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BROADBAND DIELECTRIC SPECTROSCOPY -
BASICS AND SELECTED APPLICATIONS
Andreas Schönhals 9th International Conference on Broadband Dielectric Spectroscopy and its Applications September 11-16, 2016 in Pisa (ITALY)
11.09.2016
Table of Content
Basics of Dielectric Spectroscopy
Electrostatics
Dynamics
Analysis
Scaling of the dynamic glass transition (-relaxation)
Chain dynamics – Normal mode
Conclusion
11.09.2016 Broadband Dielectric Spectroscopy – Basics and Applications 2
Dielectric Spectroscopy
11.09.2016 Broadband Dielectric Spectroscopy – Basics and Applications 3
Maxwell´s Equations:
Bt
Erot
Electric field Magnetic induction
0Bdiv
Dt
jHrot
Magnetic field
Current density
Dielectric displacement
Ddiv
Density of charges
Material Equation:
Small electrical field strengths:
E*D 0
E)1*(DDP 00
Polarization
Complex Dielectric Function * is time dependent if time dependent processes taking place within the sample
0 – permittivity of vacuum
Dielectric Spectroscopy
11.09.2016 Broadband Dielectric Spectroscopy – Basics and Applications 4
System under investigation
Input Output
E(t) P(t) (t)
Time
E
E(t
); I
nput
Time
PS
P
P(t
); O
utp
ut Relaxational Contribution
Instantaneous Response
Simplest Case : Step-like Input E
P)t(P)t(
Dielectric Spectroscopy
11.09.2016 Broadband Dielectric Spectroscopy – Basics and Applications 5
System under investigation
Input Output
E(t) P(t) (t)
Arbitrary input Approximation of the Input by step-like changes
E(t
); I
np
ut
Time
t*t
E
t*
t
E)0(E)t(E
dt*dt
dx
'dt'dt
)'t(Ed)'tt(P)t(P
t
0
Basics of Linear Response Theory
Linearity
Causality
Dielectric Spectroscopy
11.09.2016 Broadband Dielectric Spectroscopy – Basics and Applications 6
System under investigation
Input Output
E(t) P(t) (t)
E(t
) ;
P(t
)
Time
Phase shift
)tsin(EtiexpE)t(E 00
)tsin(P)t(P 0
- Angular Frequency
Complex Numbers
)(''i)(')(* Complex Dielectric Function
Dielectric Spectroscopy
Phase angle
14.10.2015 Molecular Dynamics of plasma polymerized layers by relaxation spectroscopy 7
System under investigation
Input Output
E(t) P(t)
)(''i)(')(* Complex Dielectric Function
Real Part (in Phase) Imaginary or Loss Part
(90 ° Phase shifted)
´
´´
*
Complex Plane '
''tan
Dielectric Spectroscopy
Kramers-Kronig relationship
11.09.2016 Broadband Dielectric Spectroscopy – Basics and Applications 8
Real Part Related to the energy stored reversibly during one cycle
Loss Part Related to the energy dissipated during one cycle
Law of energy conservation
Relationship between both quantities
Kramers – Kronig Relationships
d
)(''1)('
d)('1
)(''
Dielectric Spectroscopy
Modulus
11.09.2016 Broadband Dielectric Spectroscopy – Basics and Applications 9
'dt'dt
)'t(Ed)'tt(P)t(P
t
0
Linear Equation
Relationship between (t) and M(t)
System under investigation
Input Output
E(t) P(t)
M(t)
Electrical Modulus
(t)
)t('dt)'t(M)'tt(
(t) – Dirac function
1)ω(*)(*M
Fourier Transformation
Can be inverted
Dielectric Spectroscopy
Molecular quantities
11.09.2016 Broadband Dielectric Spectroscopy – Basics and Applications 10
Thermodynamic quantities are average values. Because of the thermal movement of the molecules these quantities fluctuate around their mean values.
