Potential dependence of polaron and bipolaron densities in conducting polymers: theoretical description beyond the Nernst equations

The charged species in most conducting polymers are polarons (P) and bipolarons (BP) (eventually transverse or interchain bipolarons), The electrochemical behaviour of such systems is determined (apart from kinetics) by the dependence of the P and BP densities on the electrochemical potential and on the temperature. Until now a statistics for the high density-limit (needed for high degrees of oxidation) was not known. We present here a novel approximation for finite temperatures which contains exactly both the low-density (non-degenerate) limit and the zero temperature limit. Our result can be expressed in terms of conventional Nernst equations describing oxidation by two one-electron steps, followed by thermodynamic equilibrium. This equivalence yields the connection between the two standard potentials and the formation energies and degeneracy factors of P's and BP's. For high densities we approximate the dependence of the P and BP formation energies on the densities by few-parameter interpolations based on numerical results of the discrete Brazovskii-Kirova model for polymers with a non-degenerate ground state. The theory yields a consistent description for typical experimental observations which are in complete disagreement with the conventional Nernst equations. The most important facts we describe correctly are: In a region of several hundreds mV above the CV-peak one has a capacitive current plateau with a volume-proportional capacitance of the order of 100 Fcm(-3) and a small and almost constant charge transfer resistance; the spin concentration shows an asymmetric peak, with a considerable spin concentration in the plateau region, These features arise from increase of the standard potentials with increasing degree of oxidation in our theory, owing to the increase of the P and BP formation energies at high densities. (C) 1998 Elsevier Science B.V.