# Cyclic Voltammetry

The cyclic voltammetry is an analytical technique used to analyze electrochemical systems. The method involves a linear sweep over time of the potential difference between a working electrode and a reference potential from a potential start vertex, and vice versa. The resulting current in the working electrode is plotted against the potential in a voltammogram. The information, on both the electrochemical reactivity and transport properties of an electrochemical system can be obtained simultaneously. The interface of electroanalysis, uses equations of chemical transport for species reactant and product. The domain equation is the diffusion equation (also known as Fick’s second law) to describe the transport of substances chemicals of the species electroactive A and B:

At the upper limit (x = L), a uniform concentration, is assumed equal to the highest concentration of the reactant. The product has a concentration of zero here; on the edge of the electrode (x = 0), the reactive species A, is oxidized (loses an electron) to form product B. By convention, the electrochemical reactions are written in the direction of the reduction:

The stoichiometric coefficient is -1 for B (the reagent in the direction of the reduction), and +1 for A (the product in the direction of the reducing); the number of electrons transferred, n equals one. The current density for this reaction is given by the electroanalytical Butler-Volmer equation for oxidation:

where k_{0} is the rate constant of the reaction heterogeneous, a_{c} is the coefficient of transfer and n is the cathodic overpotential on the working electrode. The overpotential is the difference between the potential applied and the equilibrium potential (formal potential of the reduction) of redox couple of species A and B. According to the Faraday laws of electrolysis, the flow of reactive and products are proportional to the density of current expended:

This is expressed in the boundary condition of the electrode surface. The triangular waveform applied to the study of cyclic voltammetry specified in the boundary condition of the electrode surface according to the two vertices of potential, forming a window in potential between -0.4 and 0.4 V, on each side of the potential of reduction on the equilibrium, and a scan rate voltammetric, v (v s ^{1}), which is the rate at which the applied potential changed. The total current is related to the current density by simply multiplying by the electrode area, A: