Curie–von Schweidler law

The Curie–von Schweidler law refers to the response of dielectric material to the step input of a direct current (DC) voltage first observed by Jacques Curie[1] [2] and Egon Ritter von Schweidler.[3]

Overview

According to this law, the current decays according to a power law:

${\displaystyle I\left(t\right)\propto t^{-n},}$

where ${\displaystyle I\left(t\right)}$ is the current at a given charging time, ${\displaystyle t}$, and ${\displaystyle n}$ is the decay constant such that ${\displaystyle 0<n<1}$. Given that the dielectric has a finite conductance, the equation for current measured through a dielectric under a DC electrical field is:

${\displaystyle I\left(t\right)=at^{b}+c,}$

where ${\displaystyle a}$ is a constant of proportionality, ${\displaystyle b}$ is the decay constant (i.e., ${\displaystyle b=-n}$), and ${\displaystyle c}$ is the intrinsic conductance of the dielectric. This stands in contrast to the Debye formulation, which states that the current is proportional an exponential function with a time constant, ${\displaystyle \tau }$, according to:

${\displaystyle I\left(t\right)\propto \exp \left\{-t/\tau \right\}}$.

The Curie–von Schweidler behavior has been observed in many instances such as those shown by Andrzej Ka Johnscher[4] and Jameson et al.[5] It has been interpreted as a many-body problem by Jonscher, but can also be formulated as an infinite number of resistor-capacitor circuits. This comes from the fact that the power law can be expressed as:

${\displaystyle t^{-n}={\frac {1}{\Gamma \left(n\right)}}\int _{0}^{\infty }\tau ^{-\left(n+1\right)}e^{-t/\tau }d\tau ,}$

where ${\displaystyle \Gamma \left(n\right)}$ is the Gamma function. Effectively, this relationship shows the power law expression to be equivalent to an infinite weighted sum of Debye responses.

References

1. Curie, Jaques (1889). "Recherches sur le pouvoir inducteur spécifique et sur la conductibilité des corps cristallisés". Annales de Chimie et de Physique. 17: 384–434.
2. Curie, Jaques (1889). "Recherches sur la conductibilité des corps cristallisés". Annales de Chimie et de Physique. 18: 203–269.
3. Schweidler, Egon Ritter von (1907). "Studien über die Anomalien im Verhalten der Dielektrika (Studies on the anomalous behaviour of dielectrics)". Annalen der Physik. 329 (14): 711–770. Bibcode:1907AnP...329..711S. doi:10.1002/andp.19073291407.
4. Jonscher, Andrzej Ka (1983), Dielectric Relaxation in Solids, Chelsea Dielectrics Press Limited, ISBN 978-0-9508711-0-3
5. Jameson, N. Jordan; Azarian, Michael H.; Pecht, Michael (2017). Thermal Degradation of Polyimide Insulation and its Effect on Electromagnetic Coil Impedance. Proceedings of the Society for Machinery Failure Prevention Technology 2017 Annual Conference.