Ranko Richert

► non-linear basics► experimental techniques► summary of effects► chemical effects► energy absorption► electroviscous effects

Tuto

rial o

rgan

ized

by

"Int

erna

tiona

l Die

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ric S

ocie

ty"

Wisła

,Pol

and

23Ju

ly20

17

Non-linear approach to complex dynamics

E ε ε D 0

0 E 0 E

T kμE B

dielectric relaxation: static permittivity

fieldelectric

E dV

A

I

AQ D

ntdisplacemedielectric t

00

R. R

ichert, Adv. C

hem. P

hys. 156 (2015) 101

Q

V

+

constitutive equation:

Nonlinear Basics

P. Debye, Polar Molecules, Chemical Catalog Company, 1929:

"Here we see that the mean moment is not a linear function for largevalues of the argument, and for such values the dielectric constant

would not be a true constant but would depend upon the field intensity."

limits to linear dielectric behavior

linear

pola

rizat

ion

P

field E

cos cos

EP

E

E MNP

el

or

orelA

1cos

non-linear

pola

rizat

ion

P

field E

1cos

A real dipolar system is

limited to:

dielectric saturation for non-interacting dipolesP

. Debye, P

olar Molecules (C

hemical C

atalog Com

pany, 1929)

753

4

cos4

cos

94502

9452

451

31

1cotanhcos

: ,function Langevin

coscos

aaaaaL

aLa

a

kTEa

de

dekTE

kTE

0.1 1 10

0.1

1

L(a)a / 3

cos = 1

L(a) a/3

a = E / kT

cos

Langevin saturation effect(for dipole gas)

non-linear dielectric effects: static limit

linear

'saturation'

po

lariz

atio

n P

field E

10

E P

0

5533

0

EEEP

beyond the static limit: ac- versus dc-field approachR

. Richert, P

hys. Rev. E

88 (2013) 062313

linear

'saturation'

Pdc

+ac(t

)P

ac(t)

pola

rizat

ion

P

field E

Edc+ac(t)Eac(t)

Eacdcn tEE ,,,ˆ

gauging deviation from linear dielectric response

pola

rizat

ion

resp

onse

time

pola

rizat

ion

resp

onse

time

pola

rizat

ion

resp

onse

time

low field Plo(t)

high field Phi(t) = P1(t) + P3(t)high field Phi(t) P1(t)high field Phi(t)

Experimental Techniques(polar viscous liquids)

experimental techniques: high field impedanceU

. Pathak, R

. Richert, C

olloid Polym

. Sci. 292 (2014) 1905

GEN

V-1

V-2

SI-1260 PZD-350(350 V, 200 mA)

100

100

Buffer Amp.Vin 500 Vp 800 kHz

Zs() 1

Csam

E0 650 kV/cmμE 0.1 kT

= 0.1 Hz ... 350 kHz

-1 0 1 2 3 4 5 6

101

102

103

| Z s | /

log10( / Hz)

Cblock(for DC)

experimental techniques: time resolved techniquesU

. Pathak, R

. Richert, C

olloid Polym

. Sci. 292 (2014) 1905

GEN

Ch 1

Ch 2

DS-345

200

200

R

Sigma-100

Trig Csam

SRS DS-345:Arbitrary Waveform

Signal Generator(16300 points, 12 bit)10 Hz 30 MHz

Nicolet Sigma 100:Digital Storage Oscilloscope4 channels, 100 MS/svertical: 14 bithorizontal: 106 points

PZD-700(700 V, 100 mA)

00

22

2

2

22

2

2

cos , sin

arctan

cos

sin

arctan

cos

sin

2 : periodeach for analysisFourier

CAAte

CAAte

IIIIA

tdtItI

tdtItI

VVVVA

tdtVtV

tdtVtV

tt

V

VII

V

VII

I

It

t

t

t

V

Vt

t

t

t

L.-M. W

ang, R. R

ichert, Phys. R

ev. Lett. 99 (2007) 185701

W. H

uang, R. R

ichert, J. Phys.C

hem. B

112 (2008) 9909adding time-resolution capabilities to high-field technique: ac

t = 0

curre

ntI(t

)

time

volta

geV

(t)

time

2 tt

S. S

amanta, R

. Richert, J. C

hem. P

hys. 142 (2015) 044504adding time-resolution capabilities to high-field technique: dc

