Dielectrics

Discussion

the basic idea

Dielectrics are insulators, plain and simple. The two words refer to the same class of materials, but are of different origin and are used preferentially in different contexts.

The plastic coating on an electrical cord is an insulator. The glass or ceramic plates used to support power lines and keep them from shorting out to the ground are insulators. Pretty much anytime a nonmetallic solid is used in an electrical device it's called an insulator. Perhaps the only time the word dielectric is used is in reference to the nonconducting layer of a capacitor.

Dielectrics in capacitors serve three purposes:

  1. to keep the conducting plates from coming in contact, allowing for smaller plate separations and therefore higher capacitances;
  2. to increase the effective capacitance by reducing the electric field strength, which means you get the same charge at a lower voltage; and
  3. to reduce the possibility of shorting out by sparking (more formally known as dielectric breakdown) during operation at high voltage.

what's going on here

When a metal is placed in an electric field the free electrons flow against the field until they run out of conducting material. In no time at all, we'll have an excess electrons on one side and a deficit on the other. One side of the conductor has become negatively charged and the other positively charged. Release the field and the electrons on the negatively charged side now find themselves too close for comfort. Like charges repel and the electrons run away from each other as fast as they can until they're distributed uniformly throughout; one electron for every proton on average in the space surrounding every atom. A conducting electron in a metal is like a racing dog fenced in a pasture. They are free to roam around as much as they want and can run the entire length, width, and depth of the metal on a whim.

Life is much more restrictive for an electron in an insulator. By definition, charges in an insulator are not free to move. This is not the same thing as saying they can't move. An electron in an insulator is like a guard dog tied to a tree — free to move around, but within limits. Placing the electrons of an insulator in the presence of an electric field is like placing a tied dog in the presence of a mailman. The electrons will strain against the field as far as they can in much the same way that our hypothetical dog will strain against its leash as far as it can. Electrons on the atomic scale are more cloudlike than doglike, however. The electron is really spread out over the whole volume of an atom and isn't concentrated in any one location. A good atomic dog wouldn't be named Spot, I suppose.

When the atoms or molecules of a dielectric are placed in an external electric field, the nuclei are pushed with the field resulting in an increased positive charge on one side while the electron clouds are pulled against it resulting in an increased negative charge on the other side. This process is known as polarization and a dielectric material in such a state is said to be polarized. There are two principal methods by which a dielectric can be polarized: stretching and rotation.

Stretching an atom or molecule results in an induced dipole moment added to every atom or molecule.

Polarization By Stretching [animate]

Rotation occurs only in polar molecules — those with a permanent dipole moment like the water molecule shown in the diagram below.

Polarization by Rotation [animate]

Polar molecules generally polarize more strongly than nonpolar molecules. Water (a polar molecule) has a dielectric strength 80 times that of nitrogen (a nonpolar molecule that is the major component of air). This happens for two reasons — one of which is usually trivial. First, all molecules stretch in an electric field whether they rotate or not. Nonpolar molecules and atoms stretch, while polar molecules stretch and rotate. This combination of actions only has a tiny effect on the overall degree to which a substance will polarize, however. What's more important is that polar molecules are already strongly stretched — naturally. The way the hydrogen atoms sit themselves on the arms of an oxygen atom's electron clouds distorts the molecule into a dipole. All of this takes place on an interatomic or molecular scale. At such tiny separations, the strength of the electric field is relatively huge for what would otherwise be an unremarkable voltage. (13.6 V for an electron in a hydrogen atom, for example.)

Stretching and rotation are not the end of the story when it comes to polarization. They are just the methods simplest to describe to the casual observer. In general, the polarization of a dielectric material is microscopic electrostatic strain in response to a macroscopic electrostatic stress. An external field applied to a dielectric can't make charges move macroscopically, but it can stretch and distort them microscopically. It can push them into uncomfortable positions and when released allow them to fall back into a relaxed state. The thing that makes the polarizing in an insulator different from stretching an elastic body like a spring is that eliminating the stress doesn't necessarily release the strain. Some insulators will remain in their polarized state for hours, days, years, or even centuries. The longest characteristic times have to be extrapolated from incomplete observations more reasonable duration. No one is going to sit around and wait two thousand years to see the polarization of a chunk of plastic dwindle away to zero. It isn't worth the wait.

