Simplifications of Butler-Volmer Equation

We will consider here three important cases to simplify Equation 6.6 (1) q is very close to 0, (2) q 0, and (3) q 0  

At a very small overpotential (Iql 10 mV), the exponents in Equation 6.6 are small enough to expand both of them taking into account that e +x  

When the electrode is highly cathodically polarized, q 0, the first term of Equation 6.6 is very small and the equation is simplified to 

---