STATISTICAL THERMODYNAMICS OF POLYNUCLEAR LINEAR COMPLEXES WITH MIXED-VALENCE STATES BY MEANS OF THE CORRELATED WALK

Expressions for the equilibrium electrode potential of linear N-nuclear complexes with homoredox centers were derived by the theory of the correlated walk as a function of the molar fraction of the oxidized moiety, the nearest-neighbor interaction energies and N. When the interaction energy was large in two-, three- and four-nuclear complexes, the expressions predicted two, three and four voltammetric peaks respectively owing to the formation of mixed valence states. The intuitive extension that the N-nuclear complex might exhibit N peaks was invalid. There were three peaks for any odd number of N. In contrast, four peaks appeared for any even number of N more than 4. For a polynuclear complex with N-->infinity, the number of the peaks was reduced to two, as if the complex might be a binucleus. The log plot for the fraction vs. potential curve at large values of N deviated from a straight line. The averaged inverse slope was ca. 90 mV at 25 degrees C. From the concentration distribution of a predominant species varying with the potential, the deviation of the log plot was ascribed to the coexistence of various isomers with different interaction energies. The difference in the voltammetric peak potential was approximately linear with the interaction energy for any N. Approximate equations for the potential difference for N = 2, 3 and 4 were obtained, and were applied to the experimental data available for polyferrocenes.