Transcript PPT - Jordan University of Science and Technology

The electric properties of dielectric materials are usually
described in terms of the dielectric constant .
When an ideal dielectric body is exposed to an electric
field there exist only bound charges that can be displaced
from their equilibrium positions. This phenomenon is
called displacement polarization.
In molecular dielectrics, bound charges form permanent
dipoles. The molecular dipoles can only be rotated by an
electric field.
In an external field the permanent
dipoles rotate with the electric field
direction and this process is called
orientational polarization.
There are three kinds of
polarization processes we can see in
this case, ionic,electronic and
orientational.
The most important phenomenon
in dielectric materials when exposed
to an external alternating electric
field is the relaxation in these
permanent dipoles, which is the
subject of our project.
When we apply an external static field to a dielectric
material
the electric displacement written as:
--[1]
The electric displacement also equal:
--[2]
Then,the polarization given by :
--[3]
In static field case
--[4]
We can write Ps as :
Where,
--[5]
:The part due to the polarizability of the particles.
:The part of due to permanent dipoles.
Equ.[4] can be written as:
--[6]
The time needed by dipoles to reach the equilibrium
distribution is in the range (10-6 to10-13 s) .[due to static
external electric field].
During this interval of time :
(Ps)dip built up as shown in Fig.[1].
P increased from P∞ to Ps .
where, the polarization
is given by :
where,
L is Langevin
function.
Fig.[1]- The polarizability as a function of time.
After an interval of time ( t ) :
--[7]
Due to relaxation mechanism, the rate of which dipole
build up in the material is given by Drude’s model as:
--[8]
 : The relaxation time of the mechanism.
When the static electric field is suddenly switched off
Eq.[8] becomes:
--[9]
Integrating Eq.[9] we get :
--[10]
From Eq's.[4],[5]and[6] we get :
--[11]
From Eq.[8]
--[12]
The solution of this equation
--[12]
Then, the steady state solution,
--[13]
And ,Equ.[7] gives:
--[14]
Then,
This means that:
--[15]
We get it by Comparing the relation of the complex
electric displacement
and Eq.[15]
--[16]
By separating the real & imaginary parts
Comparing it with:
We get :
--[17]
--[18]
ε∞ = 2
εs = 20
τ = 10-2
ε`
ε``
ε`
ε∞ = 2
εs = 20
τ = 10-4
ε˝
ε`
ε``
ε∞ = 2
εs = 20
τ = 10-6
ε`
ε∞ = 1
εs = 25
τ = 10-6
ε˝
ε∞ = 2
εs = 10
τ = 10-6
ε`
ε˝
ε`
ε∞ =2
εs = 20
τ = 10-6
ε˝
ε˝
ε∞ = 2
εs = 20
έ
ε˝
20
17.5
15
12.5
ε∞ = 2
εs = 20
10
7.5
ε∞ = 2
εs = 10
5
2.5
2.5
5
7.5
10
12.5
15
17.5έ
20
For this general case Equ.[16] can be written as:
Then ,
This gives :
--[20]
Separation of the real and imaginary parts leads to :
--[21]
&
--[22]
ε˝
ε∞ = 2
εs = 20
ideal
θ
έ
From Fig.[7] we can see clearly that :
The center of a semi circle of the Cole-Cole plots when
we consider a series of relaxation processes is not on the
real axes of έ .but, it deviates by a small angle θ from the
έ axes which is called the dip angle.
The center of the deviation semi circle is at the point
( 11 , -2.9 ).then, we can get the dip angle from
--[23]
The dip angle equal:
then,
From Equ.[23] we can find that the value of n is 0.8.
where this value agrees with our assumption
The following variables can be measured in the
laboratory for any dielectric material:
Cexp as a function of frequency. The phase angle 
Where,C is the capacitor
capacitance.
The real part of the impedance Z’ and the imaginary
part Z”. Then the dielectric components are calculated
as:
’ = Cexp/C0,
and
” = ’ tan ()
Here are some experimental data for an
organomettalic polymer before and after being exposed
to carbon dioxide.
8
3.0x10
8
2.5x10
8
Z'()
2.0x10
8
1.5x10
Z' A0 (before CO)
Z' A0 (after CO)
Z A3 (before CO)
Z' A3 (after CO)
8
1.0x10
7
5.0x10
0.0
0
10
1
10
2
10
3
10
log frequancy(Hz)
4
10
8
Z"()
1.0x10
Z" A0 before CO
Z" A3 before CO
Z" A0 after CO
Z" A3 after CO
7
5.0x10
0.0
0
10
1
10
2
10
3
10
log frequancy(Hz)
4
10
4e+8
4e+8
3e+8
3e+8
Z"
2e+8
2e+8
2e+8
Before
1e+8
8e+7
4e+7
After
0e+0
0e+0 4e+7 8e+7 1e+8 2e+8 2e+8 2e+8 3e+8 3e+8 4e+8 4e+8
Z'
Sample A0 before and after exposure to CO