Correlation function of Polarization Fluctuations
2
i
i
i ji
ji
i
ii
)(
)()0(2)()0(
)(
2P
)0(P)(P)(
iμV
1P
Fluctuation Dissipation Theorem
d)i(exp)(2
P)P(
22
Spectral Density
Measure for the frequency distribution of the fluctuations
ε
1)τ(ε
Tk
1)τ(
1)(''
kT
1)P( 2
Links microscopic fluctuations and macroscopic reactions
For a small (linear) disturbance a system reacts only in the way as it fluctuates
Dielectric Spectroscopy
Propylene glycol
11.09.2016 Broadband Dielectric Spectroscopy – Basics and Applications 11
-4 0 4 8
0
20
40
60
80
-4 -2 0 2 4 6 8 10
0
10
20
30
40
''
'
313 K258.5 K215 K185.4 K168.5 K
log ( f [Hz])
Time Domain
Fourier Correlation Analysis
Bridges
Coaxial Reflectometer
Network Analysis
A. Schönhals, F. Kremer, E. Schlosser, Phys. Rev. Lett. 67, 999 (1991)
Linear Response Theory
11.09.2016 Broadband Dielectric Spectroscopy – Basics and Applications 12
System under Investigation
Input Output
Disturbance x(t)
Reaction y(t)
Material function
Molecular Motions
Electric field E Polarization P
Shear tension Shear angle
Magnetic field H Magnetization M
Temperature T Entropy S
Linear Response Theory
11.09.2016 Broadband Dielectric Spectroscopy – Basics and Applications 13
System under Investigation
Input Output
Disturbance x(t)
Reaction y(t)
Molecular Motions
Material function Disturbance Reaction
Intensive - independent of V Extensive ~ V Generalized Modulus G(t)
Tensile Strain Strain Elastic Modulus
Extensive ~ V Intensive - independent of V Generalized Compliance J(t)
Strain Tensile Stress Elastic Compliance
Relaxation
Retardation
Linear Response Theory
11.09.2016 Broadband Dielectric Spectroscopy – Basics and Applications 14
Type of Experiment
Disturbance x(t)
Response y(t)
Compliance J(t) or J*()
Modulus G(t) or G*()
Dielectric Electric field E
Polarization P
Dielectric Susceptibility *()=(*()-1)
Dielectric Modulus
Mechanical Shear
Shear tension
Shear angel
Shear compliance J(t)
Shear Modulus G(t)
Isotropic Compression
Pressure p
Volume V
Volume compliance B(t) V
Compression Modulus K(t)
Magnetic Magnetic field H
Magnetization M
Magnetic susceptibility *()=(*()-1)
-
Heat Temperature T
Entropy S
Heat capacity cp(t)
Temperature Modulus GT(t)
System under investigation
Input Output
x(t) y(t)
Dielectric Spectroscopy
Information of a measurement
11.09.2016 Broadband Dielectric Spectroscopy – Basics and Applications 15
log ( /p)
log
''
p = 2 f
p=1/
S
= S -
'
Three essential measurement information
Frequency position fp
Dielectric relaxation strength
Shape of the relaxation time spectra
Dielectric Spectroscopy
Dielectric relaxation strength
11.09.2016 Broadband Dielectric Spectroscopy – Basics and Applications 16
Time
S
(t
)=P
/E
Induced dipoles
Orientational polarization
Capacitor with N permanent Dipoles, Dipole Moment
Polarization :
PμV
NPμ
V
1P
i
Mean Dipole Moment
Mean Dipole Moment: Counterbalance
EWel
kTWth
Thermal Energy Electrical Energy
4
4
d)kT
Eexp(
d)kT
E(exp
The factor gives the probability that the dipole moment vector has an orientation between and + d.
