Nonlinear Dielectric Effectsin Simple Fluids
High-Field Dielectric Response:Coulombic stressLangevin effectEnergy absorptionTime-resolved technique
Ranko RichertNO
N-L
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IELE
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XPER
IMEN
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ust 2
009
dielectric relaxation techniques
0
1
0
1ε''
(ω)
ε'(ω)log(ωτ)
( )( )[ ]
Negami -
Havriliak
1 *
⎭⎬⎫
⎩⎨⎧
+
−+= ∞
∞ γαωτ
εεεωεis
( ) Debye1
*
ωτεεεωε
is
+−
+= ∞∞
E ε ε D 0=
fieldelectric
ntdisplacemedielectric
E dV
AQ D ≡∝≡
typical case near the glass transition
10-1 100 101 102 1030
10
20
30
40
50
60
70
ε'
ν [Hz]10-1 100 101 102 1030
10
20
30 174 K - 198 K (3K)
propylene glycol
ε''
ν [Hz]
non-linear susceptibility
( ) ( ) ( ) ( )
( )( ) ( )
( ) ( ) K
K43421321321
+++=
−−==
++++++====
4422
0
44
symmetry0
3322
symmetry0
1
causality00
:symmetry00 :causality
EE
EEEEelectret
χχχε
χχχχχχε
EP
EPEPP
EEEEEP
( ) ( ) [ ]( )
ss
s
ss
E
E
EE
λεε
ελ
λεε
−=∆
∆−=
−×=
2
2
22
:factorPiekara ln
10
( ) ( ) ( ) ( )∫∫ ∞−∞−−==
ttdtEdPtP θθϕθχεθ 0 :principle ionsuperposit
( ) ( ) dttJJkTVLFLJ
J
L
eee
e
FFeF
F
∫∞
===
=
==0
000
0
0
flux conjugate in the nsfluctuatio mequilibriu theoffunction n correlatio-auto
torelated are tscoefficiennsport linear tra :s)(1950' Kubo R. Green, S. M.
variety of high field techniques
0 5 10 15-60
-40
-20
0
20
40
60
volta
ge
time0 5 10 15
-60
-40
-20
0
20
40
60
volta
ge
time0 5 10 15
-60
-40
-20
0
20
40
60
volta
ge
time
high DC fieldlow AC fieldmainly 1ω
high AC fieldno bias1ω + 3ω
low AC fieldon high pulse
NDE(t)
Coulombic stress
Coulombic stress exercise
QVEnergyd
ACCVQ
VQC
21
0
=
===εε
( )( ) ( )
[ ][ ] A
FL
Lstrainstress
E
tVtVtV
∆=≡
=
=
0
0
modulus mechanical
GPa 1 modulus sYoung'hspacer witTeflon assume
measuredon effect calculatesin
voltagefrom resulting force calculate
εω
rFrF 3304 r
qqr
qqcgsSI
′=
′=
πε10 µm
top electrode 16 mm Øbottom electrode 30 mm Øring outer: 20 mm Øring inner: 14 mm Ø
Coulombic stress solutions
10 µm
( )
QVEdA
C
VQC
rqq
SI
21
0
30
1
4
=
==
=
′=
εε
πεrF
( )
( )
( )
( )[ ]
( ) ( )[ ]
[ ][ ] A
FL
LstrainstressE
tV
tVVVdA
tVVdA
