Dielectric Materials [Compatibility Mode].pdf

8/9/2019 Dielectric Materials [Compatibility Mode].pdf

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Part I Dielectric MaterialsDefinition: is the material that does not conduct electricity

readily, i.e., an insulator

Applications: range from power engineering to

Lecture StructureReview of basic electrostatic theory

CapacitorComplex permittivityPolarisation processesElectrets


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Basic Electrostatic TheoryCoulomb's law

Experiments on electrically-charged bodies yield thefollowing observations-Like charges repel and opposite charges attract eachother

-The force between the charges isinversely proportional to the square of the distancebetween them

dependent on the medium in which they areembeddedacts along the line joining the chargesproportional to the product of the charge magnitudes.


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041

0 221

221 rrF

r

QQ

r

QQ

or k ==

F= force of one charge on the other, newtons (N)

Q1 and Q 2 = charge quantities, coulombs (C)r= distance between charges, metres (m)k=constant of proportionality

r= relative permittivity of the dielectric0=8.85x10 -12F/m, permittivity of free space or vacuum


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Electric field

An electric field is region where forces actThe resulting force per unit charge is defined asthe electric field intensity E

104

1

2

21 == NC

Q r Q

or r

FE

An equivalent unit for the electric field intensity isthe volt per metre (Vm -1)

The total or resultant electric field at a point isthe vector sum of the individual componentfields at the point.


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Electric flux densityThe electric field --forces on charge

-- magnitude of the

charges

,density with a symbol D is defined as

E D r o =


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Electric potential and potential differenceElectric field is inconvenient to work with(vector).

Any system of charges at rest is unstable.The inverse square law causes charges ofunlike sign to collide and charges of like sign

position by force which are not electrostatic.Work has to be done to assemble systems of

charges and this work can be recoveredwhen they are released.The systems possess potential energy

electric potential.


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We often are interested in the change of electricpotentialelectric potential difference.It is defined as the work done when unit positive

charge is moved from one point to the other.Consider the figureThe force on the charge is E.

The work done on the chargeby the external force when itis moved through a small distance d l is the product ofthe external force and the distance moved in thedirection of that force, ie

unitcharge

= lE d dV


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The potential difference between two points A

and B can be calculated by integrating along asuitable path between them.

The potential difference depends only on the ==

B

A

B

A dl E d V V A B coslE

starting and finishing points, not on the pathwhich taken between them.

Consider a charge is moved from A to B in thefield of another charge Q at O


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The potential difference from

a small movement of dl of aunit charge at P is

ThereforeQ

dl

E

BA r

P

rArB

dlrdlE == 204 r

QdV

BB

Using the principle of superposition theconclusion can be extended to the field of anycombination of charge.

)11

(44

4

02

0

20

A B

B

A

A B

r r Q

dr r

Q

r V V

==

==

dlrdlE AA


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CapacitorDefinition : a device for storing electric charge and, hence,electric energy. It consists of two conductors separated by aninsulating medium.

Capacitance is defined as the ratio of the storedcharge to the voltage applied.

Its unit is Coulombs/Volt=farads.

The capacitance is independent of the charge andvoltage. Thus, an increase in applied voltageincreases the charge stored, but the ration of charge

to voltage remains the same.

V C =


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Energy stored in a capacitorIt requires work to charge a capacitor energy is stored bya charged capacitor.Consider a capacitor of capacitance C charged to a

potential difference V (Q=CV)The potential is work per charge. In terms of infinitesimals itis the infinitesimal work dW per infinitesimal charge dq, i.e.