Dielectric Spectroscopy
Dielectric relaxation strength
11.09.2016 Broadband Dielectric Spectroscopy – Basics and Applications 17
Spherical Coordinates:
Only the dipole moment component which is parallel to the direction of the electric field contributes to the polarization
dsin2
1)
kT
cosE(exp
dsin2
1)
kT
cosE(expcos
0
0
x = ( E cos ) / (kT) a = ( E) / (kT)
)a(a
1
)aexp()aexp(
)aexp()aexp(
dx)xexp(
dx)xexp(x
a
1cos
a
a
a
a
0 2 4 6 8 100.0
0.2
0.4
0.6
0.8
1.0(a)=a/3
Langevin function
a
(a
) 1.0kT
Ea
Tk1.0E
Langevin function
(a)a/3 ETk3
2
V
N
Tk3
1 2
0S
Debye-Formula
Dielectric Spectroscopy
Dielectric relaxation strength
11.09.2016 Broadband Dielectric Spectroscopy – Basics and Applications 18
Shielding effects:
E
eff
= + Eloc
Polar Molecules; Onsager – Theory, Reactions Field
V
N
TkF
3
1 2
0S
)2(3
)2(F
S
2S
Onsager Factor F= 2 … 3
eff
Interaction effects:
inter
2
2
.Interact
2
jiji
i
N1g
V
N
TkgF
3
1 2
0
S
z nearest neighbors: cosz1g
Kirkwood / Fröhlich Correlation Factor g= 0.5 … 5
Dielectric Spectroscopy
Dynamics - Debye model
11.09.2016 Broadband Dielectric Spectroscopy – Basics and Applications 19
2
ii
i jiji
iii
)(
)t()0(2)t()0(
)t(Dynamics is due to the dipole – dipole correlation function
Debye model: Change of the polarization is proportional to the actual value )t(P1
td
)t(Pd
D
D
texp)t(
Time domain Frequency domain
Di1)(*
2
D )(1'
2
D
D
)(1''
Rotational Diffusion Model Double Potential Model
)t(P2nn2dt
dn
dt
dn
dt
Pd21
21
A rigid isolated fluctuating dipole is regarded in viscous media under the influence of a stochastic force
)]t,r(fkT
)t(E)t,r(f[D
t
)t,r(fRot
)tD)1m(m(exp))t((cosP))0((cosP Rotmm
Dielectric Spectroscopy
Model functions
11.09.2016 Broadband Dielectric Spectroscopy – Basics and Applications 20
In most cases the half width of measured loss peaks is much broader than predicted by Debye equation and in addition their shapes are asymmetric.
Di1)(*
Debye function:
Cole/Cole function:
)i(1)(
CC
*
CC 0<1
symmetric
symmetric broadening
Cole/Davidson function:
)i1()(
CD
*
CD 0<1 asymmetric broadening
Havriliak/Negami function:
))i(1()(
HN
*
HN 0<; 1 asymmetric and symmetric broadening
Dielectric Spectroscopy
Data Analysis
11.09.2016 Broadband Dielectric Spectroscopy – Basics and Applications 21
-2 0 2 4 6-2
-1
0
'' = 0 / (2 f
0)
-1
log
''
log (f [Hz])
min)f(**w2
iModelii
i
PVAC
0.0 0.2 0.4 0.6 0.8 1.00.0
0.2
0.4
0.6
0.8
1.0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
1819
2021
22
23
24
25
2627
28
2930
31
3233
34
35
C o
l e
- D
a v
i d
s o
n
K W W
C o l e - C o l e
D e b y e
Most general function is the formula of Havriliak / Negmai
Overview about the dynamics of
polymers
11.09.2016 Broadband Dielectric Spectroscopy – Basics and Applications 22
Polymers are complex systems For an isolated macromolecule a large number of atoms (100 to 1000 000) are covalently bonded.
Almost unlimited number of conformations in space and time.
Most properties depend on this large conformation.
Chain flexibility
Mean End-to-End vector (shape)
Mean Square dipole moment
… and many more
Behavior is complex ….
