To characterize the electrocatalytic activity of the microelectrodes, the effective surface area was determined using the equation proposed for cylindrical microelectrodes by (Szabo, 1987). But, I don't understand why the current density decreases as the effective surface area increases.
This is intuitive if you consider that the same current will be spread over a larger 2-dimensional space. It might help if you think of the current as a flow of water out of a shower head, with water pressure determined by voltage. A small shower head will concentrate the water into a dense stream, while a wide shower head will spread the water flow at a lower density and a wider stream.
It is important to understand the relevant length scale when measuring the effective electrde area. There is an IUPAC review by Trasatti and Petrii that discusses real electrde areas. If the electrode reaction is diffusion-limited, the relevant length scale in one dimension is sqrt(2Dt), so for any time t, any features smaller than sqrt(2Dt) will not increase the electrode area except at very short times, since the concentration gradient will be smeared out. The effective electrode area will them be close to the projected geometric area. Increasing surface roughness can only lead to an increased electrode current if the gaps between the asperities are larger than the concentration boundary layer. Measurements of capacitance will have a characteristic length scale of the Debye length. If you measure the area of eg a gold or platinum electrode using gold oxide peaks or beta-hydride peaks, then the area will scale as the unit cell for the oxide or beta hydride respectively. So the electrode area will depend on how you measure it and you need to decide which measure characterises the problem that you're trying to solve.
Maybe the surface of the electrode is saturated in this case the current will be blocked
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