Understanding hopping transport and thermoelectric properties of conducting polymers

We calculate the conductivity $\ensuremath{\sigma}$ and the Seebeck coefficient $S$ for the phonon-assisted hopping transport in conducting polymers poly(3,4-ethylenedioxythiophene) or PEDOT, experimentally studied by Bubnova et al. [J. Am. Chem. Soc. 134, 16456 (2012)]. We use the Monte Carlo technique as well as the semianalytical approach based on the transport energy concept. We demonstrate that both approaches show a good qualitative agreement for the concentration dependence of $\ensuremath{\sigma}$ and $S$. At the same time, we find that the semianalytical approach is not in a position to describe the temperature dependence of the conductivity. We find that both Gaussian and exponential density of states (DOS) reproduce rather well the experimental data for the concentration dependence of $\ensuremath{\sigma}$ and $S$ giving similar fitting parameters of the theory. The obtained parameters correspond to a hopping model of localized quasiparticles extending over 2--3 monomer units with typical jumps over a distance of 3--4 units. The energetic disorder (broadening of the DOS) is estimated to be 0.1 eV. Using the Monte Carlo calculation we reproduce the activation behavior of the conductivity with the calculated activation energy close to the experimentally observed one. We find that for a low carrier concentration a number of free carriers contributing to the transport deviates strongly from the measured oxidation level. Possible reasons for this behavior are discussed. We also study the effect of the dimensionality on the charge transport by calculating the Seebeck coefficient and the conductivity for the cases of three-, two-, and one-dimensional motion.