Harnessing, and understanding the mechanisms of growth and activity of, biofilms of electroactive bacteria (EAB) on solid electrodes is of increasing interest, for application to microbial fuel and electrolysis cells. Microbial electrochemical cell technology can be used to generate electricity, or higher value chemicals, from organic waste. The capability of biofilms of electroactive bacteria to transfer electrons to solid anodes is a key feature of this emerging technology, yet the electron transfer mechanism is not fully characterized as yet. Acetate oxidation current generated from biofilms of an EAB, Geobacter sulfurreducens, on graphite electrodes as a function of time does not correlate with film thickness. Values of film thickness, and the number and local concentration of electrically connected redox sites within Geobacter sulfurreducens biofilms as well as a charge transport diffusion co-efficient for the biofilm can be estimated from non-turnover voltammetry. The thicker biofilms, of 50 +/- 9 mm, display higher charge transport diffusion co-efficient than that in thinner films, as increased film porosity of these films improves ion transport, required to maintain electro-neutrality upon electrolysis.