charge‐transfer organic salts.
1.1.5.3.3 Conducting Polymers
The temperature dependence of the conductivity of conducting polymers is different because they are disordered systems. The charge transport is dominated by the interchain charge hopping. In general, the conductivity of conducting polymers follows the one‐dimensional variable range hopping model,
(1.17)
In terms of this model, the resistivity increases with the increasing temperature. The kT 0 value suggests the energy barrier for the charge hopping. It decreases with the increasing crystallinity. It is easy to confuse the charge hopping mechanism with the metallic band structure of conducting polymers. At high doping level, the conducting polymers can have energy band structure like metals. This picture is applicable for an individual chain. For a conducting polymer sample, the charge transport is dominated by interchain charge hopping.
Figure 1.16 Temperature dependence of the resistance of a PEDOT:PSS treated with H2SO4.
Source: Xia et al. [21]. © John Wiley & Sons.
However, semimetallic or metallic behavior, that is, the conductivity is insensitive to temperature or decreases with the increasing temperature, was reported on a few conducting polymers with high conductivity. For example, H2SO4 treatment can enhance the conductivity of a PEDOT:PSS film prepared from the Clevious PH1000 aqueous dispersion from ~0.2 S cm−1 to >3000 S cm−1 [21]. As shown in Figure 1.16, when the temperature is lower than 230 K, the temperature dependence of the resistance still follows the one‐dimensional variable range hopping model. Nevertheless, when the temperature is higher than 230 K, the thermal energy can overcome the energy barrier for the interchain charge hopping. As a result, the resistance becomes insensitive to temperature. This indicates semimetallic or metallic behavior. Metallic or semimetallic behavior was also observed on highly conductive polyaniline [27].
1.1.5.4 Conductivity of Composites
Some composites particularly the dispersion of inorganic nano‐fillers in polymer matrix can exhibit high thermoelectric properties [28, 29]. There can be three different structures for a two‐phase composite (Figure 1.17). The resistivity (ρ c) of the composites depends on the volume fractions and the resistivity of the two phases. When the two phases α and β are in series, the resistivity of the composite is given by,
Figure 1.17 Structures of a composite with two phases of α and β (a) in series, (b) in parallel, and (c) one phase dispersed in another phase.
(1.18)
where χ α and χ β are the volume fractions of the α and β phases, respectively, and ρ α and ρ β are the resisitivities of the two phases, respectively. The resistivity of the composite is dominated by the phase of higher resistivity.
When the two phases of α and β are parallel, the conductivity (σ c) of the composites is related to the conductivities of the two phases by the following equation,
(1.19)
The phase with higher conductivity will be the dominant one for the conductivity of the composite.
If a composite has a structure of the α phase dispersed in the β phase, the α phase is the dispersed phase and the β phase is the matrix. The resistivity of the composite depends on the relative resistivities of the two phases. If the α phase is more resistive than the β phase, ρ α > 10 ρ β, the resistivity of the composite is given by
(1.20)
If the α phase is less resistive than the β phase, ρ α < (1/10)ρ β, the resistivity of the composite is given by
(1.21)
The Seebeck coefficient of the composites is also related to the microstructure of the two phases. When the α and β phases are in series, the Seebeck coefficient (S c) of the composite is given by,
(1.22)
where S α and S β are the Seebeck coefficients of the α and β phases, respectively, and κ α and κ β are the thermal conductivities of the two phases, respectively. When the two phases are in parallel, the Seebeck coefficient of the composite is given by
(1.23)
1.1.6 Thermal Conductivity
The thermal conductivity (κ) of an electronic material include the lattice thermal conductivity (κ L) and the electronic thermal conductivity (κ e),
(1.24)