**1. Introduction**

Recently, the polymer film capacitors have received growing attention due to their advantages of a low cost, facile fabrication, excellent flexibility and high operating voltage [1]. To also attain high energy storage density, one employs nanosized inclusions with a high dielectric constant, thus increasing the effective dielectric permittivity of such polymer-based nanocomposites [2–5]. This can be performed, however, at the expense of a decrease in the capacitor breakdown strength [6–8] that diminishes to some extent the advantages of this approach.

To properly design nanocomposite capacitors, one needs a deep understanding of the factors which control the electrical breakdown in them. For relatively low volume fractions of inclusions, which do not create deep traps for electrons [9–13], the primary effect of their embedding is a modification of the electric field in the capacitor. Among different approaches which aim to account for this influence, only the Maxwell Garnett approximation [14,15] follows from first principles, while the other ones are rather phenomenological models (see, for example, a review of different models in Ref. [7]). This approximation treats the spherical inclusions as point dipoles with a dipole moment which is determined by the sphere polarizability. It is applicable, however, to composite media provided they extend throughout a space of dimensions which are much larger than the wavelength of the external field or to unbounded media in the static case. For a nanocomposite capacitor, this criterion is not fulfilled, and one must take into account the polarization of electrodes and, resulting from it, the image potential [16].

In the present paper, we develop a first-principles approach to the static electric field in a nanocomposite capacitor which is based on a rigorous account of the image potential for point dipoles between parallel metallic electrodes. The obtained results are used to find the parameters which characterize the electrical breakdown in a nanocomposite capacitor.

**Citation:** Bordo, V.; Ebel, T. Theory of Electrical Breakdown in a Nanocomposite Capacitor. *Appl. Sci.* **2022**, *12*, 5669. https://doi.org/ 10.3390/app12115669

Academic Editor: Alberto Vomiero

Received: 19 May 2022 Accepted: 31 May 2022 Published: 2 June 2022

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The predicted dependencies are compared with the available experimental data on the breakdown field strength as a function of the volume fraction of inclusions and temperature.