F
VVdA
VdA
ddAVF
dAVCVVVCCVV
QVVQQVdFQVenergyFdwork
dcdc
dc
acdc
∆==
⎟⎟⎠
⎞⎜⎜⎝
⎛−+−=
−=
+==∂
∂=
∂=∂+∂=∂
=∂+∂=∂=∂
=
−
−
=
=
0
20
02
20
202
0
22
022
01
02
21
10
2212
21
0
21
21
21
0
21
21
21
modulus sYoung'
2cos12
sin22
sin2
22
ωωε
ωε
εεε
ε43421
321
( ) ( ) ( )[ ]
4
0
0
25
20
00
20
020
107.6ln
MPa 0.67N 31
(Teflon) GPa 1mm) 16-14d ring,(Teflon m 107.4
4ln
2cos142
−
−
×≤∆
−=∆
==
==×=
=+=∆
−=∆
−×==
dd
aFFYa
EaY
AaYF
dd
tEAtEAtF
s
ss
ε
εεε
ωεεεε
dielectric saturation
expected non-linearity: dielectric saturation, Langevin effect
0 2 4 6 8 100.0
0.2
0.4
0.6
0.8
1.0
a/3
⟨cosθ⟩ = 1
L(a) ≈ a/3
a = µE / kT
L(a)
= ⟨c
osθ⟩
( ) ( )
kTEa
akTEa
aaL
kTEa
kTEL
kTE
kTE
de
de
kTE
kTE
33cos
1or if
1cotanhcos
with
function Langevin
cos
cotanhcos
cos
cos
10
cos
0
cos
µθ
µ
θ
µ
µθ
µµθ
θ
θθθ π
θµ
πθµ
=≈
<<<<
−==
=
⎟⎟⎠
⎞⎜⎜⎝
⎛⎟⎠⎞
⎜⎝⎛=
⎟⎠⎞
⎜⎝⎛−⎟
⎠⎞
⎜⎝⎛=
⇒=
−
∫
∫
saturation in water at 293 K
( ) ( )( )
( )( ) ( )222
44
30
4
2
2
2
2
222
450vanVleck
Piekara
∞∞
∞
+++
×−=−
=∆
−=∆
εεεεεε
εµεεε
λεε
ss
ssss
ss
kTVN
EE
E
E
H. A. Kolodziej, G. Parry Jones, M. Davies, J. Chem. Soc. Faraday Trans. 2 71 (1975) 269
J. H. van Vleck, J. Chem. Phys. 5 (1937) 556A. Piekara, Acta Phys. Polon. 18 (1959) 361
time resolved NDE experimens
M. Gorny, J. Ziolo, S. J. Rzoska, Rev. Sci. Instrum. 67 (1996) 4290
high field impedance
10-1 100 101 102 1030
10
20
0
20
40
60
ε''
ν [Hz]
propylene glycol
ε'
S. Weinstein, R. Richert, Phys. Rev. B 75 (2007) 064302S. Weinstein, R. Richert, J. Phys.: Condens. Matter 19 (2007) 205128
GEN
V - 1
V - 2
SI-1260 PZD-700
× 100
÷ 200
Cgeo = 136 pF
Vin ≤ 300 VR = 100 Ω
10 µm
× 1
GEN
V - 1
V - 2
SI-1260 PZD-700
× 100
÷ 200
Cgeo = 136 pF
Vin ≤ 300 VR = 100 Ω
10 µm
× 1
analyzer input protection
S. Weinstein, R. Richert, Phys. Rev. B 75 (2007) 064302S. Weinstein, R. Richert, J. Phys.: Condens. Matter 19 (2007) 205128
RPROTECT = 3 MΩ:protects against 300 V (no time limit)
102 103 104 1050.0
0.2
0.4
0.6
0.8
1.0
[ 1 + (ωτ)2 ] -1/2
τ = 5.95 × 10-6 s
f-6dB = 26750 Hz
Am
plitu
deν / Hz
AD 549 LRin = 1015 ΩCin = 0.8 pFIbias = 40 fA
field effect results for propylene glycol[ 71 - 282 kV/cm steady state harmonic measurement ]
