Transcript absorption coefficient

Infrared Spectroscopy in thin films
Periklis Papadopoulos
Universität Leipzig, Fakultät für Physik und Geowissenschaften
Institut für Experimentelle Physik I, Abteilung "Molekülphysik“
[email protected]
Outline

Techniques

Transmission

Reflection

Out-of-plane dipole moments

Transition Moment Orientational Analysis

Example: Liquid crystal elastomers
2
Transmission – reflection modes

Simplified: no interference, etc.
Transmission - absorption
Absorbance
A   log
Absorption coefficient α
Molar absorption coefficient ε=α/c
Lambert-Beer law:
Specular reflection
I1
I0
I1  I 0 e  l  I 0 e  cl
l
 cl
A

ln10 ln10
Reflectivity
R
I ref
I0
Normal incidence in air
 n  1 
R  
 n 1
2
3
Thin films – coatings
incident

Absorption is too low

Reflection might be more important

(Spectroscopic) Ellipsometry: reflected intensity for s and p polarizations

Attenuated total reflection
reflected
transmitted
4
Ultrathin polystyrene films

Spin-coated polystyrene

Measured in transflection geometry

Possible to measure thin samples, below 5 nm
0.002
thickness of PS card: 30 µm
refractive index of PS:
0.0004
doi:10.1016/j.optmat.2006.07.010
~ 20 nm
2
Absorbance
~ 4.8 nm
0.001
0.0002
1
0
3500
0.0000
3000
2500
2000
wavenumber / cm
1500
1000
0.000
500
-1
5
Complex refractive index
n  n  in
 The imaginary part is proportional to the absorption coefficient
Et  x   E0 exp  i 2 n x  
I t  I 0 exp  i 4 n x  exp  4 n x  


  4 n
Dielectric function
    n 
2
Real and imaginary parts are related through Kramers-Kronig relations
Example:
polycarbonate
Fourier Transform Infrared Spectrometry,
P. R. Griffiths, J.A. de Haseth, Wiley
6
IR spectral range
Polarization dependence


Example: salol crystal

All transition dipoles (for a certain transition) are perfectly aligned

Intensity of absorption bands depends greatly on crystal orientation
Dichroism: difference of absorption coefficient between two axes

Biaxiality (all three axes different)
salol
Vibrational Spectroscopy in Life Science, F. Siebert, P. Hildebrandt
J. Hanuza et al. / Vib. Spectrosc. 34 (2004) 253–268
7
IR spectral range
Order parameter


Non-crystalline solids: molecules (and transition dipole moments) are not (perfectly) aligned

Rotational symmetry is common

Different absorbance A|| and A 

Dichroic ratio R= A|| / A 
Reference
axis
Molecular order parameter
Molecular
segment
S mol  P2   
“parallel” vibration
  0 : S mol 
“perpendicular” vibration


2
3 cos2   1
Transition
dipole
2
R 1
R2
: S mol  2
R 1
R2
||

8
Quantitative IR spectroscopy
Limitations of polarization-dependent measurements in 2D

Lambert-Beer law


Direct application may be problematic
Cx
ln10
No correction for reflection


I  I0 exp  Cx   A 
Problem near strong absorption bands
IR ellipsometry?

Needs model, unsuitable for thick samples in NIR

Too many free parameters

Biaxiality ?

Complex n*=n’-i n” ?

Tensor of refractive index ?

Arbitrary principal axes
9
Setup
Arbitrary direction of electric field – 3D
z


By tilting the sample (0 ... ±70°) the E-field can
have almost any direction (x,y,z)
The complex refractive index for every
wavelength can be measured

Transmission mode: better than ellipsometry for
the absorption coefficient
x
W. Cossack et al. Macromolecules 43, 7532 (2010)
y
10
Setup
Experimental setup
Detector

Simultaneous IR and mechanical measurements

Temperature variation
(RT – 45 °C)
W. Cossack et al. Macromolecules 43, 7532 (2010)
11
Theory
Propagation in biaxial lossy medium – complicated!