Lo
g (
Sh
ea
r M
od
ulu
s G
)
Temperature
glass-like behavior
viscoelastic
behavior liquid-like
behavior
glass transition G ~109
Pa
G ~106
Pa flow transition
Tg
Shear modulus vs. Temperature
… and related to the molecular mobility
Molecular dynamic in polymers
11.09.2016 Broadband Dielectric Spectroscopy – Basics and Applications 23
CH
CH
CH
3
2
3
C
OO
Local
CCH
2
Seg Chain
r
Local Motion
Localized bond rotations
Fluctuations in a side group
LOCAL < 1 nm
Segmental Motion
SEG ~ 1 .. 2 nm
Chain Motion
Chain < = r
“Glassy State” Glass Transition, -Relaxation
Flow Transition
11.09.2016 Broadband Dielectric Spectroscopy – Basics and Applications 24
Scaling of segmental dynamics
Dynamic glass transition
Dynamics in glass-forming materials
11.09.2016 Broadband Dielectric Spectroscopy – Basics and Applications 25
Thermal Response
Dynamic Response
-relaxation, dynamic glass transition
Slow-relaxation
Fast-relaxation
Boson-peak
Activation Diagram
Aexp
ET
kTSlow-relaxation
0
0
1( ) exp
2 ( )
DTT v
T T T
-relaxation
15 orders of magnitude
The temperature dependence of the dynamical relaxation times correlates with the glass transition temperature
at ca. 102 s.
Dynamics in glass-forming materials
11.09.2016 Broadband Dielectric Spectroscopy – Basics and Applications 26
Crossover Phenomena form a high to a low temperature regime at TB ~ 1.2 .. 1.3 Tg
Non-Debye behavior of the Relaxation function
Formation of dynamic heterogeneities below TB
t
exp~ KWW-function
Size : few nanometers
Dielectric Spectroscopy
Poly(methyl phenyl siloxane) (PMPS) ; Mw=1000 g/mol
11.09.2016 Broadband Dielectric Spectroscopy – Basics and Applications 27
-4 -2 0 2 4 6 8 10
-3.0
-2.5
-2.0
-1.5
-1.0
log
''
log (f [Hz])
Alpha-Analyzer
HP4191A
?
Dielectric Spectroscopy
Poly(methyl phenyl siloxane) (PMPS) ; Mw=1000 g/mol
11.09.2016 Broadband Dielectric Spectroscopy – Basics and Applications 28
Mean Relaxation Rate fp
Dielectric Strength 3.0 3.5 4.0 4.5 5.0
-4
-2
0
2
4
6
8
log(f
p [
Hz])
1000 / T [K-1]
-2 0 2 4 6-2.5
-2.0
-1.5
-1.0
-0.5 161.7 K155.7 K
log
''
log (f [Hz])
152. 7 K
))i(1()(
HN
*HN
VFT- equation:
0pp
TT
Aflogflog
?
Specific Heat Spectroscopy
11.09.2016 Broadband Dielectric Spectroscopy – Basics and Applications 29
System under investigation
Input Output
T(t) S(t) cp(t)
Furnace
Thermocouples
Te
mp
era
ture
Time
Temperature Modulated DSC
)t*sin(At*T)t(T
Ch. Schick, Temperature Modulated Differential Scanning Calorimetry - Basics and Applications to Polymers in Handbook of Thermal Analysis and Calorimetry edited by S. Cheng (Elsevier, p 713. Vol. 3, 2002).
The modulated temperature results in a modulated heat flow
The heat flow is phase shifted if time dependent processes take place in the sample
c*p()= c´p() – i c´´p()
Specific Heat Spectroscopy
Example - Polystyrene
11.09.2016 Broadband Dielectric Spectroscopy – Basics and Applications 30
340 360 380 400-0.05
0.00
0.05
0.10
1.50
1.75
2.00
Gaussfit
Tg(q)
T( )
cp''
cp'
total cp
Sp
ec
ific
He
at
Ca
pa
cit
y i
n J
g -1
K -1
Temperature in K
Hensel, A., and Schick, C.: J. Non-Cryst. Solids, 235-237 (1998) 510-516.
