in this aspect. Current work in our laboratory aims at elucidating the performance of the method used here and other procedures for curve resolution of mid-IR data from reaction monitoring and the effects of the nonfulfilled bilinearity assumption.
Received for review October 15, 1997. Accepted February 7, 1998. AC9711403
