A FREQUENCY-DEPENDENT CAPACITANCE MODEL AND ANALYSIS OF THE AC-IMPEDANCE OF CONDUCTING POLYANILINE FILMS

Impedance measurements were made of polyaniline-coated electrodes in sulfuric acid solution. The a.c. current vs. potential curve was sigmoidal although polyaniline involves a reversible redox couple. The susceptance and the conductance corrected for the solution resistance varied with the 1.1 and 1.4 powers of frequency respectively in the capacitive potential domain for frequencies less than 1 kHz. Microscopic mechanical dynamics of the conducting chains were thought to be responsible for the relaxation of the double layer capacitance. A model incorporating the dynamics is a two-dimensional array of straight conducting chains which interact electrostatically with each other in a randomly fluctuating viscous medium. It can be interpreted as a number of parallel conducting plates to which two potentials are applied. A plate experiences a coulombic force from the neighboring plates, a frictional force from the medium, and thermal fluctuations. Balancing these forces resulted in a Langevin equation. Linearization of the coulombic force was reduced to an equation of the Rouse model which consists of beads linked with springs. The initial and boundary value problem was solved using Fourier transformation to yield a time-dependent expression for the capacitance. A long-time approximation of the capacitance shows a linear relation with t(-1/2). This is an explanation of the frequency dependence pf the susceptance and the conductance. The frequency dependence is not due to conventional dielectric losses but is thought to belong to a cooperative phenomenon commonly observed in strongly interacting systems.