Test of the Anderson–Stuart model and correlation between free volume and the ‘universal’ conductivity in sodium silicate glasses

Abstract

Experimental ionic conductivity σ and activation energy E A data in the binary sodium silicate system are reviewed. Analysis and brief discussion based on 48 glasses in a wide compositional range (between 4 and 45 Na2O mol%) are presented. Emphasis is placed on the application of the Anderson–Stuart model to describe the variation of activation energy E A with sodium concentration. In this analysis were considered experimental parameters such as shear modulus G and relative dielectric permittivity e, also in wide compositional range. A ‘universal’ finding is obtained using log10σ vs. E A/k B T in 47 of the 48 glasses investigated, where E A is the activation energy for conduction, k B is the Boltzmann constant and T is the absolute temperature. Using conductivity and molar volume from density data, both measured at 20 °C in the same glasses, it was found a remarkable common cubic scaling relation between conductivity enhancement of the free volume due to increase in alkali content. The drastic drop in conductivity by 16 orders of magnitude for so many ion-conducting binary sodium silicate glasses is then caused by structure and ion content. The effects of shear modulus, relative dielectric permittivity and free volume are taken into account, as also the problem of phase separation. In particular, it is suggested that the glass network expansion, which is related to the available free volume, is a parameter that could partially explain the increase in ionic conductivity for this binary system.