10.3 Molecular Orientation and Polarization Analysis
255
The procedure of polarization analysis is simply summarized into two steps as
follows.
SFG
spectra
(i)
− −→
ratios of
(2)
elements
(ii)
−−→
molecular
orientation
Essentially, the experimental measurements evaluate the ratios of different χ (2) tensor elements, such as B = χ
(2)
yyz /χ
(2)
yzy and C = χ
(2)
zzz /χ
(2)
yyz . There are some methods
for the step (i) to evaluate the ratios of χ (2) elements experimentally. A simple way
is to compare the relative intensities of relevant polarization combinations. More
sophisticated methods using interference of different polarizations have been also
developed and utilized [5, 9, 10, 23, 30, 32, 38]. In any events, the obtained tensor
elements in step (i) have to be analyzed in order to derive the microscopic molecular
orientation. The theory of the analysis in the step (ii) is also an integral part of the
polarization analysis of orientation, and we have depicted the theoretical procedure
(ii) to derive the molecular orientation from the ratios of tensor elements in Sect. 4.2.
The present section focuses on the analysis step (ii), and further examines the
procedure.
When we apply the theoretical procedure (ii) to actual interfaces, it often requires
some assumptions on microscopic properties of the systems. As we discuss in the
following, the reliability of these assumptions may have significant influences on the
results of molecular orientation. The MD simulation can help clarifying the relation
between the tensor elements and the microscopic molecular orientation without
resort to those assumptions, and help examining the reliability of the assumptions
involved in the polarization analysis. In this section the polarization analysis of the
methyl group is examined with two examples, methanol and acetonitrile, with the
help of MD simulation.
10.3.1 Methanol
The SFG band of the methyl symmetric stretching has been discussed in Sect. 10.1.
As illustrated in Fig. 10.2, the C–H band consists of the low-frequency component at
∼2830 cm −1 and high-frequency one at ∼2950 cm −1 , and the former is attributed to
the methyl symmetric stretching, while the latter is a mixture of the Fermi splitting
and the antisymmetric stretching. Therefore, the intensity of the former component
becomes an index of methyl symmetric C–H stretching, which could be governed
by the number density of methyl groups at interface and their orientation.
The experimental intensity of methyl symmetric stretching (ss) band shows an
intriguing behavior when the methanol is diluted with water. In the methanol/water
mixture solutions, the SFG intensity of this band shows a turn-over behavior as
255
The procedure of polarization analysis is simply summarized into two steps as
follows.
SFG
spectra
(i)
− −→
ratios of
(2)
elements
(ii)
−−→
molecular
orientation
Essentially, the experimental measurements evaluate the ratios of different χ (2) tensor elements, such as B = χ
(2)
yyz /χ
(2)
yzy and C = χ
(2)
zzz /χ
(2)
yyz . There are some methods
for the step (i) to evaluate the ratios of χ (2) elements experimentally. A simple way
is to compare the relative intensities of relevant polarization combinations. More
sophisticated methods using interference of different polarizations have been also
developed and utilized [5, 9, 10, 23, 30, 32, 38]. In any events, the obtained tensor
elements in step (i) have to be analyzed in order to derive the microscopic molecular
orientation. The theory of the analysis in the step (ii) is also an integral part of the
polarization analysis of orientation, and we have depicted the theoretical procedure
(ii) to derive the molecular orientation from the ratios of tensor elements in Sect. 4.2.
The present section focuses on the analysis step (ii), and further examines the
procedure.
When we apply the theoretical procedure (ii) to actual interfaces, it often requires
some assumptions on microscopic properties of the systems. As we discuss in the
following, the reliability of these assumptions may have significant influences on the
results of molecular orientation. The MD simulation can help clarifying the relation
between the tensor elements and the microscopic molecular orientation without
resort to those assumptions, and help examining the reliability of the assumptions
involved in the polarization analysis. In this section the polarization analysis of the
methyl group is examined with two examples, methanol and acetonitrile, with the
help of MD simulation.
10.3.1 Methanol
The SFG band of the methyl symmetric stretching has been discussed in Sect. 10.1.
As illustrated in Fig. 10.2, the C–H band consists of the low-frequency component at
∼2830 cm −1 and high-frequency one at ∼2950 cm −1 , and the former is attributed to
the methyl symmetric stretching, while the latter is a mixture of the Fermi splitting
and the antisymmetric stretching. Therefore, the intensity of the former component
becomes an index of methyl symmetric C–H stretching, which could be governed
by the number density of methyl groups at interface and their orientation.
The experimental intensity of methyl symmetric stretching (ss) band shows an
intriguing behavior when the methanol is diluted with water. In the methanol/water
mixture solutions, the SFG intensity of this band shows a turn-over behavior as