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New concept of electret-based capacitance, as shown for solder and other conductors

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A Correction to this article was published on 28 November 2022

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Abstract

An electret refers to a permanent electric dipole. Nonconductive electrets (polymers and ceramics) have long been studied and utilized, but conductive electrets (metals and carbons) are emerging. This paper introduces the concept of the electret-based capacitance C′ to elucidate the discharge behavior of conductive electrets in the form of unpoled solder and other conductors (metals). The C′ is defined as the electret charge Q′ (determined by integrating the discharge curve) divided by the DC electret voltage V′. The conventional permittivity-based capacitance C (measured) is lower than C′ by orders of magnitude. For Sn–4Ag lead-free solder, C′ (given by Q′/V′) is 620 F, whereas C is 175 pF. The electret stems from the interaction of a small fraction of the carriers (free electrons) with the atoms, as supported by DC polarization asymmetry. For Sn–4Ag, this fraction is 3.5 × 10–9. Electret discharge (V′ decreasing to zero) occurs upon short circuiting. Self-charge (V′ restored) occurs upon subsequent open circuiting, being slightly more sluggish than discharge. The electret discharge/charge amounts to discharge/charge of C′. The discharge/charge time constant is found to approximately equal RC′ (R = resistance) and the discharge/charge energy is found to approximately equal ½ C′V′2, as expected for the discharge/charge of C′ and shown for Sn–4Ag, copper (0 and 37% cold work) and low-carbon steel. This two-fold agreement between theory and experiment for each of the metals studied strongly supports the C′ concept. Strong correlation occurs among high fraction of carriers that participate, high participating charge density and high discharge time constant.

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Data and material are available by contacting the corresponding author.

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Change history

Abbreviations

C :

Capacitance stemming from the permittivity

C ′ :

Capacitance stemming from the electret

Q :

Charge magnitude associated with the capacitance stemming from the permittivity

Q ′ :

Charge magnitude associated with the capacitance stemming from the electret

V :

Voltage applied to cause the charge stemming from the permittivity

V ′ :

Inherent voltage in the electret

V 1 ′ :

Inherent voltage in the electret, obtained without polarity removal

V 2 ′ :

Inherent voltage in the electret, obtained after polarity removal, being opposite in sign from V1′

J ′ :

Current density (current per unit area) in the electret

J 1 ′ :

Current density (current per unit area) in the electret, based on V1′

J 2 ′ :

Current density (current per unit area) in the electret, based on V2′, being opposite in sign from J1′

E :

Electric field applied to cause the charge stemming from the permittivity.

E ′ :

Inherent electric field in the electret

E 1 ′ :

Inherent electric field in the electret, based on V1′

E 2 ′ :

Inherent electric field in the electret, based on V2′, being opposite in sign from E1′

P :

Power density (i.e., power per unit volume) stemming from the permittivity

P ′ :

Power density (i.e., power per unit volume) stemming from the electret

l :

Inter-electrode distance, which is the proximate distance between two electrodes

A :

Cross-sectional area of the specimen in the plane perpendicular to the capacitance, voltage or resistance

R :

Resistance

ρ :

Resistivity

κ :

Relative permittivity

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Funding

The authors declare that no funds, grants, or other support were received during the preparation of this manuscript.

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Authors and Affiliations

  1. Composite Materials Research Laboratory, Department of Mechanical and Aerospace Engineering, University at Buffalo, The State University of New York, Buffalo, NY, 14260-4400, USA

    D. D. L. Chung & Xiang Xi

  2. College of Mechanics and Materials, Hohai University, Nanjing, 211100, China

    Xiang Xi

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  1. D. D. L. Chung
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Contributions

DDLC provided the study conception and design. Material preparation, data collection and analysis were performed by XX. The first draft of the manuscript was written by DDLC and both authors commented on previous versions of the manuscript. Both authors read and approved the final manuscript.

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Correspondence to D. D. L. Chung.

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Chung, D.D.L., Xi, X. New concept of electret-based capacitance, as shown for solder and other conductors. J Mater Sci: Mater Electron 33, 27022–27039 (2022). https://doi.org/10.1007/s10854-022-09366-4

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