Nonlinear Dielectric Effects in Simple Fluidsthe-dielectric- .Nonlinear Dielectric Effects in Simple

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Transcript of Nonlinear Dielectric Effects in Simple Fluidsthe-dielectric- .Nonlinear Dielectric Effects in Simple

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