new approaches to generalized two-dimensional correlation...

New Approaches to GeneralizedTwo-Dimensional Correlation Spectroscopy

and Its Applications

Young Mee Jung

Department of Chemistry, Kangwon National University, Chunchon,

Korea

Isao Noda

The Procter & Gamble Company, West Chester, Ohio, USA

Abstract: This review is focused on the recent approaches to generalized 2D

correlation spectroscopy, a technique widely used for the analysis of spectral data. A

brief introduction of generalized 2D correlation spectroscopy is described first. Then

the powerful combination of generalized 2D correlation spectroscopy and multivariate

chemometircs techniques, such as the data reconstruction by principal component

analysis (PCA), eigenvalue manipulation transformation (EMT), and self-modeling

curve resolution (SMCR) analysis are explored. Examples of successful applications

of new approaches to generalized 2D correlation spectroscopy are highlighted.

Keywords: Two-dimensional (2D) correlation spectroscopy, principal component

analysis, eigenvalue manipulating transformation, self-modeling curve resolution

INTRODUCTION

Generalized two-dimensional (2D) correlation spectroscopy has attracted a

high level of interest of analytical science community, as it provides considera-

ble utility and benefit in many fields of spectroscopic studies (1–8). In gene-

ralized 2D correlation spectroscopy, a sample is subjected to an external

Received 16 April 2006, Accepted 30 June 2006

Address correspondence to Young Mee Jung, Department of Chemistry, Kangwon

National University, Hyoja 2-dong, Chunchon 200-701, Korea. E-mail: ymjung@

kangwon.ac.kr

Applied Spectroscopy Reviews, 41: 515–547, 2006

Copyright # Taylor & Francis Group, LLC

ISSN 0570-4928 print/1520-569X online

DOI: 10.1080/05704920600845868

515

perturbation (e.g., temperature (9–21), pressure (22–24), concentration

(25–37), of pH (88) while being monitored with an appropriate spectroscopic

probe, such as IR (17, 18, 20, 25, 27, 39–68), Raman (21, 32–36, 69–74), NIR

(11–15, 28–32, 75–84), fluorescence (85–87), UV-Vis (88–90), and X-ray

(91, 92). The systematic variation in the spectral signal intensities induced

by the perturbation is then treated as a function of the physical variable repre-

senting the perturbation. 2D correlation is finding applications even outside of

conventional spectroscopic studies. For example, an interesting application of

generalized 2D correlation spectroscopy to gel permeation chromatography

was reported by Izawa et al. (93–95).

Some of the most notable features of generalized 2D correlation spectra

are simplification of complex spectra consisting of many overlapped peaks;

enhancement of spectral resolution by spreading peaks along the second

dimension; establishment of unambiguous assignments through the corre-

lation of bands of selectively coupled by various interaction mechanisms;

and determination of the sequence of the spectral peak emergence.

A very intriguing possibility in 2D correlation spectroscopy is the idea of

2D hetero-spectral correlation analysis, where two completely different types

of spectra obtained for a system using multiple spectroscopic probes under a

similar external perturbation are compared (35, 73, 74, 84, 91, 96–98). If there

is any commonality between the response patterns of system constituents

monitored by two different probes under the same perturbation, one should

be able to detect the correlation even between different classes of spectral

signals. There are two types of applications of 2D hetero-spectral correlation

analysis. One is the investigation of the correlation between closely related

spectroscopic measurement (35, 73, 74, 84, 97) as IR and Raman spectra,

which is very attractive from the point of better understanding of its comp-

lementary vibration spectra. It provides especially rich insight and clarifica-

tion into the in-depth study of vibrational spectra. Another is the hetero-

correlation between completely different types of spectroscopic or physical

techniques, which is useful for investigating the structural and physical prop-

erties of materials under a particular external perturbation (91, 96, 98). It has,

for example, been applied to X-ray absorption and Raman spectroscopy (91).

Hetero-spectral correlation has become one of the most active areas of

research in 2D correlation spectroscopy.

