Ionic conduction in solids: Comparing conductivity and modulus representations with regard to scaling properties

In the literature, the electric modulus representation has been used to provide comparative analysis of the ion transport properties in different ion-conducting materials. In this paper we show that the modulus representation is not a suitable tool for such purposes. Our arguments derive from an examination of the scaling properties of both the ac conductivity ${\ensuremath{\sigma}}^{*}(\ensuremath{\nu})$ and the modulus ${M}^{*}(\ensuremath{\nu})$ which demonstrates how scaling that is inherent in ${\ensuremath{\sigma}}^{*}(\ensuremath{\nu})$ is lost in ${M}^{*}(\ensuremath{\nu})$ by inclusion of the high frequency permittivity ${\ensuremath{\varepsilon}}^{\ensuremath{'}}(\ensuremath{\infty}),$ the latter quantity being unrelated to ion transport processes. Furthermore, we show how highly regarded shape changes of the modulus that occur with varying ion concentration are merely a manifestation of including ${\ensuremath{\varepsilon}}^{\ensuremath{'}}(\ensuremath{\infty})$ in the definition of ${M}^{*}(\ensuremath{\nu}).$ We conclude then that the electric modulus formalism has resulted in misleading interpretations of the ion dynamics and, hence, should be discouraged.