Quantifying dielectric permittivities in the nonlinear regime

In contrast to the static dielectric permittivity, ϵ, associated with linear response, its high-field counterpart, ϵ E , is not a material specific quantity, but rather depends on the experimental method used to determine the nonlinear dielectric effect (NDE). Here, we define ϵ E in a manner consistent with how high field permittivities are typically derived from a capacitance measurement using high voltages. Based upon characterizing the materials nonlinear behavior via its third order susceptibility, χ 3, the relations between a given χ 3 and the observable ϵ E is calculated for six different experimental or theoretical approaches to NDEs in the static limit. It is argued that the quantity χ 3 is superior over ϵ E or the Piekara factor, (ϵ E - ϵ)/E 2, because it facilitates an unambiguous comparison among different experimental techniques and it provides a more robust connection between experiment and theory.