High proton conductivity at low and moderate temperature in a simple family of Prussian blue analogs, divalent transition metal hexacyanocobaltates (III)

Control of Proton‐Conductive Behavior with Nanoenvironment within Metal–Organic Materials

“…activation energies below 0.21 eV. [55] This trend actually was similar to the quantity of adsorbed water molecules rather than the Lewis acidity of the metal components, indicating that the number of defective sites would significantly affect their conducting properties. Conventionally, the arrangement of vacancies in these Perovskite Blue analogs was believed to be random.…”

The Debye length and anionic transport properties of composite membranes based on supported ionic liquid-like phases (SILLPS)

“…In this work we assume that the contribution of the conductivity at low frequencies is generally due to impurities, and it can be omitted. Secondly, when the Maxwell-Wagner-Sillars (MWS) conditions are accomplished (i.e., when the bulk conductivity dominates as for a pure ohmic conduction at high frequencies), then e 00 (o,T) = s dc (o,T)/e 0 o, and the loss tangent, tan d = e 00 /e 0 , can be expressed as follows 25,42,50…”

“…where the relaxation time obtained as t m represents a time constant, which is related with the electrode polarization time relaxation t EP , and to the sample relaxation time t through the equation t m 2 = tÁt EP . 25,38,42,50 Furthermore, the parameter M also defined as 38 can be expressed for a Cole-Cole model in the form:…”

“…Both the L D and the charge density experience abrupt changes with temperature, depending significantly on the involved transition metal. 50 The effective Debye length associated with this kind of membranes, can play a key role to rationalize the observed behavior. As mentioned earlier, the values for M have been used Finally, when the values of the inverse Debye length can be obtained from the peaks of the loss tangent, the values of static permittivity e s or e N , can be estimated from an indirect method following eqn (6).…”

“…In this work we assume that the contribution of the conductivity at low frequencies is generally due to impurities, and it can be omitted. Secondly, when the Maxwell–Wagner–Sillars (MWS) conditions are accomplished (i.e., when the bulk conductivity dominates as for a pure ohmic conduction at high frequencies), then ε ′′( ω , T ) = σ dc ( ω , T )/ ε 0 ω , and the loss tangent, tan δ = ε ′′/ ε ′, can be expressed as follows 25,42,50 with M = Δ ε EP / ε ∞ and Δ ε EP = ε − ε ∞ , where ε is the dielectric constant, ε ∞ is the static permittivity, τ EP is the electrode polarization relaxation time, and the parameter α gives us the indication of a cumulative process in the system as a consequence of the interactions among charge carriers.…”