Wave equation from Maxwell‘s equations:


The wavevector depends on the orientation
Effective refractive index neff


1
1
k  Ek 
D
εE
2
2
 0 neff
 0 neff
 
 ε 1 I  kk T


E
ε  ε 0n 2
1
E
2
 0 neff
When reflection is negligible, or can be removed (e.g. baseline correction in NIR) the tensor of
absorption coefficient can be easily obtained

Effective optical path (Snell’s law):
deff  d
Re


neff
2
neff
 sin 2 
θ

W. Cossack et al. Macromolecules 43, 7532 (2010)
d
12
Theory
Propagation in biaxial lossy medium

Boundary conditions of Maxwell equations are taken into account

E//, k// and D are the same at both sides of reflecting surface
2


k

 2 ε 
 0
 2
 c  0  k k
 


0
k 2  k2
0
k k
0
k2


E  0


Two values of the refractive index
are allowed



Birefringence
θ
k// k
The polarization eigenstates are
not necessarily s and p
The values can be used in the
Fresnel equations
W. Cossack et al. Macromolecules 43, 7532 (2010)
13
Analysis of spectra
Analysis

The absorption coefficient (or absorbance) as a function of polarization and tilt angles can be fitted with
6 parameters

3 eigenvalues and 3 Euler angles

No assumption for the orientation of the principal axes is necessary
C-O stretch
Absorbance tensor
 3.52 0.44 0.15 


A   0.44 0.14 0.07 
 0.15 0.07 0.04 


2
1
Po
lari
zat
60
ion
a
90
ngl
e
0
12
0
15
-60
e
0
-20
- 40
gl
30
Not diagonal!
an
0
60
40
20
lt
0
Ti
Absorbance
3
A  QΛQ1
0
18
14
Applications
PEDOT:PSS spin-coated on Ge

Spin coated sample ~ 20 nm
thick
Molecular chains lie on the xyplane

0.02
2D study would be inadequate
z
y
x
x
y
z
Absorbance

0.01
0.00
1300
1200
1100
1000
900
-1
wavenumber [cm ]
15
Applications
Smectic C* elastomer: vibrations
Repeating unit of main chain

Main chain is LC

Sample is too thick for MIR


In NIR the combination bands and overtones are
observed
C=O
C-O
  3330 cm -1
  3430 cm -1
Doping with chiral group
Crosslinker
0.6
Absorbance

0.4
x
y
z
0.2
0.0
7000
6500
6000
5500
5000
4500
4000
3500
-1
wavenumber [cm ]
W. Cossack et al. Macromolecules 43, 7532 (2010)
16
Applications
Smectic C* elastomer: biaxiality

Stretching parallel to director


No effect on biaxiality
z
Biaxiality at 25 °C (smectic X) comparable with 40
°C (smectic C)
Carbonyl C=O
Aliphatic C-H
x
y
Ester C-O
17
Applications
Smectic C* elastomer: director reorientation

Shear

z
After small threshold, reorientation starts
x
Reorientation on xy-plane
Rotation angles
y
Biaxiality
18
Applications
Smectic C* elastomer: model

Unlike NLCE, the director is strongly coupled to the network
19
Summary

Absorbance from thin films is low, reflection must be taken into account

Ellipsometry is commonly applied

New technique: TMOA

Applied to thick biaxial films

Promising for thin films as well
20
Applications
Liquid crystalline elastomers:
Nematic

The elastomer has LC side chains


Nematic phase
With TMOA it is possible to find
the order of the backbone and the
mesogen
21
Applications
Nematic elastomer: vibrations

C-H out-of-plane bending:

Si-O- stretching (overtone):
  844 cm-1
  2110 cm -1
Si
O
Si
O
2
Absorbance
x
y
z
1
0
2200
2000
1800
1600
1400
1200
1000
800
600
-1
wavenumber [cm ]
22
Applications
Nematic elastomer: biaxiality

3D polar plot of absorbance

The main chains are oriented along the stretching direction

The mesogen is perpendicular to the main chain

No perfect rotational symmetry
z
z
y
y
z
x
y
x
x
Main chain (Si-O)
Side chain (mesogen)
23
Applications
Nematic elastomer: biaxiality
C-C mesogen

Strething parallel to the director:

Small change of biaxiality

No reorientation
stretch //
z

Stretching perpendicular:

x
y
No reorientation either!
stretch 
24
Applications
Nematic elastomer: model

Only the polymer network is deformed

Different from previous studies on NLCE
Macromol. Chem. Phys. 206, 709 (2005)
25