Does Flexoelectricity Drive Triboelectricity?

The triboelectric effect, charge transfer during sliding, is well established but the thermodynamic driver is not well understood. We hypothesize here that flexoelectric potential differences induced by inhomogeneous strains at nanoscale asperities drive tribocharge separation. Modeling single asperity elastic contacts suggests that nanoscale flexoelectric potential differences of $\pm 1–10\mathrm{V}$ or larger arise during indentation and pull-off. This hypothesis agrees with several experimental observations, including bipolar charging during stick slip, inhomogeneous tribocharge patterns, charging between similar materials, and surface charge density measurements.

Figure 1

Schematic of asperity contact between a rigid sphere (blue) and an elastic body (red). During indentation and pull-off the elastic body will deform, developing a net strain gradient opposite to the direction of the applied force ($F$).

Figure 2

(a)–(e) Symmetrically inequivalent strain gradients arising from Hertzian indentation of an elastic half-space that can flexoelectrically couple to the normal component of the electric field. Lines indicate constant strain gradient contours in units of ${10}^6{\mathrm{m}}^{-1}$, $z$ is the direction normal to the surface with positive values going into the bulk, $x$ is an in-plane direction, and the origin is the central point of contact. Data correspond to 1 nN of force (a conservatively small number) applied to an elastic half-space with a Young’s modulus of 3 GPa and a Poisson’s ratio of 0.3 (typical polymer) by a 10 nm rigid indenter. (f) The magnitude of the average effective strain gradient ($|(\overline{\partial \epsilon }/\partial z){|}_{\mathrm{eff}}|$) as a function of indenter radius ($R$). The average effective strain gradient corresponds to a sum of the strain gradient components shown in (a)–(e) averaged over the indentation and pull-off volumes.

Figure 3

(a) Normal component of the electric field induced by Hertzian indentation via a flexoelectric coupling. Lines indicate constant electric field contours in units of $\mathrm{MV}/\text{m}$, $z$ is the direction normal to the surface with positive values going into the bulk, $x$ is an in-plane direction, and the origin is the central point of contact. Data correspond to 1 nN of force applied to an elastic half-space with a Young’s modulus of 3 GPa and Poisson’s ratio of 0.3 (typical polymer) by a 10 nm indenter. A flexocoupling voltage of 1 V is assumed. (b) Magnitude of the average electric field ($|\overline{E_z}|$) in the indentation or pull-off volumes as a function of indenter radius ($R$) assuming a flexocoupling voltage of 1 (dashed) and 10 V (solid).

Figure 4

Electric potential difference along the surface of the deformed body for indentation (solid) and pull-off (dashed). $x$ is an in-plane direction and the origin is the central point of contact. Data correspond to 1 nN of force applied to an elastic half-space with a Young’s modulus of 3 GPa, Poisson’s ratio of 0.3, adhesion energy of $0.06\mathrm{N}/\mathrm{m}$ (typical polymer), and flexocoupling voltage of 10 V by a 10 nm indenter.