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)(

+

=