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Created page with "{{Language_sel|LANG=ger|ARTIKEL=Dielektrische Eigenschaften}} {{PSM_Infobox}} Dielectric properties and dielectric loss factor __FORCETOC__ ==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 d..."

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{{Language_sel|LANG=ger|ARTIKEL=Dielektrische Eigenschaften}}
{{PSM_Infobox}}
Dielectric properties and dielectric loss factor
__FORCETOC__

==Physical fundamentals==

Most amorphous and semi-crystalline [[Plastics|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 [[Polymers & Structure|structure]] and processing-related [[Microscopic Structure|morphology]], as well as the [[Particle-filled Thermoplastics#Technically used fillers|fillers]] and [[Fibre-reinforced Plastics#Types of reinforced plastics|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|vulcanization]] process or the [[Curing|curing]] of resins to be observed.

The dielectric properties of a [[Material & Werkstoff|material]] are primarily represented by the [[Material Parameter|parameters]] dielectric constant ''ε''r (also referred to as relative dielectric constant or permittivity), the [[Dielectric Loss Factor|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 ''ε''0 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].

{|
|- valign="top"
|width="550px"|<math>\varepsilon = \varepsilon_{0} \cdot \varepsilon_{r}</math>
|width="50px"|(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 [[Material Value|characteristic value]] for material characterisation.

==Determination of the dielectric constant==

The dielectric constant of a [[Material & Werkstoff|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 [[Specimen|test specimen]] with a thickness ''h'' serves as the dielectric.

[[File:Dielectric Properties-1.jpg|600px]]
{|
|- valign="top"
|width="50px"|'''Fig. 1''':
|width="600px"|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 (''C''0) according to '''Eq. (2)'''.

{|
|- valign="top"
|width="550px"|<math>\varepsilon_{r}=\frac{C}{C_{0}}</math>
|width="50px"|(2)
|}

Based on '''Eq. (3)'''

{|
|- valign="top"
|width="550px"|<math>C_{0}=\frac{\pi}{4}\cdot \varepsilon_{0}\cdot \frac{(D_{m}+g)^{2}}{d}</math>
|width="50px"|(3)
|}

the identical distance ''h'' between the electrodes must be set for determining the two capacitances ''C'' and ''C''0 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|dielectric loss factor]]).

{|
|- valign="top"
|width="550px"|<math>\varepsilon_{r}(\omega)=\varepsilon_{r}^{\prime}+\varepsilon_{r}^{\prime\prime}=Re(\varepsilon_{r})+i\cdot lm(\varepsilon_{r})</math>
|width="50px"|(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)'''

{|
|- valign="top"
|width="550px"|<math>\frac{1}{Z}=\sqrt{\frac{1}{R^{2}}+(\omega\cdot C)^{2}}
</math>
|width="50px"|(5)
|}

[[File:Dielektische_Eigenschaften-2.jpg|250px]]
{|
|- valign="top"
|width="50px"|'''Fig. 2''':
|width="600px"|Equivalent circuit diagram of a real capacitor
|}

==Determination of the dielectric loss factor==

The [[Dielectric Loss Factor|dielectric loss factor]] for the circuit in '''Fig. 2''' is defined according to '''Eq. (6)'''.

{|
|- valign="top"
|width="550px"|<math>\tan\delta=\frac{1}{\omega\cdot R\cdot C}</math>
|width="50px"|(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.

{|
|- valign="top"
|width="550px"|<math>\varepsilon_{r}^{\prime\prime}(\omega)=\frac{1}{\omega \cdot R \cdot C_{0}}</math>
|width="50px"|(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|Dielectric loss factor]]
* [[Volume Resistance|Volume resistance]]

'''References'''

{|
|-valign="top"
|[1]
|Schönhals, A.: Electrical and Dielectrical Properties. In: [[Grellmann, Wolfgang|Grellmann, W.]], [[Seidler, Sabine|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-Büchersammlung|AMK-Library]] under A 22)
|-valign="top"
|[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)
|-valign="top"
|[3]
|DIN 53483-1 (1969-07): Testing of Insulating Materials – Determination of Dielectric Properties, Definitions, General Information (withdrawn)
|-valign="top"
|[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)
|-valign="top"
|[5]
|ASTM D 149 Standard Test Method for Dielectric Breakdown Voltage and Dielectric Strength of Solid Electrical Insulating Materials at Commercial Power Frequencies
|}

[[Category:Electrical and Dielectrical Testing]]

Dielectric Properties - Revision history