Impedances of thin and layered systems: cells with even or odd numbers of interfaces

Impedance data, e.g., system responses, from perturbing small amplitude applied sinusoid signals of near DC to high kilohertz frequencies, give chemical information. Analysis of frequency-dependent imaginary and real impedance proceeds from equivalent analog circuit elements to chemical and physical significance determined from many model systems. Already, it is possible to interpret bulk transport processes, surface kinetic effects, diffusion phenomena, and dependencies on the type of contacts: symmetric ion contact, symmetric metal contact or asymmetric metal-ion interfaces, and cell design; even (battery or sensor) and odd numbered (constrained junction or immiscible liquid) interfaces in a system. These analyses cover the chemical origins, locations and meanings of the lumped resistances, capacitances and transmission lines that are introduced by engineers in their strict analog interpretations of the impedance data. Examples cover simple ohmic, simple diffusive behavior, complex behavior with surface interfacial kinetics or surface resistances, and with finite (nonblocking) or infinite (blocking) DC impedance. High and low frequency responses may show so-called constant phase element character that suggests fractal behavior. Low frequency data occasionally appear in the second quadrant of impedance plane plots. These results are caused by negative capacitances and resistances. In this paper, chemical interpretations of analog circuit elements are mainly based on theory and observations of thin cells of electrolytes and solid and liquid films (membranes) that are ionic or mixed ionic/electronic conductors. The information should carry over into thickened, gelled, and tissue electrolyte phases and serve as a basis for medically-oriented, perhaps diagnostic impedance measurement applications already pioneered by Herman Schwan.