POTENTIAL DEPENDENCE OF POLARON AND BIPOLARON DENSITIES IN CONDUCTINGPOLYMERS - THEORETICAL DESCRIPTION BEYOND THE NERNST EQUATIONS

The charged species in most conducting polymers are polarons (P) and b ipolarons (BP) (eventually transverse or interchain bipolarons), The e lectrochemical behaviour of such systems is determined (apart from kin etics) by the dependence of the P and BP densities on the electrochemi cal potential and on the temperature. Until now a statistics for the h igh 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 z ero temperature limit. Our result can be expressed in terms of convent ional Nernst equations describing oxidation by two one-electron steps, followed by thermodynamic equilibrium. This equivalence yields the co nnection between the two standard potentials and the formation energie s and degeneracy factors of P's and BP's. For high densities we approx imate the dependence of the P and BP formation energies on the densiti es by few-parameter interpolations based on numerical results of the d iscrete Brazovskii-Kirova model for polymers with a non-degenerate gro und state. The theory yields a consistent description for typical expe rimental observations which are in complete disagreement with the conv entional Nernst equations. The most important facts we describe correc tly 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 trans fer resistance; the spin concentration shows an asymmetric peak, with a considerable spin concentration in the plateau region, These feature s arise from increase of the standard potentials with increasing degre e of oxidation in our theory, owing to the increase of the P and BP fo rmation energies at high densities. (C) 1998 Elsevier Science B.V.