• Kontogeorgis, Georgios M.
• Liang, Xiaodong
• Silva, Gabriel M.

Abstract

In this work we present Hückel’s original derivation and considerations, verifying the approximations that were done in his paper. More complex equations are obtained by not applying some of Hückel’s approximations, and these equations are compared to the original Hückel equation. We explore the use of both a linear and an experimental concentration dependency of the relative permittivity to represent experimental data. We show that Hückel’s equation, as known today in its semi-empirical form, is not the full model or even the approximate model the author had derived in his original work, being only an approximation of his full theoretical method. Both the original Hückel equation, and the equation used in literature, represent important developments when compared to the original Debye-Hückel equation. We also show that Hückel had already derived and used the Born term in his work, clarifying thus the connection between the Hückel equation and the Born term. Finally, we derive different equations from Hückel and estimate the error introduced by his method of considering the concentration-dependency of the dielectric constant only after deriving the charge work.

Topics

• impedance spectroscopy
• dielectric constant