Nonlinear Dielectric Effects in Simple Fluidsthe-dielectric- .Nonlinear Dielectric Effects in Simple
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Nonlinear Dielectric Effectsin Simple Fluids
High-Field Dielectric Response:Coulombic stressLangevin effectEnergy absorptionTime-resolved technique
Ranko RichertNO
N-L
INEA
R D
IELE
CTR
IC E
XPER
IMEN
TS
Rom
a, D
iele
ctric
Tut
oria
l30
Aug
ust 2
009
dielectric relaxation techniques
0
1
0
1''
()
'()log()
( )( )[ ]
Negami -
Havriliak
1 *
+
+=
is
( ) { } Debye1
*
is
+
+= E 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
'
[Hz]10-1 100 101 102 1030
10
20
30 174 K - 198 K (3K)
propylene glycol
''
[Hz]
non-linear susceptibility
( ) ( ) ( ) ( )
( )( ) ( )
( ) ( ) K
K43421321321
+++=
==
++++++====
4422
0
44
symmetry0
3322
symmetry0
1
causality00
:symmetry00 :causality
EE
EEEEelectret
EP
EPEPP
EEEEEP
( ) ( ) [ ]( )
ss
s
ss
E
E
EE
=
=
=
2
2
22
:factorPiekara ln
10
( ) ( ) ( ) ( ) ==tt
dtEdPtP 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 1
high AC fieldno bias1 + 3
low AC fieldon high pulse
NDE(t)
Coulombic stress
Coulombic stress exercise
QVEnergyd
ACCVQ
VQC
21
0
=
===
( )( ) ( )
[ ][ ] A
FL
Lstrainstress
E
tVtVtV
=
=
=
0
0
modulus mechanical
GPa 1 modulus sYoung'hspacer witTeflon assume
measuredon effect calculatesin
voltagefrom resulting force calculate
rFrF 3304 r
qqr
qqcgsSI
=
=
10 m
top electrode 16 mm bottom electrode 30 mm ring outer: 20 mm ring inner: 14 mm
Coulombic stress solutions
10 m
( )
QVEdA
C
VQC
rqq
SI
21
0
30
1
4
=
==
=
=
rF
( )
( )
( )
( )[ ]
( ) ( )[ ]
[ ][ ] 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
43421
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
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
cos = 1
L(a) a/3
a = E / kT
L(a)
= c
os
( ) ( )
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
=
saturation in water at 293 K
( ) ( )( )
( )( ) ( )222
44
30
4
2
2
2
2
222
450vanVleck
Piekara
+++
=
=
=
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
''
[Hz]
propylene glycol
'
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
10 m
1
GEN
V - 1
V - 2
SI-1260 PZD-700
100
200
Cgeo = 136 pF
Vin 300 VR = 100
10 m
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 M:protects against 300 V (no time limit)
102 103 104 1050.0
0.2
0.4
0.6
0.8
1.0
[ 1 + ()2 ] -1/2
= 5.95 10-6 s
f-6dB = 26750 Hz
Am
plitu
de / Hz
AD 549 LRin = 1015 Cin = 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 22244
30
4
2
+++
=
ss
ss
kTVN
E
10-1 100 101 102 103 1040
10
20
0
20
40
60
'' [Hz]
propylene glycol
'0 2 4 6 8
-8
-6
-4
-2
0
E0 2 [1010 V 2 cm-2 ]
ln '5.6 Hz - 100 Hz
propylene glycol
1000
ln
'
energy absorbtion
(less) expected non-linearity: sample heating via dielectric loss
1 0 -1 -2 -3 -40.0
0.1
0.2
0.3 KWW = 0.5
log10( / KWW)
heating
g KW
W(ln
)( )
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
spectrally selective dielectric experiments
( ) ( )tEtE bb sin=
b 1321
( ) 20 bb EQ =1 0 -1 -2 -3 -4
0.0
0.1
0.2
0.3
anti-hole
hole
KWW = 0.5
log10( / KWW)
spectrallyselective'heating'
g KW
W(ln
)
1 0 -1 -2 -3 -40.0
0.1
0.2
0.3 KWW = 0.5
log10( / KWW)
heatingg K
WW
(ln)
B. Schiener, R. Bhmer, A. Loidl, R. V. Chamberlin, Science 274 (1996) 752B. Schiener, R. V. Chamberlin, G. Diezemann, R. Bhmer, J. Chem. Phys. 107 (1997) 7746R. V. Chamberlin, B. Schiener, R. Bhmer, Mat. Res. Soc. Symp. Proc. 455 (1997) 117
E E
: 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 = 3105 V / cm E = 0 V / cm
''
100
ln
''log10(HN)
0
20
40
60
80
-2 -1 0 1 2 3 40
5
10
15
20
25
E = 3105 V / cm E = 0 V / cm'
log10(HN)
HN = 0.95HN = 0.58HN = 285 s = 72
= 3.7
Dgeo = 20 mmsgeo = 6.4 mCp = 1.5 J/K/cm