t = 0

curr

ent

I(t)

time

volta

geV

(t)

time

00

22

2

2

22

2

2

cos , sin

arctan

cos

sin

arctan

cos

sin

2 : periodeach for analysisFourier

CAAte

CAAte

IIIIA

tdtItI

tdtItI

VVVVA

tdtVtV

tdtVtV

tt

V

VII

V

VII

I

It

t

t

t

V

Vt

t

t

t

2 tt

S. S

amanta, R

. Richert, J. C

hem. P

hys. 142 (2015) 044504adding time-resolution capabilities to high-field technique: dc

t = 0

curr

ent

I(t)

time

volta

geV

(t)

time

-2 0 2 4 6 8 10

-600

-400

-200

0

200

400

600

T = 213 K = 4 kHz

glycerol

EB = 225 kV/cm

EB = 225 kV/cm

I 0 / A

time / ms

componentsFourier even all eliminates2

, 2

tItItI

tVtVtV negposnegpos

NDE Summary( AC / DC )

NDE summary: dielectric saturationR

. Richert, J. P

hys.: Condens. M

atter (in press)10-2 10-1 100 101 1020

2

4

6

8

10

12

14DC

''hi

'hi

''lo

'lo

log10( / max )

' , ''

10-2 10-1 100 101 1020

2

4

6

8

10

12

14AC

''hi

'hi

''lo

'lo

log10( / max )

' , ''

DC: amplitude reduction at all frequenciesAC: amplitude reduction fades for > max

(depending on number of Tfic for structural recovery)

NDE summary: chemical effectR

. Richert, J. P

hys.: Condens. M

atter (in press)10-2 10-1 100 101 1020

2

4

6

8

10

12

14DC

''hi

'hi

''lo

'lo

log10( / max )

' , ''

10-2 10-1 100 101 1020

2

4

6

8

10

12

14AC

''hi

'hi

''lo

'lo

log10( / max )

' , ''

DC: amplitude enhancement at all frequenciesAC: amplitude enhancement can fade for > max

(depends on nature of chemical effect)

NDE summary: energy absorptionR

. Richert, J. P

hys.: Condens. M

atter (in press)10-2 10-1 100 101 1020

2

4

6

8

10

12

14DC

''hi

'hi

''lo

'lo

log10( / max )

' , ''

10-2 10-1 100 101 1020

2

4

6

8

10

12

14AC

''hi

'hi

''lo

'lo

log10( / max )

' , ''

DC: no energy absorbed from static fieldAC: reduction of relaxation times for > max

NDE summary: electroviscous effect (entropy reduction)R

. Richert, J. P

hys.: Condens. M

atter (in press)10-2 10-1 100 101 1020

2

4

6

8

10

12

14DC

''hi

'hi

''lo

'lo

log10( / max )

' , ''

10-2 10-1 100 101 1020

2

4

6

8

10

12

14AC

''hi

'hi

''lo

'lo

log10( / max )

' , ''

DC: increased relaxation times for all frequenciesAC: increased relaxation times only for < max(always combined with dielectric saturation)

Chemical Effect(Monohydroxy Alcohols)

special case of 5-methyl-3-heptanolA

. R. Y

oung-Gonzales, R

. Richert, J. C

hem. P

hys. 145 (2016) 074503

low

tem

pera

ture

1Kg

1Kg

high

tem

pera

ture

cos1 zgK

W. Dannhauser, J. Chem. Phys. 48 (1968) 1911

10-1 100 101 102 103 104 105 1060

1

2

3

4

5

T = 215 K

T = 180 K

''

/ Hz

5-methyl-3-heptanol

180190200210

0.5

1.0

1.5

g K

T / K

EfxxK

ring

chainrc E

special case of 5-methyl-3-heptanolA

. R. Y

oung-Gonzales, R

. Richert, J. C

hem. P

hys. 145 (2016) 074503

101 102 103 104 105-2

0

2

4

6

8

10

max

ED = 11.0 %ElnD = 12.6 %

5-methyl-3-heptanolT = 203 K

EB = 171 kV/cm

100

( 'hi

' lo

) / (

'lo

)

/ Hz

101 102 103 104 1050

5

10

15

20

25

max

ED = 11.0 %ElnD = 12.6 %

5-methyl-3-heptanolT = 203 K

EB = 171 kV/cm

100

( '' hi

'' lo )

