In-situ spectroelectrochemistry provides dynamic electrochemical and spectroscopic information concurrently with the redox reaction occurring on the electrode surface. Although different spectroelectrochemical configurations can be used, simple equations explain how to relate electrochemistry and spectroscopy for each experimental setup.

This Application Note describes how the quantification of one electrochemical parameter (the diffusion coefficient) is calculated from the spectroscopic data as a proof of this concept. 

The Lambert–Beer law relates absorbance (Abs) to the molar absorption coefficient (ε), the optical path length (b), and the electroactive compound concentration (C):

Taking into account the following electrochemical reaction:

the spectroscopic monitoring process in a normal transmission configuration means that the light beam passes through each infinitesimal layer (n) until it arrives at the electrode surface. 

Each layer is considered as a homogeneous solution (Figure 1) and the absorbance can be expressed as the sum of the absorbance of these layers.

Considering also that a segment of solution of thickness dy and cross-sectional area A is uniformly illuminated and only B species absorb light, the differential absorbance registered upon passage of the light though this segment is [1]: 

and then, the total absorbance is given as:  

If B species are stable, the integral is the total amount of B species per unit area and is equal to Q/nFA. Then, the absorbance is calculated as: 

Furthermore, considering that the charge Q is given by the integrated Cottrell equation: 

The total absorbance is therefore: 

The methodology followed is exactly the same when the spectroelectrochemical experiment is carried out in normal reflection configuration (Figure 2), but in this case the light passes though the solution two times: when it goes to the electrode surface and when is reflected back. 

For that reason, the absorbance equation is expressed as such:

If the light does not arrive completely perpendicular to the electrode surface, the angle of incidence must be taken into consideration: 

where 𝜃 is the angle of incidence. Therefore, spectroelectrochemical experiments in different configurations allow analysts to calculate electrochemical parameters such as the diffusion coefficient from the spectroscopic data. 

Taking into account that the molar absorption coefficient of ferricyanide is 1040 L·mol^-1·cm^-1 [2], the diffusion coefficient of ferrocyanide can be easily calculated from the spectroscopic information:

Then, D_ferrocyanide = 6.5 × 10^-6 cm² ·s^-1. This value agrees with literature [3,4]. In case the molar absorption coefficient is an unknown parameter, it can be calculated with the calibration curve of absorbance obtained by working in total electrolysis or thin layer configuration for a different reagent concentration.