Recently, many interesting developments in generalized 2D correlation

spectroscopy have been proposed (82, 99–115). For example, sample-sample

2D correlation spectroscopy was promoted by Sasic et al. (82, 102–104). In

the sample-sample 2D correlation spectroscopy, which has two independent

sample axes defining the 2D correlation coordinates instead of traditional

variable axes (e.g., wavenumber or wavelength), the relationship between

different samples observed under different states of perturbation (time, tem-

perature, concentration, etc.) is studied by examining the similarity or difference

of their spectral trace patterns along the spectral variable. Information obtained

by conventional (variable-variable) and sample-sample 2D correlation

Y. M. Jung and I. Noda516

spectroscopy is often complementary, and general features of variable-variable

correlation maps are expected to be equally applicable to the sample-sample cor-

relation maps. Recently, to further extend the concept of sample-sample 2D cor-

relation spectroscopy, Wu et al. proposed hybrid 2D correlation spectroscopy for

two spectral data sets obtained separately, which can potentially explore the

latent correlation between different perturbation variable (108, 109). Classical

statistical analysis (99–101) and global phase 2D maps (105–107) were also

explored by Morita et al., which is much more straightforward to extract pure

correlation information. A very powerful recent development in generalized

2D correlation spectroscopy is the incorporation of multivariate chemometrics

techniques proposed by Jung et al., (110–115).

In this review, the principle of generalized 2D correlation spectroscopy

and recent developments in the field are reviewed. The fruitful combination

of multivariate chemometircs techniques and generalized 2D correlation spec-

troscopy is discussed in detail, and its applications are explored.

BACKGROUND

Generalized 2D Correlation Spectroscopy

In a generalized 2D correlation spectroscopy experiment, a series of a

perturbation-induced dynamic spectra are collected first in a systematic

manner, e.g., in sequential order during a process. Such a set of spectra

y(v, t) observed as a function of the perturbation variable t (e.g., time, temp-

erature, or concentration) during the interval between Tmin and Tmax, is then

transformed into a set of 2D correlation spectra by a form of cross correlation

analysis. The dynamic spectrum y(v, t) of a system induced by the application

of an external perturbation is formally defined as

~yðv; tÞ ¼yðv; tÞ � �yðvÞ for Tmin � t � Tmax

0 otherwise

�ð1Þ

where y(v) is the reference spectrum of the system. Reference spectrum is

customary to set y(v) to be the stationary or averaged spectrum given by

�yðvÞ ¼1

Tmax � Tmin

ðTmax

Tmin

yðv; tÞ dt ð2Þ

The intensity of 2D correlation spectrum X(v1, v2) represents the quantitative

measure of a comparative similarity or dissimilarity of spectral intensity varia-

tions y(v, t) measured at two different spectral variables, v1 and v2, during a

fixed interval. In order to simplify the mathematical manipulation, X(v1, v2)

is treated as a complex number function

Xðv1; v2Þ ¼ Fðv1; v2Þ þ iCðv1; v2Þ ð3Þ

Generalized Two-Dimensional Correlation Spectroscopy 517

comprising two orthogonal (i.e., real and imaginary) components, known

respectively as the synchronous and asynchronous 2D correlation intensities.

The generalized 2D correlation function given below

Fðv1; v2Þ þ iC ðv1; v2Þ ¼1

p ðTmax � TminÞ

ð1

0

~Y1ðvÞ � ~Y�

2ðvÞdv ð4Þ

formally defines the synchronous and asynchronous correlation intensity

introduced in Eq. (3). The term Y1(v) is the forward Fourier transform of

the spectral intensity variations y(v1, t) observed at a given spectral variable

v1 with respect to the external variable t. It is given by

~Y1ðvÞ ¼

ð1

�1

~yðv1; tÞe�ivtdt

¼ ~YReðvÞ þ i ~Y

Im

1 ðvÞ ð5Þ

where Y1Re (v) and Y1

Im (v) are, respectively, the real and imaginary com-

ponents of the Fourier transform. It is useful to remember that the real

component Y1Re(v) is an even function of v, while Y1

Im (v) is an odd

function. The Fourier frequency v represents the individual frequency

component of the variation of y(v1, t) traced along the external variable t.

According to Eq. (1), the above Fourier integration of the dynamic

spectrum is actually bound by the finite interval between Tmin and Tmax.

The conjugate of the Fourier transform Y2

�

(v) of the spectral intensity

variation y(v2, t) observed at another spectral variable v2 is given by

~Y�

2ðvÞ ¼

ð1

�1

~yðv2; tÞeþivtdt

¼ ~YRe

2 ðvÞ þ i ~YIm

2 ðvÞ ð6Þ

Once the appropriate Fourier transformation of the dynamic spectrum y(v1, t)

defined in the form of Eq. (1) is carried out with respect to the variable t,

Eq. (4) will directly yield the synchronous and asynchronous correlation

spectrum, F(v1, v2) and C(v1, v2).

