# Electrical breakdown and ultrahigh electrical energy density in poly(vinylidene fluoride-hexafluoropropylene) copolymer

[Edited by Jianyu Li for AP 225, fall, 2010.]

## Summary

The paper reports a new method to predict the electrical breakdown of poly(vinylidene fluoride-hexafluoropropylene). This polymer exhibits an extraordinary capability to store electrical energy, with a series of lower electrical breakdown strength than the prediction by the conventional Stark-Garton electromechanical breakdown model. Its curves of discharged energy density and breakdown strength-temperature are illustrated in the figure 1, . The figure 1b shows that the breakdown strength tends to decreases with temperature increasing, the prediction curve from Stark-Garton model is well above the experimental result, while the new model matches it perfectly. Experiments also demonstrated its thickness independence, combined with the temperature dependence, the authors concluded there is a certain correlation between the Young's modulus and the dielectric constant.

## Summary of Theory

The difference behind the two model lies on the consideration of potential plastic deformation. The authors claim that Stark-Garton model overestimates the breakdown strength, because it mistakenly assumes the deformation is purely elastic, which follow the elastic stress-strain relastionship <math>Yln(d_0/d)</math> where Y represents the Young's modulus, <math>ln(d_0/d)</math> refers to the true stain. What's worse, the model simply ignores the potential plastic deformation, leading the failure to occur below the critical stress. To improve the model,the authors gave up the elastic model and used the power law relation instead. It goes like <math>\sigma=Ke^N=K(log\frac{d_0}{d})^N</math>. When N=1, we have K equal Y which is the linear elastic relation. By contrast, N=0, an ideal plasticity occurs. Based on this new model, the predicted result is improved, reflected in the better fitting result of the experimental curves, as showed in the figure 3