# Two dimensional correlation spectroscopy applications in vibratioal and optical spectroscopy - Isao N.

ISBN 0-471-62391-1

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The idea of statistical 2D correlation spectroscopy used by Sasic and Ozaki,23’24 constructing 2D correlation coefficient maps, is essentially the same as the approach originally introduced by Barton II et at.21 Sasic and Ozaki used a concise matrix algebra notation to describe the derivation of 2D correlation coefficient spectra. They noted that the scope of statistical 2D correlation strictly based on product-moment correlation coefficients is different from the full-scale generalized 2D correlation, but such maps can be interpreted in an analogous way to those obtained by a synchronous 2D spectrum in the generalized correlation. However, an asynchronous

Statistical 2D Correlation Spectroscopy

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Wavelength (nm)

Wavenumber (cm 1)

Figure 7.2 (A) NIR spectrum of beeswax from the 1100 to 2500 nm region. (B) IR spectrum of the same sample from the 4000 to 6000 cm-1 region (Reproduced with permission from F.E. Barton II et al, Appl. Spectrosc., 46, 420 (1992) (Ref. 21). Copyright (1992) Society for Applied Spectroscopy.)

2D spectrum or even the basic concept of asynchronicity does not exist in statistical 2D correlation spectroscopy. As in the case of the generalized 2D correlation spectroscopy, one can develop both variable-variable and sample-sample 2D correlation spectra for the statistical 2D correlation spectroscopy.

In the statistical 2D correlation of Sasic and Ozaki, the correlation coefficient matrix is calculated directly from the experimental data matrices, X and Y, by

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Other Types of Two-dimensional Spectroscopy

Wavelength (nm)

•2650 cm 1 Aliphatic Stretch

Wavelength (nm)

Figure 7.3 (A) IR correlation slice of the NIR spectrum at 2919 cm-1 in the 1100-2500 nm region. (B) IR correlation slice of the NIR spectrum at 2850 cm-1 in the 1100-2500 nm region (Reproduced with permission from F.E. Barton II et al, Appl. Spectrosc., 46, 420 (1992) (Ref. 21). Copyright (1992) Society for Applied Spectroscopy.)

a simple pretreatment operation called autoscaling. The autoscaling of a data matrix column is given by the form

dr, = {d’J~dj) (7.5)

J

Statistical 2D Correlation Spectroscopy

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(A)

Cl)

o

O

> 2312 nm C-H Aliphatic Stretch Combination

Wavenumbers (cm 1)

Wavenumbers (cm 1)

:.C: »1380 nm C-H Aliphatic Stretch 2 nd Overtone

Wavenumbers (cm 1)

Figure 7.4 (A) NIR correlation slice of the IR spectrum at 2312 nm in the 4000-600 cm-1

region. (B) NIR correlation slice of the IR spectrum at 1729 nm in the 4000-600cm-1 region. (C) NIR correlation slice of the IR spectrum at 1390nm in the 4000-600cm-1 (Reproduced with permission from F.E. Barton II et al., Appl. Spectrosc., 46, 420 (1992) (Ref. 21). Copyright (1992) Society for Applied Spectroscopy.)

where djj represents the autoscaled element of the i 111 row and j (It column of the original data matrix. Column parameters, dj and sj, are the mean value and standard deviation of the jth column. Autoscaling equalizes variances of all variables and transforms the spectra into shapes that are visually very far from the common spectral shapes. Once the autoscaling has been carried out on the data matrices to generate a new set of data matrices Xscaled and Yscaled, the correlation coefficient matrix is given simply as a matrix product.

R = Xscaled Yscaled (7 ?6)

The autoscaling makes all the variances comparable and limits the vectors to the unit lengths, and thus, all possible scalar products between these vectors take the values between 1 and -1. These two figures mean perfect correlation, while 0 corresponds to the absence of correlation. It is also noted the correlation

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Other Types of Two-dimensional Spectroscopy

coefficients can be directly transformed into angles. For variable-variable correlation maps, correlation coefficients (or angles) between concentration profiles are measured. On the other hand, for sample-sample correlation maps, the similarities of autoscaled spectra are measured. Since all the correlation coefficients are displayed in one map, one must choose the ranges of the highest and smallest coefficients to be investigated.

Statistical 2D correlation spectroscopy was applied to short wave NIR spectra of raw milk,23 IR spectra measured during polymerization of bis-(hydroxyethyl terephthalate) (BHET),23 and model chemical reactions.24 Here, we outline statistical 2D correlation spectroscopy study of the IR spectra measured during the polymerization of BHET. Figure 7.5(A) shows IR spectra measured on line during polymerization of BHET that yields poly(ethylene therephthalate) (PET) as a final product and one molecule of ethylene glycol (EG) per each condensation reaction.23 This polymerization reaction is described in more detail in Chapter 11. EG is expelled from the system, and it is expected that the spectra contain a very weak contribution from EG mainly due to the difference between the rates of EG production and evacuation. The model shown in Figure 7.5(A) consists of 44 spectra. Spectra of pure components, BHET, PET, and EG, shown in Figure 7.5(B) illustrate the degree of overlapping of bands.23 The only available spectrum of PET was that of the cast film, which does not correspond truly to the spectrum of PET produced during the reaction, hence having limited usefulness.

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