Therefore, the energy stored in a capacitor:

W vdqqC

dqQC

CV QV QQ

= = = = =00

221

212

12

V dW dq

=


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Imperfect dielectrics & Complexpermittivity

Ideal dielectric no loss

I

I=jC0

Defects and impurities lead to variouscharge carriers in dielectrics. Under theinfluence of electric field, current flows

through the dielectrics

C0 V


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V

I

IC

IR

V C I R 0" =

V C I C 0' =0* C C =

V C jV C j I

0=

=


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V C j j

V C jV C jI I V C j I C R

0

00

0

)"'(

'"*

=

+=+==

"'* is called complex permittivity

From the equivalent circuit:

0'C C p =0

"1

C R p

=


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The physical meaning of complex permittivity

Real part is the same as permittivity

Imaginary part represents the resistance inparallel with capacitor

is an important angle. In practice, it oftenappears in terms of tan

'"

'"tan

0

0

===

V C V C

I I

C

R


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Power loss per unit capacitanceWhen considering the parallel equivalentcircuit of a capacitor, the power loss in thecapacitor is due to R p. If V is the rms value ofthe voltage across the capacitor, then the

power ss pa e per un capac ance, cap ,is

tan'"

'"1 22

0

022

V V A

d d

AV C R

V W p

cap ====


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Example: Consider the three dielectric materials listed

in Table with the real and imaginary dielectric constants, ' and 'at 1 kHz.(i) At a given voltage, which dielectric will have the

lowest power dissipation per unit capacitance at 1 kHzand at an operating temperature of 50 C?(ii) Is this also true at 120 C?

T =50 oC T =50 oC T = 120 oC T = 120 oC

Materials

Polycarbonate 2.47 0.003 2.535 0.003PET 2.58 0.003 2.75 0.027

PEEK 2.24 0.003 2.25 0.003


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PolarisationWhat happens when an insulating material isinserted between the plates of a capacitor?

Experimental evidence+

---

++

--

++

-+Q 0

CC0 -Q+Q-Q 0

+

+

+

-----

+++++

-

-

-

-

+

+

+

+

-

-

-

E Et

(a) (c)(b)

V VV


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According to , the capacitance has been

increased due to the insertion of a dielectricbetween the plates.Why?Electrons in an insulator are bound to theatoms and are not free to wander through the

V

QC =

mater a un er t e act on o an e ectr c e .

+E=0 E0

_


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This leads to dipoleoriented along theelectric field.

Inside the material manyatoms overlap no noticeable

- - - - - - - - - - -

-- - - - - - - - - -

+ + + + + + + + + ++ + + + + + + + + + +

-q

+q

e ec pos ve an nega ve cance eacother) At the edges of the material surfacelayers of charge appear.

Much the same as if there were free chargesin the material, but the amount of surfacecharge is always less in an insulatingmaterial than in a conductor.


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Let Q be the charge on the metal plates and q

the induced charge on the insulators surfaceThe electric field between theplates is now due to Q and q.

-q

+q

+Q

-

E=? d

S

S

qQ E

0

=

p.d. is

capacitance

is called the relative permittivity

of the insulating material

d S EdlV 0 ==

d

S

d

S

qQ

Q

V

QC

r

00

=

==

qQ

Qr

=


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q is proportional to the applied field E, i.e.

E is proportional to E (Q-q)

e is called the electric susceptibility which is a

E q

)( qQq e =

constant

The capacitance is increased by inserting aninsulating material

111 >+=

+=

+=

= er qQ

qqQ

qqQqQ

Q


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The product of 0 and r is called the

absolute permittivity, represented by

q is bound to atoms (cant move within thematerial) -- bound chargeQ comes from power source -- free charge

0 r =

- uFrom the definition of D,

(Q-q) is proportional to E D only depends on the free charge Q

qQ

Q

E

Dr

== 00


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Imagine that the electric flux density in adielectric is due to two causes:(i) the flux density set up by an applied field

and(ii) the polarisation of the dielectric resulting

Therefore

Polarisation is related to permittivity of the

dielectric.

P E D += 0

E E E E DP r r )1(0000 ===


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PolarisationThe total effect of an electrical field on adielectric material is called the polarizationof the material.Polarisation is related to permittivity of

.Two questions :1. Given the atomic structure of the material -What is its dielectric constant ?2. How does the dielectric constant dependon the frequency of the external field?