S. Weinstein, R. Richert, Phys. Rev. B 75 (2007) 064302S. Weinstein, R. Richert, J. Phys.: Condens. Matter 19 (2007) 205128
( )( )
( ) ( )( )Vleckvan
222
45 222
44
30
4
2∞∞
∞
+++
×−=∆
εεεεεε
εµε
ss
ss
kTVN
E
10-1 100 101 102 103 1040
10
20
0
20
40
60
ε''ν [Hz]
propylene glycol
ε'0 2 4 6 8
-8
-6
-4
-2
0
E0 2 [1010 V 2 cm-2 ]
∆ ln ε'5.6 Hz - 100 Hz
propylene glycol
1000
× ∆
ln ε
'
energy absorbtion
(less) expected non-linearity: sample heating via dielectric loss
1 0 -1 -2 -3 -40.0
0.1
0.2
0.3 βKWW = 0.5
log10(τ / τKWW)
heating
g KWW
(lnτ)( )
K 1.0
cm K J 2
cm J 22.0
MVm 2.2810
31
3
10
200
≈=∆
≈
=
=
≈′′
′′=
−−
−
−
p
eq
p
eq
eq
cq
T
c
qE
Eq
υ
υ
ε
ωεπευ
spectrally selective dielectric experiments
( ) ( )tEtE bb ωsin=
bωτττ 1321 ≈≈≈
( ) 20 bb EQ ωεπε ′′=∆
1 0 -1 -2 -3 -40.0
0.1
0.2
0.3
anti-hole
hole
βKWW = 0.5
log10(τ / τKWW)
spectrallyselective'heating'
g KWW
(lnτ)
1 0 -1 -2 -3 -40.0
0.1
0.2
0.3 βKWW = 0.5
log10(τ / τKWW)
heatingg KW
W(ln
τ)
B. Schiener, R. Böhmer, A. Loidl, R. V. Chamberlin, Science 274 (1996) 752B. Schiener, R. V. Chamberlin, G. Diezemann, R. Böhmer, J. Chem. Phys. 107 (1997) 7746R. V. Chamberlin, B. Schiener, R. Böhmer, Mat. Res. Soc. Symp. Proc. 455 (1997) 117
E E
ε : polarization at constant field E
'burn cycle' (n = 3) 'measure cycle''wait'
time
dielectric hole-burning technique: what do we look for?
-3 -2 -1 0 1 20.0
0.5
1.0original
responseP(t)
plainheating
P*(t)
selectiveheating
P*(t)
P(t)
, P*(
t)
log10(t/s)
model prediction for 300 kV/cm steady state harmonic field
0
5
10
15
20
25
30
-2 -1 0 1 2 3 4
0
5
10
E = 3×105 V / cm E = 0 V / cm
ε''
100
× ∆
ln ε
''log10(ωτHN)
0
20
40
60
80
-2 -1 0 1 2 3 40
5
10
15
20
25
E = 3×105 V / cm E = 0 V / cmε'
log10(ωτHN)
αHN = 0.95γHN = 0.58τHN = 285 s∆ε = 72ε
∞ = 3.7
Dgeo = 20 mmsgeo = 6.4 µm∆Cp = 1.5 J/K/cm3
T = 187.30 KEact = 20000 KV0 = 200 V
ε''
R. Richert, S. Weinstein, Phys. Rev. Lett. 97 (2006) 095703
high field impedance
high field impedance technique
GEN
V - 1
V - 2
SI-1260 PZD-700
× 100
÷ 200
Cgeo = 136 pF
Vin ≤ 300 VR = 100 Ω
10 µm
× 1
GEN
V - 1
V - 2
SI-1260 PZD-700
× 100
÷ 200
Cgeo = 136 pF
Vin ≤ 300 VR = 100 Ω
10 µm
× 1
101 102 103 1040
5
10