The intensity of a synchronous 2D correlation spectrum represents the

simultaneous or coincidental changes of two separate spectral intensity varia-

tions measured at v1 and v2 during the interval between Tmin and Tmax of the

externally defined variable t. The intensity of peaks located at diagonal

positions mathematically corresponds to the autocorrelation function of

spectral intensity variations observed during an interval between Tmin and

Tmax. The diagonal peaks are therefore referred to as autopeaks, and the

slice trace of a synchronous 2D spectrum along the diagonal is called the

autopower spectrum. The magnitude of an autopeak intensity, which is

always positive, represents the overall extent of spectral intensity variation

observed at the specific spectral variable v during the observation interval


between Tmin and Tmax. Thus, an autopeak represents the overall susceptibility

of the corresponding spectral region to change in spectral intensity as an

external perturbation is applied to the system. Cross-peaks located at the

off-diagonal positions of a synchronous 2D spectrum represent simultaneous

or coincidental changes of spectral intensities observed at two different

spectral variables v1 and v2. Such a synchronized change, in turn, suggests

the possible existence of a coupled or related origin of the spectral intensity

variations. The sign of synchronous cross-peaks becomes positive if the

spectral intensities at the two spectral variables corresponding to the coordi-

nates of the cross-peak are either increasing or decreasing together as

functions of the external variable t during the observation interval.

However, the negative sign of cross peaks indicates that one to the spectral

intensities is increasing while the other is decreasing.

The intensity of an asynchronous 2D correlation spectrum represents

sequential or successive, but not coincidental, changes of spectral intensities

measured separately at v1 and v2. Cross-peaks develop only if the intensity

varies out of phase with each other for some Fourier frequency components

of signal fluctuations. The sign of asynchronous cross-peak provides useful

information on sequential order of events observed by the spectroscopic

technique along the external variable. If the signs of synchronous and asyn-

chronous cross-peaks are the same, the intensity change at v1 occurs before

v2. If the signs of synchronous and asynchronous cross-peaks are different,

the intensity change at v1 occurs after v2.

Principal Component Analysis–Based 2D (PCA 2D) CorrelationSpectroscopy

It is natural to consider the combined use of various multivariate chemo-

metrics tools and 2D correlation spectroscopy. However, most workers have

focused their attention to the parallel or sequential use of 2D correlation

analysis (1–8) and chemometrics (116–118) as complementary but essen-

tially independent data analysis techniques (59, 77, 79, 81, 119, 120). Jung

et al. have recently reported the promising possibility of the combination of

2D correlation spectroscopy and principal component analysis (PCA) (110–

115). In this approach, PCA treatment of spectral data set now becomes an

essential and integral part of the subsequent 2D correlation analysis.

Let us set the raw data matrix A, comprising the original set of pertur-

bation-dependent spectra, to be an n � m matrix with n spectra and m wave-

number points. The loading matrix V is an m � r matrix, where each column

is the loading (i.e., the eigenvector of the dispersion matrix ATA) obtained by

PCA. Here, AT stands for the transpose of A. The total number of loadings r

selected for the analysis must be less than or equal to n. It is customary to

normalize each column of V (i.e., each loading), such that the product VT

V is an identity matrix. Associated with the PCA loading factors are


the scores (sometime called latent variables). Score matrix W is a relatively

small n � r matrix.

The fundamental idea of factor analysis based on PCA is that the signifi-

cant part of the data matrix can be expressed as the product of score and

loading matricies

A ¼W VT þ E ¼ A�� þ E ð7Þ

where E is the residual matrix often associated with pure noise. Thus, the

matrix product A�� can be regarded as the noise-free reconstructed data

matrix of the original data A.

A�� ¼W VT ð8Þ

In generalized PCA-based two-dimensional (PCA 2D) correlation

analysis, the reconstructed data matrix A�� is utilized for the calculation of

2D correlation spectra instead of the original data matrix. The analysis of

this new data matrix, reconstructed strictly from a few selected significant

scores and loading vectors of PCA, has been proposed as a useful method

to substantially improve the data quality for 2D correlation analysis by

focusing the attention more efficiently to the dominant feature of spectral

intensity variations. Furthermore, the 2D correlation analysis of such a recon-

structed data matrix accentuates only the most important features of synchro-

nicity and asynchronicity without being hampered by the noise, or even by

minor signal components, if the number of principal components is restricted.

Eigenvalue Manipulating Transformation (EMT)

Jung et al. have also proposed a new concept of eigenvalue manipulating

transformation (EMT) for the generalized PCA-2D correlation analysis

(111–113). The PCA-reconstructed data matrix A�� is expressed in the

familiar form known as the singular value decomposition (SVD) (116–118).

A�� ¼ USVT ð9Þ

and

S ¼ L1=2 ð10Þ

where U, S, and V are, respectively, the orthonormal score matrix, diagonal

matrix containing the singular values, and loading matrix. Here L ¼W0 Wis a diagonal matrix where each diagonal element corresponds to the eigen-

value of principal component. The score matrix W is expressed in the form

W ¼ U S and can be obtained directly from W ¼ A V.


