M
p
j ¼
cos β j
Ài n
2
j
^
ξ j
sin β j
Ài
ξ
n 2
j
^
sin β j cos β j
2
6
6
6
6
6
4
3
7
7
7
7
7
5
ð2:20Þ
M
s
j ¼
cos β j
Ài
ξ j
sin β j
Àiξ j sin β j cos β j
2
4
3
5
ð2:21Þ
where ξ j ¼n j
^ cos φ
j
i , φ i is the angle of incidence at the phase boundary j
th and n j is
the refractive index of the j
th phase and β j ¼
2πξ j d j
λ and d j is a finite thickness of a j
th
phase (here electrolyte and film adsorbed on the mirror surface, as shown in
Fig. 2.4). Multiplication of individual matrices of the stratified medium gives the
characteristic matrix. For an incoming radiation of wavelength λ, the reflectivity and
transmission coefficients, MSEFS and phase shift as a function of the angle of
incidence φ i and thickness d j of a finite layer of the j
th phase (here d 3 , thickness of
the electrolyte layer) can be calculated.
MSEFS was calculated for the stratified system representing the
spectroelectrochemical cell composed of either CaF 2 or ZnSe optical windows;
D 2 O solvent and Au mirror and electrode. The calculation was performed using a
computation program received form Zamlynny [18]. The calculation was done for
collimated and converged (Æ 5%) IR beams. In the calculation the wavenumber of
the incoming IR radiation is set to 2900 cm
À1 (λ ¼ 3.34 μm). In this spectral range
the IR absorption modes of the methyl and methylene groups occur. These modes
are commonly present in organic compounds and often analyzed in
spectroelectrochemical studies. Figure 2.5 shows the plots of the MSEFS as a
function of the angle of incidence and electrolyte layer thickness.
First are discussed the plots of MESFS as a function of the angle of incidence
(Fig. 2.5a, b). In a stratified system containing CaF 2 as the optical window MSEFS
reaches a maximum of 7.5 at φ i ¼ 52.4
and 18.7 at φ i ¼ 58.4
for converged and
collimated beams, respectively (Fig. 2.5a). When ZnSe is used as the optical window
the maximum of MESFS is close to 11 at φ i ¼ 24.5
and 33 at φ i ¼ 29.2
for
converged and collimated beams, respectively (Fig. 2.5b). The enhancement of
MSEFS of the collimated beam reflected from the Au surface arises from multiple
reflections and constructive interference of the IR radiation in the thin electrolyte
layer between the mirror and optical window. When a collimated beam is used,
MSEFS versus φ i curves are very narrow while in the case of converged beam these
plots become broader (Fig. 2.5a, b). These results have practical consequences for
the performance of in situ experiments. The use of a converged IR beam leads to a
decrease in the intensity of the reflected light approaching the detector. However, the
presence of a broad maximum does not cause a large decrease in MESFS at angle of
2.2 Application of IRRAS to the Electrochemical Interface
15
p
j ¼
cos β j
Ài n
2
j
^
ξ j
sin β j
Ài
ξ
n 2
j
^
sin β j cos β j
2
6
6
6
6
6
4
3
7
7
7
7
7
5
ð2:20Þ
M
s
j ¼
cos β j
Ài
ξ j
sin β j
Àiξ j sin β j cos β j
2
4
3
5
ð2:21Þ
where ξ j ¼n j
^ cos φ
j
i , φ i is the angle of incidence at the phase boundary j
th and n j is
the refractive index of the j
th phase and β j ¼
2πξ j d j
λ and d j is a finite thickness of a j
th
phase (here electrolyte and film adsorbed on the mirror surface, as shown in
Fig. 2.4). Multiplication of individual matrices of the stratified medium gives the
characteristic matrix. For an incoming radiation of wavelength λ, the reflectivity and
transmission coefficients, MSEFS and phase shift as a function of the angle of
incidence φ i and thickness d j of a finite layer of the j
th phase (here d 3 , thickness of
the electrolyte layer) can be calculated.
MSEFS was calculated for the stratified system representing the
spectroelectrochemical cell composed of either CaF 2 or ZnSe optical windows;
D 2 O solvent and Au mirror and electrode. The calculation was performed using a
computation program received form Zamlynny [18]. The calculation was done for
collimated and converged (Æ 5%) IR beams. In the calculation the wavenumber of
the incoming IR radiation is set to 2900 cm
À1 (λ ¼ 3.34 μm). In this spectral range
the IR absorption modes of the methyl and methylene groups occur. These modes
are commonly present in organic compounds and often analyzed in
spectroelectrochemical studies. Figure 2.5 shows the plots of the MSEFS as a
function of the angle of incidence and electrolyte layer thickness.
First are discussed the plots of MESFS as a function of the angle of incidence
(Fig. 2.5a, b). In a stratified system containing CaF 2 as the optical window MSEFS
reaches a maximum of 7.5 at φ i ¼ 52.4
and 18.7 at φ i ¼ 58.4
for converged and
collimated beams, respectively (Fig. 2.5a). When ZnSe is used as the optical window
the maximum of MESFS is close to 11 at φ i ¼ 24.5
and 33 at φ i ¼ 29.2
for
converged and collimated beams, respectively (Fig. 2.5b). The enhancement of
MSEFS of the collimated beam reflected from the Au surface arises from multiple
reflections and constructive interference of the IR radiation in the thin electrolyte
layer between the mirror and optical window. When a collimated beam is used,
MSEFS versus φ i curves are very narrow while in the case of converged beam these
plots become broader (Fig. 2.5a, b). These results have practical consequences for
the performance of in situ experiments. The use of a converged IR beam leads to a
decrease in the intensity of the reflected light approaching the detector. However, the
presence of a broad maximum does not cause a large decrease in MESFS at angle of
2.2 Application of IRRAS to the Electrochemical Interface
15