15
20
25
30
glycerol
E0 = 14 kV/cm
T = 213 K
E0 = 283 kV/cm
ε''ν / Hz
R. Richert, S. Weinstein, Phys. Rev. Lett. 97 (2006) 095703
fields up to 450 kV/cm
µE up to 0.082 kT
0.1 Hz to 50 kHz range
ξ
dynamically correlated domains
-2 -1 0 1 2 3 4 5
ε''
log10(ω)
τ1
τ2τ3
τ4
τ5
ω0
τ1
τ2τ3τ4
τ5
heat
ext.field
-2 -1 0 1 2 3 4 5
ε''
log10(ω)
τ1
τ2τ3
τ4
τ5
ω0
τ1τ1
τ2τ2τ3τ3τ4τ4
τ5τ5
heat
ext.field
heterogeneous dynamics and configurational temperatures
W. Huang, R. Richert, J. Phys. Chem. B 112 (2008) 9909
calorimetric modes
dielectric modes
DT ττ =
model for high-field steady-state harmonic measurement
( )
( )
( )
22
22200
DT
200
200
0
12
:h domain wit single afor
0
: re temperatuionalconfigurat excess22
:periodover averaged power
:periodper energy statesteady :applied sin field harmonic
τωτωεε
τττ
ττ
ωωεεπω
ωεπε
ω
+∆∆
+=
==
+=⇒=−
−=
′′==
′′=
pcfg
p
Tcfg
T
cfg
p
cfg
b
cE TT
cpTT
TTcp
dtdT
VEQp
p
VEnQ
nQtE
R. Richert, S. Weinstein, Phys. Rev. Lett. 97 (2006) 095703W. Huang, R. Richert, J. Chem. Phys. 130 (2009) 194509
0.00
0.10
0.20
100 101 102 103 104-0.05
0.00
0.05
0.10
0.15tan δ
(c)
∆ ln
(tan
δ)
ν / Hz
0.00
0.10
0.20
0.30
ε'' (b)
∆ ln
ν
0.0
0.2
0.4
( Tcfg −T
) / K
ε'' (a)
PCT = 166 K
∆ ln
ε''
propylene carbonate(E0 = 177 kV/cm)
analogous to 'box'-model:B. Schiener, R. Böhmer, A. Loidl, R. V. Chamberlin, Science 274 (1996) 752
L.-M. Wang, R. Richert, Phys. Rev. Lett. 99 (2007) 185701W. Huang, R. Richert, J. Phys.Chem. B 112 (2008) 9909
adding time-resolution capabilities to high-field technique
( ) ( ) ( )
( ) ( )
( )
( ) ( )
( )ϕ
ωπω
ϕ
ωπω
ωπ
ωπ
sin
cos
cos
sin
or
2
0
2
0
A
dttStI
A
dttStR
tItVtS
=
=
=
=
=
∫
∫
-1
0
1
-4 -2 0 2 4 6 8
-1
0
1
voltage
V(t)
/ V 0
current
I(t) /
I 0
time / ms
GEN
Ch 1
Ch 2
DS-345 PZD-700
× 100
÷ 200
Vin ≤ 300 V
R = 1 kΩ
× 1
Sigma-100
Trig
GEN
Ch 1
Ch 2
DS-345 PZD-700
× 100
÷ 200
Vin ≤ 300 V
R = 1 kΩ
× 1
Sigma-100
Trig
⎟⎠⎞
⎜⎝⎛ ∆−=
⎟⎠⎞
⎜⎝⎛=+=
ϕπδ
ϕ
2tantan
arctan22
RIIRA
single/multiple frequency technique
Stanford Research DS-345 Generator
Nicolet Sigma 100 Digital Oscilloscope
-4 -2 0 2 4 6 8-2
-1
0
1
2
V(t)
/ V0
time / ms
4 channels
1 Ms depth
12 bit @ 100 Ms/s14 bit @ 1 Ms/s
