IDMRCS8 2017 TUT nonlin -...
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Ranko Richert ► non-linear basics ► experimental techniques ► summary of effects ► chemical effects ► energy absorption ► electroviscous effects Tutorial organized by "International Dielectric Society" Wisła, Poland 23 July 2017 Non-linear approach to complex dynamics
Transcript of IDMRCS8 2017 TUT nonlin -...
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
lect
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
