ρ ¼ k À k
0
¼ k 1 À
k
0
k
ffi k 1 À e
1:15 ΔεC l
À
Á
ð15:10Þ
and I 0 is equal to the square of the complex amplitude of the initial light source.
Now, we can calculate the following S CD value:
S CD ¼
I R À I L
I R þ I L
¼
I θ, δ
ð ÞÀI Àθ, δ
ð
Þ
I θ, δ
ð ÞþI Àθ, δ
ð
Þ
:
ð15:11Þ
When Δε C l ¼ (ε L À ε R ) C l < < 1,
ρ ffi À1:15 k Δεcl,
ð15:12Þ
and
S CD ¼
I R À I L
I R þ I L
¼
1:15 Δε C l
sin 2θ tan
δ
2
,
ð15:13Þ
where C and l are the molar concentration of the sample and optical path length of
the sample cell, respectively.
Equation 15.13 gives the relationship between the experimentally observed
values (S CD ) and molar circular dichroism (Δε). In Eq. 15.13, we realize that two
parameters, θ and δ, need to be known to evaluate Δε.
The angle between the polarization plane of the initial linearly polarized light
after the first prism and the first axis of the retarder is defined as θ. In Fig. 15.1, the
retarder is mounted on the θ-stage; thus, θ is well known when the experiment is
performed.
To determine δ, we should understand the effect of δ on the polarization of
transmitted light through all optics without any light absorber (sample solution) in
Fig. 15.1. By calculation similar to that mentioned above, we have an equation
indicating the polarized light intensity as follows:
I θ, δ
ð Þ ¼ I 0 sin
2 2θ sin
2 δ
2
:
ð15:14Þ
Thus, we can estimate δ by the following equation:
δ ¼ 2 sin
À1
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
I θ, δ
ð Þ
I 0 sin
2 2θ
s
:
ð15:15Þ
Through Eq. 15.13, we account that S CD value may have a θ-value dependency;
moreover, S CD increases with decreasing θ-value. Such a characteristic feature is
represented in Fig. 15.4.
15 Transient Circular Dichroism Approach to Chirality Detection in Dark. . .
333
0
¼ k 1 À
k
0
k
ffi k 1 À e
1:15 ΔεC l
À
Á
ð15:10Þ
and I 0 is equal to the square of the complex amplitude of the initial light source.
Now, we can calculate the following S CD value:
S CD ¼
I R À I L
I R þ I L
¼
I θ, δ
ð ÞÀI Àθ, δ
ð
Þ
I θ, δ
ð ÞþI Àθ, δ
ð
Þ
:
ð15:11Þ
When Δε C l ¼ (ε L À ε R ) C l < < 1,
ρ ffi À1:15 k Δεcl,
ð15:12Þ
and
S CD ¼
I R À I L
I R þ I L
¼
1:15 Δε C l
sin 2θ tan
δ
2
,
ð15:13Þ
where C and l are the molar concentration of the sample and optical path length of
the sample cell, respectively.
Equation 15.13 gives the relationship between the experimentally observed
values (S CD ) and molar circular dichroism (Δε). In Eq. 15.13, we realize that two
parameters, θ and δ, need to be known to evaluate Δε.
The angle between the polarization plane of the initial linearly polarized light
after the first prism and the first axis of the retarder is defined as θ. In Fig. 15.1, the
retarder is mounted on the θ-stage; thus, θ is well known when the experiment is
performed.
To determine δ, we should understand the effect of δ on the polarization of
transmitted light through all optics without any light absorber (sample solution) in
Fig. 15.1. By calculation similar to that mentioned above, we have an equation
indicating the polarized light intensity as follows:
I θ, δ
ð Þ ¼ I 0 sin
2 2θ sin
2 δ
2
:
ð15:14Þ
Thus, we can estimate δ by the following equation:
δ ¼ 2 sin
À1
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
I θ, δ
ð Þ
I 0 sin
2 2θ
s
:
ð15:15Þ
Through Eq. 15.13, we account that S CD value may have a θ-value dependency;
moreover, S CD increases with decreasing θ-value. Such a characteristic feature is
represented in Fig. 15.4.
15 Transient Circular Dichroism Approach to Chirality Detection in Dark. . .
333