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

Abstract

Experimental ionic conductivity r 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 Na 2 O 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 log 10 r 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 ionconducting 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.

Structural investigation of amorphous Na2O–P2O5–B2O3 correlated with its ionic conductivity

“…(12) we can think of sodium ion mobility in terms of the energy it needs to leave one charge compensating site and "hop" to another site with an activation energy E a . Anderson and Stuart [49] proposed that the activation energy consisted of the energy required to move the ion from one charge compensating site to another E b [50] and the energy required to deform the network structure by generating a hole large enough for the ion to pass through, E s [49], known as the electrostatic binding and strain energy, respectively. The binding energy is described by the sum of the forces of Coulomb acting on the ion as it moves away from its charge-compensating site.…”

Ionic transport in mixed-alkali glasses: hop through the distinctly different conduction pathways of low dimensionality

“…If the mobile ions in the DLCA percolation cluster hop to an adjacent cluster after moving through the first branch of the fractal structured pathway, then we may obtain the power-law exponent β = 0.76 in equation (19). This is because the fractal dimension of DLCA is D f = 1.75 and β = 1 − α = 4 3 − 1 D f for the ions in the first branch in the pathway.…”

“…The values of power-law exponent β fitted from equation (19) x = 0.5, respectively (see table 1). As shown in figures 5(a) and (b), the power-law exponent β increases with increasing temperature at relatively lower ranges of temperature in the SA glass but it shows a nearly independent trend with temperature in the MA with x = 0.5 glasses, even Table 1.…”

“…The experimental conductivity data for the SA glasses and the MA glasses have been fitted to equation (18), which is a Jonscher fit of ac conductivities. The hopping rates are obtained from the conductivity spectrum in equation (19) by the substitution (σ (ω h ) = 2σ dc ), and the other parameters, σ dc , K and β, are determined by linear least-squares fitting procedures. E ac (1) is equal to E ac (x = 0) or E ac (x = 1), and E ac (2) is the same as E ac (x = 0.5).…”

“…where A 1 and B 1 are constants, σ exp is the experimentally determined conductivity, T is the temperature, M is the mass of a cation, E A is the activation energy and k B is the Boltzmann constant. The correlation between the free pathway volume, F, and the electrical conductivity was also tested for binary sodium silicate glasses [19].…”