The new transformed data matrix A�� will be obtained by manipulating

and replacing eigenvalues of A�� as

A�� ¼ US��VT ð11Þ

where S�� is given by varying the corresponding eigenvalues in S by raising

them to the power of m.

S�� ¼ Sm ð12Þ

The concept of EMT of spectral data involves the systematic substitution of

individual eigenvalues associated with the original data set. This process

will generate a new set of transformed data with a very different emphasis

place on specific information content. This new EMT-reconstructed data

matrix A�� will be used instead of A�� for the calculation of enhanced 2D

correlation spectra.

By uniformly raising the power of a set of original eigenvalues, the

influence of factors associated with major eigenvalues becomes more

prominent, while the minor eigenvectors primarily arising from the noise

component are no longer strongly represented (111). Thus, this transformation

of the data matrix becomes a gradual noise reduction scheme with attractive

flexibility of continuously fine-tuning the balance between the desired noise

suppression and retention of pertinent spectral information.

However, by uniformly lowering the power of a set of eigenvalues associ-

ated with the original data, the smaller eigenvalues becomes more prominent

and the contributions of minor components but potentially interesting factors

become amplified (112, 113). Thus, much more subtle difference of spectral

behavior for each component is now highlighted.

When the power parameter m is reduced to near zero, the singular value

matrix S is essentially replaced with the identity matrix I. The final trans-

formed data matrix approaches A�� ¼ U VT. The synchronous 2D correlation

analysis of such reconstructed data generates the so-called projection

spectrum, F ¼ V VT (associated with the subspace spanned by the set of

object eigenvectors) instead of more familiar form of the synchronous 2D cor-

relation spectrum based on the covariance or dispersion matrix F ¼ AT A.

The intensity at the diagonal of a synchronous 2D projection spectrum corre-

sponds to the squared Mahalanobis distance of the spectral intensity variations

of the data set from the reference (mean) spectrum.

In more advanced case of the spectral selectivity enhancement, where the

power parameter m is now taken to be a negative number, EMT operation will

further exaggerate the effect of minor PC factors such that asynchronicity is

very strongly accentuated. When the power parameter m becomes 21, the

diagonal matrix S is replaced with S21, which by definition is the inverse

matrix of S. It is interesting to point out that the corresponding synchronous

spectrum V S22 VT is nothing but the Moore-Penrose pseudo inverse of the

conventional 2D synchronous spectrum V S2 VT. In such an inverted 2D


spectrum, the information content associated with small eigenvalues of the

original data matrix is preferentially represented, while the contribution

from the dominant variance is mostly attenuated.

The elimination of the contribution of the first PC, which is closely

aligned to the autopower spectrum, results in the PC1-free data matrix A��

given by

A�� ¼ A�� s1U1VT1 ð13Þ

where s1 is the first (i.e., most dominant) singular value of the data matrix,

and U1 and V1 are the first eigenvectors of matrices A AT and AT A.

The motivation behind the elimination of PC1 is similar to that of the

negative power EMT discussed earlier. The beneficial outcome of such

selective manipulation of data is the efficient detection and discrimination

of individual features of spectral intensity variations. Thus, highly overlapped

signals with only slight differences in the variational pattern can be readily

identified. It is noted that, the obtained PC1-free data matrix A�� is the

same as that reconstructed by using only PC2 and PC3 in regular PCA 2D

correlation analysis.

2D Correlation–Based Self-Modeling Curve Resolution (SMCR)

Analysis

Furthermore, Jung et al. have reported the use of 2D correlation spectroscopy

in conjunction with alternating least-squares (ALS)-based self-modeling

curve resolution (SMCR) analysis of spectral data see (114). A classical

problem of SMCR is to extract a set of concentration profiles and spectra of

pure components from a set of unknown mixture spectra A without any

prior knowledge about the system.

For a given spectral data matrix A, where each row corresponds to a

spectrum of a mixture, one have the following bilinear form

A ¼ TPT þ E ð14Þ

Here, T and P are the score and loading vector matricies comprising the

information on concentration profile of pure components and their spectra,

respectively; PT stands transpose of P, and E is the residuals comprising

mainly noise. The total number of pure variables should be the same as the

total number of components to be modeled. It can be estimated by the

simple PCA or SVD, where the number of “significant” eigenvectors will

be equated to the number of components.

Asynchronous 2D correlation spectrum will provide the excellent can-

didates for the most distinct variation points of spectral intensities (corre-

sponding closely to the concept of pure variables). Although they may not


be the best estimates in terms of the lack of signal overlaps, the correlation

peak base band positions will give the clearest idea of how the most

dominant individual component intensities are changing with samples.

