Scheme 1. Hydrolysis of acetic anhydride to 2 M acetic
acid
measurements for robust multivariate process analytical
technology (PAT) and suggests the extension to real-time
analysis and control of manufacturing processes.
Theoretical Method
Band-Target Entropy Minimization (BTEM). As pre-
viously mentioned, the primary use of BTEM is to extract
the pure-component spectra out of a set of mixture spectra.
Subsequently, the individual concentration profiles are
obtained, which contain significant information on the
dynamical changes of each compound involved in the system.
Let Ik×ν represent the Raman intensity in the consolidated
spectroscopic data matrix where k denotes the number of
spectra taken and ν denotes the number of data channels
associated with the spectroscopic range. The experimental
intensities Ik×ν have a bilinear data structure and can be
described as a product of two submatrices, namely, the
concentration matrix Ck×s and the Raman pure-component
scattering coefficient matrix Js×ν (where s denotes number
of observable species in the chemical mixture). Accordingly,
the associated error matrix ꢀk×ν contains both experimental
error and model error (nonlinearities).24
mixed-component spectrum is just a linear superposition of
pure-component spectra and their concentrations.
Among the currently available SMCR techniques, band-
target entropy minimization (BTEM) is one of the newer
and robust methods,10 which was developed on the basis of
Shannon’s information entropy concept.11 Thus far, BTEM
has been successfully applied to resolve pure-component
spectra from various one-dimensional (1D) spectra from
multicomponent systems, measured by FT-IR,12-18 Ra-
man,19,20 XRD,21 and MS.22 In addition, recently it has also
been applied to two-dimensional (2D) spectra, such as COSY
and HSQC 2D NMR data.23 The main strengths of BTEM,
which make it unique and different from other SMCR
methods, are the following: (1) its ability to recover pure-
component spectra of species at sub-ppm levels, (2) consid-
erably enhanced signal-to-noise ratio of recovered minor
compounds, (3) no requirement for any a priori estimate of
the number of species present in a system, and (4) goal-
oriented approach, whereby the user targets a single spectral
feature of interest, and the algorithm yields the full-range,
reconstructed, pure spectrum associated with the targeted
feature.
The use of BTEM to recover pure-component spectra
from Raman data of a mixture has been thus far limited to
nonreactive and off-line systems. In the present contribution,
we combine the use of Raman spectroscopic measurements
and the novel multivariate data analysis method, BTEM, to
monitor the hydrolysis of acetic anhydride to acetic acid
(Scheme 1). Raman spectroscopy is a better choice than FT-
IR for this reaction since water has an intrinsically weak
Raman signal, and thus the Raman signals of other reactants
and product can be more easily observed and measured. Two
different monitoring setups, consisting of static and flow-
through modes were employed. This contribution demon-
strates the applicability of combined BTEM and Raman
Ik×ν ) Ck×s
J
s×ν + ꢀk×ν
(1)
The BTEM algorithm proceeds by first decomposing Ik×ν
into its singular vectors using singular value decomposition
(SVD).25 This is then followed by the appropriate transfor-
mation of right singular vectors, VT, into physically mean-
ingful, pure-component spectra.
Ik×ν ) Uk×k
Σ
k×νVTν×ν
(2)
Different from other SMCR methods, BTEM is uniquely
developed to resolve one pure spectrum at a time. The
number of eigenvectors, z, taken for inclusion in the
transformation is usually much larger than s due to the
nonlinearities present (nonstationary spectral characteristics).
The number z is usually determined by identifying the vectors
which possess localized signals of clear physical significance
and retaining these, while discarding the vectors that are
more-or-less randomly distributed noise.
(10) Widjaja, E. DeVelopment of Band-Target Entropy Minimization (BTEM)
and Associated Software Tools. Ph.D. Thesis, National University of
Singapore, 2002.
Jˆ1×ν ) T1×z VTz×ν
(3)
(11) Shannon, C. E. Bell Syst. Tech. J. 1948, 3, 379- 423.
(12) Chew, W.; Widjaja, E.; Garland, M. Organometallics 2002, 21, 1982-
1990.
To extract a pure spectrum Jˆ1×ν, a selected band present
in the first few VT vectors is targeted. The BTEM algorithm
then retains this feature and, at the same time, returns an
entire spectrum which has a minimum entropy. This routine
is repeated for all important observable physical features in
the selected VT vectors. A superset of reconstructed spectra
is obtained, and this set is reduced to eliminate redundancies.
This results in an enumeration of all observable pure-
component spectra.
(13) Widjaja, E.; Li, C. Z.; Garland, M. Organometallics 2002, 21, 1991-1997.
(14) Li, C. Z.; Widjaja, E.; Chew, W.; Garland, M. Angew. Chem., Int. Ed.
2002, 41, 3785-3789.
(15) Li, C. Z.; Widjaja, E.; Garland, M. J. Am. Chem. Soc. 2003, 125, 5540-
5548.
(16) Li, C. Z.; Widjaja, E.; Garland, M. J. Catal. 2003, 213, 126-134.
(17) Widjaja, E.; Li, C. Z.; Chew, W.; Garland, M. Anal. Chem. 2003, 75, 4499-
4507.
(18) Widjaja, E.; Li, C. Z.; Garland, M. J. Catal. 2004, 223, 278-289.
(19) Ong, L. R.; Widjaja, E.; Stanforth, R.; Garland, M. J. Raman Spectrosc.
2003, 34, 282-289.
(20) Widjaja, E.; Crane, N. J. Chen, T.-S.; Morris, M. D.; Ignelzi, M. A., Jr.;
McCreadie, B. R. Appl. Spectrosc. 2003, 57, 1353-1362.
(21) Guo, L. F.; Kooli, F.; Garland, M. Anal. Chim. Acta 2004, 517, 229-236.
(22) Zhang, H. J.; Garland, M.; Zeng, Y. Z.; Wu, P. J. Am. Soc. Mass Spectrom.
2003, 14, 1295-1305.
The targeted bands are retained during the reconstruction.
As part of the process, the resulting pure spectral patterns
(24) Garland, M.; Visser, E.; Terwiesch, P.; Rippin, D. W. T. Anal. Chim. Acta
1997, 351, 337-358.
(23) Guo, L. F.; Wiesmath, A.; Sprenger, P.; Garland, M. Anal. Chem. 2005,
77, 1655-1662.
(25) Golub, G. H.; Van Loan, C. F. Matrix Computations; Johns Hopkins
University Press: Baltimore, 1996.
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