Protonic conductivity of polycrystalline materials evaluated with effective medium percolation approach: A case study on lithium-carboxylate based MOF

A model of random walk of protons previously proposed for the evaluation of conductivity data of polycrystalline metal-organic framework compound, lithium tetrahydrofuran-2,3,4,5-tetracarboxylate (LiTFTA), is reexamined using a percolation path approximation (PPA). PPA is a useful technique for analyzing electronic and ionic transports in inhomogeneous media and in this paper it is applied to interpret unclear effects encountered in the study of conductivity properties of LiTFTA measured in the form of a polycrystalline material. Random distribution of grain size produces dispersive conductivity, it means that ac conductivity of a polycrystalline sample depends on the frequency almost linearly, a phenomenon completely different from that observed in single crystals. The local conductance fluctuation due to the grain size variation is the origin of the dispersive conductivity. The frequency, at which dispersive loss occurs, is determined by macroscopic dielectric relaxation time but not by microscopic hopping time of protons. This reasoning leads to conductivity data analysis based on PPA, from which the values of conductivity inside the grains and at the interface of the grains can be determined. In addition, we were able to estimate the change of the density of the charge carriers in dependence on temperature, based on previously established idea of ionic diffusion.