Let us start the ALS iteration as

P ¼ ATðTT TÞ�1ð15Þ

P is the estimated loading matrix calculated from the initial guess of T. One

then replace all the negative elements of P with zero according to the

so-called non-negativity constraint for spectral intensities. One then nor-

malizes each column of P by dividing the Euclidian norm (i.e., square

root of pTp).

One can then estimate new T from the constrained and normalized P as

T ¼ AT PðPT PÞ�1ð16Þ

and then replace all negative elements with zero according to the non-negative

constraint for component concentrations. The process is repeated until T and P

are stabilized. If the above process converges successfully, one should have T

and P consisting strictly with non-negative elements. The ALS-estimated

scores and loading matricies come very closely to the true concentrations

and pure spectra of individual chemical components. Thus, the reconstructed

data matrix can be

A� ¼ TPT ð17Þ

Applications of PCA 2D Correlation Spectroscopy

In this review, we give an overview of applications of new approaches to

generalized 2D correlation spectroscopy very briefly, instead of reviewing

extensive amount of its applications. Two examples of recent applications

of PCA 2D correlation are discussed. One is the applications of PCA 2D cor-

relation analysis to experimental spectra with a finite but unknown level of

noise contribution (115, 121). This work demonstrates the potential of PCA

2D correlation analysis for noise filtering effect. Another is the application

of PCA 2D correlation spectroscopy with EMT operations for spectral selec-

tivity enhancement (122, 123). EMT technique which uniformly lowers the

power of a set of eigenvalues associated with the original data highlights

the subtle contributions from minor eigenvectors. Thus, subtle differences in

the thermal responses of polystyrene-block-poly(n-pentyl methacrylate)

(PS-PnPMA) copolymer, which are difficult to observe by conventional 2D

correlation analysis, are accentuated much more strongly than the original

data.


Application of PCA 2D Correlation Spectroscopy for Noise Filtering

Effect

The PCA 2D correlation spectroscopy was applied to the time-dependent

FTIR spectra of a mixture of methyl ethyl ketone (MEK), deuterated

toluene, and polystyrene (PS) during the solvent evaporation, which were

combined with a substantial amount of artificial noise to emphasize the

practical benefit of this technique (121).

Figure 1 shows the original data set examined in this study, where sub-

stantial amount of artificial noise is injected to the raw transient IR spectra

of a PS/MEK/toluene solution mixture during the solvent evaporation

process. A detailed information of these spectra including bands assignment

was already given elsewhere (4) This original spectral data set was decom-

posed into the scores and loading vectors by standard PCA analysis. PCA

factor 1 (PC1), factor 2 (PC2), and factor 3 (PC3) accounts, respectively,

for 83.0, 16.1, and 0.2% of the total variance of spectral intensities along

the time axis.

Figure 1. Synthetic noisy spectra in which substantial amount of artificial noise is

injected to the time-dependent FTIR spectra of a mixture of a PS/MEK/toluene

solution mixture during solvent evaporation, measured every minute over a time

range of 0 to 12 min, in the region of 1320–1520 cm21. Reproduced with permission

from Bulletin of the Korean Chemical Copyright Society, 24 (9): 1345. Copyright

(2003) Korean Chemical Society.


Figure 2 displays the conventional asynchronous 2D correlation spectrum

from these original spectra in Figure 1. The basic properties and interpreta-

tional procedure of asynchronous 2D correlation spectrum have already

been described in more detail previously (4), so no further in-depth discussion

will be given here. In this demonstration, the asynchronous 2D correlation

spectrum is focused, because the asynchronous 2D correlation spectrum is

often contaminated heavily by artifactual peaks attributed to the fortuitous

correlation of noise, while the synchronous 2D correlation spectrum is

relatively insensitive to noise contribution.

The reconstructed data matrix A�� obtained by Eq. 8 from the only two

principal components was used instead of the original spectral data matrix

A for the subsequent 2D correlation analysis. Figure 3(a) depicts the PCA-

reconstructed spectra represented in the matrix A�� from loading vectors and

scores of PC1 and PC2 with average spectrum added back. Figure 3(b)

shows the raw transient IR spectra of a PS/MEK/toluene solution mixture

during the solvent evaporation process for comparison. It shows clearly that

the reconstructed spectra (Figure 3(a)) are sufficiently close enough to the

original spectra (Figure 3(b)), suggesting that most of the pertinent infor-

mation is retained in the PCA-reconstructed data.

