Time-difference impedance spectroscopy of growing films containing a single mobile charge carrier, with application to surface films on Li electrodes

In this paper we present a new approach to the analysis of electrochemical impedance spectroscopy (EIS) data for electrodes covered by passivating sur face films that grow in time. The impedance of such electrodes increases in time due to the gradual growth of their thickness as well as to the change of their local characteristics. The growing part of the surface films may either be homogeneous in its structure and properties or inhomogeneous, wit h gradually changing properties as a function of the distance of the newly formed surface species from the metal-film interface. We show herein that t he time-difference impedance spectra (DIS), i.e., the difference between tw o complex impedance curves, Z(omega, t(1)) - Z(omega, t(2)), measured after different periods of storage, tl and t(2), as a function of frequency may provide a very useful tool for characterizing the nature of the growing pas sivating films. These time-difference impedance curves (e.g., plotted in co ordinates Z(imag) vs Z(real)) can be simulated both for homogeneous growing surface films on electrodes and for situations in which local properties s uch as the surface film's resistivity are nonuniform across the growing fil m. The prospects of this approach have been demonstrated in the analysis of the surface films at lithium electrodes freshly prepared and stored in alk yl carbonate mixture (ethylene-dimethyl carbonates) with a Li salt, and mea sured periodically by EIS. The analysis of DIS of this system has shown tha t during a period of several hours after the electrode's preparation in sol ution, the process of the surface film deposition is very complicated. Prop erties of the new portions of the film are varying in time so that the depo sited film possesses a highly nonuniform structure. Moreover, the local cha racteristics of earlier formed portions are modified gradually inside the f ilm. However, as the storage time is longer, the growth of the surface Film s on the lithium electrodes becomes more homogeneous, probably due to the i ncreased selectivity of the Li-solution reactions when the surface films ar e thicker.