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dielectric spectroscopy
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DIELECTRIC SPECTROSCOPY
&
Comparison With Other Techniques
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
Dielectric properties
Complex dielectric permittivity relative to vacuum
*()=()-i()
Complex conductivity
*()=()+i()
Complex electric modulus
*()=()+i()
as a function of temperature
Medium in an external electric field
ElectricField
D=0sE
D=0E+PP=0sEs= s+1
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
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
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
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)(
+
=