Application of Heywang model to the apparent PTCR effect in water-adsorbing layered materials

Surface proton/hydroxide conduction predominates at ambient conditions prior to levelling off at elevated temperatures due to water evaporation and subsequent loss of charge carriers. This water-induced charge transport results in the “apparent” positive temperature coefficient of resistivity (PTCR) effect. Herein, we show that Heywang model typical of classical ferroelectric PTCR ceramics is applicable to a wide range of water-adsorbing layered materials (0.17–4.76 wt% H 2 O). Several examples include layered alkali titanates with negatively-charge sheets; one van der Waals material (g‒C 3 N 4 ) with neutral sheets; and a NiFe layered double hydroxide with positively-charge sheets. The linear log ρ DC vs ( ε ′ DC T ) -1 plots ( ρ DC = static resistivity, ε ′ DC = static dielectric permittivity, and T temperature) are observed from 25 to 250 °C where resistivity and dielectric permittivity varied up to five orders of magnitude. Using Cs 2 Ti 6 O 13 as a representative sample, the density of acceptor states at the grain boundary N s (the exact nature to be elucidated) is ∼10 10 -10 11 cm -2 , slightly dependent on the heating/cooling rates (0.5, 2 and 5 °C·min -1 ). Complex plane analyses show that capacitances at grain/grain boundaries alike are constant regardless of temperatures, but resistances in both cases peak at 150–200 °C. While rigorous theoretical basis is yet to be constructed, the observed linearity suggests that there could be a common foundation between these two classes of PTCR materials which have been treated separately so far. The linear log ρ DC vs ( ε ′ DC T ) -1 plots ( ρ DC = static resistivity, ε ′ DC = static dielectric permittivity, and T temperature) are observed in many layered materials, following Heywang model typical of classical PTCR ceramics. • Successful demonstration of conformity to Heywang model in many water-containg layered materials. • Examples include many metal oxides, one Ni 2.8 FeLDH, and g-C 3 N 4 . • Effects of heating/cooling rates and frequency are examined.