6 Two-Dimensional Correlation Spectroscopy
119
Another type of moving-window technique, PCMW2D correlation spectroscopy,
was proposed by Morita et al. [20] In this case, both synchronous and asynchronous
correlation spectra were calculated as
, j =
1
2w
j+w
J = j−w
˜
y(ν, t J ) · ˜
t J
(6.13)
, j =
1
2w
j+w
J = j−w
˜
y(ν, t J ) ·
j+w
K = j−w
M J K · ˜
t K
(6.14)
where ˜
t and M are dynamic perturbation and Hilbert–Noda transformation matrix,
respectively. As similar to MW2D correlation spectroscopy, following relations were
found by Morita et al.
(ν, t) ∼
∂ y(ν, t)
∂t
ν
(6.15)
(ν, t) ∼ −
∂
2 y(ν, t)
∂t 2
ν
(6.16)
i.e., synchronous and asynchronous PCMW2D correlation intensities are proportional to a perturbation derivative and the opposite sign of a perturbation second
derivative [20]. In the case of linear perturbation, therefore, synchronous and asynchronous PCMW2D correlation intensities are proportional to a gradient and a curvature of the spectral intensity variations along the perturbation direction, respectively
[20].
Figure 6.6 shows synchronous PCMW2D correlation map constructed from the
temperature-dependent NIR spectra of MCC shown in Fig. 6.4a. Positive and negative
correlation intensities in the map represent increase and decrease of the spectral
intensities along the temperature direction, respectively. A slice spectrum at 90 °C is
also plotted in the figure. A positive correlation peak located at 6961 cm
−1 is reported
to be intermediate hydrogen bonds in MCC [17].
6.3 Applications of Two-Dimensional Correlation NIR
Spectroscopy
The simplicity in obtaining of 2D correlation spectra resulted in a fast development
of this approach. In a short time, a number of successful applications of 2DCOS to
various fields of chemistry were reported. In 1996, Noda et al. published the first
application of 2DCOS in NIR region (2DCOS-NIR) to study self-association of
oleyl alcohol in the liquid phase [21]. Due to the resolution enhancement, a number
119
Another type of moving-window technique, PCMW2D correlation spectroscopy,
was proposed by Morita et al. [20] In this case, both synchronous and asynchronous
correlation spectra were calculated as
, j =
1
2w
j+w
J = j−w
˜
y(ν, t J ) · ˜
t J
(6.13)
, j =
1
2w
j+w
J = j−w
˜
y(ν, t J ) ·
j+w
K = j−w
M J K · ˜
t K
(6.14)
where ˜
t and M are dynamic perturbation and Hilbert–Noda transformation matrix,
respectively. As similar to MW2D correlation spectroscopy, following relations were
found by Morita et al.
(ν, t) ∼
∂ y(ν, t)
∂t
ν
(6.15)
(ν, t) ∼ −
∂
2 y(ν, t)
∂t 2
ν
(6.16)
i.e., synchronous and asynchronous PCMW2D correlation intensities are proportional to a perturbation derivative and the opposite sign of a perturbation second
derivative [20]. In the case of linear perturbation, therefore, synchronous and asynchronous PCMW2D correlation intensities are proportional to a gradient and a curvature of the spectral intensity variations along the perturbation direction, respectively
[20].
Figure 6.6 shows synchronous PCMW2D correlation map constructed from the
temperature-dependent NIR spectra of MCC shown in Fig. 6.4a. Positive and negative
correlation intensities in the map represent increase and decrease of the spectral
intensities along the temperature direction, respectively. A slice spectrum at 90 °C is
also plotted in the figure. A positive correlation peak located at 6961 cm
−1 is reported
to be intermediate hydrogen bonds in MCC [17].
6.3 Applications of Two-Dimensional Correlation NIR
Spectroscopy
The simplicity in obtaining of 2D correlation spectra resulted in a fast development
of this approach. In a short time, a number of successful applications of 2DCOS to
various fields of chemistry were reported. In 1996, Noda et al. published the first
application of 2DCOS in NIR region (2DCOS-NIR) to study self-association of
oleyl alcohol in the liquid phase [21]. Due to the resolution enhancement, a number