Due to heating rate
Due to modulation
Specific Heat Spectroscopy
11.09.2016 Broadband Dielectric Spectroscopy – Basics and Applications 31
System under
investigation
Input Output
T(t) S(t) cp(t)
AC Chip calorimetry Pressure gauge, Xsensor Integration
10 mm 2 mm 0.1 mm
H. Huth, A. Minakov, Ch. Schick, Polym. Sci. B Polym. Phys. 44, 2996 (2006).
Fast heating and cooling
Specific Heat Spectroscopy
11.09.2016 Broadband Dielectric Spectroscopy – Basics and Applications 32
System under investigation
Input Output
T(t) S(t) cp(t)
H. Huth, A. Minakov, Ch. Schick, Polym. Sci. B Polym. Phys. 44, 2996 (2006).
Differential setup
U*
Increase of sensitivity
Complex differential Voltage
Specific Heat Spectroscopy
Example - PMPS
11.09.2016 Broadband Dielectric Spectroscopy – Basics and Applications 33
180 200 220 240 260 280 300
70
75
80
85
90
95
T [K]
UR [V
]
0.0
0.5
1.0
1.5
C
orr [d
eg
]
f=240 Hz
Frequency range : 10 Hz …. 5000 Hz
A. Schönhals et al. J. Non-Cryst. Solids 353 (2007) 3853
3.0 3.5 4.0 4.5 5.0
-4
-2
0
2
4
6
8
log
(f p
[H
z])
1000 / T [K-1]
Dielectric
3.0 3.5 4.0 4.5 5.0
-4
-2
0
2
4
6
8
log
(f p
[H
z])
1000 / T [K-1]
Specific Heat
AC Chip Calorimetry
TMDSC
Both methods measure the same process….
… Glassy dynamics of PMPS
Analysis of the temperature
dependence of the relaxation rate
11.09.2016 Broadband Dielectric Spectroscopy – Basics and Applications 34
3.4 3.6 3.8 4.0 4.2 4.4 4.6 4.8
-4
-2
0
2
4
6
8
10
log
(f p
[H
z])
1000 / T [K-1]
3.4 3.6 3.8 4.0 4.2 4.4 4.6 4.8
-4
-2
0
2
4
6
8
10
log
(f p
[H
z])
1000 / T [K-1]
VFT- equation:
… cannot be described by the VFT-equation in the whole temperature range
0
loglogTT
Aff pp
Derivative: 02/1
2/11log
TTATd
fd p
Straight Line, T0>0
Analysis of the temperature
dependence of the relaxation rate
11.09.2016 Broadband Dielectric Spectroscopy – Basics and Applications 35
160 180 200 220 240 260 280 300
0
2
4
6
8
{ lo
g (
f p [
Hz])
/
dT
[K
] }-1
/2
T [K]
160 180 200 220 240 260 280 300
0
2
4
6
8
{ lo
g (
f p [
Hz])
/
dT
[K
] }-1
/2
T [K]
low and high temperature regime
two VFT - dependencies
T0,Low
T0,high Crossover temperature
TB = 250 K
TB
160 180 200 220 240 260 280 300
0
2
4
6
8
{ lo
g (
f p [
Hz])
/
dT
[K
] }-1
/2
T [K]
Thermal and dielectric data have the same temperature dependence
red : dielectric data
blue: thermal data
Analysis of the temperature
dependence of the dielectric strength
11.09.2016 Broadband Dielectric Spectroscopy – Basics and Applications 36
V
N
Tkg
3
1
B
2
0
Dipole moment
Debye Theory:
Interaction parameter
3.2 3.6 4.0 4.4 4.8
20
40
60
80
T*
1000 / T [K-1]
3.2 3.6 4.0 4.4 4.8
20
40
60
80
T*
1000 / T [K-1]
TB
Temperature dependence of is much stronger than predicted
Cooperative effects
Change of the temperature dependence of at TB
Analysis of the temperature
dependence of the dielectric strength
11.09.2016 Broadband Dielectric Spectroscopy – Basics and Applications 37
The change in the temperature dependence of is not much pronounced
A. Schönhals Euro. Phys. Lett. 56 (2001) 815
Plot of vs. log fp
-2 0 2 4 6 8 10 12
0.1
0.2
0.3
0.4
log (fp [Hz])
TB Sharp transition from a low temperature to a high temperature branch
The crossover frequency corresponds to TB
11.09.2016 Broadband Dielectric Spectroscopy – Basics and Applications 38
Chain dynamics
Normal mode
Dipole moments of polymers
11.09.2016 Broadband Dielectric Spectroscopy – Basics and Applications 39
rrrrr
