dielectric properties of ion - conducting materials f. kremer coauthors: j. rume, a. serghei,
TRANSCRIPT
DIELECTRIC PROPERTIES OF ION -CONDUCTING MATERIALS
F. Kremer
Coauthors: J. Rume, A. Serghei,
The relationship between the complex dielectric function and the complex conductivity
Phenomenology of the conductivity of charge – conductingmaterials
The dielectric properties of zwitterionic polymethacrylate
The dielectric properties of „Ionic Liquids“
Theoretical descriptions of the observed frequencyand temperature dependemce of the complex conductivity
The spectral range of Broadband Dielectric Spectroscopy (BDS) and its information content
for studying dielectric relaxations and charge transport.
Dcurl H j
t
0D E j E (Ohm‘s law)
The linear interaction of electromagnetic fields with matter is described by Maxwell‘s equations
Current-density and the time derivative of D are equivalent
0i
i i
Dielectric spectroscopy
2( )1s
2( )1
s
*
(1 )s
i
Debye relaxation
2.0
2.4
2.8
3.2
3.6
'=s
'==s-
'10
010
110
210
310
410
510
6
0.0
0.2
0.4
0.6
0.8
''max
max
'' [rad s-1]
complex dielectric function
electric field E
E
t0
polarization P
PD( )
P
PS
P
t0
10-2
10-1
100
101
102
103
104
105
106
100
101
102
103
104
105
235 K220 K
205 K
190 K
propylene glycol
´
frequency [Hz]
10-2
10-1
100
101
102
103
104
105
106
100
101
102
103
104
´
frequency [Hz]
Analysis of the dielectric spectra
(sample amount required < 5 mg)
The spectral range (10-3 Hz to 1011 Hz) of Broadband Dielectric Spectroscopy (BDS)
Brief summary concerning Broadband Dielectric Spectroscopy (BDS)
1. The spectral range of BDS ranges from 10-3 Hz to 1011 Hz.
2. Orientational polarisation of polar moieties and charge transport are equivalent and observed both.
3. The main information content of dielectric spectra comprises for fluctuations of polar moieties the relaxation- rate, the type of its thermal activation, the relaxational strength and the relaxation-time distribution function. For charge transport the mean attempt rate to overcome the largest barrier determining the d.c.conductivity and its type of thermal activation can be deduced
Phenomenology of the conductivity of charge – conducting materials
407K417K427K438K448K
458K468K478K488K491K
1 2 5 6-10
-9
-8
-7
-6
4
log ( [H z ])3
log
([S
cm])
’-1
Frequency and temperature dependence of the conductivity of a mixed alkali-glass 50LiF-30KF-20Al(PO3)3
3 4 5 6 7-11
-10
-9
-8
-7
-6
log( [rad/s])
100 mol%
log
(' [
Scm
-1])
396 K 391 K 382 K 373 K 364 K 355 K 346 K
Frequency and temperature dependence of the conductivity of a zwitterionic polymer
T [K]
295285
262250
236
223
210
1 3 5 7
-4
-2
log ( [H z ])
-6
log
([S
cm])
’-1
Frequency and temperature dependence of the electronic conductivity of poly(methyl-thiophene)
p
0 .1 00
0 .0 75
0 .0 50
0 .0 30
0 .0 20
0.015
0.012 5
0 .0 10
2 3 4 5 6 7 8 9
log( [Hz])
1
0
-1
-2
-3
-5
-4
-6
-7
-8
-9
-10
Frequency and concentration dependence of the electronic conductivity of composites of carbonblack
and poly(ethylene terephthalate)
-2 0 2 4 6
0
1
2
3
4
- 396 K - 391 K - 382 K - 372 K - 364 K - 355 K
log
('/
o)
log()
Mixed alkali-glass: Scaling with temperature is possible
-4-6-8-10-12-1
0
1
2
3
4
5
log e 2kT 0
log
’ 0
poly(methyl-thiophene): Scaling with temperature is possible
2 4 8 10 12
log(a [Hz])p
3
2
1
0
composites of carbonblack and poly(ethylene terephthalate): Scaling with concentration is possible
-1 0 1 2 3 4 5 6 7 8
-12
-10
-8
-6
-4
-2
log
(0
[Scm
-1])
log(1/e [Hz])
- 0 mol% - 100 mol% - 200 mol% - conductor-polymer composite - mixed alkali glasses - polymer
The Barton-Nakajima-Namikawa (BNN) – relationship holds for all materials examined:
Experimental findings
In all examined materials the conductivity shows a similarfrequency and temperature (resp. concentration) dependence
There is no principle difference between electron – and ion –conducting materials
The conductivity „scales“ with the number of effective charge-carriers as determined by temperature or concentration
A characteristic frequency exists where the frequencydependence of the conductivity sets in
With increasing number of effective charge-carriers the conductivity increases.
