Dielectric

For Dielectric Shader (Mental Ray), see Dielectric Shader.

A dielectric, or electrical insulator, is a substance that is highly resistant to the flow of electric current. Although a vacuum is also an excellent dielectric, the following discussion applies primarily to physical substances.

Dielectrics have the property of making space seem bigger or smaller than it is dimensionally to electric charges and electromagnetic waves. For example, when a dielectric material is placed between two electric charges it increases the force between them, as if they have moved closer together. When an electromagnetic wave travels through a dielectric, the velocity of the wave will be reduced and it will behave as if it had a shorter wavelength.

Electrically, the dielectric constant is a measure of the extent to which a substance concentrates the electrostatic lines of flux. More specifically it is the ratio of the amount of electrical energy stored in an insulator, when a static electric field is imposed across it, relative to vacuum (which has a dielectric constant of 1). Thus, the dielectric constant is also known as the static permittivity.

Explanation

When an electric field is applied to a dielectric medium, a current flows. The total current flowing in a real dielectric is in general made of two parts: a conduction and a displacement current. The displacement current can be thought of as the elastic response of the dielectric material to the applied electric field. As the magnitude of the electric field is increased, the displacement is stored in the dielectric material, and when the electric field is decreased the material releases displacement current. The electric displacement can be separated into a vacuum contribution and one arising from the dielectric by

\mathbf{D} = \varepsilon_{0} \mathbf{E} + \mathbf{P} = \varepsilon_{0} \mathbf{E} + \varepsilon_{0}\chi\mathbf{E} = \varepsilon_{0} \mathbf{E} \left( 1 + \chi \right),

where P is the polarization of the medium and $\chi$ its electric susceptibility. It follows that the relative permittivity and susceptibility of a dielectric are related, $\varepsilon_{r} = \chi + 1$ .

Complex permittivity in dielectrics

Apart from a vacuum, the response of normal dielectrics to external fields generally depends on the frequency of the field. This frequency dependence is because a material's polarization does not respond instantaneously to an applied field. The response must always be causal (arising after the applied field). For this reason permittivity is often treated as a complex function of the frequency of the applied field $\omega$ , $\varepsilon \rightarrow \widehat{\varepsilon}(\omega)$ . The definition of permittivity therefore becomes

D_{0}e^{i \omega t} = \widehat{\varepsilon}(\omega) E_{0} e^{i \omega t},

where $D_{0}$ and $E_{0}$ are the amplitudes of the displacement and electrical fields, respectively, $i=\sqrt{-1}$ is the imaginary unit. The response of a medium to static electric fields is described by the low-frequency limit of permittivity, also called the static permittivity or dielectric constant $\varepsilon_{s}$ (also $\varepsilon_{DC}$ ):

\varepsilon_{s} = \lim_{\omega \rightarrow 0} \widehat{\varepsilon}(\omega).

At the high-frequency limit, the complex permittivity is commonly referred to as ε_∞. At the plasma frequency and above, dielectrics behave as ideal metals, with electron gas behavior. The static permittivity is a good approximation for altering fields of low frequencies, and as the frequency increases a measureable phase difference $\delta$ emerges between D and E. The frequency at which the phase shift becomes noticeable depends on temperature and the details of the medium. For moderate fields strength ( $E_{0}$ ), D and E remain proportional, and

\widehat{\varepsilon} = \frac{D_0}{E_0}e^{i\delta} = |\varepsilon|e^{i\delta}.

Since the response of materials to alternating fields is characterized by a complex permittivity, it is natural to separate its real and imaginary parts, which is done by convention in the following way:

\widehat{\varepsilon}(\omega) = \varepsilon'(\omega) - i\varepsilon''(\omega) = \frac{D_0}{E_0} \left( \cos\delta - i\sin\delta \right).

In the equation above, $\varepsilon''$ is the imaginary part of the permittivity, which is related to the rate at which energy is absorbed by the medium (converted into thermal energy, etcetera). The real part of the permittivity, $\varepsilon'$ .

Dielectrics in Parallel-Plate Capacitors

Putting a dielectric material between the plates in a parallel plate capacitor causes an increase in the capacitance in proportion to k, the dielectric constant of the material:

C = \frac{k \epsilon_0 A}{d}

where

\epsilon_0

is the permittivity of free space, A is the area covered by the capacitors, and d is the distance between the plates.

This happens because an electric field polarizes the molecules of the dielectric, producing concentrations of charge on its surfaces that create an electric field opposed (antiparallel) to that of the capacitor. Thus, a given amount of charge produces a weaker field between the plates than it would without the dielectric, which reduces the electric potential. Considered in reverse, this argument means that, with a dielectric, a given electric potential causes the capacitor to accumulate a larger charge.

Applications

The use of a dielectric in a capacitor presents several advantages. The simplest of these is that the conducting plates can be placed very close to one another without risk of contact. Also, if subjected to a very high electric field, any substance will ionize and become a conductor. Dielectrics are more resistant to ionization than air, so a capacitor containing a dielectric can be subjected to a higher operating voltage. Layers of dielectric are commonly incorporated in manufactured capacitors to provide higher capacitance in a smaller space than capacitors using only air or a vacuum between their plates, and the term dielectric refers to this application as well as the insulation used in power and RF cables.

Some practical dielectrics

Dielectric materials can be solids, liquids, or gases. In addition, a high vacuum can also be a useful, lossless, dielectric even though its relative dielectric constant is only unity.

Solid dielectrics are perhaps the most commonly used in electrical engineering and many solids are very good insulators. Some examples include porcelain, glass, and most plastics. Air, nitrogen and sulfur hexafluoride are the three most commonly used gaseous dielectrics.

Industrial coatings such as parylene provide a dielectric barrier between the substrate and its environment.
Mineral oil is used extensively inside electrical transformers as a fluid dielectric and to assist in cooling. Dielectric fluids with higher dielectric constants, such as electrical grade castor oil, are often used in high voltage capacitors to help prevent corona discharge and increase capacitance.

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Explanation

Complex permittivity in dielectrics

Dielectrics in Parallel-Plate Capacitors

Applications

Some practical dielectrics

See also