Comment on "ac Conductivity of Scandium Oxide and a New Hopping Model for Conductivity"

In the paper by Pike on ac conductivity, the relaxation time for classical (over-the-barrier) hopping is assumed proportional to $\phi \left(\frac{R}{a}\right)\exp \left(\frac{W}{\mathrm{kT}}\right)$, where $W$ is the barrier height and $\phi \left(\frac{R}{a}\right)$ is a function which depends on the site separation $R$. For the classical hopping mechanism the correct form of $\phi \left(\frac{R}{a}\right)$ varies weakly with $\frac{R}{a}$, but the paper may have inadvertently implied that $\phi \left(\frac{R}{a}\right)$ had the strong exponential dependence encountered in the quantum hopping or tunneling process. This comment is to clarify the situation by discussing the processes which contribute to $\phi \left(\frac{R}{a}\right)$ in more detail.