I considered the following reaction:

• Re Ox + e-

Both species can be adsorbed at the electrode's surface following a Langmuir isotherm. I considered that the adsorbed species can go through a redox process and I asummed that the redox paramters of adsorbed species are different from those of the bulk solution. Finally, I defined the total current, jt, as

• jt = jads + jbulk

Where

• jads is the current due to the adsorbed species defined as:
• jads = -n⋅F⋅A⋅(dΓRe/dt) Γ is the interfacial concentration of Re
• jbulk is the current due to the bulk species defined as:
• jbulk = -n⋅F⋅A⋅DRe(d[Re]/dx)x=0

I attach some results how the total current is affected by the increase of the maximum capacity of adsorption Γmax accosing to Langmuir model.

although i did not do a research on this area, i will try to put my opinion. adsorption on electrochemistry is the process of accumulation of ions, molecules, on the surface of electrodes. the condition may helps us to control and adjust the cathode reaction, and interfacial phenomena.

In my case, I only considered the adsorption of neutral molecules—specifically, the species involved in the redox reaction:

• Re Ox + e-

I did not take into account the adsorption of charged species. Including them would affect the structure of the electrical double layer and ultimately influence the system's capacitance. Unfortunately, modelling the capacitive component of electrochemical systems is currently beyond the scope of my skills. From a numerical perspective, incorporating this aspect would also significantly increase the complexity of the simulations.