W. Huang, R. Richert, J. Chem. Phys. 130 (2009) 194509
curre
nt
time
1ω versus 3ω data analysis
low field response
high field response
1ω approximation
1ω + 3ω response
εhi - εlo
A3ω / Aω
rise of configurational temperature for different frequencies
-2 0 2 4 6 8 10
0%
1%
2%
3%
4%
∆ ln
(tan
δ)
ν t →
0 5 10 15 20
0.00
0.02
0.04
0.06
MTHFT = 96.1 K
ν = 500 Hz ν = 1 kHz ν = 2 kHz
∆ ln
(tan
δ)
time / ms
W. Huang, R. Richert, J. Chem. Phys. 130 (2009) 194509
rise of configurational temperature for pumping with 1 kHzand probing at higher frequencies
0.00 0.020.0
0.5
1.0
0.00 0.02 0.04 0.06 0.08
0.00
0.01
0.02
0.03
0.04
0.05PC
T = 166 K
1 kHz4 kHz8 kHz16 kHz
∆ ln
(tan
δ)
time / s
1 kHz 4 kHz 8 kHz 16 kHz
time / s
W. Huang, R. Richert, J. Chem. Phys. 130 (2009) 194509
( ) ( )
( ) ( )22
2
0
2
0 3cos
3sinIRA
dttVtI
dttVtR+=
⎪⎪⎭
⎪⎪⎬
⎫
=
=
∫
∫ωπ
ωπ
ωπω
ωπω
3ω signal during field change
0.00 %
0.02 %
0.04 %
-0.1 0.0 0.1 0.2 0.3 0.40.00 %
0.20 %
0.40 %
0.60 %
voltage
V 3ω /
V ω
current
I 3ω /
I ω
time / s
( )
( )( ) ( ) ( )
( ) ( )
4ln
ln3sin
sinsin
sin
ln
1
3
0041
3
413
003
00
433
0000
0
20
2000
300000
ε
εεεωλεε
εεωλεεωεε
ω
ελ
λεε
λεεεε
ω
ω
ω
ω
ω
ω
∆=
∆=⇒
−=
≈⇒
+=
=
∆=
+×=
+=
AA
EAtEtD
EAtEtEtD
tEE
E
EE
EED
agreement between experiment and model
0.00 0.02 0.04 0.06 0.08
0
1
2
3
4
5
0
1
2
3
4
5
PCT = 166 K
∆ ln(tan δ) 4 I3ω
/ Iω
4 I3ω / Iω × 100
∆ ln
(tan
δ) ×
100
time / s
( ) ( )
( ) ( )
⎟⎠⎞
⎜⎝⎛ ∆−=
⎟⎠⎞
⎜⎝⎛=
+=
=
=
∫
∫
ϕπδ
ϕ
ωπω
ωπω
ωπ
ωπ
2tantan
arctan
cos
sin
22
2
0
2
0
RI
IRA
dttStnI
dttStnR
ν = 1000 Hz
W. Huang, R. Richert, J. Chem. Phys. 130 (2009) 194509
non-steady state version of 'box'-model
-2 -1 0 1 2 3 4 5
ε''
log10(ω)
τ1
τ2τ3
τ4
τ5
ω0
τ1
τ2τ3τ4
τ5
heat
ext.field
-2 -1 0 1 2 3 4 5
ε''
log10(ω)
τ1
τ2τ3
τ4
τ5
ω0
τ1τ1
τ2τ2τ3τ3τ4τ4
τ5τ5
heat
ext.field
( )( )
( ) ( )( ) ( ) ( )
( )( )( )
( ) ( ) ( ) ( )( )
( ) ( ) ( )
( )( )
( ) ( )
( ) ( ) ( ) ( )⎟⎠⎞
⎜⎝⎛ +=+=
=
∆−=
⎥⎦
⎤⎢⎣
⎡⎟⎟⎠
⎞⎜⎜⎝
⎛−−=
−−
∆∆=
−∆
==
==
∆=∆⇒∆=∆
∆=∆⇒∆=∆
∑∑
∑
∑∑
∞∞
∞
tjdt
tdEAtjAAjtI
dtEtV
CC
tTtT
dtdT
TkE
TTtT
t
tTtT
CVttj
dttdT
ttD
ttE
tjdt
tdDTTD
CCdgCC
dg
ii
ip
ip
i
i
B
Aiii
i
i
ipi
iii
i
i
i
ii
i
ii
pi ippip
i ii
εε
τ
ττ
τεετ
ττεε
ττ
εεττεε
0
.