Figure 2. Conventional asynchronous 2D correlation spectrum obtained from the

spectra in Figure 1. Solid and dashed lines represent positive and negative cross-

peaks, respectively. Reproduced with permission from Bulletin of the Korean Chemical

Society, 24 (9): 1345 Copyright (2003) Korean Chemical Society.


Figure 4 depicts the asynchronous 2D correlation spectrum generated

from the PCA 2D reconstructed spectral data matrix A�� with PC1 and PC2.

It is similar to the conventional 2D correlation spectrum in Figure 2, but is

remarkably less noisy and somewhat simplified. The noise component E

can be successfully truncated from A to calculate A�� by applying classical

PCA treatment to the original data without using a mathematical smoothing

filter. This result confirms again that the key features of 2D correlation

spectrum can be faithfully reconstructed from PC loading vectors and scores.

In addition, finer features appearing in the asynchronous 2D correlation

spectrum now can be taken as real manifestations with a much higher level

of confidence, since the possibility of noise-induced correlation intensity

effect is now substantially eliminated.

Application of PCA 2D Correlation Spectroscopy with EMT

Operation for Spectral Selectivity Enhancement

Polystyrene-block-poly(n-pentyl methacrylate) [PS-PnPMA] exhibits a

closed-loop phase behavior bounded by a lower disorder-to-order transition

(LDOT) at lower temperature and an upper order-to-disorder transition

(UODT) at higher temperature. The analysis of conventional 2D IR

Figure 3. (a) PCA-reconstructed spectra from loading vectors and scores of PC1 and

PC2 with average spectrum added back. Reproduced with permission from Bulletin of

the Korean Chemical Society, 24 (9): 1345. Copyright (2003) Korean Chemical Society

(b) The raw time-dependent IR spectra of a PS/MEK/toluene solution mixture during

the solvent evaporation process. Reproduced with permission from Applied

Spectroscopy, 57 (5): 564. Copyright (2003) Society for Applied Spectroscopy.


correlation spectra revealed that the conformation of C-C-O group of PS-

PnPMA is changed near the transitions and two disordered states occurring

at lower and higher temperatures are different(20). Jung et al. then demon-

strated that the phase behavior of PS-PnPMA is more clearly understood by

using PCA 2D correlation spectroscopy through EMT technique (123). To

better understand the different characteristics of the two disordered states

found in PS-PnPMA more clearly, PCA 2D correlation spectroscopy

through EMT of spectral data set was applied to temperature-dependent IR

spectra of PS-PnPMA copolymer.

Figure 5 shows the temperature-dependent IR spectra of PS-PnPMA

measured during heating from 100 to 2608C at an interval of 58C. The

original spectral data set in Figure 5 was decomposed into the scores and

loading vectors by standard PCA analysis. PCA factor 1 (PCl), factor 2

(PC2), and factor 3 (PC3) account for 98.4, 1.3, and 0.2%, respectively, of

the total variance of spectral intensities along the time axis. The reconstructed

data matrix A�� obtained by Eq. 8 from the three principal components was

used instead of the original raw spectral data matrix A for the subsequent

2D correlation analysis.

Figure 4. Asynchronous 2D correlation spectrum obtained using reconstructed data

from the reconstructed spectral data matrix A� with PC1 and PC2. Solid and dashed

lines represent positive and negative cross-peaks, respectively. Reproduced with per-

mission from Bulletin of the Korean Chemical Society, 24 (9): 1345. Copyright

(2003) Korean Chemical Society.


Since synchronous 2D correlation spectra constructed from these raw

spectra are already reported (20), the interpretation of conventional synchro-

nous 2D correlation spectra is not further discussed. For comparison, conven-

tional synchronous 2D correlation spectra for two disordered states are shown

in Figure 6. Figure 7 shows the spectrum of the new reconstructed data

obtained by varying the value of the power parameter m, as m ¼ 1, 1/2,

1/3, etc. Such a data matrix will emphasize the subtle contributions from

minor eigenvectors much more strongly than the original data. It looks like

the EMT effect is already apparent at m ¼ 1/2, well before reaching the

m ¼ 0 condition.

