Molecular theory of chemically modified electrodes by redox polyelectrolytes under equilibrium conditions: Comparison with experiment

A molecular theory is presented to describe chemically modified electrodes by redox polymers. The theory is based on writing the free energy functional of the system which includes the size, shape, charge distribution, and conformations of all of the molecular species as well as all of the inter and intramolecular interactions, the acid-base equilibrium for the ionizable groups of the weak polyelectrolyte, and the redox equilibrium of the electrochemical active sites with the metal. The minimization of the free energy leads to the molecular organization of the film as a function of bulk pH, salt concentration, and applied electrode potential. The approach is applied to the experimental system composed by osmium pyridine-bipyridine complex covalently bound to poly(allylamine) backbone, which is adsorbed onto a mercapto-propane sulfonate thiolated gold electrode. The redox and nonredox capacity of the electrode and its dependence on the electrode potential calculated with the molecular theory shows very good agreement with linear scan voltammetric experiments under reversible conditions (equilibrium scans) without the use of any free adjustable parameter. The predicted film thickness is in line with ellipsometric measurements. Further, the theory predicts the swelling of the film as a function of the electrode potential. The molecular theory provides the link between the molecular organization within the film and the electrochemical behavior. It is shown that the electrostatic, excluded volume, and van der Waals interaction fields are strongly coupled in a nontrivial way. Furthermore, the degree of charge regulation and distribution of oxidized states couples to the molecular distributions and the interaction fields. The application of the theory to different model systems demonstrates the importance of incorporating molecular information into the theoretical approach and the very strong coupling that exists between molecular structure, film organization, interactions fields, and electrochemical behavior.