Size-Dependent Same-Material Tribocharging in Insulating Grains

Observations of flowing granular matter have suggested that same-material tribocharging depends on particle size, typically rendering large grains positive and small ones negative. Models assuming the transfer of trapped electrons can account for this trend, but have not been validated. Tracking individual grains in an electric field, we show quantitatively that charge is transferred based on size between materially identical grains. However, the surface density of trapped electrons, measured independently by thermoluminescence techniques, is orders of magnitude too small to account for the scale of charge transferred. This reveals that trapped electrons are not a necessary ingredient for same-material tribocharging.

Figure 1

(a) Schematic of free-fall charge measurements. (b) Normalized particle size distribution determined by optical microscopy for unsifted grains (dotted grey line), sifted small grains (solid blue line), and sifted large grains (dashed red line). Inset: Microscope image of small and large grains. (c) Radius distribution (pixels) of all grains as determined by the analysis of the free-fall video (we measure here the “radius of gyration”; see Ref. [21] for details). Dashed vertical line indicates cutoff between large and small grains. Inset: Small portion of an image from the high-speed video.

Figure 2

Size-dependent charging. (a) Acceleration distribution of small (solid blue line) and large (dashed red line) grains for $V=3000\mathrm{V}$. (b) Mean acceleration $\overline{a}$ of small (blue solid diamonds) and large (red open circles) grains vs. $V$. Fits are of the form $\overline{a}=sV$. (c) Width of acceleration distributions ${\mathrm{\Delta }}_a$ for small and large gains vs. $V$ with the same symbols as (b). Fits are of the form ${\mathrm{\Delta }}_a=\sqrt{{\delta }_0^2+(kV{)}^2}$.

Figure 3

TL measurements of the trapped state density. (a) TL curves of photon count rate $\dot{N}$ vs temperature $T$ at ramp rate $6\mathrm{K}/\mathrm{s}$ for untreated grains (blue diamonds), grains exposed to $\sim 12$ hours sunlight (red circles), and grains exposed to $\sim 12$ hours UV lamp (green squares). Inset: Schematic of the TL measurement. (b) Total number of photons counted are for the same data as in (a).