papadopoulos@physik.uni-leipzig.de

Periklis Papadopoulos

Universität Leipzig, Fakultät für Physik und Geowissenschaften

Institut für Experimentelle Physik I, Abteilung "Molekülphysik“

Infrared Spectroscopy in thin films

2

Outline

Techniques Transmission Reflection

Out-of-plane dipole moments Transition Moment Orientational Analysis

Example: Liquid crystal elastomers

3

Transmission – reflection modes

Simplified: no interference, etc.

Transmission - absorption Specular reflection

Absorbance

Absorption coefficient αMolar absorption coefficient ε=α/c

Lambert-Beer law:

1

0

logI

AI

1 0 0e el clI I I

ln10 ln10

l clA

Reflectivityref

0

IR

I

Normal incidence in air2

1

1

nR

n

4

Thin films – coatings

Absorption is too low Reflection might be more important (Spectroscopic) Ellipsometry: reflected intensity for s and

p polarizations Attenuated total reflection

incident reflected

transmitted

5

Ultrathin polystyrene films

Spin-coated polystyrene Measured in transflection geometry Possible to measure thin samples, below 5 nm

6

Complex refractive index

The imaginary part is proportional to the absorption coefficient

Dielectric function Real and imaginary parts are related through Kramers-

Kronig relations

Example:polycarbonate

n n in

0

0

exp 2

exp 4 exp 4

4

t

t

E x E i n x

I I i n x n x

n

2n

Fourier Transform Infrared Spectrometry,P. R. Griffiths, J.A. de Haseth, Wiley

7

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)

IR spectral range

salol

Vibrational Spectroscopy in Life Science, F. Siebert, P. HildebrandtJ. Hanuza et al. / Vib. Spectrosc. 34 (2004) 253–268

8

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

Molecular order parameter

IR spectral range

Reference axis

Molecular segment

Transition dipole

||

2

2

3 cos 1

2molS P

1

0 :2

mol RS

R

1

: 22 2

mol RS

R

“parallel” vibration

“perpendicular” vibration

9

Limitations of polarization-dependent measurements in 2D

Lambert-Beer law Direct application may be problematic

No correction for reflection 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

Quantitative IR spectroscopy

0 expln10

CxI I Cx A

10

Arbitrary direction of electric field – 3D

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

Setup

x y

z

W. Cossack et al. Macromolecules 43, 7532 (2010)

11

Experimental setup

Setup

Detector

Simultaneous IR and mechanical measurements

Temperature variation (RT – 45 °C)

W. Cossack et al. Macromolecules 43, 7532 (2010)

12

Propagation in biaxial lossy medium – complicated!

Wave equation from Maxwell‘s equations: The wavevector depends on the orientation Effective refractive index 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):

Theory

2 20 0

1 1

eff effn n k E k D εE

12

0

1T

effn ε I kk E E

d eff

eff2 2

effRe sin

nd d

n

θ

20ε ε n

W. Cossack et al. Macromolecules 43, 7532 (2010)

13

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

Theory

k//k

θ

22

20 2

2

2

0

0 0 0

0

k

kc

k k

k k

k

k

εE

Two values of the refractive index are allowed Birefringence

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)

14

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

Analysis of spectra

030

6090

120

150

180

0

1

2

3

-60-40

-200

2040

60

Abs

orba

nce

Tilt an

gle

Polarization angle

3.52 0.44 0.15

0.44 0.14 0.07

0.15 0.07 0.04

A

Absorbance tensor

Not diagonal!

1A QΛQ

C-O stretch

15

PEDOT:PSS spin-coated on Ge

Spin coated sample ~ 20 nm thick

Molecular chains lie on the xy-plane

2D study would be inadequate

1300 1200 1100 1000 900

0.00

0.01

0.02

Abs

orba

nce

wavenumber [cm-1]

x y z

Applications

z

x

y

16

Smectic C* elastomer: vibrations

Main chain is LC Sample is too thick for MIR

In NIR the combination bands and overtones are observed

C=O C-O

-13430 cm

-13330 cm

Applications

Repeating unit of main chain

Doping with chiral group Crosslinker

7000 6500 6000 5500 5000 4500 4000 3500

0.0

0.2

0.4

0.6

Abs

orba

nce

wavenumber [cm-1]

x y z

W. Cossack et al. Macromolecules 43, 7532 (2010)

17

Smectic C* elastomer: biaxiality

Stretching parallel to director No effect on biaxiality Biaxiality at 25 °C (smectic X)

comparable with 40 °C (smectic C)

Applications

Carbonyl C=O Aliphatic C-H Ester C-O

y

z

x

18

Smectic C* elastomer: director reorientation

Shear After small threshold,

reorientation starts

Applications

y

z

x

Reorientation on xy-plane Rotation angles Biaxiality

19

Smectic C* elastomer: model

Unlike NLCE, the director is strongly coupled to the network

Applications

20

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

21

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

Applications

22

Nematic elastomer: vibrations

C-H out-of-plane bending:

Si-O- stretching (overtone):

-1844 cm

-12110 cm

2200 2000 1800 1600 1400 1200 1000 800 6000

1

2

x y z

Ab

sorb

an

ce

wavenumber [cm-1]

Applications

Si O Si O

23

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

Main chain (Si-O) Side chain (mesogen)

Applications

x

z

yy

x

z

x

y

z

24

Nematic elastomer: biaxiality

Applications

Strething parallel to the director: Small change of biaxiality No reorientation

Stretching perpendicular: No reorientation either!

C-C mesogen

stretch //

stretch

y

z

x

25

Nematic elastomer: model

Only the polymer network is deformed Different from previous studies on NLCE

Applications

Macromol. Chem. Phys. 206, 709 (2005)