This is not a simple question! It all depends on why you want to know the surface area and how you measure it. The length scale is critical. Estimating the surface area using the diffusion limited current will be insensitive to any feature smaller than the average diffusional distance, sqrt(2Dt), in one dimension. So for typical diffusion coefficients of 10^-10 m^2/s and an experiment lasting 100 s, any asperity, scratch or nanoparticle smaller than 100 um, a little larger than the diameter of human hair, will not contribute. This is however a useful parameter for giving the effective area for sensing. However, it will be insensitive to defects in construction such as cracks in the insulator-metal interface. Capacitance measurements will give the area with a linear resolution of the order of the Debye length, which for most aqueous electrochemistry experiments will be sub nanometre. However capacitance is supersensitive to adsorbed impurities and is potential and electrolyte dependent. For Pt, the charge associated with adsorbed hydrogen atoms will give the area with atomic scale resolution. For Pt and Au electrodes, the oxide reduction peak in dilute sulfuric acid will also give near atomic scale resolution. The ratio of the area from oxide reduction to the diffusion area gives the useful parameter of surface roughness which tells you how successful you have been at polishing your electrode. Scratches and cracks will contribute to charging current through double layer and through thin-layer electrolysis. This can affect response times in sensors. There is an authoritative IUPAC report on real electrode areas by Trasatti and Petrii Pure & Appl. Chern., Vol. 63, No. 5, pp. 71 1-734, 1991 which discusses the relative merits and significance of the different electrode area methods.
For the diffusion coefficient, cyclic voltammetry is not recommended as the diffusion limited current has only a weak dependence of sqrt(D) and so is relatively noise-prone. This is made worse by the narrow range of real diffusion coefficients of most electroactive entities, 10^-10- 10^-9 m^2/s. The most reliable electrochemical method is probably plotting the diffusion limited current at a rotating disc electrode versus sqrt (angular velocity). This should be a straight line with a slope that depends on D^2/3. The straight line gives you confidence that the experiment has been correctly executed and it is straightforward and fast to get a good few data points. Otherwise, for a non-electrochemical method, use radiolabelled molecules and measure the dispersion from a point or line. The standard deviation in one dimension will equal sqrt(2Dt). This method is useful for media where it is not convenient to do an electrochemical experiment. Again, the quality of fit to a Gaussian can give confidence in the results and show how effective you have been in minimising convection effects.
Dera Abera Demeke Ambaye
the calculation of surface area is available in the supporting information file, and the diffusion constant is calculated on paper.
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