Multiple charge carrier species as a possible cause for triboelectric cycles

The tendency of materials to order in triboelectric series has prompted suggestions that contact electrification might have a single, unified underlying description. However, the possibility of "triboelectric cycles," i.e., series that loop back onto themselves, is seemingly at odds with such a coherent description. In this work, we propose that if multiple charge carrying species are at play, both triboelectric series and cycles are possible. We show how series arise naturally if only a single charge carrier species is involved and if the driving mechanism is approach toward thermodynamic equilibrium, and simultaneously, that cycles are forbidden under such conditions. Suspecting multiple carriers might relax the situation, we affirm this is the case by explicit construction of a cycle involving two carriers, and then extend this to show how more complex cycles emerge. Our work highlights the importance of series and cycles towards determining the underlying mechanism(s) and carrier(s) in contact electrification.