Dielectric Properties

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Dielectric properties and dielectric loss factor

Physical fundamentals

Most amorphous and semi-crystalline plastics used in technical applications are electrical insulators, which is why they are often used for cable sheathing, housings or in capacitors. Their electrical or dielectric properties are largely determined by their chemical structure and processing-related morphology, as well as the fillers and reinforcing materials used. Conversely, specific properties of the polymer structure or morphology can be determined by dielectrometry, which allows, for example, the dynamics of the vulcanization process or the curing of resins to be observed.

The dielectric properties of a material are primarily represented by the parameters dielectric constant ε_r (also referred to as relative dielectric constant or permittivity), the dielectric loss factor tan δ and the susceptibility χ, as well as the polarisation. These parameters reflect the reaction of the material to the application and permeability of an electric field. The electric field constant ε₀ corresponds to the dielectric function ε when using a vacuum as the dielectric, and the permittivity of a material ε_r corresponds to a multiple of the field constant, whereby the material parameter ε_r is frequency-dependent (Eq. 1) [1, 2].

$\varepsilon =\varepsilon _{0}\cdot \varepsilon _{r}$

(1)

The dielectric constant is particularly important in practical terms. It describes a material's ability to align electric dipoles in insulators and is structure-sensitive and highly dependent on temperature. It is therefore used as a characteristic value for material characterisation.

Determination of the dielectric constant

The dielectric constant of a material is measured in a measuring capacitor specified in accordance with DIN 53 483 and ASTM D 149 [3–5]. It consists of two circular plate electrodes, one of which is divided into a ring electrode, which acts as a protective electrode, and a measuring electrode (diameter D_m) in order to keep the alternating electric field to be measured homogeneous (Fig. 1). The distance between these two electrodes (protective gap g) is usually 0.5 mm. The test specimen with a thickness h serves as the dielectric.

Fig. 1:

Schematic measurement setup for determining the relative permittivity εr

The dielectric constant ε_r is determined from the ratio of the capacitances C of the filled (test specimen) and empty (air) measuring capacitor (C₀) according to Eq. (2).

$\varepsilon _{r}={\frac {C}{C_{0}}}$

(2)

Based on Eq. (3)

$C_{0}={\frac {\pi }{4}}\cdot \varepsilon _{0}\cdot {\frac {(D_{m}+g)^{2}}{d}}$

(3)

the identical distance h between the electrodes must be set for determining the two capacitances C and C₀ for calculating ε_r.

The measurements are performed at the frequencies commonly used in practice, namely 50 Hz, 1 kHz and 1 MHz (DIN 53 483-2) [4]. The dielectric constant ε_r is frequency-dependent and complex (Eq. 4) and is defined as the sum of the real part and the imaginary part (dielectric loss factor).

$\varepsilon _{r}(\omega )=\varepsilon _{r}^{\prime }+\varepsilon _{r}^{\prime \prime }=Re(\varepsilon _{r})+i\cdot lm(\varepsilon _{r})$

(4)

The following equivalent circuit diagram, shown in Fig. 2, is used to determine the dielectric loss factor. This results in the complex resistance Z or the apparent conductance 1/Z according to Eq. (5)

${\frac {1}{Z}}={\sqrt {{\frac {1}{R^{2}}}+(\omega \cdot C)^{2}}}$

(5)

Fig. 2:

Equivalent circuit diagram of a real capacitor

Determination of the dielectric loss factor

The dielectric loss factor for the circuit in Fig. 2 is defined according to Eq. (6).

$\tan \delta ={\frac {1}{\omega \cdot R\cdot C}}$

(6)

With ε ''_r = ε '_r ⋅ tan δ, the frequency-dependent dielectric loss factor can be calculated according to Eq. (7). The dielectric parameter tan δ is referred to as the dielectric loss factor.

$\varepsilon _{r}^{\prime \prime }(\omega )={\frac {1}{\omega \cdot R\cdot C_{0}}}$

(7)

The properties of the dielectric are implicitly expressed in Eq. (7) in the parallel resistance R. Instead of Eq. (1), the loss factor can also be determined according to Eq. (7) to characterise the properties of the dielectric.

See also

• Dielectric loss factor
• Volume resistance

References

[1]	Schönhals, A.: Electrical and Dielectrical Properties. In: Grellmann, W., Seidler, S. (Eds.): Polymer Testing. Carl Hanser, Munich (2022) 3rd Edition, pp. 330–368 (ISBN 978-1-56990-806-8; E-Book: ISBN 978-1-56990-807-5; see AMK-Library under A 22)
[2]	Lindner, H., Siebke, W., Simon, G., Wuttke, W.: Physik für Ingenieure. Fachbuchverlag Leipzig im Carl Hanser Verlag (2006), 17th Edition, (ISBN 978-3-446-40609-4)
[3]	DIN 53483-1 (1969-07): Testing of Insulating Materials – Determination of Dielectric Properties, Definitions, General Information (withdrawn)
[4]	DIN 53483-2 (1970-03): Testing of Insulating Materials – Determination of Dielectric Properties, Testing at Standard Frequencies of 50 Hz, 1 kHz, 1 MHz (withdrawn)
[5]	ASTM D 149 Standard Test Method for Dielectric Breakdown Voltage and Dielectric Strength of Solid Electrical Insulating Materials at Commercial Power Frequencies