Dielectric measurement of low-concentration aqueous solutions: assessment of uncertainty and ion-specific responses

Abstract

Excessive amounts of chemicals and ions flowing into water sources cause serious environmental and human-health related concerns. The lack of affordable and real-time monitoring systems for these contaminants limits effective conservation and management strategies. To establish a basis for developing an effective, fast, real-time, and affordable sensing system, a dielectric spectroscopy method has been employed to characterize aqueous solutions of sodium chloride (NaCl), sodium nitrate (NaNO3), and sodium sulphate (Na2SO4) at environmentally-relevant (low) concentrations. Dielectric spectra were measured over a frequency range of 200 MHz to 20 GHz, at a temperature of 25.00 °C ± 0.01 °C and for concentrations 0–20 mmol l−1. The measured spectra were fitted with a Debye model using a non-linear, weighted, least-squares analysis. A method of judiciously exploiting the resulting fitting parameters is proposed, that allows the concentration and type of ions to be uniquely determined. Uncertainties due to random and systematic errors that contribute to the measured dielectric spectra and become critical in the context of low concentration aqueous solutions have been assessed. Furthermore, two methods of calculating associated uncertainties of the indicator parameters, viz. covariance matrix and Monte Carlo methods have been performed. The results show the numerical approach taken by a Monte Carlo method, while yielding the same estimates, reduces the tediousness accompanied by the analytical covariance matrix method.