,
,0
2
0
,,
case adiabaticfor
10
0 and 00:conditions initial
sepa
rate
ly fo
r eac
h do
mai
n i
W. Huang, R. Richert, J. Chem. Phys. 130 (2009) 194509
what do we learn ?
high voltage impedance results for glycerol
101 102 103 104
4
6
810
20
glycerol
E0 = 14 kV/cm
T = 213 K
∆ε = 71.8τHN = 1.8 msαHN = 0.93γHN = 0.65
E0 = 282 kV/cm
ε''
ν [Hz]
( ) ( )∫∞
∞ +∆+=
+×
∆∆
×−=
0
22
22200
2*
*11ˆ
12 lnln
:modelcurrent
τωτ
τεεωε
τωτωεεττ
di
g
cE
TT
p
A
( )( )[ ]γαωτ
εεεωεi
s
+
−+= ∞
∞1
:fit Negami-Havriliak
*
R. Richert, S. Weinstein, Phys. Rev. Lett. 97 (2006) 095703
summary of relevant non-linear effects (~E2)
S. Weinstein, R. Richert, Phys. Rev. B 75 (2007) 064302
0 2 4 6 80
2
4
6
8∆ ln ε''
422 Hz - 42.2 kHz
100
× ∆
ln ε'
'
E0 2 [1010 V 2 cm-2 ]
-8
-6
-4
-2
0
∆ ln ε'5.6 Hz - 100 Hz
propylene glycol
1000
× ∆
ln ε'
( )( )
( ) ( )( )Vleckvan
222
45
:saturation dielectric
222
44
30
4
2∞∞
∞
+++
×−=∆
εεεεεε
εµε
ss
ss
kTVN
E
( )
( ) ( )∫∞
∞ +∆+=
+×=
+×
∆∆
=
0
220
2200
e220
220
200
*11ˆ
1
12
:absorptionenergy
τωτ
τεεωε
τωτω
τωτωεετ
di
g
Tc
ETp
e
( ) ( ) ( )tEAEAtEAtF
dACCVQQVFd
sss ωεεεεεεεε
2cos442
,,:stress Coulombic
20
0
N 31
20
020
021
−==
===
≈43421
continuous harmonic (impedance) measurement(glycerol)
101 102 103 1040
5
10
15
20
25
30
glycerol
E0 = 14 kV/cm
T = 213 K
E0 = 282 kV/cm
ε''
ν [Hz]
10 µm
101 102 103 1040
5
10
15
20
25
30
glycerolT = 213 K
ε''
ν [Hz]
GEN
V - 1
V - 2
SI-1260 PZD-700× 100
÷ 200
D.U.T.
500 Ω
50 Ω
R. Richert, S. Weinstein, Phys. Rev. Lett. 97 (2006) 095703
082.0 K 213
MVm 2.28D 56.2
1 =⎪⎭
⎪⎬
⎫
==
=−
kTE
TE
GLY µµ
L.-M. Wang, R. Richert, Phys. Rev. Lett. 99 (2007) 185701
100 101 102 103 104
02468
E0 → 100 kV/cm
∆cp = 0.47 J K
-1 cm-3
(b)
100
× ∆l
nε''
ν / Hz
106 kV/cm 141 kV/cm 177 kV/cm
100
101
102
(a) 14 kV/cm 177 kV/cm
ε''
propylene carbonateT = 166 K
the case of propylene carbonate
loss increases
by up to 20 %
at electric field
of 177 kV/cm
∆Tcfg = 0.185 K
L.-M. Wang, R. Richert, Phys. Rev. Lett. 99 (2007) 185701
differential scanning calorimetry of propylene carbonate
140 150 160 170 1800.0
0.5
1.0
1.5
2.0
2.5
3.0propylene carbonate
Cp /
J K
-1 c
m -3
T / K
1.04 J K-1 cm-3
0.47 J K-1 cm-3
?
40 60 80 100 120 1400
2
4
6
8(a)
SOR
B
PC
NM
EC
24PD
12PD
GLY
PG
E0 → 100 kV/cm
100
× ∆l
nε''
m
0.0
0.5
1.0(b)
Cp,
cfg /
Cp,
exc
measuring the configurational heat capacity
cp ∞
τ1
cp1 ...
