Randles-Sevcik equation: The Cyclic Voltammetry peak current (Ip)

Randles-Sevcik equation is the formulated mathematical equation to calculate the peak current (i_p) using scan rate (v) in an observed voltammogram. For redox reaction cycles like ferrocene/ferrocenium couple, peak current (i_p) depends on the concentration (C), the diffusion coefficient (D), the scan rate (V), and the electrode surface area ( A), of redox-active species. Along with these variables, several constants like Faradays constant (F), gas constant (R), and absolute temperature (T) are implied.

Prerequisites
Cyclic Voltammetry
Scan rate in Cyclic Voltammetry
Voltammetric determination of diffusion coefficients

Prerequisites

Cyclic Voltammetry

Scan rate in Cyclic Voltammetry

Voltammetric determination of diffusion coefficients

Voltammetric signals are the measurements of current flowing through electrodes as a function of electrode potential of the electroactive (redox-active) species. Randles Sevcik equation predicts the square root dependence of peak current on scan rate.

Randles-Sevcik equation and units

$\fn_phv i_{p}=0.4463\left ( \frac{n^{3}F^{3}}{RT} \right )^{1/2}A.C\left ( D.v \right )^{1/2}$

where,

i_p= Peak current (amperes)
n = Number of electrons transferred in a redox cycle
F = Faraday’s constant (96485.339 C/mol)
R = Universal gas constant (8.31447 J.K^-1.mol^-1)
T = Absolute temperature
A = The electrode surface area in working (cm²)
C = Molar concentration of redox-active species (mol/cm³)
D = The diffusion coefficient (cm²/s)
v = Scan rate in V/s

The Randles Sevcik equation is often abbreviated by assuming a temperature of 298.15 °K (25 °C). Now that the constant terms can be evaluated as a single constant, the equation becomes;

$\fn_phv i_{p}=\left ( 2.687\times 10^{5} \right )n^{3/2}A.C(D.v)^{1/2}$

The constant term 2.687×10⁵has the unit [ C.mol^-1.V^-1/2].

Randles-Sevcik equation evaluation examples

In a Cyclic Voltammetric process, the evaluation of diffusion constants is done for materials such as magnetic iron oxide nanoparticles, with coating materials named, cation-hexadecyltrimethylammonium bromide (CTAB), Bovine serum albumin (BSA), and Dextran. The calculation of such diffusion coefficients and their comparison enables us to compare the effects of coating and the resistance to the corrosion effect of solvent.

Materials studied by CV	Diffusion constant (cm²/s)
Magnetic Iron oxide nanoparticles (MNPs)	1.27x10^-4
MNPs with CTAB	0.40x10^-4
MNPs with BSA	3.11x10^-4
MNPs with CTAB and BSA	0.90x10^-4
MNPs with Dextran	0.88x10^-4
MNPs with CTAB and Dextran	0.21x10^-4

Reversibility of Redox reactions by Randles-Sevcik equation

A cyclic voltammogram is shown depicting the reversibility criterion of redox reversible and irreversible reactions. After a throughout potential scan, a redox process is said to be reversible if the following parameters are met.

A peak current ratio (i_pa/i_pc) of 1 at all scan rates evaluated by the Randles Sevcik equation.
The peak current function (i_p/ v^1/2) is independent of scan rate (v), where the peak current is given by the Randles Sevcik equation.
A peak potential separation (ΔE_p) at all scan rates is to be ~ 52.9/n mV.

For a reversible redox process, E^ois given by the mean peak potentials.

Predictions of Randles-Sevcik equation

Generally, the Randles Sevcik equation evaluations are opposite to expected results. For example, the peak current (i_p) increases at faster voltage scan rates in cyclic voltammetry. This is due to the electrode potential establishment against the concentration gradient of diffusing species. By changing the cell voltage, the concentration of species at the electrode surface also alters, and therefore, a faster voltage sweep will cause a larger concentration gradient near the electrode, making the peak current (i_p) larger.

Uses of Randles-Sevcik Equation

Application of the Randles Sevcik equation are listed as:

Calculation of the diffusion coefficient of electroactive (redox-active) species.
Provision of evidence of reversibility in a redox process.
The stoichiometry of redox processes can be estimated by using slopes of plots (i_pvs. v^1/2) only if the diffusion coefficients are known.

The high sensitivity of the technique cyclic voltammetry is due to the evaluation capabilities of the Randles Sevcik equation. Moreover, CV is also moderately selective and requires less procedure/preparation time.

Concepts Berg

What equation indicates the relationship between the peak current and the scan rate?

In Cyclic Voltammetry, The Randles-Sevcik equation is used to indicate the dependence of peak current (i_p) and scan rate (v).

How is the Randles Sevcik equation used?

The Randles Sevcik equation can be used as the electrochemical evidence of reversibility or irreversibility of redox reactions. Moreover, the diffusion coefficients and stoichiometric calculations are also the uses of Randles Sevcik equation.

How to get i_p for Randles Sevcik equation?

The peak current (i_p) for a cyclic voltammetric process, can be calculated using the Randles-Sevcik equation. It uses scan rate (v) and diffusion coefficient (D) to find the peak current using various constants.

How to find peak current in cyclic voltammetry?

In cyclic voltammetry, the peak current (i_p) can be calculated using the Randles Sevcik equation.

What is i_p in cyclic voltammetry?

Ip stands for the peak current value in cyclic voltammetry.

What do the peaks in cyclic voltammetry mean?

The peaks in cyclic voltammetry in cyclic voltammetry mean the positive and negative peak currents.

Randles-Sevcik equation slope:

The slope of the graph (i_pvs. v^1/2) is used for the stoichiometric determination of the redox-active compound.

Cottrell equation:

$\fn_phv i=\frac{nFAc_{j}^{o}\sqrt{D_{j}}}{\sqrt{\pi t}}$

where,

i = current (amperes)

n = number of molecules to reduce or oxidize one molecule of analyte

F = Faraday’s constant (96485.339 C/mol)

A = Area of electrode in cm²

c_j^o = initial concentration of analyte

D_j = Diffusion coefficient of analyte (j)

t = time in secs.