Electrical Conductivity

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Electrical conductivity

Fundamentals

Electrical conductivity σ or γ, also referred to as conductance, is a physical material parameter and corresponds to the reciprocal of the specific resistance of a dielectric located in a measuring capacitor. It characterises the practically significant ability of a material to conduct electrical current.

In general, electrical conductivity is defined with the unit S/m (Siemens per metre) as the proportionality constant between the current density and the electric field strength, whereby this relationship in the case of constant conductivity corresponds de facto to OHM's law (named after the German physicist Georg Simon Ohm).

The conductivity of materials depends largely on the presence and density of mobile charge carriers, such as free (delocalised) electrons or ions, in the conductive medium. If materials with low electrical resistance are present, which consequently have many freely mobile charge carriers, then these are referred to as conductive or conductors; otherwise, they are non-conductors or insulators.

In practical or metrological applications, almost all materials, even those described as ideal non-conductors or insulators, exhibit low, albeit often negligible, conductivity. They cannot completely prevent the flow of current through the material, especially at high currents and/or voltages.

Unreinforced or unfilled plastics are usually described as almost ideal non-conductors, which are used specifically in the electrical and electronics industry as cable sheathing, printed circuit boards or protective housings. However, under certain circumstances or for special applications, the conductivity of plastics is of interest. Conductive plastics, also known as intrinsically conductive polymers, such as polyacetylene (abbreviation: PAC), polythiophene (abbreviation: PT), polyaniline (abbreviation: PAni) or polypyrrole (abbreviation: PPy), have conductivity levels that are almost comparable to those of metallic materials and are successfully used, for example, in lithium polymer batteries, rechargeable batteries or organic light-emitting diodes (OLEDs) to achieve weight savings while maintaining the same functionality (organic microelectronics) [1].

Electrical conductivity therefore also requires freely movable charge carriers in special plastics in order to generate a current flow. For this reason, electrically self-conducting polymers have delocalised electrons (π-electron system) that cannot be clearly assigned to an atomic group or molecule, but belong to a so-called electron cloud. Such conjugated double bonds with defect electrons typically occur in aromatic polymer molecules such as benzene.

In special plastics such as polyacetylene and poly-p-phenylene (abbreviation: PPV), a negatively charged polymer structure is also observed as a result of oxidation processes, with anions serving as counterions to this oxidised polymer structure in the case of current flow. The total resistance of the plastic is the sum of the resistances in the polymer chains and the resistances between the polymer chains to be bridged.

Another way of producing conductive plastics is to fill them with suitable additives or fillers. The addition of carbon black, aluminium flakes or other conductive additives can significantly improve the conductivity of, for example, polyethylene (abbreviation: PE) or polypropylene (abbreviation: PP), which naturally has a positive effect on both the electrical volume resistance and the electrostatic charge. In contrast to glass fibre reinforcement, the use of carbon fibres in thermosetting matrix materials also results in a significant improvement in electrical conductivity, depending on the filler content and fibre orientation, which can also be used for defect detection purposes with eddy current testing, for example.

Analogous to the mechanical properties of plastics, the electrical parameters of this group of materials are also highly dependent on time and temperature [2], i.e. there is a clear difference between the resistance values under short-term and long-term stress. For example, local heating processes can cause thermal breakdown, while local discharges or electrical ageing can cause sudden long-term breakdown of the tested material (see also: electric breakdown strength).

Derivation of electrical conductivity

In principle, electrical conductivity when a direct current is applied can be described by the characteristic parameters, volume resistance or specific volume resistance, surface resistance or specific surface resistance, and insulation resistance [2, 3]. In each specific measurement case, the specific electrical conductivity σ behaves proportionally to the current I under direct current stress according to Eq. (1).

$\sigma \sim I\!$

(1)

The resistance R of a homogeneous conductor with a constant cross-sectional area A is thus defined according to Eqs. (2) and (3).

$R={\frac {U}{I}}={\frac {1}{\sigma }}\cdot {\frac {I}{A}}$

(2)

$\sigma ={\frac {1}{R}}\cdot {\frac {I}{A}}$

(3)

Fig. 1:

Circuitry of the measuring capacitor for determining the surface resistivity

If the special design of the measuring capacitor is taken into account (Fig. 1), the following calculation Eq. (4) according to [4] applies (see: surface resistance), whose circuitry is analogous to the determination of the specific surface resistance [2–6].