/ '' lo

/ Hz

100 101 102 103 1040

1

2

3

4170 kV/cm28 kV/cm

T = 195 K5-methyl-3-heptanol

''

[Hz]

4

6

8 '

''

'

L.P. Singh, R. Richert, Phys. Rev. Lett. 1009 (2012) 167802

time resolved changes: structural recoveryA

. R. Y

oung-Gonzales, R

. Richert, J. C

hem. P

hys. 145 (2016) 074503

0 2 4 60.0

0.5

1.0

0.0 2.5 5.0 7.50.00.51.01.5

0 4 8 120.0

1.0

2.0

1.27 %

= 8.0 kHz = 0.24 ms

t / ms

1.56 %

= 6.4 kHz = 0.24 ms

100

( e'' hi

'' lo ) /

'' lo

T = 203 K D= 0.18 ms EB = 171 kV/cm

= 4.0 kHz = 0.24 ms

2.30 %

5-methyl-3-heptanol

-8 0 8 16 24 32 40 48

0

2

4

6

8

10

8.75 %

5-methyl-3-heptanol

T = 203 KD = 0.18 ms

EB = 171 kV/cm = 1.0 kHz

10

0

( e'' hi

'' lo )

/ '' lo

t / ms

Origin of Debye peak D

Energy Absorption

I

V

volta

ge ,

cur

rent

time

I

V

volta

ge ,

cur

rent

time

I

V

volta

ge ,

cur

rent

time

5

1

2

2 4

3

3

-2 -1 0 1 2 3 4 5

''

log10()

1

23

4

5

30 sin)( tEtE

p=VI

R. R

ichert, Eur. P

hys. J. Special Topics 189 (2010) 223

energy absorption with heterogeneous dynamics

B. Schiener, R. Böhmer, A. Loidl, and R. V. Chamberlin, Science 274 (1996) 752

101 102 103 1040

5

10

15

20

25

30

glycerol

E0 = 14 kV/cm

T = 213 K

E0 = 283 kV/cm

''

/ Hz

glycerol(E0 = 283 kV/cm)

propylene carbonate(E0 = 177 kV/cm)

100 101 102 103 104

0.00

0.10

0.20

0.30

/ Hz

'' (b)

ln

0.0

0.2

0.4

( Tcfg T

) / K

0.00

0.10

0.20

'' (a)

PCT = 166 K

ln

''

R. R

ichert, S. W

einstein, Phys. R

ev. Lett. 97 (2006) 095703

W. H

uang, R. R

ichert, J. Chem

. Phys. 130 (2009) 194509

high field impedance of glycerol and propylene carbonate

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 )

ln

(tan )

1

00

time / s = 1000 Hz

measured atconstant temperature

propylenecarbonate

(E0 = 177 kV/cm)

time resolved increase of fictive

temperature,

at isothermal conditions

W. H

uang, R. R

ichert, J. Chem

. Phys. 130 (2009) 194509

agreement between experiment and model

S. S

amanta, R

. Richert, J. C

hem. P

hys. 140 (2014) 054503observations at high frequencies

not yet steady stateafter 30 000 periods

t

e

0 100 200 3000.00

0.05

0.10

0.15(c)

= 100 Hz = 105 s

= 0.61

PC

E0 = 283 kV/cmT = 155 K

time / s

0 200 400 600 8000.000.100.200.300.40 (b)

= 1 Hz = 105 s

= 0.61

PCE0 = 283 kV/cm

T = 155 K (

'' hi

'' lo

) /

'' lo 0 200 400 600 8000.000.050.100.150.20

(a)

= 1 Hz = 25 s

= 0.61

PCE0 = 200 kV/cm

T = 156 K

time correlation function of ’s is structural recovery :

not seen in linear response experiments, homogeneous in excess wing.