The BNN-relationship is fulfilled
The dielectric properties of zwitterionic poly-methacrylate: poly{3-[N-[-oxyalkyl)-N,N-
dimethylammonio]propanesulfonate}
H C3 C C O O
C H 2
(C H )2 m
x
N +
C H 3
C H 3
(C H )2 3 S O 3
Dielectric data as displayed for the complex dielectric function T)
3 4 5 6 7 8101
102
103
log( [rad/s])
396 K 391 K 382 K 373 K 364 K 355 K 346 K
'
3 4 5 6 710-1
100
101
102
103
104 396 K 391 K 382 K 373 K 364 K 355 K 346 K
"
log( [rad/s])
Dielectric data as displayed for the complex conductivity T)
3 4 5 6 7
-9,5-9,0-8,5-8,0-7,5-7,0-6,5-6,0-5,5-5,0
log( [rad/s])
log
(' [
Scm
-1])
3 4 5 6 7
-9
-8
-7
-6
-5
396 K 391 K 382 K 373 K 364 K 355 K 346 K
log(
" [S
cm-1
])log( [rad/s])
3 4 5 6 7 8
0.00
0.02
0.04
0.06
0.08
0.10
M'
Log (Rad/s)3 4 5 6 7 8
0.00
0.01
0.02
0.03
0.04
M"
log( [rad/s])
Dielectric data as displayed for the complex
electrical modulus M*T) =1/ T)
Dyre‘s random free energy barrier model
Hopping Conduction in a spatially randomly varying energy barrier :
22 2 2
0 arctan1
ln 1 arctan4
e e
e e
2 2
22 2 2
0 ln 1
1ln 1 2 arctan
2
e e
e e
Fits using the Dyre theory „work well“
3 4 5 6 7 8
-9,5-9,0-8,5-8,0-7,5-7,0-6,5-6,0-5,5-5,0
log( [rad/s])
lo
g('
[S
cm-1])
340 350 360 370 380 390 4002
3
4
5
6
7
log
(c,
M, 1
/ e)
T [K]
c
M
1/e
The rates c, M and 1/e nearly coincide and have - over 5 decades - a similar temperature dependence
-1 0 1 2 3 4 5 6
-13
-12
-11
-10
-9
-8
-7
-6
log
( 0 [S
cm-1])
log(1/e [Hz])
- 0 mol% - 100 mol% - 200 mol%
The BNN-relationship holds for varying the charge carrier concentration
Summary
The dielectric properties of the zwitterionic poly-methacrylate:poly{3-[N-[-oxyalkyl)-N,N-dimethylammonio]propanesulfonate} are characterized by a pronounced frequency -and temperature dependence.
It should be analysed in terms of the complex dielectric function T), the complex conductivity T) and the complex electrical modulus M*T) =1/ T)
The data can be well described by Dyre‘s random freeenergy barrier model
The BNN-relation is fulfilled
At low frequencies electrode polarisation effects show up
The dielectric properties of „Ionic Liquids“
BMIM BF4 BMIM SCN
1-n-butyl-3-methylimidazolium thiocyanate
1-butyl-3-methylimidazolium tetrafluoroborate
Temperature dependence
Imaginary and real part of the complex dielectric function are strongly temperature dependent
10-1 101 103 105 107101
103
105
107
109
280 K 270 K 260 K 250 K 240 K 230 K'
Frequency (Hz)
BMIM BF4
10-1 101 103 105 10710-1
101
103
105
107
280 K 270 K 260 K 250 K 240 K 230 K
" Frequency (Hz)
BMIM BF4
Temperature dependence
The complex conductivity of the ionic liquid BMIM BF4 is also strongly temperature dependent
10-1 101 103 105 107
10-6
10-5
10-4
10-3
280 K 270 K 260 K 250 K 240 K 230 K
' (S/c
m)
Frequency (Hz)
BMIM BF4
10-1 101 103 105 10710-9
10-8
10-7
10-6
10-5
10-4
10-3
280 K 270 K 260 K 250 K 240 K 230 K
" (S/c
m)
Frequency (Hz)
BMIM BF4
Broadband dielectric measurements displayedfor the complex dielectric function T)
10-2 100 102 104 106 108 101010-210-1100101102103104105106107
268 K 258 K 248 K 238 K
"
Frequency (Hz)
MMIM Me2PO
4
Thickness= 50µm
10-2 100 102 104 106 108 1010100
102
104
106
268 K 258 K 248 K 238 K'
Frequency (Hz)
MMIM Me2PO
4
Broadband dielectric measurements displayedfor the complex conductivity T)
10-2 100 102 104 106 108 101010-8
10-7
10-6
10-5
10-4
10-3
268 K 258 K 248 K 238 K
' (S/c
m)
Frequency (Hz)
MMIM Me2PO
4
10-2 100 102 104 106 108 1010
10-8
10-7
10-6
10-5
10-4
10-3
268 K 258 K 248 K 238 K
" (S/c
m)
Frequency (Hz)
MMIM Me2PO
4
Scaling with temperature possible
10-10 10-8 10-6 10-4 10-2 100 102 104100
101
102
103
104
105
106
107
e
268 K 258 K 248 K 238 K