$\sigma ={\frac {1}{R_{x}}}\cdot {\frac {g}{p_{o}}}$

(4)

where:	g	–	width of the protective gap
	po	–	specific surface resistance

However, in the case of semi-crystalline plastics, electrical conductivity also depends on the crystallite size of the plastic being examined [7].

Test method for determining electrical conductivity

In practice, conductivity is often used as a parameter to characterise electrostatic discharge (ESD) in order to verify the suitability of clothing and flooring for this work area by means of measurement. This is particularly important in microelectronics, as even minor electrostatic discharges can destroy electronic components. A certain conductivity must not be exceeded to prevent electrostatic charges from building up on equipment or components in industry and causing damage. In this case, electrical conductivity is determined according to Eq. (4) (see Fig. 2) [8].

Fig. 2:

Schematic measurement setup with voltage source, series resistor and megaohmmeter

See also

• Electrical strength
• Tracking
• Volume resistance
• Insulation resistance
• Creep current resistance

References

[1]	Rehahn, M.: Elektrisch leitfähige Kunststoffe: Der Weg zu einer neuen Materialklasse, Chem. Unserer Zeit 37 (2003) 1, pp. 18–30 DOI: https://doi.org/10.1002/ciuz.200390000
[2]	Schönhals, A.: Electrical and Dielectrical Properties. In: Grellmann, W., Seidler, S. (Eds.): Polymer Testing. Carl Hanser Munic (2022) 3. Edition, pp. 330–368 (ISBN 978-1-56990-806-8; e-book ISBN: 978-1-56990-807-5; ePub ISBN: 978-1-56690-808-2; see AMK-Library under A 22)
[3]	Recknagel, A.: Physik – Elektrizität und Magnetismus. Vol. 1, Verlag Technik, Berlin (1980)
[4]	DIN IEC 60093 (1993-12): Methods of Test for Insulating Materials for Electrical Purposes – Volume Resistivity and Surface Resistivity of Solid Electrical Insulating Materials (withdrawn; replaced by DIN EN IEC 62631-3-1 (2023-10); DIN EN IEC 62631-3-2 (2024-10))
[5]	DIN EN IEC 62631-3-1 (2023-10): Dielectric and Resistive Properties of Solid Insulating Materials – Part 3-1: Determination of Resistive Properties (DC Methods) – Volume Resistance and Volume Resistivity – General Method
[6]	DIN EN IEC 62631-3-2 (2024-10): Dielectric and Resistive Properties of Solid Insulating Materials – Part 3-2: Determination of Resistive Properties (DC Methods) – Surface Resistance and Surface Resistivity
[7]	Leute, U.: Elektrisch leitfähige Polymerwerkstoffe. Springer Fachmedien Wiesbaden (2015) doi. 10.1007/978-3-658-10539-6, ISBN 978-3-658-10538-9
[8]	DIN EN IEC 61340-5-1 (2025-06): Protection of Electronic Devices from Electrostatic Phenomena – General Requirements

Additional literature references

• Dhakal, K. N., Krause, B., Lach, R., Wutzler, A., Grellmann, W., Le, H. H., Das, A., Wießner, S., Heinrich, G., Adhikari, R.: Electrically conductive nanocomposites based on poly(lactic acid)/flexible copolyester blends with multiwalled carbon nanotubes]: J. Appl. Polym. Sci., 2022, 139, 51554
• Dhakal, K. N., Khanal, S., Krause, B., Lach, R., Grellmann, W., Lee, H. H., Das, A., Wießner, S., Heinrich, G., Pionteck, J., Adhikari, R.: Electrically conductive and piezoresitive polymer nanocomposites using multiwalled carbon nanotubes in a flexible copolyester: Spectroscopic, morphologicat, mechanical an electrical properties: Nano-Structures & Nano-Objects 29 (2022) 100806
• Dhakal, K. N., Lach, R., Grellmann, W., Krause, B., Piontek, J., Adhikari, R.: Piezoresitivity and strain-sensing behavior of poly (butylene adipate-co-terephthalate)/multiwalled carbon nanotube nanocomposites. Royal Society of Chemistry. RSC Advances (RSC Adv.) 14 (2024) 35715–35726 DOI: https://doi.org/10.1039/d4ra04826a