...τ2
cp2
τ3
cp3
τ4
cp4
τN
cpN
phonon bath cp ∞
τ1
cp1 ...
...τ2
cp2
τ3
cp3
τ4
cp4
τN
cpN
phonon bath
( ) ( )∫∞
∞ +∆+=
+×
∆∆
×−=
0*
22
2200
2*
11ˆ
12 lnln
:modelcurrent
DD
D
D
TD
p
ADD
di
g
cE
TT
τωτ
τεεωε
τωττωεεττ
L.-M. Wang, R. Richert, Phys. Rev. Lett. 99 (2007) 185701
configurational heat capacity
configurational versus excess-vibrational heat capacity
(d)
T1 < T2 < T3
Cp''
(ω)
log ω
(c)
× ×ex.-vib.
crystal
liquid
config
glass
log ω
Cp'(ω
)(b)
heat capacity
config
Tg↓
liquid
glass
crystal
Cp(T
)
T
(a)
entropy
config
↑ TK
↑Tm
Tg↓
crystal
liquid
glass
S(T
)
T
testing the claim: τT = τD versus τT = τD/h
L.-M. Wang, R. Richert, Phys. Rev. Lett. (submitted)
0.00 0.01 0.02 0.03 0.04 0.05
0
1
2
3
4
5
0
1
2
3
4
5
h = 2.00 h = 1.41 h = 1.00 h = 0.71 h = 0.50
PCT = 166 K
∆ ln
(tan
δ) ×
100
time / s
⎥⎥⎦
⎤
⎢⎢⎣
⎡−
+×
∆∆
×−=⎥⎥⎦
⎤
⎢⎢⎣
⎡−
+×
∆∆
×−=−−
ht
D
DD
pB
AD
t
D
TD
pB
ADD
DT ehhc
ETk
Eec
ETk
E ττ
τωττω
ρεετ
τωττω
ρεεττ 1
12 ln1
12 ln*ln 22
2200
222
2200
2
why not look at a RTIL 1-butyl-3-methyl-imidazolium + hexafluorophosphate −
W. Huang, R. Richert, Phys. Chem. Chem. Phys. (submitted)
0.0 0.4 0.8 1.2 1.6
0.00
0.02
0.04
0.06
0.08
0.10
ν = 1000 Hz same for :ν = 500 Hzν = 2000 Hzν = 4000 Hz
Std.Dev. of tanδ ≈ 8 × 10-5
BMIM-HFPT = 200 K
E0 = 283 kV/cm
∆ ln
(tan
δ)
time / s
explanation: mild decoupling of τM from τα
10-2 10-1 100 101 102 103 1040.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
structuralrelaxationKWW-fit:
τ = 47.5 msβ = 0.37
diel. modulusHN-fit:
∆M = 0.20τM = 16.0 ms
α = 0.93γ = 0.44
BMIM-HFPT = 200 K
M''
ν / Hz10-3 10-2 10-1 100
0.00
0.02
0.04
0.06
0.08
0.10
KWW A = 0.089
τ = 47.5 msβ = 0.37
BMIM-HFPT = 200 K
E0 = 283 kV/cm
∆ ln
(tan
δ)
time / s
W. Huang, R. Richert, Phys. Chem. Chem. Phys. (submitted)
configurational temperature lifetime of Debye peak
0 5 10 15 200.00
0.01
0.02
0.03
0.04 2-ethyl-1-butanolT = 175 K
average:500 Hz - 3000 Hz
∆ ln
ε''
E02 [1010 V2 / cm2 ]
453 kV / cm
100 101 102 103 104 105
10-1
100
101
-5 0 5 10 150.1400
0.1405
0.1410
0.1415
0.1420
↓
'D'
(a)'α'
∆ε = 20.2τ = 8.6 ms
ν0 = 1 kHz
2-methyl-3-pentanol
ε"
ν / Hz
(b)
← 39 kV/cm 193 kV/cm →
ν0 = 1 kHz
tan
δ
t / ms
W. Huang, R. Richert, J. Phys.Chem. B 112 (2008) 9909