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6 Using Individual Carbon Fiber Electrodes to Quantify Effects of Thermal Activation Perhaps the source of conjecture is that it is currently difficult to quantify the effect on the felt performance from each felt property. For example, the measured current at an electrode is related to the electrochemically active surface area and the inherent rate constant of a material, as described by the Butler-Volmer equation: 0 βπΌππΉ(πΈβπΈπππ£ ) (1βπΌ)ππΉ(πΈβπΈπππ£) π=πΉπ΄π (πΆπ πππ π π βπΆππ₯π π π ) (6.1) Where; π is the recorded current, π΄ is the electrochemically active surface area of the electrode, π0 is the inherent rate constant, πΆπ ππ is the concentration of the reduced species at the surface of the electrode, πΆππ₯ is the concentration of the oxidised species at the surface of the electrode, π is the universal gas constant and π is the temperature of the system in kelvin. In this work and often in literature, the electrochemically active surface area (π΄ππ), is assumed to be equal to the geometric area of the electrode (π΄π). For instance, this assumption is often applied when using the Nicholson method at planar electrodes and is acceptable as the electrodes are typically finely polished to produce a very smooth surface. However, when using carbon fibers the π΄ππ is likely larger than the geometric surface area, due to surface roughness and or the presence of pores. This means the rate constant value that is calculated from electrochemical measurements is not the inherent rate constant (π0 ), but in fact an apparent ππ rate constant (π0 ): πππ π΄Γπ0 =π΄Γπ0 π πππ ππ ππ (6.2) As mentioned previously, both the wettability and roughness of an electrode will change the electrochemically active surface area relative to the geometric area: π΄π Γ π = π΄π‘ππ‘ (6.3) π΄π Γ π Γ π = π΄ππ (6.4) Where π is the roughness factor of the electrode, π΄π‘ππ‘ is the total area of the electrode and π is the wetted fraction of the electrode. 74PDF Image | Electron Transfer Kinetics in Redox Flow Batteries
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