Symmetry Coefficient
The physical meaning of the symmetry coefficient (or charge transfer coefficient) is a difficult subject. I have approached it here by simply setting it to various values and plotting the results. In Figure 1 the solid red curve is a plot of current density with a=0.5. Cathodic current density is plotted downward from the zero current line in this plot. At a=0.5 the curve is symmetrical in that the anodic and cathodic portions are equivalent.
The dotted blue curve is the result of the same equation but with a=0.6. The dashed green curve has a=0.7. Examination of the plots show that for a reduction reaction and a >0.5 a negative overpotential results in a greater current density than an equivalent positive overpotential.
Figure 1.
This can be interpreted as meaning that for a>0.5 the activation energy for the reduction process is decreased while the activation energy for the oxidation process is increased aside from the effect of the potential difference between the electrode and the solution.