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

ISBN 0-471-62391-1

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Ass(j, j) = yjôss(i, i) ? &ssU, j) - &ss2(i, j) (5-6)

where Ô^(³, j) is the ith row and j th column element of the synchronous sample-sample correlation matrix (Equation 5.4). Here, the dissimilarity between two spectral features is most prominently analyzed, more so than asynchronous analysis. Any slight discrepancies between two spectral traces belonging to different samples can be detected by the positive intensity of disrelation spectra.

5.1.4 APPLICATION OF SAMPLE-SAMPLE CORRELATION

In the previous chapter (Section 4.1), we examined the IR spectra of a polymer solution mixture system undergoing spontaneous evaporation of volatile components using the standard variable-variable correlation analysis. Coordinated changes of band intensities arising from the same species were depicted in the synchronous 2D correlation spectrum (Figure 4.3), and the sequential order of the compositional changes was sorted out in the asynchronous spectrum (Figure 4.4). It was found that highly volatile methyl ethyl ketone (MEK) disappears first, followed by the gradual evaporation of deuterated toluene (d-toluene), which leads to the accumulation of nonvolatile polystyrene (PS). We now revisit the same solution mixture system, but this time using the sample-sample correlation analysis.

A series of time-dependent IR spectra of the solution mixture undergoing evaporation is presented again in Figure 5.1 Based on this set of spectral data, a sample-sample 2D correlation spectrum (Figure 5.2) is calculated using Equation

(5.4). The time-averaged spectrum is used as the reference to obtain so-called mean-centered dynamic spectra. Although this selection of reference is somewhat

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Further Expansion of Generalized 2D Correlation Spectroscopy

0 min

—I---------1------1-----1------1------1-----1------1------r

1520 1320

Wavenumber, v

Figure 5.1 Time-dependent IR spectra of a mixture of MEK, d-toluene, and PS during the spontaneous evaporation process

arbitrary, it often brings out more detailed features of sample-sample correlation spectra. Note that axes of the 2D correlation spectrum are no longer in the wavenumber scale as in Figures 4.3 or 4.4 but are replaced by the two orthogonal time axes. The autopower spectrum, which corresponds to the correlation intensity at the main diagonal position, is provided at the top and left side of the 2D spectrum for reference.

In this example (Figure 5.2), the correlation intensity is the highest at the bottom left corner of the 2D spectrum, corresponding to the early stage of the evaporation process. For the first few minutes of the evaporation process, the correlation intensity is high even at the off-diagonal position, as the sample spectra collected during this period all have very similar spectral features dominated by the contribution from MEK. As the evaporation process continues, new spectral features show up with more contributions from d-toluene and PS. Thus, the correlation intensity becomes much weaker between the MEK-rich samples collected after only several minutes of evaporation and those after 6 or 7 min with

Sample-Sample Correlation Spectroscopy

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Time, t, (min)

Figure 5.2 Synchronous sample-sample 2D correlation spectrum for a solution mixture of MEK, d-toluene, and PS undergoing evaporation

higher relative content of d-toluene. Samples collected after 9 min are negatively correlated with the rest of the region of the 2D spectrum, reflecting the fact that the solvents are mostly gone leaving only the residual PS component with spectral features very different from those of the original solution mixture. As apparent from this example, sample-sample correlation is especially useful in detecting trends or transitions along a series of spectral traces.

There have been increasing numbers of the application of sample-sample correlation. In this book one can find examples of sample-sample correlation spectroscopy in Chapters 7 and 9. The sample-sample correlation has been used for the analysis of temperature-induced NIR changes of oleic acid to detect the existence of two phase transition temperatures (see Section 9.2).2 Other sample-sample correlation applications include 2D IR and NIR studies of polycondensation reaction of bis(hydroxyethylterephthalate) (see Section 7.2.2),10 raw milk,6 and other reaction kinetics studies.7 Sample-sample correlation was used by Wu et al.9 to study the temperature effect on intermolecular hydrogen bonding for a supramolecular assembly of azobenzene derivatives. Normalized sample-sample correlation for field-induced reorientation dynamics of ferroelectric liquid crystals was reported on the 2D analysis based on polarization angle dependence.11

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Further Expansion of Generalized 2D Correlation Spectroscopy

5.2 HYBRID 2D CORRELATION SPECTROSCOPY

5.2.1 MULTIPLE PERTURBATIONS

Hybrid correlation deals with the 2D correlation analysis between two separately obtained data matrices.3 4 It may be regarded as one of several useful variants of heterocorrelation methods.12 Another example of heterocorrelation, heterospectral correlation, has already been discussed in Section 2.2.4. In heterospectral correlation, two sets of data matrices are obtained by making two different types of spectroscopic measurements under the same perturbation. In hybrid correlation, on the other hand, a single type of spectroscopic measurement is usually carried out under multiple perturbation variables. Most importantly, hybrid 2D correlation spectroscopy is often concerned with both variable-variable and sample-sample 2D correlation spectroscopy. If coupled with sample-sample correlation, hybrid correlation furthermore can potentially explore the latent correlation between different perturbation variables.

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