Size-dependent same-material tribocharging in insulating grains
Scott R. Waitukaitis, Victor Lee, James M. Pierson, Steven L. Forman, Heinrich M. Jaeger
SSize-dependent same-material tribocharging in insulating grains
Scott R. Waitukaitis, Victor Lee, James M. Pierson, Steven L. Forman, and Heinrich M. Jaeger James Franck Institute and Department of Physics, The University of Chicago, Chicago, IL 60637 Department of Earth and Environmental Sciences,University of Illinois at Chicago, Chicago, Illinois, 60607 (Dated: September 3, 2018)Observations of flowing granular matter have suggested that same-material tribocharging dependson particle size, typically rendering large grains positive and small ones negative. Models assumingthe transfer of trapped electrons can account for this trend, but have not been validated. Trackingindividual grains in an electric field, we show quantitatively that charge is transferred based on sizebetween materially identical grains. However, the surface density of trapped electrons, measuredindependently by thermoluminescence techniques, is orders of magnitude too small to account forthe scale of charge transferred. This reveals that trapped electrons are not a necessary ingredientfor same-material tribocharging.
PACS numbers: 45.70.-n, 47.60.Kz, 37.20.+j, 51.10.+y
Although tribocharging is typically assumed to arisefrom frictional contact between dissimilar materials, itcan also be caused by interaction between objects madeof the same material [1, 2]. Several observations indicatethat the mechanism for same-material tribocharging ingranular systems is related to particle size, with largergrains typically charging positively and smaller ones neg-atively. The electric field of dust devils, for example, isknown to point upward, consistent with smaller, nega-tively charged grains being lifted higher into the air [3].A similar mechanism is suspected to be responsible forthe large electric fields and consequent lightning gener-ated in volcanic ash clouds [4–8]. Zhao et al. showed thatthe charge-to-mass ratio for a variety of powder samplescrossed from negative to positive as the particle diameterincreased, indicating a similar trend [9]. More recently,Forward et al. conducted experiments which revealed acorrelation between charge polarity and grain size forsamples with a binary particle size distribution (PSD)[10–13].Lowell and Truscott showed that dragging an insulat-ing sphere across a plane made of the same material usu-ally caused the sphere to charge negatively [14]. Theydeveloped a model based on a combination of asymme-try between two contacting surfaces and the transfer oftrapped electrons [14, 15], which they suggested tunnelbetween surfaces when contact offers the possibility forrelaxing into an empty, lower energy state. If the initialsurface density of trapped electrons is uniform, contin-ually rubbing some small region of contact (such as thetip of sphere) across a larger region ( e.g. a plate) leads tonet transfer of charge to the smaller region. Lacks andcoworkers later showed how the same geometrical asym-metry also arises with random collisions among particlesof different size [16–18]. However, while in most situa-tions the transferred charge species is negative, there aresome materials, such as nylon, where the polarity is re-versed, which points to the possibility that other chargespecies might be responsible (Hu et al. recently suggestedtrapped holes might explain the polarity reversal [19]). Given these observations and the lack of quantitativedata specifically linking charge transfer to the presence oftrapped electrons, their role in same-material tribocharg-ing is uncertain.Here we test whether or not trapped electrons are nec-essary for same-material tribocharging. First, we de-velop a non-invasive experimental technique that allowsus to measure the charge of individual grains while si-multaneously differentiating them by size. For a binary-sized sample, we show that charge is indeed transferredbetween the different sizes, with large grains becomingmore positively charged and small ones more negativelycharged. Assuming the trapped electron model is correct,the amount of charge transferred allows us to put a lowerbound on the required trapped electron surface densitybefore mixing. To test this assumption, we then directlymeasure the density of trapped electrons on the materialsurface prior to mixing with a