Flexible Thermoelectric Polymers and Systems. Группа авторов

increased through post treatment. As a result, the conductivity can be enhanced by several orders of magnitude. When a chemical is used for the post treatment, the post treatment method is usually called “secondary doping.” Secondary doping has been extensively reported for solution‐processable conducting polymers including polyaniline and PEDOT:PSS [15–19]. Polyaniline doped with a large counter anion like camphorsulfonic acid (HCSA) can be dispersed in organic solvent such as m‐cresol and chloroform [20]. The solvent significantly affects the crystallinity and the conductivity of polyaniline:HCSA (PANi:HCSA) because it can affect the conformation of the polymer chains in solution. When a PANi:HCSA film is prepared from chloroform, its conductivity is only 10⁻¹ S cm⁻¹, while it can be >100 S cm⁻¹ when it is obtained from m‐cresol. This difference in conductivity is attributed to the effect of the solvents on the crystallinity of polyaniline. As shown in Figure 1.14, there is a strong absorption in the infrared range for the PANi:HCSA film cast from its m‐cresol solution [15]. This suggests a high crystallinity and the delocalization of the charge carrier. Instead, only a band appears in the near infrared (NIR) range when chloroform is used as the solvent. This is consistent with the low crystallinity.

Figure 1.14 UV–visible–NIR absorption spectra of PANi:HCSA films casted from solutions with (a) m‐cresol or (b) chloroform as the solvent, respectively.

      Source: MacDiarmid and Epstein [15]. © Elsevier.

Figure 1.15 Conductivity of PEDOT:PSS after secondary doping with H₂SO₄.

      Source: Xia et al. [21]. © John Wiley & Sons.

      A couple of secondary doping methods were also reported for PEDOT:PSS. PEDOT:PSS can be dispersed in water [17–19]. The conductivity of an as‐prepared PEDOT:PSS film is only 10⁻¹ S cm⁻¹, and it can be significantly enhanced by secondary doping. The chemicals for the secondary doping can be organic solvents like dimethyl sulfoxide (DMSO), ethylene glycol (EG) and even methanol, cosolvent of water and organic solvents, aqueous or organic solutions, ionic liquids, and acids. Particularly, the conductivity of PEDOT:PSS can be enhanced from 10⁻¹ S cm⁻¹ to higher than 3000 S cm⁻¹ through a post acid treatment [21–24]. The conductivity enhancement is ascribed to the partial removal of the insulating PSSH from PEDOT:PSS and the conformational change of PEDOT from coil to expanded‐coil or linear structure. Less PSSH chains and linear PEDOT conformation can lead to high crystallinity and thus high conductivity.

      Mechanical stretching can orient polymer chains along the tensile direction and thus increase the crystallinity. It has been used to increase the conductivity of conducting polymers as well [25, 26]. For example, it can increase the conductivity of polyacetylene up to 10⁵ S cm⁻¹.

      1.1.5.3 Temperature Dependence of Conductivity

Temperature dependence of the conductivity is often used to study the charge transport mechanism because metals and semiconductors have different temperature dependences of their conductivity. Conducting polymers are considered as disordered systems. Their charge transport is dominated by interchain charge hopping, that is different from those of both metals and semiconductors.

       1.1.5.3.1 Metals

      The temperature dependence of the conductivity is related to the charge transport mechanism. Varying the temperature does not affect the charge carrier density but the charge carrier mobility of metals. As the lattice vibrations become stronger at higher temperature, the scattering of the conduction electrons by lattice vibrations becomes more significant at higher temperature. This lowers the charge carrier mobility. The conductivity of metals thus decreases with the increasing temperature. There are two empirical formulas for the temperature dependence of the resistance of metals. One is the power law form,

      (1.15)

      The resistivity (ρ) at temperature (T) is related to the resistivity (ρ ₀) at the reference temperature (T ₀). The resistivity linearly increases with temperature in another form, and the temperature effect is characterized by the temperature coefficient of resistivity (α ₀),

      (1.16)

      In both forms, the resistivity of metals increases with the increasing temperature.

       1.1.5.3.2 Semiconductors

The temperature dependence of the conductivity of semiconductors is quite different from metals. The temperature can affect both the charge carrier density and the charge carrier mobility of semiconductors. There are three temperature ranges in terms of the temperature effect on the charge carrier density. At the low temperature range below the saturation temperature (T _s), the thermal energy is less than the ionization energy of the doping atoms. As a result, not all the doping atoms ionize. The electron (or hole) density in the conduction band (or valence band) depends on the thermal excitation of the electrons (or holes) from the dopant to the conduction band (or valence band). The charge carrier density increases with the increasing temperature. In the medium temperature of T _s < T < T _i with T _i being the intrinsic temperature, the thermal energy is high enough for the ionization of all the dopants, but it is lower than the energy bandgap between the valence band and the conduction band. The charge carrier density equals the dopant density, and it is constant in this temperature range. At the high temperature range of T > T _i, the thermal energy can excite the electrons from the conduction band to the valence band. This produces electrons in the conduction band and holes in the valence band. In this high temperature range, both the electron and hole densities increase with the increasing temperature.

      There are two temperature regimes for the temperature dependence of the charge carrier mobility of semiconductors. At low temperature regime, the ionized impurities are the charge carrier scattering centers. In this temperature range, the charge carrier mobility increases with the increasing temperature because the scattering area decreases. At high temperature, the scattering by the lattice vibration becomes the dominant factor for the charge carrier mobility. Similar to metals, the charge carrier mobility decreases with the increasing temperature in the high temperature regime.

      Therefore, the temperature dependence of the conductivity of semiconductor is more complicated than that of metals. At low and high temperature range, the conductivity of semiconductor increases with the increasing temperature. The conductivity can be less sensitive to the temperature or even decrease in the medium temperature range.

      The temperature dependence of the conductivity is usually used to determine whether a conductor is metallic or semiconductive. In general, if the conductivity decreases with the increasing temperature, it is metallic. In contrast, if the conductivity increases with the increasing temperature, it is considered as semiconductive behavior. This is also frequently used to judge the charge transport mechanism of non‐conventional