Type A Type B Type C
Dipole Moment “Parallel” to the Chain
Dipole Moment “Perpendicular” to the Chain
Dipole Moment in a Side Group
Poly(cis-1,4-isoprene)
Poly(propylene glycol)
Polystyrene
Poly(vinyl chloride)
Poly(methyl phenyl siloxane)
Poly(methyl methacarylate)
Segmental Dynamics Chain Dynamics
Dielectric Spectroscopy
Polypropylene glycol; Mw=4000 g/mol
11.09.2016 Broadband Dielectric Spectroscopy – Basics and Applications 40
-4 -2 0 2 4 6 8 10
-1.5
-1.0
-0.5
0.0
0.5
303.3 K
273.2 K
253.3 K233.7 K332.8 K204.5 K
log
''
log ( f [Hz])Time Domain Spectrometer Frequency Response
Analysis
Coaxial Reflectometer
Dynamic Glass Transition, - relaxation
Normal Mode Relaxation
Data analysis
11.09.2016 Broadband Dielectric Spectroscopy – Basics and Applications 41
-4 -2 0 2 4 6
-2.0
-1.5
-1.0
-0.5
0.0
0.5233.7 K204.5 K
log
''
log ( f [Hz] )
The two model function of Havriliak and Negami are fitted to the data.
Relaxation rate fp
Dielectric strength
fp,
fp,n
… for each process
Theory of chain dynamics
Rouse motion, Reptation
11.09.2016 Broadband Dielectric Spectroscopy – Basics and Applications 42
r
A
A
A
A
A
A
N-1
N-2
0
1
2
3
l
l
l
lN1
2
3
lN-1
Fig. 7.2
Beads
Springs
Monomeric friction
xi
dxi
dt+ 3 kT 2xi − xi−1 − xi+1 = 0
Rouse Model:
Friction Chain connectivity (Entropy springs)
Solution:
) t / ( exp p
1
8 =
> r <
> ) t ( r ) 0 (r <)t( p2
N
1p22
Short chains:
Long chains (Entanglements):
3... 1, = p , M~p Tk 3
b N = 2
22
22
p
3
222
43
p M~p a kT
b N =
Molecular weight dependence
Temperature dependence of the relaxation rates of segmental and chain dynamics should be similar
Predictions:
Chain dynamics – Normal mode
Poly(cis-1,4 isoprene)
11.09.2016 Broadband Dielectric Spectroscopy – Basics and Applications 43
200 250 300 3500.00
0.01
0.02
0.03
0.04
200 250 300 3500.00
0.01
0.02
0.03
0.04
200 250 300 3500.00
0.01
0.02
0.03
0.04
H
T [K]
H
´´
f=1000 Hz
MW 1400 3830 8400 g/mol
Schönhals, A. Macromolecules 26 (1993) 1309
Chain dynamics – Normal mode
Poly(cis-1,4 isoprene)
11.09.2016 Broadband Dielectric Spectroscopy – Basics and Applications 44
3.0 3.5 4.0 4.5 5.0
-8
-6
-4
-2
0
Anstieg = 2 ( Rouse )
Anstieg = 3.7
log
( n
[s])
log (MW
[g/mol])
Reptation
T=320 K
M~p Tk 3
b N = 2
22
22
p
3
222
43
p M~p a kT
b N =
Critical molecular weight for the formation of entanglements
Chain dynamics – Normal mode
Self diffusion
11.09.2016 Broadband Dielectric Spectroscopy – Basics and Applications 45
p kT 3
b N =
22
22
p
Relaxation times:
Diffusion coefficient: N
kTDSelf
p
22
2
Selfp3
rD
2.5 3.0 3.5 4.0-15
-14
-13
-12
-11
log
(D
Se
lf [
m2/s
])
1000 K / T
Blue - dielectric
Red - NMR
Poly(propylene glycol) MW=4000 g/mol DSelf can be measured by
Pulsed Field Gradient NMR
Both quantities agree in both there absolute values and in there temperature dependence
Normal mode corresponds to translatorial diffusion
Appel, M.; Fleischer, J. Kärger, G.; Chang, I.; Fujara, F.; Schönhals, A.; Colloid and Polymer Sci. 275 (1997) 187
Chain dynamics
Temperature dependence relaxation rates
11.09.2016 Broadband Dielectric Spectroscopy – Basics and Applications 46
2.0 2.5 3.0 3.5 4.0 4.5 5.0
-4
-2
0
2
4
6
8
10
2 3 4 5
-4
0
4
8
Blue: PPG2000
Green: PPG3000
Red: PPG4000
Black: PPG5300
log (
f p [
Hz])
1000 K / T
log (
f p [H
z])
1000 K / T
Segmental dynamics
Chain dynamics
The relaxation rates of the segmental dynamics are independent of the molecular weight.
