Capacitors in EIS experiments often do not behave ideally. Instead they act like a constant phase element (CPE) as defined below. The impedance of a CPE has the form:
When this equation describes a capacitor, the constant Y0 = C (the capacitance) and the exponent α = 1. For a constant phase element, the exponent α < 1. The "double-layer capacitor" on real cells often behaves like a CPE instead of like a capacitor. Several theories have been proposed to account for the non-ideal behavior of the double layer, but none has been universally accepted. In most cases, you can safely treat a as an empirical constant and not worry about its physical basis.