Is Voltammetric Current Proportional to the Number of Transferred Electrons for Multi‐Charged Ions or to 3/2 Power of the Number?

Abstract

Particles with a large number of electrons to transfer, such as nanoparticles and colloidal redox particles, give voltammetrric currents that were demonstrated theoretically to be proportional directly to the number of the electrons, n, rather than to n 3/2 . The latter quantity is included in the conventional expression for voltammetric peak currents of multi-charge transfer processes. This apparent contradiction appears depending on whether the charge transfer occurs concurrently (n 3/2 ) or consecutively (n). The expression for the linear sweep voltammetric current was derived from a combination of the diffusion equation for large particles with n electrons and the Nernst equation for the n-time consecutive one-electron reactions at the electrode. The power in n for the peak currents, in several voltammetric techniques, was demonstrated to be ascribed to the convolution of the Nernst equation and the diffusion equation.

Voltammetric Determination of Both Concentration and Diffusion Coefficient by Combinational Use of Regular and Microelectrodes

“…However, for n ! 2 this equation is valid only for concomitant n-electron transfer reactions rather than successive nelectron transfer reactions [3]. There are very few examples of concomitant n-electron transfer reactions [24], whereas successive transfer reactions have often been found.…”

“…Mass-transfer controlled voltammetric currents depend on the concentration, c, of an electroactive species, its diffusion coefficient, D, and the number of electrons transferred, n, [1] in the form of their product, ncD x , [2] if n electrons are transferred sequentially [3], where x (x 1) is proper to electrochemical techniques as well as the mass transport mode. A value of n is often known or can readily be estimated, whereas D-values range widely, depending on the viscosity of solutions and hydrodynamic radii of the diffusing species.…”

Size-dependent efficiency of electron transfer at suspended ferrocenyl jumbo particles

“…We estimate the dependence of the peak current on the radii through the expression for the diffusion-controlled current of multi-electron transfer [17]:…”

“…Furthermore, an essential problem lies in the concept of which reaction actually occurs [17], R n M O n + ne À or n(R M O + e À ) even in equilibrium. More complications can be included in currents owing to not only translational diffusion of particles but also rotational diffusion [18], partial electron transfer of the redox sites on the particle surface in contact with an electrode [9,10], detachment of redox sites from particles [9], and charge transport within particles.…”

Voltammetric discrete current of polyaniline-coated latex particles at microelectrodes

“…3, revealing the proportionality. According to the theory for linear sweep voltammetry of multi-charged particles, the diffusion-controlled peak current density is expressed by [49] …”