The relaxation rates of the chain dynamics depends of the molecular weight.
The temperature dependence of both relaxation rates seems to follow the Vogel/Fulcher/Tammann formula.
0
loglogTT
Aff pp
Both processes seems to merge close to Tg.
Chain dynamics
Temperature dependence relaxation rates
11.09.2016 Broadband Dielectric Spectroscopy – Basics and Applications 47
200 225 250 275 300 3251.0
1.5
2.0
2.5
3.0
3.5
PPG2000
PPG3000
PPG4000
log
(f p
/
fp
n)
T [K]
Detailed investigation of the temperature dependence of the relaxation rates!
Ratio of both relaxation rates Plateau
Decrease
Chain dynamics – Normal mode
Crossover of segmental dynamics
11.09.2016 Broadband Dielectric Spectroscopy – Basics and Applications 48
-2 0 2 4 6 8 10 12 140
1
2
3
4
log (f [Hz])
Polypropylene glycol; Mw=4000 g/mol
A low temperature branch
A high temperature branch
TB =240 K
=0
150 200 250 300 350 4000
2
4
6
8
244 K
(d lo
g f
p / d
T)-1
/2
T [K]
Chain dynamics – Normal mode
11.09.2016 Broadband Dielectric Spectroscopy – Basics and Applications 49
150 200 250 300 350 400
0
2
4
6
8
10
(lo
g f
pN
/ d
T)
-1/2
T [K]
02/1
2/11log
TTATd
fd p
Derivative:
The temperature dependence of the -relaxation rate shows a change at T=244 K as it was observed also for the dielectric strengths
No change of the temperature dependence of the relaxation rate of the normal mode at TB.
The reason for the different temperature dependencies of - and normal mode relaxation is the crossover in the dynamic glass transition.
Decoupling of rotational and
translatorial diffusion
11.09.2016 Broadband Dielectric Spectroscopy – Basics and Applications 50
Segmental dynamics – rotational diffusion
Chain dynamics – translatorial diffusion
3.0 3.5 4.0 4.5 5.0 5.5
1.0
1.5
2.0
2.5
3.0
3.5 PPG2000
PPG3000
PPG4000
log (
f p /
fp
n)
~ l
og
(DR
ot/D
Tra
ns)
T [K]
Different temperature dependencies of - and normal mode relaxation is due to the decoupling of rotational
and translatorial diffusion at TB.
Decoupling of Rotation and translation in low molecular weight glass-forming liquids
Rössler, E.; Phys. Rev. Lett. 69 (1992) 1620, 65 (1990) 1595
Can be explained by different averaging of modes with different length scales
Conclusion
11.09.2016 Broadband Dielectric Spectroscopy – Basics and Applications 51
Dielectric spectroscopy is a powerful tool to study the structure and dynamics of matter.
Extremely broad dynamical range.
Extremely high sensitivity.
Careful data analysis is needed.
This can be done by model functions.
Employing theoretical approaches.
Combination with other spectroscopic methods.
Mechanical spectroscopy
Thermal spectroscopy
Neutron spectroscopy
NMR spectroscopy
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