thermoluminescence (TL)technique. This data puts an upper bound on the ac-tual surface density of trapped electrons that is orders ofmagnitude smaller than the lower bound required by thetrapped electron model. This demonstrates that trappedelectrons are not necessary for same-material tribocharg-ing and suggests that other candidate charge carriers andmechanisms should be considered.Our apparatus for measuring individual grain chargeswhile simultaneously differentiating grains by size isshown in Fig. 1(a). [Here we only discuss the essential de-tails of the measurement technique. For a full discussion,see Ref. [20].] For the granular material, we use fused zir-conium dioxide - silicate (ZrO :SiO , Glenn Mills Inc.)because it exhibits strong charging behavior and becauseit is known to the thermoluminescence community forits capacity to store trapped electrons [22–25]. To en-sure the grains are as materially identical as possible, webegin with an initially broad size distribution of grainsfrom a single factory batch. (We have further confirmedthat there is no difference in the composition of the grainswith energy dispersive X-ray spectroscopy.) We take thisinitial batch and mechanically sieve it into tighter distri- a r X i v : . [ c ond - m a t . s o f t ] A ug butions. We choose two cuts at the tails of the originaldistribution, the “large” and “small” grains, and mea-sure their average diameters with an optical microscope,as in Fig. 1(b). For the experiments here, ¯ d l = 326 ± µ m and ¯ d s = 251 ± µ m. We use a Faraday cup [26]to do a baseline measurement of the mean charges ofthe large and small grains before mixing, which gives¯ q l = − (3 . ± . × e and ¯ q s = − (5 . ± . × eper grain (here we take “e” to be the magnitude of theelementary charge, +1 . × − C). We then mix the twosizes by fluidizing with air in the grain-coated hopper forapproximately 30 minutes. At this point we put the hop-per into the vacuum chamber, as indicated in Fig. 1(a).Opening an orifice in the nozzle at the bottom of the hop-per allows the grains to fall freely via gravity between twolarge copper plates held at potential difference V . The re-sulting electric field causes a grain of charge q and mass m to experience a horizontal acceleration a = qV /ml .Outside the chamber a high-speed, high-resolution videocamera (Phantom v9.1, 1000 frames per second) guidedby low-friction rails falls alongside the grains, which en-ables us to track their horizontal trajectories with preci-sion and fit with parabolas to extract the accelerations a .The magnification and depth of field of our setup is highenough to allow us to distinguish a particle as “large”or “small”, as shown in Fig. 1(c). Performing approxi-mately 25 camera drops at a given V allows us to measurethe acceleration of several thousand grains and constructindependent acceleration distributions for the large andsmall grains.In Fig. 2(a), we plot the acceleration distributions forthe large and small grains at V = 3 . | E | = 59kV/m), which shows that the small grains have predom-inantly negative accelerations, i.e. negative charge, whilethe large grains generally have positive accelerations. Toextract the average charges ¯ q l and ¯ q s , we calculate themean accelerations ¯ a l and ¯ a s for each size and plot themas a function of V , as in Fig. 2(b). The proportionalitybetween ¯ a and V confirms that the charge distributionis unaffected by the field and thus reflects the state ofthe sample as it exits the hopper (this proportionalitywould break down if particles collided and transferredcharge inside the electric field, as in the mechanism pro-posed by P¨ahtz et al. [27]). From ¯ a = sV , the slope s = ¯ q/l ¯ m then gives access to the mean grain charge ifthe mass is known. Similarly, the width of the acceler-ation distribution, ∆ a , is related the the width of thecharge distribution,∆ q , via ∆ a = (cid:112) δ a + ( kV ) , where k = ∆ q /l ¯ m and δ a is the average uncertainty in an indi-vidual acceleration measurement, independent of appliedfield.From the specific material density ρ = 3800 kg/m andthe PSD in Fig. 1b we compute the average grain massesas ¯ m l = (7 . ± × − kg and ¯ m s = (3 . ± . × − kg. Using the fit values for the slope s this leads to meancharges ¯ q l = (1 . ± . × e and ¯ q s = − (2 . ± . × e for the two particle sizes. For the widths we obtain(2 . ± . × e and (1 . ± . × e for the large FIG. 1: (color