## Table of Contents

One of the key tools used in electrochemistry research is the Randles-Sevcik Equation. This equation has multiple applications in energy storage, biosensors and surface science. In this blog post, we will discuss the history and significance of the equation, as well as how it can be used to calculate the electrochemical active area and diffusion coefficient.

## Brief History of the Randles-Sevcik Equation

### The Authors of the Randles-Sevcik Equation

The Randles-Sevcik Equation was developed by two researchers, J.E.B. Randles and C.I. Sevcik, in the 1940s.

### Goal of the Randles-Sevcik Equation

Both scientist were interested in the study electrochemical reactions and were looking for new ways to analyze data from electrochemical experiments.

The equation was developed with linear sweep voltammetry in mind and describes the behavior of redox reactions in electrochemical cells under potentiodynamic conditions.

### First Appearance of the Randles-Sevcik Equation in Scientificl Literature

Despite being developed earlier, it was first published in Discussions of the Faraday Society in 1959 in a paper entitled “Kinetics of Rapid Electrode Reactions”. Since its conception, the Randles-Sevcik equation has made a lasting impact on the field of electrochemistry, becoming an essential tool with applications in a wide variety of fields, from energy storage to sensor development.

## What is The Randles-Sevcik Equation?

This equation describes the behavior of a redox reaction under linear sweep potentiomery conditions by taking into account the electron transfer rate, the concentration of the electroactive species, and its diffusion coefficient as follows:

where:

i_{p }is the peak current of the redox reaction in the voltammogram in A

n is the number of electrons of the reaction

F is Faraday’s Constant, 96485 C/mol

A is the surface area of the working electrode in cm^{2}

C is the concentration of the redox species in mol/cm^{3}

v is the scan rate used to collect the voltammogram in V/s

D is the diffusion coefficient of the redox species in cm^{2}/s

R is the Gas Constant 8.3144 J/molK

and T is the temperature in K

## How to Use the Randles-Sevcik Equation?

The Randles-Sevcik equation is a powerful tool in electrochemistry because it relates three key parameters: surface area, diffusion coefficient and redox concentration.

In most cases, one of these 3 parameters will be unknown which opens a wide range of applications for this equation.

## Top 3 Applications of the Randles-Sevcik Equation

### 1. Surface chemistry characterization

If the diffusion coefficient and redox concentration are known, then the Randles-Sevcik Equation can be used to determine what is known as the Electrochemical Active Area (EAA) of the electrode.

For a perfectly planar metallic electrode, the EAA is expected to be equal to the geometric area of the electrode. However, sometimes this may not be the case. Below are 3 examples of cases where the EAA is unknown:

- Dirty electrodes: often electrodes can behave poorly because a significant area of the electrode is fouled with an insulating layer of, most commonly, organic material. In this case, determining the EAA can help optimize cleaning procedures.
- Porous electrodes: in this type of electrodes the macroscopic area does not relate to the actual area contributing to the electrochemical signal. In this case, determining the EAA can help understand the behavior of these electrodes and optimize its manufacturing process.
- Electrode functionalisation: when developing sensors, the surface of the electrode often requires modification with specific chemicals or molecules such as thiols, DNA or antibodies. In this case, by monitoring the decrease of the EAA, it is possible to control the quality and coverage of these coatings.

### 2. Electroactive species characterisation

Working with novel redox molecules is exciting, but often it also means there is very little known about them. One of the key parameters of electroactive species is its diffusion coefficient.

The diffusion coefficient plays a crucial role in the applicability of electroactive species and is often influenced by environmental factors such as the electrolyte composition, temperature and pressure.

With the Randles-Sevcik equation, it is possible to characterize the diffusion coefficient of electroactive species. This allows researchers to have quantitative data of how different factors affect this crucial parameter and helps optimize the electrochemical system.

### 3. Determining concentration of redox molecules

If both the area and diffusion coefficients are known, then the Randles-Sevcik equation can be used to determine the total concentration of the redox species in solution. While this application is not as common as the two prior ones in research settings, it is certainly useful for the development of sensors.

## The Randles-Sevcik Plot

In practice, the Randles-Sevcik equation is mostly used in experiments that measure the sample at multiple different scan-rates. This is done to be able to generate the so-called Randles-Sevcik Plot, which displays the peak currents of the redox reactions versus the square root of the scan-rate.

This type of plot is useful for the characterisation of electrochemical systems and also provides qualitative information.

### What does symmetry mean in a Randles-Sevcik plot?

One of the qualitative bits of information that can be extracted from the Randles-Sevcik plot is regarding reversibility of a redox reaction.

For a redox reaction to be fully reversible, the peak current of the oxidation and reduction need to be of equal magnitude. This means that as many electroactive molecules are oxidised and reduced each cycle.

However, some times this will not be apparent, yet the reaction will be reversible. This is often the case when dealing with electrodes displaying a high IR drop where the background signal has not been properly corrected for. In these cases, a Randles-Sevcik plot can qualitatively indicate that the reaction is reversible if the anodic and cathodic lines are symmetric.

### What does linearity mean in a Randles-Sevcik plot?

For a diffusion-controlled redox system, the plot of the peak current versus the square root of the scan-rate shows a linear trend. If this is not the case, it mainly shows that the system is irreversible or quasi-reversible.

A typical irreversible redox rection only shows either oxidation or reduction, and as its name suggests, once it has happened it can’t go back to its original state. An example of this would be the electropolymerization of monomers.

A quasi-reversible reaction, is a type of reaction that is not able to oxidize and reduce to the same amount each time. One of the main sources of a quasi-reversible reaction is surface adsorption of the redox molecules onto the electrode, like aromatic mediators on carbon electrodes.

As you can see, the Randles-Sevcik Equation is a key tool for electrochemists that is used in a variety of applications to optimize electrode design and performance, as well as study the behavior of electrochemical systems. By understanding how to use the equation it is possible to gain valuable insights into the behavior of electrochemical systems and develop new materials . If you are interested in learning more about electrochemistry, we encourage you to explore our blog.