Broadband Dielectric Spectroscopy (BDS) in soft matter research F.Kremer.
Dielectric Spectroscopy
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Transcript of Dielectric Spectroscopy
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DIELECTRIC SPECTROSCOPY
&
Comparison With Other Techniques
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DIELECTRIC SPECTROSCOPY
measures the dielectric and electric properties of a medium as a function of frequency (time)
is based on the interaction of an external electric field with the electric dipole moment and charges of the medium
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Dielectric properties
Complex dielectric permittivity relative to vacuum
*()=()-i()
Complex conductivity
*()=()+i()
Complex electric modulus
*()=()+i()
as a function of temperature
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Medium in an external electric field
ElectricField
D=0sE
D=0E+PP=0sEs= s+1
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Medium in an external electric field
Relation between macroscopic and microscopic quantities
=i
ipVP 1
Dipole moments can have an induced or a permanent character
Permanent dipole moments, Induced polarization, P
+=+= PVNP
VP
ii
1
Is determined by:The interaction between the dipolesThe local electric field at the location of the dipole
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Medium in an external electric field
EkT3
2 =
No interaction between dipoles and local electric field equal to the outer applied fieldthermal energy interaction energy between the dipole and the electric field
VN
kTs2
031
=
Interactions between molecules, effect of polarization of environment
VN
kTFgs
2
031
=
( )( )
++
=
s
sF23
2 2 Internal field Onsager factor
cos122
int zg +== Dipole interactions Kirkwood-Froehlich factor
Onsager-Kirkwood-Froehlich equation
Langevin equation
Relation between macroscopic and microscopic quantities
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Dielectric dispersion in time domain
PerturbationElectricField
E(t)(t)
ResponseElectricDisplacement
D(t)
E0
0
E(t)
t
oo0E0
0
D(t)
t
0sE0 ( ) ( ) 00 EttD =
( ) ( ) ( )tt s +=
( ) 00 = ( ) 1=
( ) ( )tt = 1
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Dielectric dispersion in frequency domain
PerturbationElectricField
E()*()
ResponseElectricDisplacement
D*()
D(t)=D0sin(t-)
t
E(t)=E0sin(t)
( ) ( ) ( ) DiDD +=*
( ) ( ) cos0DD =
( ) ( ) sin0DD =
( ) ( )
cos00
0
ED
=
( ) ( )
sin00
0
ED
=
-
Time-frequency domain
( ) [ ]dttidt
td
=
exp)(0
*( )( ) [ ] pi
dtidt
tdexp
21)(
0
*
=
( ) ( )[ ]tt s = 1)(
( ) ( ) [ ]dttidt
tds
=
exp)(0
*
0)( = t
( ) ( ) ( ) ( )2
020)(
+
=