Effects of the Gaussian energy dispersion on the statistics of polarons and bipolarons in conducting polymers

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Abstract
We discuss the interpretation of usually broad oxidation peaks observed in electronically conducting polymers, in terms of the statistical distributions functions of polarons and bipolarons. The analysis is based on examining the chemical capacitance, that relates the change of concentration to a modification of the chemical potential of a given species, for different statistical models. We first review the standard models for single energy species that provide a nernstian dependence, and the limitations of these models are discussed. A new model that assumes a Gaussian distribution of energies related to molecular geometry fluctuations is suggested, and this model shows excellent agreement with the results of electrochemical oxidation of polypyrrole in quasiequilibrium conditions. From a fit of the data, it is found that the density of conjugated chain segments in polypyrrole, Ns≈1021 cm−3, shows a Gaussian distribution of half width σ≈170 meV, tentatively attributed to bipolaron formation energies.