# Diffusion Layer Thickness and Electrochemistry – Everything you need to know

Electrochemistry plays a critical role in a wide range of fields like energy storage and conversion or (bio)sensing. One important factor that influences electrochemical reactions is the so-called diffusion layer thickness, which determines the amount of reactants that can reach the electrode’s surface. In this blog post, we will explore the theoretical background of diffusion layer thickness in electrochemistry, what are the factors that affect its thickness, methods for measuring it, as well as some special cases to bear in mind.

## What is the Diffusion Layer?

In electrochemistry, the diffusion layer is described as the region of the electrolyte in contact with the electrode that will be able to interact with it.

The thickness of this layer plays a crucial role in electrochemical reactions, as only the reactants within this region will undergo redox transformations. This is because only the molecules within this area have the time to diffuse to the electrode surface to exchange electrons.

Therefore, the diffusion layer has serious implications on electrochemical experiments that cannot be ommitted.

## How to calculate the thickness of the diffusion layer?

Calculating the diffusion layer thickness is quite straightforward and can be done using the equation below:

where:

l is the diffusion layer thickness in cm,

D is the diffusion coefficient of the analyte/reactant, in cm2/s

and t is time in s.

## Special cases of the diffusion layer thickness

### Special case 1: Chronoamperometry

One particularly interesting point about the diffusion layer is that its thickness depends on time. This is because the longer the experiment time, the more time we allow reactants to diffuse to the electrode surface.

As a result of this feature, experiments where a set potential is applied constantly over time are considered to have an “infinite” thickness. Because the experiment is not limited by the thickness of the diffusion layer, but by the total time of the reaction.

### Special case 2: Cyclic voltammetric techniques

Cyclic voltammetric techniques such as cyclic voltammetry, are influenced by the diffusion layer thickness. Proof of that is how the overall charge measured for a redox couple like potassium ferri/ferrocyanide increases with decreasing scan rates.

This is because the slower scan-rates allow more time for molecules to diffuse to the electrode surface resulting in more molecules being oxidised or reduced.

Similarly, if the scan rate is too fast, the voltammograms end up looking rectangular and showing just the capacitive contribution of the electrolyte because the reactants were not able to travel to the electrode surface within the timeframe of the experiment.

One curious feature of cyclic voltammetry is that, thanks to the cyclic nature of the measurement, the oxidation state of the species in the diffusion layer is reset after each cycle. Therefore, for fully reversible reactions the peak intensities should remain constant across the different cycles.

### Special case 3: Unidirectional voltammetric techniques

This is one of those cases where the diffusion layer thickness can be troublesome.

Cyclic voltammetry is a great technique for laboratory based characterisation, but it’s not great for developing real-world applications -specially for sensing. The reason for this? Time.

Cyclic voltammetry measurements are lengthy if a good signal-to-noise ratio is desired. So, in an attempt to shorten the time, researchers ofter shift towards pulsed techniques. More specifically, square wave voltammetry.

While square wave voltammetry is a great and quick technique that can provide a lot of insights and is used commonly for sensing applications, one must remember that this technique is unidirectional. This means that the reactant’s oxidation state within the diffusion layer is not reset after each measurement. And being oblivious to this fact can lead to a complete loss of the signal

### Special case 4: Surface bound reactants

This is an interesting case, specially for biosensing applications.

Often, when developing biosensors, a biological receptor is bound to the surface of the electrode. This allows to concentrate biochemical reactions near the electrode and helps maximize the signal obtained.

In some cases, these biological receptors have been chemically modified to also contain a redox active molecule. In these cases, the signal is typically generated by the ability of this redox molecule to undergo oxidation or reduction reactions with the electrode.

The best example of one such type of electrochemical biosensor is DNA sensors utilizing stem-loops (also known as DNA hairpins).

DNA stem-loops have been utilized extensively for the detection of molecules using electrochemistry. This type of DNA structure folds on itself as a single-stranded DNA (ssDNA) and becomes a straight double helix after interacting with its complementary DNA strand, or the target DNA that we would want to detect.

Thanks to this unique property, if we attach a redox molecule to one of the ends of the DNA hairpin, we can use the redox reaction as a way to detect, quantitatively, how much target DNA is in our sample.

And the best thing is that, since the DNA is attached to the electrode surface… the diffusion layer is irrelevant! All the redox molecules are already next to the electrode.

#### 2 things to bear in mind with surface bound reactants

While the diffusion layer is irrelevant because redox molecules do not have to diffuse to the electrode surface, there’s a couple of things that you should bear in mind when working with this type of experiments:

• Remember to reset the oxidation state for “real-time” experiments. This can be done by either using cyclic techniques or setting up an appropriate pre-conditioning DC potential.
• Be wary of reading times. When working with DNA, remember that it is not necessarily a stiff molecule, specially with long strands. So if your reading time is too long, even if the redox marker is far from the electrode surface it may still have enough time to diffuse to the electrode. After all, once we apply a potential, charged molecules will be attracted, or repelled, by the potential applied. This may lead to false negatives. The best way to avoid this effect is by optimizing reading times.

In conclusion, the diffusion layer thickness is an important concept to understand for all electrochemists. It has implications in all areas of electrochemistry, from plating to, energy storage, to sensing. Therefore, it is an essential concept that must not be overlooked.

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