Flexoelectricity driven elastic contact–separation model for triboelectrification

Triboelectrification is the transfer of electrical charge between surfaces during contact. When the contact is purely normal (i.e., no sliding), the term contact electrification is often used. It was proposed in 2019 by Laurence Marks and co-workers (Phys. Rev. Lett., 123, 116103) that flexoelectricity (i.e., strain gradient-induced polarization) might be a key driver of triboelectricity at least in insulators. They explained how to determine flexoelectric surface potentials for Hertzian sphere-on-flat contacts and calculated appreciable values when the typical small size of surface asperities was considered. However, the theory developed so far is only valid when two contacting surfaces are in the loading stage where transferred charges are restricted within the contact area. However, nearly all experimental measurements of surface charge and potential are made at the end of the unloading stage when two surfaces are completely separated. Here, we develop a Hertzian (sphere-on-flat) flexoelectric non-adhesive contact electrification model that accounts for the Hertzian contact in both the loading and unloading stages. The impetus for the model is the fact that flexoelectric polarization clearly decreases monotonically during unloading. For this reason, we find that the residual surface charges and potential (after a complete separation of two mating surfaces) are considerably altered if unloading is considered. Their magnitudes are much reduced, and their profiles take on a very different shape. The trends of increasing surface charge and potential magnitudes with increasing normal load are in agreement with experiments. The next major step will require the addition of adhesion to the loading–unloading model as this can be expected to further alter the evolution of strain gradients during the loading and unloading stages.