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Mechanisms of polarisationPermittivity is a macroscopic description of thedielectric properties. How is it linked with atomic

and molecular processes taken place in thedielectric?There are four polarisation mechanisms

responsible for frequency characteristics of and and they are(i) electronic (optical)

(ii) ionic(iii) dipolar (orientational) and(iv) interfacial


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dp qm =)(

-q +q

d

Dipole and Dipole Moment

ppppP N vol N

=+++= )(1 21


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The dipole moment of the atom

-- the polarisability and E l the localfield

lEm =

If there are n polarisable atoms per unitvolume then the polarisation

lEP n=


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Since the above dipole moment iscreated under the influence of anelectric field it is called the induceddipole moment .Many molecules contain dipolemoments for examples

ClH

H

H

O


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Electronic polarisation ( e)

When a field is applied to an atom electronclouds are displaced slightly with respect to

the positive charge

E=0 E0

d

+ -

m =edElectron cloud


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The induced dipole moment

e-- the electronic polarisabilityd

lEm e=

ere are n po ar sa e a oms per unvolume then the polarisation

lEP en=


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Ionic polarisation ( i)This type of polarisation occurs in ioniccrystals such NaCl, KCl and so forth.

The ionic crystal has distinctly identifiable ionslocated at well-defined lattice sites. Each pairof oppositely charged neighbouring ions has adipole moment.


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In the absence of an electric field, the solid has no

net polarisation as the dipole moments of equalmagnitude are lined up head to head and tail totail, so that the net dipole moment is zero.

0== + p p pnet , -

ions pushed in x direction and the Na+ ions in +xdirection about their equilibrium positions.Consequently, p+ increases and p- decreases.

0>= + p p pnet


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Based on electronic polarisation, we canwrite

lii E N P =Ni number of ion pairs/vol i ionic polarisiability


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Dipolar polarisation ( d)

Certain molecules posses permanent dipolemoments, such as HCl and H 2O.

In the absence of electric field these di oles

are randomly oriented due to thermal agitation.P net = 0

When a field E is applied, E tries to align thedipoles parallel to itself.P net > 0


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If all the molecules were simply rotated and

aligned with the E, the polarisation of thematerial would be

P net = Np 0N number of molecules/vol.

ermanent di ole moment of molecule

Due to their thermal energy, the moleculesmove around randomly and collide with eachother which destroy the dipole alignments.The higher the temperature, the lower thepolarisation P.

0 p N P

d =


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Interfacial polarisation ( m-w)All materials will have defects (lattice vacancies,impurity ions and free electrons). Under theinfluence of the applied field, migration will occur

d


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Frequency DependenceAny or all of the mechanisms of polarisation may beoperative in any material, i.e.

total = e+ i+ d+ m-wHow identify the important ones for a givenmaterial?

Polarisation will tend to follow direction of the field.AC field a continuous reversal of polarisation insympathy with the field.

What happens if frequency increases?


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Example---polar dipoles

As frequency increases, the inertia of dipoleswill make it more and more difficult for thedipoles to follow the field, resulting in a lag of

the polarisation behind the field.

permittivity of the material.

At a critical frequency, dipoles will be unableto follow the field virtually no polarisation ofthe dielectric

Th i d l i d h


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The process is termed as relaxation and the

frequency of transition is called relaxationfrequency .Different polarisation mechanisms will have

different relaxation frequencies!


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Materials used for electrets(i) Wax

(ii) Polymers

--Highly insulating substances e.g.Polytetrafluoroethylene (PTFE),Fluoroethylene-propylene (FEP)

--Polar substances e.g.Polyvinylidene flouride (PVDF)

F i h d


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Forming methodsThermal method

P o l y m e r ( m e t a l i s e do r n o n - m e t a l i s e d

H e a t i n gc h a m b e r

V o l t a g e p r o f i l e

T e m p e r a t u r ep r o f i l e

t i m e

T a n

d V


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Corona discharge method

Needle

electrodeWire mesh

polymer

metalisation


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Liquid contact method

Clothelectrode

(wet)motion

po ymer

metalisation


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Electron beam method

Scanning ordefocusing

Electron beam

Electron source

Vacuum

polymer

metalisation

chamber


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Charge measurement methods

1. Capacitive probe method

2. Kevin probe vibrating capacitive probe

3. Pulsed electroacoustic technique

C iti b ti i i l


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Capacitive probe operation principle A capacitive probe is one of the most popular devices

for surface charge and surface potentialmeasurements.

