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

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 approximately 10(21) cm(-3), shows a Gaussian distribution of half width sigma approximately 170 meV, tentatively attributed to bipolaron formation energies.

Physical electrochemistry of nanostructured devices

“…In these situations there is a significant change in the concentration of carriers that can be interpreted as a change in the chemical potential (see for example ref. 54). Additionally changes may occur in the local electrostatic level associated with self-charging of the phase or interaction of the carriers.…”

“…82 When a thin film is voltage-scanned close to equilibrium, CV provides the DOS of the film material, as discussed later. 82,83 In electrochemical devices, the counterelectrode may require special properties, for example for storing a large amount of ions expelled from the active film. High-energy density of the Li battery necessitates, in addition to high specific capacity, that the difference in equilibrium potentials between positive and negative electrodes be large, so that both anode and cathode must be optimized.…”

“…This method has been applied in many works for investigation of DOS in conducting polymers, 54,91 quantum dots, 59 and porous semiconductors. 13,82,[92][93][94] The electrochemical determination of the (10), is exponential…”

“…In addition, the effect of the Gaussian disorder on the statistics of carriers has been described. 54 Fig . 11 shows the predictions of the model 54 for the chemical capacitance with the successive formation of P and B, in the presence of Gaussian disorder.…”

“…54 Fig . 11 shows the predictions of the model 54 for the chemical capacitance with the successive formation of P and B, in the presence of Gaussian disorder. Initially, at low oxidation potentials, only P are formed, but since the B energy is lower than that of two P (in this example), in the simulation the P readily recombine to form B.…”