Synchronous 2D correlation spectra generated from the EMT-recon-

structed spectral data matrix A�� obtained by replacing the original eigen-

values with m ¼ 1/2 for disordered state at lower temperature, ordered

state, and disordered state at higher temperature are shown in Figures 8(a),

(b) and (c), respectively. By lowering the power of a set of eigenvalues associa-

ted with the original data, the contribution of the minor but potentially interes-

ting factors such as hidden property of phase transition is greatly accentuated

compared with conventional 2D correlation spectra. As shown in Figure 8, the

EMT effect for spectral selectivity enhancement is very much apparent. The

Figure 5. The temperature-dependent IR spectra of polystyrene-block-poly(n-pentyl

methacrylate) (PS-PnPMA) measured during heating from 100 to 2608C at an interval

of 58C Reprinted from Journal of Molecular Structure, published on the Web, April 24,

2006. Copyright (2006), with permission from Elsevier.


synchronous spectrum of the ordered state is completely different from those

in the two disordered states. When the EMT effect is included, the synchro-

nous spectra for two disordered states are also clearly different. The

intensity of peaks located at the diagonal positions in the synchronous 2D

spectrum represents the overall susceptibility of the corresponding spectral

region to change in spectral intensity as an external perturbation is applied

to the system. The power spectrum, extracted along the diagonal line of the

synchronous 2D correlation spectrum, given in the top of Figures 8(a) and

Figure 6. Conventional synchronous 2D correlation spectra obtained from the raw

spectra in Figure 5 for disordered states in lower (a) and higher (b) temperatures.

Solid and dashed lines represent positive and negative cross peaks, respectively.

Reprinted from Journal of Molecular Structure, published on the Web; April 24,

2006. Copyright (2006), with permission from Elsevier.

(continued )


8(c), reveals that the intensity changes with temperature for bands at 1185,

1198, 1386, 1596, 1721, and 1750 cm21 at lower temperatures are larger

than those at higher temperatures. On the other hand, the intensity change

with temperature for bands at 1496 and 1456 cm21, assigned to phenyl ring

stretching of PS, at lower temperatures is smaller than that at higher tempera-

tures. Intensities of bands from C–CiO stretching, C–H deformation, and

C55O stretching of PnPMA and those from phenyl ring of PS change

greatly at lower and higher temperature, respectively. The distinct differences

in two disordered states in the cross correlations of the bands from phenyl

group in PS with that fiom C–C–O group in PnPMA are clearly observed.

These results again confirm that the conformation of PS-PnPMA in the two

disordered states is different, and that the weak directional interaction

between phenyl group of PS and the side chain of PnPMA in the two

Figure 6. Continued.


Figure 7. Spectra of the EMT-reconstructed data obtained by replacing eigenvalues from loadings and

scores of PC1, PC2, and PC3. Each spectrum is obtained by varying the value of power parameter m, as

m¼1 (a), 1/2 (b), 1/3 (c), and 0 (d).

Gen

eralized

Tw

o-D

imen

sion

al

Co

rrelatio

nS

pectro

scop

y5

31

disordered states is different. This kind of difference was not clearly observed

in conventional 2D correlation spectra, as shown in Figure 6. Therefore, the

EMT technique with even m ¼ 1/2 could distinguish the very subtle differ-

ences of spectra which are not detected by conventional 2D correlation

spectra. Consequently, PCA 2D correlation spectroscopy with EMT

technique provides a very promising way for studying various systems.

Figure 8. Synchronous PCA2D correlation spectra obtained from the EMT recon-

structed data with m ¼ 1/2 for disordered state in lower temperature (a), ordered

state (b), and disordered state in higher temperature (c), respectively. Solid and dashed

lines represent positive and negative cross peaks, respectively. Reprinted from Journal

of Molecular Structure, published on the Web, April 24, 2006. Copyright (2006), with

permission from Elsevier.

(continued )


Application of 2D Correlation–Based Self-Modeling Curve

Resolution (SMCR) Analysis for Interpreting

Highly Convoluted Spectra

Jung et al. have demonstrated a great potential of the application of 2D

correlation-based self-modeling curve resolution (SMCR) analysis for inter-

preting highly convoluted spectra (124–126).

The system used in this article was electrochemical reduction of p-benzo-

quinone (p-BQ) in acetonitrile, which produces anion radicals and dianions at

its first and second reduction potentials (125). The dianions undergo a fast

comproporationation reaction with neutral p-BQ molecules to produce

anion radicals back, complicating the spectral analysis. For this reason, the



absorption band of a large amount of Q2† might have buried those resulting

kom Q22 or other species, which makes the spectroelectrochemical data unin-

terpretable by a simple examination of the spectra when the data are obtained

in a bulk cell, where reaction (QþQ22 O 2Q2†) is allowed to occur. In

general, the recording of Q22 spectrum was possible in the optically transpar-

ent thin layer electrochemical (OTTLE) cell because exhaustive electrolysis

was achieved in it and no neutral p-BQ molecules were available for the

following reaction. However, Kim et al. reported a complete interpretation

of the highly convoluted in situ spectroelectrochemical data obtained during

p-BQ reduction by 2D correlation analysis technique in conjunction with

the SMCR analysis.



