Free-volume model for ionic conductivity in polymers

Electrical conduction in polymers under a relatively low applied electric field is considered to be ionic and is affected strongly by the structural factors of the polymers. The following equation for the electrical conductivity σ was derived in which free volume V_f, jump energy E_j, and ionic dissociation energy W were taken into consideration: ${\mathrm{\sigma =\sigma }}_0\exp \left\{{\mathrm{-\hspace{0.17em}[\gamma \hspace{0.17em}V}}_i^{*}{\mathrm{/V}}_f{\mathrm{+(E}}_j{\text{+W/2ε)(kT)}}^{\text{−1}}]\right\}$ , where σ_o is a constant, γ the numerical factor to correct the overlap of free volume, $V_i^{*}$ the critical volume required for transport of an ion, ε the dielectric constant, k Boltzmann's constant, and T the absolute temperature. This equation describes well the conduction phenomena in polymethylmethacrylate, polystyrene, and an unsaturated polyester. Relationships between electrical conduction and free volume are discussed.