ACL Polarization Curve

Obviously, Equation 4.247 fails to describe the overpotential at zero current, when the argument of the first logarithm tends to zero. 

In an analogy to the Butler-Volmer equation, this defect can be corrected replacing the first logarithm in Equation 4.247 by arcsinh function of the halved argument. This gives 

y(/o) is given by Equation 4.127 and was taken into account Equation 4.235. Equation 4.248 is valid down toyb = 0. 

The first term in Equation 4.248 is independent of the inverse adsorption rate of methanol, meaning that this term describes the activation overpotential for the electrochemical steps of MOR. Note that at large jo, this term exhibits doubling of the apparent Tafel slope, a well-known effect of slow proton transport in the ACL. Indeed, y r asy o 1 thus, y can be neglected and the activation term reduces to 

The second term in Equation 4.248 has the form of a transport logarithm representing the overpotential required to bring methanol molecule to the catalyst surface. Though methanol adsorption is independent of overpotential, the electrochemical steps of MOR require methanol to be adsorbed on the catalyst surface. The second term in Equation 4.248 describes the respective quasi-transport voltage loss. 

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