Use of electrochemical impedance spectroscopy to determine double-layer capacitance in doped nonpolar liquids

Electrochemical impedance spectroscopy in a thin cell (10 μm) was used to infer conductivity, permittivity and the differential double-layer capacitance of solutions of dodecane doped with OLOA 11000 [poly(isobutylene) succinimide] for concentrations of dopant between 0.1% and 10% by weight. All spectra (frequencies between 1 Hz and 100 kHz) were well fit by an equivalent circuit having four elements including a constant-phase element representing the double-layer capacitance. Using Gouy-Chapman theory for small zeta potentials and assuming univalent charge carriers, the double-layer capacitances were converted into charge carrier concentration which was found to be directly proportional to the weight percent of dopant with a 1 wt% solution having 87 carriers/μm(3) (the concentration of either positive or negative charges). This is only 17 ppm of the total monomer concentration calculated from the average molecule weight of the dopant. Dividing the measured conductivities by the charge carrier concentration, we inferred the mobility and hydrodynamic diameters for the charged micelles. The hydrodynamic diameters of carriers were significantly larger than the average diameter of all micelles measured independently by dynamic light scattering. This suggests that only large micelles become charged.