alkanethiol monolayer) and of the reference sample (unmodified gold surface) differ
slightly from each other. In double modulation IR spectroscopy a differential
spectrum is measured,
ΔI
I
h i
Diff:Spectrum
¼
I s À I p
À
Á
I p þ I s
À
Á =2
ð2:31Þ
where ΔI ¼ (I s À I p ) is the intensity of the differential and hIi ¼ (I s + I p )/2 is the
intensity of the average signal of the p- and s-polarized IR light.
To obtain the differential spectrum (described by Eq. 2.31) from the PM IRRAS
experimental spectrum (described by Eq. 2.28) the signal at the detector has to be
demodulated. The signal at the high-pass filter is demodulated with a lock-in
amplifier which extracts the detector signal (I D (2ω m )) at the frequency which is
equal to the second harmonic of the voltage frequency applied to PEM [7].
I D 2ω m
ð
Þ ¼ΔIJ 2 δ 0
ð Þ
ð2:32Þ
The signal at the low-pass filter at the detector (I D (ω i )) is given in Eq. (2.33).
I D ω i
ð Þ ¼ I
h i þ
ΔI
2
J 0 δ 0
ð Þ
ð2:33Þ
The obtained I D (2ω m ) and I D (ω i ) signals provide the experimental PM IRRA
spectrum which is expressed in Eq. (2.34).
ΔI
I
h i
exp
¼
I D 2ω m
ð
Þ
I D ω i
ð Þ
¼
ΔIJ 2 δ 0
ð Þ
I
h i þ
ΔI
2 J 0 δ 0
ð Þ
ð2:34Þ
The term
ΔI
2 J 0 δ 0
ð Þin Eq. (2.34) may be neglected, because the difference signal is
significantly lower than the average signal [7, 51]. The maximum phase shift
(δ 0 ¼ π) occurs only at λ ¼ λ 0 . Thus,
I D 2ω m
ð
Þ
I D ω i
ð Þ is equal to
ΔI
I
h i only at λ ¼ λ 0 . At any
other wavelength the absorbance of the species adsorbed on the mirror surface is
overlaid with the background caused by the Bessel functions. Figure 2.14 shows the
two channel PM IRRA signals of lipid bilayers adsorbed on the gold surface
measured at the air|gold (ex situ experiment) and water|gold (in situ experiment)
interfaces. The I D (ω i ) signal is similar to the reflectance measured from a metallic
surface in air (Fig. 2.14a, black line) and in D 2 O solution (Fig. 2.14c, black line). The
contribution from the environment of the analyzed sample (CO 2 and H 2 O vapor
lines) dominates in the spectrum.
The double modulated signals I D (2ω m ) (gray lines, Fig. 2.14a, c) have different
shapes than the I D (ω i ) signals. The shape of the I D (2ω m ) spectra is influenced by the
second order Bessel function, which is overlapped with the IR absorption modes of
the absorption of CO 2 and H 2 O vapor in the sample environment (and additionally
liquid D 2 O in the spectroelectrochemical cell). In the differential spectrum the
30
2 Polarization Modulation Infrared Reflection Absorption Spectroscopy: From. . .
slightly from each other. In double modulation IR spectroscopy a differential
spectrum is measured,
ΔI
I
h i
Diff:Spectrum
¼
I s À I p
À
Á
I p þ I s
À
Á =2
ð2:31Þ
where ΔI ¼ (I s À I p ) is the intensity of the differential and hIi ¼ (I s + I p )/2 is the
intensity of the average signal of the p- and s-polarized IR light.
To obtain the differential spectrum (described by Eq. 2.31) from the PM IRRAS
experimental spectrum (described by Eq. 2.28) the signal at the detector has to be
demodulated. The signal at the high-pass filter is demodulated with a lock-in
amplifier which extracts the detector signal (I D (2ω m )) at the frequency which is
equal to the second harmonic of the voltage frequency applied to PEM [7].
I D 2ω m
ð
Þ ¼ΔIJ 2 δ 0
ð Þ
ð2:32Þ
The signal at the low-pass filter at the detector (I D (ω i )) is given in Eq. (2.33).
I D ω i
ð Þ ¼ I
h i þ
ΔI
2
J 0 δ 0
ð Þ
ð2:33Þ
The obtained I D (2ω m ) and I D (ω i ) signals provide the experimental PM IRRA
spectrum which is expressed in Eq. (2.34).
ΔI
I
h i
exp
¼
I D 2ω m
ð
Þ
I D ω i
ð Þ
¼
ΔIJ 2 δ 0
ð Þ
I
h i þ
ΔI
2 J 0 δ 0
ð Þ
ð2:34Þ
The term
ΔI
2 J 0 δ 0
ð Þin Eq. (2.34) may be neglected, because the difference signal is
significantly lower than the average signal [7, 51]. The maximum phase shift
(δ 0 ¼ π) occurs only at λ ¼ λ 0 . Thus,
I D 2ω m
ð
Þ
I D ω i
ð Þ is equal to
ΔI
I
h i only at λ ¼ λ 0 . At any
other wavelength the absorbance of the species adsorbed on the mirror surface is
overlaid with the background caused by the Bessel functions. Figure 2.14 shows the
two channel PM IRRA signals of lipid bilayers adsorbed on the gold surface
measured at the air|gold (ex situ experiment) and water|gold (in situ experiment)
interfaces. The I D (ω i ) signal is similar to the reflectance measured from a metallic
surface in air (Fig. 2.14a, black line) and in D 2 O solution (Fig. 2.14c, black line). The
contribution from the environment of the analyzed sample (CO 2 and H 2 O vapor
lines) dominates in the spectrum.
The double modulated signals I D (2ω m ) (gray lines, Fig. 2.14a, c) have different
shapes than the I D (ω i ) signals. The shape of the I D (2ω m ) spectra is influenced by the
second order Bessel function, which is overlapped with the IR absorption modes of
the absorption of CO 2 and H 2 O vapor in the sample environment (and additionally
liquid D 2 O in the spectroelectrochemical cell). In the differential spectrum the
30
2 Polarization Modulation Infrared Reflection Absorption Spectroscopy: From. . .