Jordan University Of Sceince & Technology

1. Jordan University Of Sceince & Technology Dielectric Response Function in Polarization Debye Equations Maysa'a Al-Darabseh Dr.Hassan Al-Ghanem

2. Introduction 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.

3. 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.

4. 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 polarizationgiven by : --[3] In static field case --[4]

5. We can write Psas : Where, :The part due to the polarizability of the particles. :The part of due to permanent dipoles. --[5] 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].

6. During this interval of time : (Ps)dipbuilt up as shown in Fig.[1]. Pincreased fromP∞toPs . where,the polarization is given by : where, L is Langevin function. Fig.[1]- The polarizability as a function of time.

7. 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]

8. Integrating Eq.[9] we get : --[10] For alternating field at time t From Eq's.[4],[5]and[6] we get : --[11] From Eq.[8] --[12]

9. The solution of this equation --[12] Then, the steady state solution, --[13] And ,Equ.[7] gives: --[14] Then,

10. This means that: --[15] The complex permitivity We get it by Comparing the relation of the complex electric displacementand Eq.[15] --[16] By separating the real & imaginary parts

11. Comparing it with: We get : Debye Equations --[17] --[18]

12. Variation of the real and imaginariy parts of dielectric constant with frequency ε∞ = 2 εs = 20 τ = 10-2 ε∞ = 2 εs = 20 τ = 10-4 ε` ε` ε`` ε˝ ε∞ = 2 εs = 20 τ = 10-6 ε` ε``

13. Variation of the real and imaginariy parts of dielectric constant with frequency ε∞ = 1 εs = 25 τ = 10-6 ε∞ = 2 εs = 10 τ = 10-6 ε` ε` ε˝ ε˝ ε∞ =2 εs = 20 τ = 10-6 ε` ε˝

14. Cole-Cole plots ε˝ ε∞ = 2 εs = 20 έ

15. The dependence of Niquist plots in the dielectric strength system ε˝ ε∞ = 2 εs = 20 ε∞ = 2 εs = 10 έ

16. For a distribution of relaxation times For this general case Equ.[16] can be written as: Then , This gives : --[20]

17. Separation of the real and imaginary parts leads to : --[21] & --[22]

18. The dfference between the ideal Debye model and the deviation from simple theory ε˝ ε∞ = 2 εs = 20 ideal θ έ

19. To find the dip angle 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]

20. 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

21. Experimentally 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.

22. 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.

25. Before After

26. Thank You