Determination of charge carrier concentration in doped nonpolar liquids by impedance spectroscopy in the presence of charge adsorption.

The impedance of dodecane doped with sorbitan trioleate (Span 85), sorbitan monooleate (Span 80) and sorbitan monolaurate (Span 20) was measured as a function of frequency using a 10 mV amplitude sinusoidal voltage applied across a parallel plate cell with a 10 μm spacing. The tested solutions varied in concentration from 1 mM to 100 mM and the frequency range was 10(-2)-10(4) Hz. Nyquist plots of all three surfactants showed the high frequency semicircle characteristic of parallel resistance and capacitance but often exhibited a second semicircle at low frequencies which was attributed to charge adsorption and desorption. The electrical conductivity of each surfactant was proportional to surfactant concentration for concentrations above 10mM. Fitting the data to models for charge migration, differential capacitance, and adsorption allowed extraction of both charge concentration and two kinetic parameters that characterize the rate of adsorption and desorption. Above 10 mM the ratio of charge carriers per surfactant molecule was 22 ppm for Span 20, 3 ppm for Span 80, and 0.2 ppm for Span 85. A higher number of charge carriers per molecule of surfactant was associated with larger micelles. The adsorption rate constants were independent of surfactant concentration while the desorption rate constants were proportional to the surfactant concentration. This dependence indicated that uncharged surfactant, whether in micelles or not, participated in the desorption of charge. Predictions of the adsorption/desorption model for large constant electric fields agreed qualitatively with data from the literature (Karvar et al., 2014).