Inappropriate Use of the Quasi-Reversible Electrode Kinetic Model in Simulation-Experiment Comparisons of Voltammetric Processes That Approach the Reversible Limit

Many electrode processes that approach the “reversible” (infinitely fast) limit under voltammetric conditions have been inappropriately analyzed by comparison of experimental data and theory derived from the “quasi-reversible” model. Simulations based on “reversible” and “quasi-reversible” models have been fitted to an extensive series of a.c. voltammetric experiments undertaken at macrodisk glassy carbon (GC) electrodes for oxidation of ferrocene (Fc^0/+) in CH₃CN (0.10 M (<i>n</i>-Bu)₄NPF₆) and reduction of [Ru­(NH₃)₆]³⁺ and [Fe­(CN)₆]^3– in 1 M KCl aqueous electrolyte. The confidence with which parameters such as standard formal potential (<i>E</i>⁰), heterogeneous electron transfer rate constant at <i>E</i>⁰ (<i>k</i>⁰), charge transfer coefficient (α), uncompensated resistance (<i>R</i>_u), and double layer capacitance (<i>C</i>_DL) can be reported using the “quasi-reversible” model has been assessed using bootstrapping and parameter sweep (contour plot) techniques. Underparameterization, such as that which occurs when modeling <i>C</i>_DL with a potential independent value, results in a less than optimal level of experiment-theory agreement. Overparameterization may improve the agreement but easily results in generation of physically meaningful but incorrect values of the recovered parameters, as is the case with the very fast Fc^0/+ and [Ru­(NH₃)₆]^3+/2+ processes. In summary, for fast electrode kinetics approaching the “reversible” limit, it is recommended that the “reversible” model be used for theory-experiment comparisons with only <i>E</i>⁰, <i>R</i>_u, and <i>C</i>_DL being quantified and a lower limit of <i>k</i>⁰ being reported; e.g., <i>k</i>⁰ ≥ 9 cm s^–1 for the Fc^0/+ process

A Comparison of Fully Automated Methods of Data Analysis and Computer Assisted Heuristic Methods in an Electrode Kinetic Study of the Pathologically Variable [Fe(CN)₆]^3–/4– Process by AC Voltammetry

Fully automated and computer assisted heuristic data analysis approaches have been applied to a series of AC voltammetric experiments undertaken on the [Fe­(CN)₆]^3–/4– process at a glassy carbon electrode in 3 M KCl aqueous electrolyte. The recovered parameters in all forms of data analysis encompass <i>E</i>⁰ (reversible potential), <i>k</i>⁰ (heterogeneous charge transfer rate constant at <i>E</i>⁰), α (charge transfer coefficient), <i>R</i>_u (uncompensated resistance), and <i>C</i>_dl (double layer capacitance). The automated method of analysis employed time domain optimization and Bayesian statistics. This and all other methods assumed the Butler–Volmer model applies for electron transfer kinetics, planar diffusion for mass transport, Ohm’s Law for <i>R</i>_u, and a potential-independent <i>C</i>_dl model. Heuristic approaches utilize combinations of Fourier Transform filtering, sensitivity analysis, and simplex-based forms of optimization applied to resolved AC harmonics and rely on experimenter experience to assist in experiment–theory comparisons. Remarkable consistency of parameter evaluation was achieved, although the fully automated time domain method provided consistently higher α values than those based on frequency domain data analysis. The origin of this difference is that the implemented fully automated method requires a perfect model for the double layer capacitance. In contrast, the importance of imperfections in the double layer model is minimized when analysis is performed in the frequency domain. Substantial variation in <i>k</i>⁰ values was found by analysis of the 10 data sets for this highly surface-sensitive pathologically variable [Fe­(CN)₆]^3–/4– process, but remarkably, all fit the quasi-reversible model satisfactorily

Aggregation of a Dibenzo[<i>b</i>,<i>def</i>]chrysene Based Organic Photovoltaic Material in Solution

Detailed electrochemical studies have been undertaken on molecular aggregation of the organic semiconductor 7,14-bis­((triisopropylsilyl)-ethynyl)­dibenzo­[<i>b</i>,<i>def</i>]­chrysene (TIPS-DBC), which is used as an electron donor material in organic solar cells. Intermolecular association of neutral TIPS-DBC molecules was established by using ¹H NMR spectroscopy as well as by the pronounced dependence of the color of TIPS-DBC solutions on concentration. Diffusion limited current data provided by near steady-state voltammetry also reveal aggregation. Furthermore, variation of concentration produces large changes in shapes of transient DC and Fourier transformed AC (FTAC) voltammograms for oxidation of TIPS-DBC in dichloromethane. Subtle effects of molecular aggregation on the reduction of TIPS-DBC are also revealed by the highly sensitive FTAC voltammetric method. Simulations of FTAC voltammetric data provide estimates of the kinetic and thermodynamic parameters associated with oxidation and reduction of TIPS-DBC. Significantly, aggregation of TIPS-DBC facilitates both one-electron oxidation and reduction by shifting the reversible potentials to less and more positive values, respectively. EPR spectroscopy is used to establish the identity of one-electron oxidized and reduced forms of TIPS-DBC. Implications of molecular aggregation on the HOMO energy level in solution are considered with respect to efficiency of organic photovoltaic devices utilizing TIPS-DBC as an electron donor material