Electroviscous Effects

dc-field induced change of entropy at constant temperatureG

. P. Johari, J. C

hem. P

hys. 138 (2013) 154503 log (frequency)

di

elec

tric

loss

,

''

EB >> 0 EB = 0

2ET

SV

sE

ln&ln

E

E

high vs. low

bias electric field EB

++

TTSks

cfgB

Ec

AG

*

expG. Adam and J. H. Gibbs, J. Chem. Phys. 43 (1965) 139

field induced 'entropy effect': CPDES

. Sam

anta, O. Y

amam

uro, R. R

ichert, Thermochim

. Acta 636 (2016)57

100 101 102 103 1040

1

2

3

4

5

6

7

max = 40 Hz

CPDET = 335 K

= 15.0CD = 5.8 msCD = 0.67

''

/ Hz

330 340 350

16.5

17.0

17.5

18.0

18.5

s / T = 0.073 K-1

s

T / K

cresolphthalein-dimethylether (CPDE)

2

,

0

2E

TS

VE

sE

%75.0ln%72.0ln

E

E

101 102 103

-1.5

-1.0

-0.5

0.0

0.5

100 E

ln(

)

/ Hz

101 102 103

-0.5 %

0.0 %

0.5 %

1.0 %

EB = 217 kV/cm

CPDET = 335 K

( '' hi

'

' lo ) / '

' lo

sa

t

/ Hz

1K 073.0

p

s

T

field induced change: entropy effectS

. Sam

anta, R. R

ichert, J. Chem

. Phys. 142 (2015) 044504

0

cosCA

AeV

VII

-4 -2 0 2 4 6 8 10 129.20

9.25

9.30

9.35

9.40

9.45

9.50

9.55 T = 213 K = 4 kHz

EB = 174 kV/cm

glycerol

pos neg avg

e'

'

t / ms

'heat'-corrected results: glycerol A. R

. Young-G

onzales, S. S

amanta, R

. Richert, J. C

hem. P

hys. 143 (2015) 104504

-2 0 2 4 6 8 10 12-1.5

-1.0

-0.5

0.0

0.5

1.0

1.38 %

-process: = 0.34 ms = 0.65

= 0.58 ms = 0.65

= 0.58 ms = 0.65

T = 213 K = 4 kHz

EB = 174 kV/cm

glycerol

100

( e'' hi

'' lo )

/ '' lo

t / ms

t

ǀEBǀ

0

explaining the rise/decay asymmetry A. R

. Young-G

onzales, S. S

amanta, R

. Richert, J. C

hem. P

hys. 143 (2015) 104504

20 2 B

sE E

TMS

22

22 1

1

D

D

D

D

tdecay

trise

tdecay

trise

etR

etR

etR

etR

B

sE

EP

tPT

MtS

0

2

0

0 2

""

0 2 4 6 8 100.0

0.5

1.0

t' = t 6

Rdecay(t') = exp(t' / )

Rrise(t) =1 exp(t / )

R2decay(t') =

[ exp(t' / ) ] 2

R2rise(t) =

[ 1 exp(t / ) ] 2

R

(t) ,

R2 (t)

t /

Higher Harmonics

experimental techniques: higher harmonicsP

. Kim

, A. R

. Young-G

onzales, R. R

ichert, J. Chem

. Phys. 145 (2016) 064510

GEN

V-in

SRS-830 PZD-350(350 V, 200 mA)

100

Buffer Amp.Vin 500 Vp 3.45 kHz

Rs

1

Csam

E0 650 kV/cmμE 0.1 kT

= 1 Hz ... 102 kHz

lock-in amplifierset to nth

harmonic

third harmonic susceptibility 3 : glycerolP

. Kim

, A. R

. Young-G

onzales, R. R

ichert, J. Chem

. Phys. 145 (2016) 064510

101 102 103 1040.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

E0 = 135 kV/cmglycerol

T = 210 K T = 213 K T = 216 K

T = 180 K

100

3 E

02

/ Hz

10-210-1100 1010.0

0.5

1.0

1.5E0 100 kV/cm

/ max

experiment model

101 102 103 1040.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5glycerol T = 210 K

T = 213 K T = 216 K

100

3 E

02

/ Hz

advertisementR

. Richert, J. P

hys.: Condens. M

atter (in press)

Different sources of non-linear behavior can be separted by ac vs.dc or by frequency.

Time resolved non-linear techniques provideinformation on dynamics of structural recovery, analogous to physical aging.

Effects that can be studied are: Dielectric saturation; Field induced shifts of chemical potentials; High resolution structural recovery;Electroviscous and electrocaloric effects.

Phenomenological models exist, butmuch of the general theory needed for interpretation is still missing.

Susan Weinstein Ullas Pathak Amanda R. Young-GonzalesLi-Min Wang Abidah Khalife Pyeongeun KimWei Huang Subarna Samanta

CONCLUSIONS

pola

rizat

ion

P

field E

ASU

team