Numerical modelling of impedance spectra of ionic conductor–insulator core–shell composites

Impedance spectra of ionic conductor–insulator core–shell composites are simulated in Cole–Cole and Bode representation using a 3D lattice of parallel resistance–capacitance elements. The composite model is based on a random ternary network, considering three impedance elements: good conductor (representing interface regions), conductor and insulator. The favourable interactions between the two phases lead to a significant non-random situation versus usual percolation models. Two percolation transitions are well observed: the first corresponds to ionic conduction enhancement by space charge layers. After the second transition, the conduction pathways are blocked by the insulator and the conductivity drops dramatically. Experimental impedance spectra of model copper- and lithium-ion conducting composites and nanocomposites are in good agreement with the simulation. The dc conductivity maximum can be described by a master equation: σmax ∼ N−0.79 where N is proportional to the ionic conductor grain size