online). (a) Schematic of free-fall charge mea-surements. (b) Normalized particle size distribution deter-mined by optical microscopy for unsifted grains (dotted greyline), sifted “small” grains (solid blue line), and sifted “large”grains (dashed red line). Inset: microscope image of smalland large grains. (c) Radius distribution (pixels) of all grainsas determined by analysis of free-fall video (we measure herethe “radius of gyration”–see Ref. [21] for details). Dashed ver-tical line indicates cutoff between “large” and “small” grains.Inset: small portion of an image from the high-speed video. V (V)0 1000 2000 3000 4000 50000.00.20.40.60.81.0 V (V) Δ a ( m / s ) (b)(c) –3 –2 –1 0 1 2 30.00.20.40.60.81.01.2 a (m/s ) P a a ( s / m ) (a) a ( m / s ) FIG. 2: (color online). Size-dependent charging. (a) Acceler-ation distribution of small (solid blue line) and large (dashedred line) grains for V = 3000 V. (b) Mean acceleration ¯ a ofsmall (blue solid diamonds) and large (red open circles) grainsvs. V . Fits are of the form ¯ a = sV . (c) Width of accelerationdistributions ∆ a for small and large gains vs. V with symbolssame as (b). Fits are of the form ∆ a = (cid:112) δ + ( kV ) . and small grains, respectively. Note that the values forthe mean charge are two orders of magnitude larger thanthe residual grain charge prior to mixing. Within our ex-perimental uncertainties total charge is conserved, whichmakes it explicit that the charge transfer is occurringamong the grains themselves and not with some othermaterial.Assuming the trapped electron model is correct, thescale of charge transfer between the large and small grainsallows us to put a lower bound on the surface density, σ ,of trapped electrons that must have been present before the two sizes were mixed. If σ is the same for all grainsinitially and all the excess trapped electrons of the largegrains are transferred to the small grains, it must be thecase that σ > N/ [ π ( ¯ d l − ¯ d s )], where N is the total num-ber of electrons transferred. Given the measured numberof transferred charges N ≈ . × , this implies σ > µ m − . The randomness of collisions makes this “com-plete transfer” scenario unlikely and, using the resultsof Lacks et al. [17], a more realistic estimate is σ > µ m − .To see if enough trapped electrons to account for theobserved charge transfer were present on the pre-mixedgrains, we use a technique from thermoluminescence dat-ing. This is accomplished by heating a sample of thegrains with a temperature ramp T = T + βt while simul-taneously measuring the photon emission rate ˙ N witha photomultiplier [inset to Fig. 3(a)]. If trapped elec-trons are present, one observes peaks in ˙ N vs. T becausealthough the emission rate increases with T , the avail-able population N in the trap states is being depleted.[For an introduction to thermoluminescence, we refer thereader to references [28–30]]. In Fig. 3(a), we plot typicalTL curves taken with a heating rate β = 6 K/s (with aThorn EMI 9635QB photomultiplier with peak quantumefficiency 0.29 at 375 nm). For grains from the samebatch as the ones used in the experiments of Fig. 2, weare unable to detect trapped electrons (the slight rise inthe ˙ N with T is a background “glow,” not a TL peak).If we try to load electrons into the trap states by radi-ation, either from the sun or from an ultraviolet lamp,we observe one characteristic TL peak. As explained in[26], we can vary the heating rate to show that this traphas an energy below the conduction band (cid:15) = 0 .
36 eV,typical for the trap depths encountered in other insula-tors [29]. In Fig. 3(b), we plot the integrated number ofphotons counted for each sample, which shows that evenwith maximum trap loading no more than ∼ σ = 2 πN/A s Ω,where Ω is the solid angle common to the sample ( ∼ A s is the area of the sample( ∼ ). This reveals that the actual density of trappedelectrons has an upper bound of σ ≈ × − µ m − , fiveorders of magnitude lower than the amount necessary toaccount for the charge transfer we observe in the free-fallexperiment.In principle, it is possible that additional electrons ex-ist at trap depths deeper than we can reach with the tem-perature range available to us, but several factors makethis unlikely. First, although our TL measurement shouldbe sensitive to traps as deep as ∼ ∼ − µ m − , as our chargingdata implies), we see no indication of traps beyond theone at (cid:15) ∼ .