Finally, it's somewhat important to keep in mind that the charges "stored" in a dielectric layer aren't available as a pool of free charges. To extract them, you still need metal plates. It's very important to remember that the only reason anyone seems to care about this phenomena is that it helps us to make better capacitors. I think that's where this discussion should wrap up.

capacitors with dielectrics

Place a dielectric layer between two parallel charged metal plates with an electric field pointing from right to left. (Why not left to right? Well, I read from right to left, so it makes the diagrams easier for me to "read".) The positive nuclei of the dielectric will move with the field to the right and the negative electrons will move against the field to the left. Field lines start on positive charges and end on negative charges, so the electric field within each stressed atom or molecule of the dielectric points from left to right in our diagram — opposite the external field from of the two metal plates. The electric field is a vector quantity and when two vectors point in opposite directions you subtract their magnitudes to get the resultant. The two fields don't quite cancel in a dielectric as they would in a metal, so the overall result is a weaker electric field between the two plates.

[slide]

Let me repeat that — the overall result is a weaker electric field between the two plates. Let's do some math.

Electric field is the gradient of electric potential (better known as voltage).

Ex = −  ΔV & Ey = −  ΔV & Ez = −  ΔV  ⇒  E = − ∇V
Δx Δy Δz

Capacitance is the ratio of charge to voltage.

C =  Q
V

Introducing a dielectric into a capacitor decreases the electric field, which decreases the voltage, which increases the capacitance.

V ∝ E (d constant) & C ∝  1  (Q constant) C ∝  1  (d, Q constant)
V E

A capacitor with a dielectric stores the same charge as one without a dielectric, but at a lower voltage. Therefore a capacitor with a dielectric in it is more effective.

About the first discoveries of the Leyden jar. Removing the rod lowers the capacitance. (Air has a lower dielectric constant than water.) Voltage and capacitance are inversely proportional when charge is constant. Reducing the capacitance raises the voltage.

susceptibility, permittivity, dielectric constant

The electric dipole moment of anything — be it an atom stretched in an external electric field, a polar molecule, or two oppositely charged metal spheres — is defined as the product of charge and separation.

p = q r

with the SI unit of coulomb meter, which has no special name.

[Cm = Cm]

The polarization of a region is defined as the dipole moment per unit volume

P =  Σp
V

with the SI unit of coulomb per square meter.


Cm  =  C
m3 m2

Calculating polarization from first principles is a difficult procedure that is best left to the experts. Don't concern yourself with the details of why the polarization has the value that it has, just accept that it exists and is a function of some variables. And what are those variables? Why they're material and field strength, of course. Different materials polarize to different degrees — we'll use the greek letter χe [chi sub e] to represent this quantity known as the electric susceptibility — but for most every material, the stronger the field (E), the greater the polarization (P). Add a constant of proportionality ε0 and we're all set.

P = ε0χe E

The electric susceptibility is a dimensionless parameter that varies with material. Its value ranges from 0 for empty space to whatever. I bet there are even some bizarre materials for which this coefficient is negative (although I don't know for sure). The constant of proportionality ε0 [epsilon nought] is known as the permittivity of free space and will be discussed a bit more later. For now, it's just a device for getting the units to work out.



