Suppose that a spherical electrode can be fabricated from a single nano onion, C60-C240-C540-C960-C1500-C2160-C2940·C3840-C4860, shown here. Nano onions comprise concentric fullerenes of increasingly larger size as indicated in the formula. Assume that the nano onion has been synthesized with a carbon nanotube tail of sufficient size and strength that it can be electrically connected to a 0.1 μm tungsten needle and that the needle and nanotube tail can be proper insulated so that only the surface of the nano onion is exposed.
(a) Given that the radius of the nano onion is 3.17 nm, find the surface area in cm', neglecting the area of the nanotube attachment.
(b) If the diffusion coefficient of analyte A is 8 X 10-10 m2/s, calculate the concentration gradient and the current for A at a concentration of 1.00 mM at the following times after the application of a voltage at which A is reduced:
(c) Find the steady-state current.
(d) Find the time required for the electrode to achieve steady-state current following the application of the voltage step.
(e) Repeat these calculations for a 3-μm spherical platinum electrode and for a spherical iridium electrode with a surface area of 0.785 mm2.
(f) Compare the results for the three electrodes, and discuss any differences that you find.
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