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Chapter 3. Characterisation Methods potential cannot be measured directly in a straightforward way, but can be determined from the half-wave potential E1/2 (which is introduced in the next section): ′ RT D1/2 E0 =E1/2+ ln Ox (3.3) where D is the diffusion coefficient. It follows that, for a redox couple with similar diffusion coefficients, E0′ ∼ E1/2. For practical purposes and unless otherwise stated, it is assumed in this work that the redox potential of a redox couple is equal to its half-wave potential. For a system at equilibrium, the net current that flows between electrode and electrolyte is 0. At any point away from equilibrium, a net positive or negative current flows, depending on the overpotential η, which is the difference between the applied and formal potential: η = E − E0′ The current-overpotential relation takes on the form cOx(0, t) αnF cRed(0, t) (1−α)nF i=i0 c∗ e−RTη−c∗ eRT η Ox Red (3.4) (3.5) nF D1/2 Red where i is the current density, i0 is the exchange current density, c(0,t) is the surface concentration at time t, c∗ is the bulk concentration, and α is the transfer coefficient. The exchange current density is the current that flows in both directions when the system is at equilibrium (and therefore resulting in a net current of 0) and is given as: i =nFk0c∗(1−α)c∗α (3.6) 0 OxRed where k0 is the standard rate constant. For a well-stirred solution where the surface concentrations are close to the bulk concentrations, Equation 3.5 simplifies to i = i e−αnF η − e(1−α)nF η (3.7) 0RT RT which is known as the Butler-Volmer equation. This equation can, among others, be used to evaluate the symmetry of the energy barrier of electrochemical reactions, which is represented by α that takes on values from 0 to 1. A fully symmetric reaction results in α = 0.5. This evaluation can be done by graphical inspection of the symmetry of current-overpotential curves, such as the ones shown in Figure 3.1. 3.2 Cyclic voltammetry One of the commonly used electrochemical techniques for initial diagnostics of redox- active compounds is cyclic voltammetry (CV). CV is a linear sweep technique where the electrode potential is scanned between two switching potentials at a controlled potential scan rate ν while the current is recorded. This results in a cyclic voltammogram, which carries information about system reversibility, diffusion behaviour, redox potentials, con- centrations, and surface capacitance. A generic potential-time profile and voltammogram 20PDF Image | Organic Redox Flow Batteries 2023
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