C  =  C2   N

m2 Nm2 C

rest my brain

The quantity κ [kappa] is unitless.

material κ   material κ
air 1.005364   quartz, crystalline (∥) 4.60
acetic acid 6.2   quartz, crystalline (⊥) 4.51
alcohol, ethyl (grain) 24.55   quartz, fused 3.8
alcohol, methyl (wood) 32.70   rubber, butyl 2.4
amber 2.8   rubber, neoprene 6.6
asbestos 4.0   rubber, silicone 3.2
asphalt 2.6   rubber, vulcanized 2.9
bakelite 4.8   salt 5.9
calcite 8.0   selenium 6.0
calcium carbonate 8.7   silicon 11.8
cellulose 3.7 - 7.5   silicon carbide (αSiC) 10.2
cement ~2   silicon dioxide 4.5
cocaine 3.1   silicone oil 2.7 - 2.8
cotton 1.3   soil 10 - 20
diamond, type I 5.87   strontium titanate, +25 ℃ 332
diamond, type IIa 5.66   strontium titanate, –195 ℃ 2080
ebonite 2.7   sulfur 3.7
epoxy 3.6   tantalum pentoxide 27
flour 3 - 5   teflon 2.1
freon 12, -150 ℃ (liquid) 3.5   tin antimonide 147
freon 12, +20 ℃ (vapor) 2.4   tin telluride 1770
germanium 16   titanium dioxide (rutile) 114
glass 4 - 7   tobacco 1.6 - 1.7
glass, pyrex 7740 5.0   uranium dioxide 24
gutta percha 2.6   vacuum 1 (exactly)
jet fuel (jet a) 1.7   water, ice, –30 ℃ 99
lead oxide 25.9   water, liquid, 0 ℃ 87.9
lead magnesium niobate 10,000   water, liquid, 20 ℃ 80.2
lead sulfide (galena) 200   water, liquid, 40 ℃ 73.2
lead titanate 200   water, liquid, 60 ℃ 66.7
lithium deuteride 14.0   water, liquid, 80 ℃ 60.9
lucite 2.8   water, liquid, 100 ℃ 55.5
mica, muscovite 5.4   wax, beeswax 2.7 - 3.0
mica, canadian 6.9   wax, carnuba 2.9
nylon 3.5   wax, paraffin 2.1 - 2.5
oil, linseed 3.4   waxed paper 3.7
oil, mineral 2.1      
oil, olive 3.1   human tissues κ
oil, petroleum 2.0 - 2.2   bone, cancellous 26
oil, silicone 2.5   bone, cortical 14.5
oil, sperm 3.2   brain, gray matter 56
oil, transformer 2.2   brain, white matter 43
paper 3.3, 3.5   brain, meninges 58
plexiglas 3.1   cartilage, general 22
polyester 3.2 - 4.3   cartilage, ear 47
polyethylene 2.26   eye, aqueous humor 67
polypropylene 2.2 - 2.3   eye, cornea 61
polystyrene 2.55   eye, sclera 67
polyvinyl chloride (pvc) 4.5   fat 16
porcelain 6 - 8   muscle, smooth 56
potassium niobate 700   muscle, striated 58
potassium tantalate niobate, 0 ℃ 34,000   skin 33 - 44
potassium tantalate niobate, 20 ℃ 6,000   tongue 38
Dielectric constant for selected materials (~300 K except where indicated)

dielectric breakdown

Every insulator can be forced to conduct electricity. This phenomena is known as dielectric breakdown.

material field
(MV/m)
  material field
(MV/m)
air 3   paper 14, 16
amber 90   polyethylene 50, 500-700, 18
bakelite 12, 24   polystyrene 24, 25, 400-600
diamond, type IIa 10   polyvinyl chloride (PVC) 40
glass, pyrex 7740 13, 14   porcelain 4, 12
mica, muscovite 160   quartz, fused 8
nylon 14   rubber, neoprene 12, 12
oil, silicone 15   strontium titanate 8
oil, transformer 12, 27   teflon 60
      titanium dioxide (rutile) 6
Dielectric breakdown in selected materials

piezoelectric effect

Say all the vowels. Piezoelectricity is an effect by which energy is converted between mechanical and electrical forms.

type sounds produce
changes in …
which cause
changes in …
which result in
changes in …
carbon granule density resistance voltage
condenser plate separation capacitance voltage
dynamic coil location flux voltage
piezoelectric compression polarization voltage
Microphones and how they work