Nonlinear Dielectric Effects in Simple...

44
Nonlinear Dielectric Effects in Simple Fluids High-Field Dielectric Response: Coulombic stress Langevin effect Energy absorption Time-resolved technique Ranko Richert NON-LINEAR DIELECTRIC EXPERIMENTS Roma, Dielectric Tutorial 30 August 2009

Transcript of Nonlinear Dielectric Effects in Simple...

Page 1: Nonlinear Dielectric Effects in Simple Fluidsthe-dielectric-society.org/sites/default/files/bds-tut-09-richert.pdf · Nonlinear Dielectric Effects in Simple Fluids High-Field Dielectric

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

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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 ≡∝≡

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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]

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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.

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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)

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Coulombic stress

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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

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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

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dielectric saturation

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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

=≈

<<<<

−==

=

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎠⎞

⎜⎝⎛=

⎟⎠⎞

⎜⎝⎛−⎟

⎠⎞

⎜⎝⎛=

⇒=

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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

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time resolved NDE experimens

M. Gorny, J. Ziolo, S. J. Rzoska, Rev. Sci. Instrum. 67 (1996) 4290

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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

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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

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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

'

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energy absorbtion

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(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

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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

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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)

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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

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high field impedance

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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

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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 =

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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

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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

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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

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curre

nt

time

1ω versus 3ω data analysis

low field response

high field response

1ω approximation

1ω + 3ω response

εhi - εlo

A3ω / Aω

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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

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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

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( ) ( )

( ) ( )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

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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

Page 32: Nonlinear Dielectric Effects in Simple Fluidsthe-dielectric-society.org/sites/default/files/bds-tut-09-richert.pdf · Nonlinear Dielectric Effects in Simple Fluids High-Field Dielectric

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

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what do we learn ?

Page 34: Nonlinear Dielectric Effects in Simple Fluidsthe-dielectric-society.org/sites/default/files/bds-tut-09-richert.pdf · Nonlinear Dielectric Effects in Simple Fluids High-Field Dielectric

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

Page 35: Nonlinear Dielectric Effects in Simple Fluidsthe-dielectric-society.org/sites/default/files/bds-tut-09-richert.pdf · Nonlinear Dielectric Effects in Simple Fluids High-Field Dielectric

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

Page 36: Nonlinear Dielectric Effects in Simple Fluidsthe-dielectric-society.org/sites/default/files/bds-tut-09-richert.pdf · Nonlinear Dielectric Effects in Simple Fluids High-Field Dielectric

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

Page 37: Nonlinear Dielectric Effects in Simple Fluidsthe-dielectric-society.org/sites/default/files/bds-tut-09-richert.pdf · Nonlinear Dielectric Effects in Simple Fluids High-Field Dielectric

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

Page 38: Nonlinear Dielectric Effects in Simple Fluidsthe-dielectric-society.org/sites/default/files/bds-tut-09-richert.pdf · Nonlinear Dielectric Effects in Simple Fluids High-Field Dielectric

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

?

Page 39: Nonlinear Dielectric Effects in Simple Fluidsthe-dielectric-society.org/sites/default/files/bds-tut-09-richert.pdf · Nonlinear Dielectric Effects in Simple Fluids High-Field Dielectric

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

Page 40: Nonlinear Dielectric Effects in Simple Fluidsthe-dielectric-society.org/sites/default/files/bds-tut-09-richert.pdf · Nonlinear Dielectric Effects in Simple Fluids High-Field Dielectric

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

Page 41: Nonlinear Dielectric Effects in Simple Fluidsthe-dielectric-society.org/sites/default/files/bds-tut-09-richert.pdf · Nonlinear Dielectric Effects in Simple Fluids High-Field Dielectric

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

Page 42: Nonlinear Dielectric Effects in Simple Fluidsthe-dielectric-society.org/sites/default/files/bds-tut-09-richert.pdf · Nonlinear Dielectric Effects in Simple Fluids High-Field Dielectric

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

Page 43: Nonlinear Dielectric Effects in Simple Fluidsthe-dielectric-society.org/sites/default/files/bds-tut-09-richert.pdf · Nonlinear Dielectric Effects in Simple Fluids High-Field Dielectric

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)

Page 44: Nonlinear Dielectric Effects in Simple Fluidsthe-dielectric-society.org/sites/default/files/bds-tut-09-richert.pdf · Nonlinear Dielectric Effects in Simple Fluids High-Field Dielectric

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