36 eV. Additionally, traps beyond ∼
300 400 500 600 70001 × × × × T (K) N ( s - )
300 400 500 600 70001 × × × × × × . T (K) N (a)(b) photonsphoto-multiplierheating platesample FIG. 3: (color online). Thermoluminescence (TL) measure-ments of trapped state density. (a) TL curves of photon countrate ˙ N vs. temperature T at ramp rate 6 K/s for untreatedgrains (blue diamonds), grains exposed to ∼
12 hours sun-light (red circles), and grains exposed to ∼
12 hours UV lamp(green squares). Inset: schematic of TL measurement. (b)Total number of photons counted for same data as in (a). loading via visible light ( ∼ . − . et al. showed that charge transfer between non-identical insulating materials can be correlated with thebreaking of molecular bonds on the surface [42]. Alter-natively, other investigations have pointed out the im-portance of molecularly thin layers of absorbed water[40, 41, 45]. In particular, McCarty and Whitesides sug-gest that contact charging between different insulatingmaterials in general might be due to the transfer of OH − ions. As they point out, the exact details of how OH − ions might transfer are not clear, but in this scenariothe density of transferrable charges is no longer an is-sue. Even with partial monolayer coverage the numberof OH − ions far exceeds the lower bound of 15 µ m − .Thus, the transfer of OH − ions in adsorbed surface wa-ter is an intriguing possibility that will be the subject offuture work.We thank Gustavo Castillo, Estefania Vidal, SuomiPonce Heredia, and Alison Koser for contributions duringthe early stages of setting up the free-fall experiment, IanSteele for performing the EDS measurements, and DanielLacks, Troy Shinbrot, Ray Cocco, and Ted Knowltonfor insightful discussions. This work was supported bythe NSF through DMR-1309611. Access to the sharedexperimental facilities provided by the NSF-supportedChicago MRSEC (DMR-0820054) is gratefully acknowl-edged. S.L.F. and J.L.P. acknowledge funding from UICNSF Grant No. 0850830 and 0602308. S.R.W. acknowl-edges support from a University of Chicago Millikan Fel-lowship and from Mrs. Joan Winstein through the Win-stein Prize for Instrumentation. [1] E. W. B. Gill, Nature , 568 (1948).[2] T. Shinbrot and H. H. Herrmann, Nature , 773(2008).[3] J. R. Leeman and E. D. Schmitter, Atmos. Res. , 277(2009).[4] M. Brook, C. Moore, and T. Sigurgeirsson, J. Geophys. Res. , 472 (1974).[5] R. Anderson, S. Gathman, J. Hughes, S. Bjornsson,S. Jonasson, D. Blanchard, C. Moore, H. Survilas, andB. Vonnegut, Science , 1179 (1965).[6] T. Mather and R. Harrison, Surv. Geophys. , 387(2006). [7] I.M.P. Houghton, K.L. Aplin, and K.A. Nicoll, Phys.Rev. Lett. , 118501 (2013).[8] C. Cimarelli, M.A. Alatorre-Ibarg¨uengoitia, U. Kuep-pers, B. Scheu, and D.B. Dingwell, Phys. Rev. Lett. ,118501 (2013).[9] H. Zhao, G. Castle, and I. Inculet, Journal of Electro-statics , 261 (2002).[10] K. M. Forward, D. J. Lacks, and R. M. Sankaran, J.Electrostat. , 178 (2009).[11] K. M. Forward, D. J. Lacks, and R. M. Sankaran, Geo-phys. Res. Lett. , 1 (2009).[12] K. M. Forward, D. J. Lacks, and R. M. Sankaran, Ind.Eng. Chem. Res. , 2309 (2009).[13] K. Forward, D. Lacks, and R. Sankaran, Phys. Rev. Lett. , 028001 (2009).[14] J. Lowell and W. Truscott, J. Phys. D. Appl. Phys. ,1273 (1986).[15] J. Lowell and W. Truscott, J. Phys. D Appl. Phys. ,1281 (1986).[16] D. J. Lacks, N. Duff, and S. K. Kumar, Phys. Rev. Lett. , 188305 (2008).[17] D. Lacks and A. Levandovsky, J. Electrostat. , 107(2007).[18] N. Duff and D. Lacks, J. Electrostat. , 51 (2008).[19] W. Hu, L. Xie, and X. Zheng, Appl. Phys. Lett. ,114107 (2012).[20] S. R. Waitukaitis and H. M. Jaeger, Rev. Sci. Instrum. , 025104 (2013).[21] J. C. Crocker and D. G. Grier, J. Colloid. Interf. Sci. ,298 (1996).[22] P. Lacconi, D. Lapraz, and R. Caruba, Phys. Stat. Sol.A , 275 (1978).[23] W.-C. Hsieh and C.-S. Su, J. Phys. D Appl. Phys. ,1763 (1994).[24] H. Hristov, N. Arhangelova, V. Velev, I. Penev, M. Bello,G. Moschini, and N. Uzunov, J. Phys. Conf. Ser. ,012025 (2010).[25] J. Azorin, T. Rivera, C. Falcony, E. Martinez, andM. Garc´ıa, Radiation protection dosimetry , 317(1999). [26] Supplemental material.[27] T. P¨ahtz, H. J. Herrmann, and T. Shinbrot, Nat. Phys.pp. 1–6 (2010).[28] J. Randall and M. Wilkins, P. Roy. Soc. A-Math. Phy. , 365 (1945).[29] M. J. Aitken, Thermoluminescence Dating (AcademicPress, 1985).[30] S. L. Forman, in
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