Triboelectricity, when rubbing or contacting materials causes electric charge transfer, is ubiquitous across many fields, and has been studied in detail for centuries. Despite this, a complete description of triboelectricity remains elusive. Here, we analyze the contact between a metal asperity and a semiconductor, including contributions from the depletion zone of the semiconductor and from flexoelectric polarization that arises due to the strain gradients at asperity contacts. The free charges involved in charge transfer are then discussed and calculated. As a result, we develop a quantitative model for triboelectric charge transfer that details how charge transfer scales with contact parameters, the relative influence of depletion and flexoelectricity, and which agrees with various trends in multiple classes of triboelectric experiments.

In this report, we look at the fundamental physics of triboelectricity, charge transfer due to contact and sliding. While much of the report focuses upon recent advances such as the incorporation of flexoelectric contributions, we also include older work, some from centuries ago, which can only now be fully understood. Basic concepts and theories ranging from elements of tribology and contact mechanics through semiconductor built-in potentials, electromechanical terms, mechanochemistry and trap states are briefly described, linking to established surface science and interface physics. We then overview the main models that have been proposed, showing that they all fall within conventional electrostatics combined with other established science. We conclude with some suggestions for the future. Based upon this overview, our conclusion is that triboelectricity is a slightly complex combination of classic tribology and standard electrostatic phenomena that can be understood using the generalized Ampère's law connecting the electric displacement field with both Coulomb and polarization contributions, and the free carrier density, that is∇⋅D=ρf. Triboelectricity may be confusing, it is not really confused if care is taken, but it is complex.

Triboelectricity has been a topic of some confusion for many years, probably because it is very diverse and some of the fundamental science has not been clear. This is now starting to change. A few years ago, the importance of flexoelectricity at asperities is pointed out. That paper exploited the established physics of compensation of bound surface or interfacial charges without going into detail. The purpose of this paper is to expand further on this, mapping from the established physics of electrostatics with contact potentials and Maxwell's displacement field to the underlying fundamentals of charge transfer in triboelectricity. Examples from the published literature are used to illustrate this. In the discussion, some of the open questions and challenges to the community are mentioned.

An enduring question in science has been why sliding plays a major role in the triboelectric generation of static electricity-the "tribo" in triboelectricity. We provide here a general explanation which is rooted in established science. When sliding is taking place, there is symmetry breaking due to elastic shear, so the front of the sliding body experiences different elastic strains from the back. Consequently the polarization and associated charges at the front and back are not the same, and the difference between the two leads to current flow similar to the difference in air pressure above and below a plane's wing leading to lift. Specific calculations are provided which show good agreement with prior experimental measurements of size and shape dependencies, and reasonable quantitative agreement with experimental current measurements.

Triboelectric and flexoelectric phenomena have seen significant recent interest for energy harvesting. However, the underlying science responsible for triboelectricity has yet to be completely understood, both the fundamentals and an understanding of how the energy output depends upon the shape of the interacting surface. Here, we investigate the role of the contacting shapes (asperities) in triboelectricity. We demonstrate that their shape and size is very important, obtaining qualitative agreement with experimental results. Further, we discuss how the impact of the shape depends on material, geometric, gradient elasticity and electronic transport details. We provide scaling rules which can be exploited to better design energy harvesting devices based upon either triboelectricity or flexoelectricity.

Neutron scattering is used to study spin waves in the three-dimensional Heisenberg ferromagnet YTiO$_3$, with spin-spin exchange disorder introduced $via$ La-substitution at the Y site. No significant changes are observed in the spin-wave dispersion up to a La concentration of 20%. However, a strong broadening of the spectrum is found, indicative of shortened spin-wave lifetimes. Density-functional theory calculations predict minimal changes in exchange constants as a result of average structural changes due to La substitution, in agreement with the data. The absence of significant changes in the spin-wave dispersion, the considerable lifetime effect, and the reduced ordered magnetic moment previously observed in the La-substituted system are qualitatively captured by an isotropic, nearest-neighbor, three-dimensional Heisenberg ferromagnet model with random antiferromagnetic exchange. We therefore establish Y$_{1-x}$La$_x$TiO$_3$ as a model system to study the effect of antiferromagnetic spin-exchange disorder in a three-dimensional Heisenberg ferromagnet.

Triboelectricity was recognized millennia ago, but the fundamental mechanism of charge transfer is still not understood. We have recently proposed a model where flexoelectric band bending due to local asperity contacts drives triboelectric charge transfer in non-metals. While this ab initio model is consistent with a wide range of observed phenomena, to date there have been no quantitative analyses of the proposed band bending. In this work we use a Pt0.8Ir0.2 conductive atomic force microscope probe to simultaneously deform a Nb-doped SrTiO3 sample and collect current-bias data. The current that one expects based upon an analysis including the relevant flexoelectric band bending for a deformed semiconductor quantitively agrees with the experiments. The analysis indicates a general ratcheting mechanism for triboelectric transfer and strong experimental evidence that flexoelectric band bending is of fundamental importance for triboelectric contacts.

The underlying mechanisms responsible for triboelectricity have yet to be completely understood. We have previously proposed a model which explains charge transfer in non-metals via band bending due to electromechanical, especially flexoelectric, effects at deformed asperities coupled with work function differences. Here, we investigate whether the shape of asperities is important for triboelectricity. The results indicate that the shape is important in general, since how the electromechanical response scales with force and asperity size depends on the shape. This is qualitatively in agreement with experimental results. Further, we discuss how the impact of the shape depends on material, geometric, and electronic transport details. Additionally, gradient elasticity is incorporated into the model. As asperity contact is a nanoscale phenomenon, size-dependent mechanics can become significant and give more physically reasonable results. In some cases, the impact of gradient elasticity terms on the electromechanical potentials is very large, indicating that standard elasticity theory is not enough to cover some relevant cases in modelling triboelectricity.

S. Hameed, ∗ S. El-Khatib, 3 K. P. Olson, B. Yu, T. J. Williams, T. Hong, Q. Sheng, K. Yamakawa, J. Zang, Y. J. Uemura, G. Q. Zhao, 6 C. Q. Jin, L. Fu, Y. Gu, F. Ning, Y. Cai, 9, 10 K. M. Kojima, J. W. Freeland, M. Matsuda, C. Leighton, and M. Greven ∗ School of Physics and Astronomy, University of Minnesota, Minneapolis, MN 55455, U.S.A. Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, MN 55455, U.S.A. Department of Physics, American University of Sharjah, P.O. Box 26666, Sharjah, United Arab Emirates Neutron Scattering Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA Department of Physics, Columbia University, New York, New York 10027, USA. Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China. Department of Physics, Zhejiang University, Hangzhou 310027, China. Department of Physics and Astronomy, University of British Columbia, Vancouver, British Columbia V6T 1Z1, Canada Stewart Blusson Quantum Matter Institute, University of British Columbia, Vancouver, British Columbia V6T 1Z4, Canada TRIUMF, Vancouver, British Columbia, V6T 2A3, Canada. X-ray Science Division, Argonne National Laboratory, Argonne, IL 60439, USA (Dated: June 10, 2021)