The phrase "electrode surface" refers to the outer part of an object that is used for conducting electricity. It is the area where electrical currents pass through or are applied to. Full definition
The devices worked, but they generated just 200 milliwatts of power per square centimeter (mW / cm2) of electrode surface area, well behind the performance of PEM fuel cells and SOFCs. (sciencemag.org)
The PBCTF is limited to membrane electrode assemblies with electrode surface area of approximately 1 cm2 with membrane surface area up to 5 cm2. (h2awsm.org)
Dendrites - deposits that form on electrode surfaces during the charging process - cause the batteries to short circuit, leading to serious safety hazards. (pnnl.gov)