Figure 9 shows a series of spectra recorded in the potential region

between 21.1 and 21.8 V, where Q2† is reduced to Q22. A dianion peak,

which can be clearly observed at 370 nm in OTTLE cell, was not identified

in Figure 9. To interpret the spectra shown in Figure 9, 2D correlation

analysis was performed on them. Figure 10 shows the 2D correlation

spectra for those shown in Figure 9.

The analysis of 2D correlation spectra reveals that the broad autopeak at

342 nm in the synchronous 2D correlation spectrum is clearly resolved into

two peaks, one at 330 and the other at 351 nm in the asynchronous 2D corre-

lation spectrum. The band at 351 nm is influenced by the band at 330 nm, and

it appears to have originated from Q22, which is not readily noticeable in the

1 D spectra. We also determine the order of peak emergence of (416 and

442)! 330! 351 nm from the analysis of the asynchronous 2D correlation

spectrum.

To confirm that the band at 351 nm observed by 2D correlation analysis

indeed arises from Q22, 2D correlation based SMCR analysis was employed

to extract individual spectra from the spectral data obtained between 21.1 and

21.8 V. For the successful fitting of the spectral data by ALS iteration, of par-

ticular importance is the initial selection of the pure variables. As an initial

pick of the pure variables, the dominant cross peaks in the asynchronous 2D

correlation spectrum (Figure 10(b)) representing the pure variable bands;

i.e., (330, 351), (351, 416), and (351, 442) nm, were selected.

Figure 9. A series of spectra recorded in the potential region between 21.1 and 21.8 V,

where Q2† is reduced to Q22.


Figure 10. (a) Synchronous and (b) asynchronous 2D correlation spectra obtained from the spectra the

potential scan between 21.1 and 21.8 V (Figure 9). Solid and dotted lines indicate regions of positive and

negative correlation respectively. Reproduced with permission from Analytical Chemistry, 76: 5236.

Copyright (2004) American Chemical Society.

Y.

M.

Ju

ng

an

dI.

No

da

53

6

Figure 11. (a) The spectra of individual chemical components obtained from 2D correlation spectroscopy based

SMCR analysis of the spectra of BQ shown in Figure 10 between 21.1 and 21.8 V and (b) their concentration profiles.

Solid, dashed, and dotted lines represent BQ2†, BQ22, and BQH†, respectively. Reproduced with permission from

Analytical Chemistry, 76: 5236. Copyright (2004) American Chemical Society.

Gen

eralized

Tw

o-D

imen

sion

al

Co

rrelatio

nS

pectro

scop

y5

37

The spectra of individual chemical components obtained from the SMCR

analysis and their concentration profiles are shown in Figures 11(a) and (b),

respectively. The SMCR-estimated spectra thus obtained show well

resolved spectra of three species from what appeared to be a single

spectrum. The 351 nm band assigned to BQ22 in the 2D correlation

analysis actually corresponds to the broad band at around 356 nm in the

SMCR-extracted spectrum. A reasonable set of concentration profiles

during the potential sweep between 21.1 and 21.8 V was also obtained. It

is seen from this figure that the intensity of the Q2† band at 320 nm (solid)

stays nearly constant, while both that for Q22 at 356 nm (dashed) and the

absorption at 330 nm (dotted), which is very similar to that of Q2†,

increases until both of them reach equilibrium concentrations at the increas-

ingly negative potential. Note that the 330 nm band has already a fairly

high concentration at 21.1 V.

It is suggested that the effective decay of Q2† via the protonation reaction

is responsible for the steady state concentration of Q2†, because the concen-

tration of the species absorbing at 330 nm is already fairly high at 21.1 V

where the dianion is not even produced. Also, this species is already

generated well before Q22 is generated as pointed out above. It is therefore

concluded that the species represented by the dotted spectrum is protonated

Q2† or QH† produced from the reaction of Q2† with a trace amount of Hþ

in acetonitrile. It is the first time that the QH† is identified spectroscopically

during the reduction of p-BQ, which explains many observations described

in the literature. Results obtained in the buk cell using the 2D and SMCR

analysis techniques is in excellent agreement with that obtained in the

OTTLE cell in that the dianion spectrum was observed and extracted.

However, the spectrum from a third species (QH†) was also extracted by

the SMCR technique, which had not been possible from a simple examination

of the spectra obtained in the OTTLE cell. In conclusion, the 2D correlation

analysis used along with the SMCR analysis offers a powerful technique for

complete analysis of complex spectroelectrochemical data due to following

chemical reactions.

ACKNOWLEDGMENTS

We thank all of our colleagues who have provided us valuable contributions to

the completion of this review paper.

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