Chemistry Reference
In-Depth Information
Symmetric stretching
Asymmetric stretching
Twisting
Scissoring
Rocking
Wagging
FIGURE 7.1
Normal modes of stretching and deformation vibrations in the CH
2
molecular
group.
I
0
I
α,
c
d
FIGURE 7.2
Principle of transmission spectroscopy.
The absorbance
A
in relation (7.1) is usually defined as the negative decadic
logarithm of
t
he transmittance
T
(
ν
)
=
I
/
I
0
.
the molar
absorptivity in m
2
/mol,
c
the concentration of absorbing species in mol/m
3
, and
d
the path length in the sample. Alternatively, the negative natural lo
g
arithm is applied
in relation (7.2)
w
ith the corresponding absorption coefficient α
(
Here α
(
ν
)
is the decadic absorption coefficient at wave number ν, ε
(
ν
)
ν
)
, the absorption
cross section σ
(
ν
)
of a single particle, and the number density of the absorbing
particles
n
.
ln
I
I
0
A
(
ν
)
=−
=
α
(
ν
)
·
d
=
σ
(
ν
)
·
n
·
d
.
(7.2)
The absorption coefficient α
(
ν
)
is connected with α
(
ν
)
and the imaginary part
k
of
the com
pl
ex refractive index
n
˜
=
n
+
ik
at the wavelength λ, respectively, at the wave
number ν, according to
4π
·
k
α
·
ln10
=
α
=
=
4π
·
ν
·
k
.
(7.3)
λ
Thus, it is possible to calculate the concentration of the absorbing species if the
absorption coefficient is known. The Beer-Lambert-Bouguer law for quantitative
analysis is only exact if no interaction occurs between the absorbing species. In
the frame of its validity, the concentration can be calculated using the maximum
