The conduction mechanism of PANI and its composite is consistent with the electron tunneling (ET) model up to 107[degrees]C, while it is consistent with the small polaron
tunneling (SPT) model above this temperature.
hopping (SPH) model: In the SPH model, the exponent s increases with increasing temperature [24, 33].
It is suggested that the electrical conductivity mechanism is small polaron
hopping process [18,19] following the equation
For example, to explain the conduction just above [T.sub.p], the variable range hopping (VRH) model has been suggested, while the small polaron hopping model is considered at temperatures beyond [[theta].sub.D]/2 (where 0D is the Debye temperature).
At the high temperature (T > [[theta].sub.D]/2), conductivity data are better fitted with the small polaron hopping (SPH) model.
A similar case was described by the Marcus-Emin-Holstein-Austin-Mott theory in various Ti[O.sup.2] minerals, where the hole also behaves as a small polaron
There are various theoretical models such as small polaron
tunneling (s increases with temperature), electron tunneling (s is independent of temperature), and CBH model (s decreases with temperature) that can provide explanation for ac conductivity [3, 4, 12, 13, 24, 26, 27].
where + and - signs correspond to hole and electron type of conductivity, [E.sub.s] is the activation energy for TEP, [alpha] is a constant and [alpha] < 1 suggests that the conductivity is small polaron
hopping, whereas for [alpha] > 2, conductivity is due to large polarons, and k is the Boltzmann constant.
Additionally, the incorporation of TM ion can be described by the mechanism of hopping of small polarons
among its different valence states, this polaron hopping mechanism depends greatly on the concentration of the doped TM ion.
Ranninger, "Dynamical properties of small polarons
," Physical Review B: Condensed Matter and Materials Physics, vol.
The presence of small polarons
is probable in solid materials with narrow conducting bands and large coupling constant .