Capacitive probe allows for non-contact and non-destructive examination of the surface charges and/orvoltages.

The principle of operation has its origin in the very basicequation defining capacitance of a capacitor:

One of the simplest constructions of a capacitorconsists of two at and parallel conductive plates.

V

Q

C =

Th fig ti i d i th iti


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The same configuration is used in the capacitive

probe: the capacitance is created by the probe andthe plane under test

U1 - a difference of potentials between the

probe and the ground (earth) Reference

U2 - the voltage between the charged planeand ground.

The voltage U between electrodes of thecapacitor is then equal to |U1-U2|.

Assume for a moment that the probe is grounded (so that U1=0 and U=U2).The charge on the tested surface can be then calculated as

D A

U Q r 0=

As long as it is possible to determine the voltage U and U1, the charge on thetested surface can be calculated.

Kelvin probe and Vibrating capacitive


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Kelvin probe and Vibrating capacitive

probeThe expression dQ/dtactually defines an electriccurrent I owing either from orto the probe when the

(I = dQ/dt ).

It is possible to nd out the

voltage between the probeand the surface under testsimply by measuring the

current I and the distance D:

The probe vibrates in the direction


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The probe vibrates in the directionperpendicular to the tested surface andthe current owing to and from the probechanges proportionally to the amplitudeand frequency of that vibration.

If the motion of the probe is sinusoidal, thenthe distance D is equal to:

D = D 0 + D 1 sin( t) [m]

D 1

is the amplitude of vibrations [m], isthe circular frequency of vibrations, = 2 f[rad/s], where f is a frequency in [Hz].

In order to nullify that current thevoltage U has to be brought to zero.In this case the probe-to-groundvoltage U1 will be equal to thevoltage on the surface U2. Thecrucial factor here is properdetection of the current, so thevoltage U1 can be appropriatelyadjusted.

The current can be determined as:

Pulsed electroacoustic method


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Pulsed electroacoustic method

transducer Vdc

Vp(t)

Sample

Vs(t)p(t)

electrode

Fig.3 Schematic diagram of PEA system

Vs(t)

electrode

(x) 1 2

Electret Applications


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Electret Applications

1 Sensor Electret Condenser Microphone (ECM)An ECM is a pressure sensorhaving a moving electret diaphragmmade of polymer film sandwiched

between two electrodes. Whensound wave is incident on thediaphragm, its movement alters thedistance between two electrodes

changes, producing voltage signalin the external circuit.

A poled piezoelectric film of PVDF is another promising polymer used asdiaphragm in electret microphone. Mechanical bending of diaphragm due toincident sound wave results in induced electric charge on the electrode.

Both these configurations are being used in ECMs. A back-plate electretmicrophone configuration has a thin electret film of non-polar material like teflon ora piezoelectric material like PVDF coated on the back electrode, with a freelysuspended diaphragm made of a conventional polymer such as polypropylene.


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Advantages(i) Compact and light weight

(ii) Insensitive to mechanical vibration &s oc

(iii) Insensitive to electromagnetic pickup

2 Filters


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2 Filters

The first application of electrets leading to apatent was for an air filter in 1929.

Airborne particles are a cause of serious

health problems. It is necessary to developsimple and reliable filters/sensors fordetection and control of air pollution.

Electret composite filters with electrostatic charged fibres behave like minicapacitors, with one side of the fibre being charged negative and the other sidebeing positive. The medium as a whole is neutral. Dust particles are attractedtowards the filter and get deposited on the fibres leaving more space between

the fibres for flow of air.

With increasing dust load, electret filters have shown high collection efficiencyand lower pressure drop owing to electrostatic force on the surface.

Advantages


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Advantages

(i) Spread into a broad web

(ii) Able to capture both charged or neutral

(iii) Capable of capturing different sizes of

particles

(iv) No significant pressure drop

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Dielectric Materials [Compatibility Mode].pdf