'
MMIM Me2PO
4
10-10 10-8 10-6 10-4 10-2 100 102 10410-2
100
102
104
106
268 K 258 K 248 K 238 K
"
e
MMIM Me2PO
4
Scaling with temperature as displayed in terms of the complex conductivity T)
10-10 10-8 10-6 10-4 10-2 100 102 10410-5
10-3
10-1
101
103
268 K 258 K 248 K 238 K
' /0
e
MMIM Me2PO
4
10-10 10-8 10-6 10-4 10-2 100 102 10410-4
10-2
100
102
104
268 K 258 K 248 K 238 K
" /0
e
MMIM Me2PO
4
All data collapse into a single characteristic curve
10-5 10-3 10-1 101 103 105102
104
106
108
s
"
317 mg/ml 44.63 mg/ml 4.09 mg/ml 0.52 mg/ml
NaCl
Scaling with concentration for NaCl solutions as displayed for the complex dielectric function
10-5 10-3 10-1 101 103 105101
103
105
107
109
s
' 317 mg/ml 44.63 mg/ml 4.09 mg/ml 0.52 mg/ml
NaCl
Scaling possible but deviations on the low frequency side
Scaling with concentration for NaCl solutions as displayed for the complex conductivity
10-5 10-3 10-1 101 103 10510-4
10-2
100
s
' /0
317 mg/ml 44.63 mg/ml 4.09 mg/ml 0.52 mg/ml
s is the angular frequency of the minimum in ´´
10-5 10-3 10-1 101 103 105
10-2
10-1
100
" (S
/cm
)
s
317 mg/ml 44.63 mg/ml 4.09 mg/ml 0.52 mg/ml
NaCl
D y r e ‘ s r a n d o m f r e e e n e r g y b a r r i e r m o d e l
H o p p i n g C o n d u c t i o n i n a s p a t i a l l y r a n d o m l y v a r y i n g e n e r g y b a r r i e r :
22 2 2
0 a r c t a n1
l n 1 a r c t a n4
e e
e e
2 2
22 2 2
0 l n 1
1l n 1 2 a r c t a n
2
e e
e e
Fits using the Dyre-model of conduction
10-2 100 102 104 106 108 101010-3
10-1
101
103
105
107
109 268 K 258 K 248 K 238 K 228 K 218 K 208 K 198 K 188 K
"
Frequency (Hz)
10-2 100 102 104 106 108 1010100
102
104
106 268 K 258 K 248 K 238 K 228 K 218 K 208 K 198 K 188 K
'
Frequency (Hz)
The Dyre –model describes the observed frequency-and temperature dependence; additionally electrodepolarization effects show up
Fits using the Dyre-model
10-2 100 102 104 106 108 101010-15
10-13
10-11
10-9
10-7
10-5
10-3
268 K 258 K 248 K 238 K 228 K 218 K 208 K 198 K 188 K
' (S/c
m)
Frequency (Hz)
10-2 100 102 104 106 108 101010-14
10-12
10-10
10-8
10-6
10-4
10-2
268 K 258 K 248 K 238 K 228 K 218 K 208 K 198 K 188 K
" (S/c
m)
Frequency (Hz)
Electrode polarization effects show up already at 100 kHz
The BNN Relation is fulfilled for 0 and e as obtained from Dyre-fits
10-2 100 102 104 106 10810-14
10-12
10-10
10-8
10-6
10-4
MMIM Me2PO
4
EMIM Et2PO
4
0(S/c
m)
1/e(Hz)
Alternative approach: Superposition of a thermally activated d.c. conductivity and „nearly constant loss“ contribution.
10-2 100 102 104 10610-15
10-13
10-11
10-9
10-7
0(T1)
0(T2)
0(T3)
0(T4)
' (S
/cm
)
Frequency (Hz)
e1
e2
e3
e4
e5
0(T5)
220 K210 K200 K190 k180 K170 K
' (S
/cm
) '
01
s
A
p
A:Near constant losscontribution
The BNN relation is a trivial consequence
Activation plots
Both 0 and 1/e show a VFT - dependence
3,6 3,8 4,0 4,2 4,4 4,6 4,8 5,010-14
10-12
10-10
10-8
10-6
10-4
MMIM Me2PO
4
EMIM Et2PO
4
0(S/c
m)
1000 K/Temperature3,6 3,8 4,0 4,2 4,4 4,6 4,8 5,0
10-2
100
102
104
106
108
MMIM Me2PO
4
EMIM Et2PO
4
1/ e(H
z)1000/Temperature (K-1)
Final Summary
The dielectric properties of „Ionic Liquids“ are similar to other ion - conducting systems
They should be analysed in terms of the complex dielectric function T), the complex conductivity T) and the complex electrical modulus M*T) =1/ T)
The data can be well described by Dyre‘s random freeenergy barrier model but as well a superposition a thermally activated d.c.conductivity,a power law and a „nearly constant loss“ contribution
The BNN-relation is fulfilled
At low frequencies electrode polarisation effects showup
A.
A.Serghei
Thanks to Joshua Rume
and
and financial support through the DFG