Modern Physics

# What is the dielectric constant?

The dielectric constant is a value associated with the material that is placed between the plates of a capacitor (or capacitor – Figure 1) and that allows it to optimize and increase its function. (Giancoli, 2006). Dielectric is synonymous with electrical insulator, that is, they are materials that do not allow the passage of electrical current.

This value is important in many ways, as it is common for everyone to use electrical and electronic equipment in our homes, recreational spaces, educational or work places, but we are certainly not aware of the complicated processes that go into making this equipment work.

For example, our mini components, televisions and multimedia devices use direct current for their functions, but the domestic and industrial currents that reach our homes and jobs are alternating currents. How is this possible?

The answer to this question lies in the same electrical and electronic equipment: the capacitors (or capacitors). These components allow, among other things, to enable the rectification of alternating current to direct current and their functionality depends on the geometry or shape of the capacitor and the dielectric material present in its design.

Dielectric materials play an important role, as they allow the plates that make up the capacitor to be very close together, without touching them, and completely cover the space between said plates with dielectric material, to increase the functionality of the capacitors.

## Origin of the dielectric constant: capacitors and dielectric materials

The value of this constant is an experimental result, that is, it comes from experiments carried out with different types of insulating materials and resulting in the same phenomenon: greater functionality or efficiency of a capacitor.

Capacitors are associated with a physical quantity called capacitance “C” which defines the amount of electrical charge “Q” that a capacitor can store, giving a certain potential difference “∆V” (Equation 1)

(Equation 1)

Experiments concluded that by completely covering the space between the plates of a capacitor with a dielectric material, the capacitors increase their capacitance by a factor κ, called the “dielectric constant”. (Equation 2).

(Equation 2)

Figure 3 shows an illustration of a capacitor C capacitor with parallel flat plates charged and, consequently, with a uniform electric field directed downwards between its plates.

At the top of the figure is the capacitor with a vacuum between its plates (vacuum – of permittivity ∊0). Then, at the bottom, the same capacitor with capacitance C ‘> C is shown, with a dielectric between its plates (of permittivity ∊).

Figueroa (2005), lists three functions for dielectric materials in capacitors:

1. They allow a rigid and compact construction with a small separation between the conductive plates.
2. They allow a higher voltage to be applied without causing a discharge (the breaking electrical field is greater than that of air)
3. It increases the capacitance of the capacitor by a factor κ known as the material’s dielectric constant.

Thus, the author indicates that, κ “is called the material’s dielectric constant and measures the response of its molecular dipoles to an external magnetic field”. That is, the dielectric constant is greater the greater the polarity of the material’s molecules.

## Atomic models of dielectrics

Materials generally have specific molecular arrangements that depend on the molecules themselves and the elements that make them up in each material. Among the molecular arrangements involved in dielectric processes is that of the so-called “polar molecules” or polarized.

In polar molecules, there is a separation between the average position of negative charges and the average position of positive charges, causing them to have electrical poles.

For example, the water molecule (Figure 4) has a permanent polarization because the center of the positive charge distribution is midway between the hydrogen atoms. (Serway and Jewett, 2005).

While in the BeH2 molecule (beryllium hydride – Figure 5), it is a linear molecule, there is no polarization, since the positive charge distribution center (hydrogen) is in the negative charge distribution center (beryllium), canceling out any polarization that may exist. This is a non-polar molecule.

In the same order of ideas, when a dielectric material is in the presence of an electric field E, the molecules will be aligned according to the electric field, causing a surface charge density on the faces of the dielectric that face the capacitor plates.

Due to this phenomenon, the electric field inside the dielectric is smaller than the external electric field generated by the capacitor. In the following illustration (figure 6), an electrically polarized dielectric is shown inside a parallel plate capacitor.

It is important to note that this phenomenon results more easily in polar materials than in non-polar materials, due to the existence of polarized molecules that interact more efficiently in the presence of the electric field. Although only the presence of the electric field causes the polarization of nopolar molecules, resulting in the same phenomenon of polar materials.

## Dielectric constant values ​​in some materials

Depending on the functionality, economy and final utility of the capacitors, different insulating materials are used to optimize their operation.

Materials such as paper are very economical, although they can fail at high temperatures or in contact with water. As for rubber, it is still malleable, but more resistant. We also have porcelain, which withstands high temperatures, although it cannot adapt to different shapes as needed.

Below is a table where the dielectric constant of some materials is specified, where the dielectric constants have no units (they are dimensionless):

## Some applications of dielectric materials

Dielectric materials are important in global society, with a wide range of applications, from terrestrial and satellite communications that include radio software, GPS, environmental monitoring via satellite, among others. (Sebastian, 2010)

Furthermore, Fiedziuszko et al. (2002) describe the importance of dielectric materials for the development of wireless technology, even for cellular telephony. In their publication, they describe the relevance of this type of material in equipment miniaturization.

In this order of ideas, modernity generated a high demand for materials with high and low dielectric constants for the development of a technological life. These materials are essential components of Internet devices in terms of data storage functions, communications and data transmission performance. (Nalwa, 1999).