Particle-Size-Dependent Triboelectric Charging in Single-Component

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Particle-size-dependent triboelectric charging in singlecomponent granular materials: Role of humidity Joseph Toth, Amber Phillips, Siddharth Rajupet, R. Mohan Sankaran, and Daniel J Lacks Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.7b02328 • Publication Date (Web): 06 Aug 2017 Downloaded from http://pubs.acs.org on August 10, 2017

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Industrial & Engineering Chemistry Research

Particle-size-dependent triboelectric charging in single-component granular materials: Role of humidity Joseph R. Toth III, Amber K. Phillips, Siddharth Rajupet, R. Mohan Sankaran, Daniel J. Lacks* Department of Chemical and Biomolecular Engineering, Case Western Reserve University, Cleveland, Ohio 44106 ABSTRACT: Granular systems undergo triboelectric charging even when the particles contacting one another are of the same chemical composition. We carry out experiments to investigate the triboelectric charging due only to particle-particle collisions as a function of humidity. At low humidity, we find that large particles tend to charge positive and small particles tend to charge negative, in agreement with previous studies. However, at high humidity, we find no significant particle-size dependence for the particle charging. To explain these results, we apply a theoretical model based on charge carriers trapped in non-equilibrium surface states characteristic of electrically insulating materials. Monte Carlo simulations show that collisions between particles enable the charge carriers to reach lower energy states on other particles. These non-equilibrium dynamics lead to an accumulation of charge carriers on small particles, and, if the charge carriers are negative (electrons or negative ions), the small particles would tend to charge negatively. We propose that humidity leads to conductive layers on the surface of particles that act as a sink for charge carriers, and thus reduce the particle-size dependent charging that follows from the presence of the charge carriers in non-equilibrium states. INTRODUCTION The process by which material surfaces become electrostatically charged as a result of physical contact is known as triboelectric charging.1 Triboelectric charging has particularly important consequences in granular systems. Since surface charge is proportional to surface area and mass is proportional to volume (for constant density), the high surface-to-volume ratio of particles leads to a large charge-per-mass ratio. In fact, the charge-per-mass ratio is often high enough that electrostatic forces exceed gravitational forces, allowing particles to adhere to or lift off surfaces. The adhesion of triboelectrically-charged particles is the basis of the digital printing and xerography industries.2 However, particle adhesion can also disrupt industrial processes involving granular materials, such as fluidized bed reactors.3 Particle lift-off is useful for removing dust from solar panels4 and can be used to protect equipment during lunar or Martian exploration missions.5,6 Intuitively, one would expect triboelectric charging to occur when the two contacting surfaces have different chemical compositions, such as particles of two different materials or particles of one material colliding with a wall of a different material, as this difference could cause a driving

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force for charge transfer. However, triboelectric charging also occurs when the two contacting surfaces have exactly the same chemical composition.7 Thus, even granular systems composed of chemically-identical particles can become highly charged from only particles colliding with and rubbing against each other. Furthermore, intuition might suggest that when two surfaces of the same chemical composition are contacted, the surface that charges positive and the surface that charges negative will be random, as there is no apparent driving force. However, many laboratory experiments find that in single-component granular systems, the smaller particles tend to charge negative while the larger particles tend to charge positive.8,9,10,11,12,13,14,15,16,17 In addition, electric field measurements in dust storms18,19,20,21,22,23,24 and other dust systems25,26 find bipolar electric fields oriented parallel to the direction of gravity with the negative pole at a higher elevation, corresponding to the smaller and lighter particles charging negative and being lifted to higher elevations, and the larger and heavier particles charging positive and staying closer to the ground. A mechanistic picture for the particle-size dependence of triboelectric charging in granular systems is perplexing.27,28 The particles are macroscopic (diameters typically 10-1000 µm) and, thus, material properties do not depend on particle size. Several ideas have been put forth to explain this effect, including particle polarization in a pre-existing electric field aligned with the direction of gravity29 and asymmetries in strain as particles of different sized particles collide.30 We have proposed a theory to explain this effect31,32 based on the non-equilibrium model of Lowell and Truscott.33 Our theory shows that one non-equilibrium effect, where some fraction of charge carriers are not in the ground state, leads to a second non-equilibrium effect, where charge carriers accumulate on the smaller particles. The fundamental idea underlying the model is that mobile charge carriers on insulator surfaces are trapped in a non-equilibrium distribution of higher energy states because the insulating nature of the material prevents charge carriers from relaxing to the lowest energy states. Contact between two material surfaces could bring a low energy state on one surface close to a charge carrier trapped in a high-energy state on another surface, and thus enable the charge carrier to relax to a lower energy state by transferring from one surface to another. We have shown that the asymmetry due to particle size differences leads to the second non-equilibrium effect, where the surface density of charge carriers becomes nonuniform across different sized particles. Note that this is a transient non-equilibrium state (although the timescale could be very long), as the equilibrium state corresponds to maximum entropy and thus equal surface densities (and charge) for all particle sizes. In the present work, we probe the existence of charge carriers in non-equilibrium high-energy states and their role in the particle-size dependence of triboelectric charging by changing the background humidity for particle charging. Humidity has been previously shown to make insulating particles behave like conductors by allowing surface charges to dissipate.34 Using our previously reported fluidized bed and on line electrostatic separator system to measure the particle-size-dependent charge, we carry out particle charging experiments at different humidities. We then propose a physical explanation for the results using a non-equilibrium model that follows from Lowell and Truscott.


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EXPERIMENTAL METHODS There are two significant challenges to carrying out controlled experiments of triboelectric charging with granular systems. The first is to disentangle the two main types of contact: particles contacting one another and particles contacting other surfaces such as the container walls. The mechanisms underlying charging in these two cases is likely different, as particleparticle contacts involve two surfaces of the same material, while particle-wall contacts involve two surfaces of different materials. In the present work, we address triboelectric charging due only to particle-particle collisions, and, thus, the experimental methodology must ensure that particles do not contact other surfaces. The second challenge is that the net charge arising from a particle ensemble is often not useful in characterizing the system, and the charge on individual particles, or the charge distribution, is needed. For example, consider that a granular system with a net charge of zero could in fact be very highly charged, with half the particles having high positive charge and the other half having high negative charge. Therefore, we need to separately determine the charge of positive and negative particles. We previously described a methodology to overcome these challenges, which was implemented in an open atmosphere.35 Briefly, a bed of particles (approximately 200 g) was first placed on a distributor plate with an array of five holes in the middle of the plate. When gas passed through these holes, the particles were fluidized in a ‘fountain-like’ manner, such that the moving particles contacted only other particles and not the walls of the bed. We then transferred a sample of particles from the bed to an electrostatic separator by using air to blow the particles from the fountain to ensure that no contact occurred between the particles and other surfaces (as would be the case if particles were picked up). The electrostatic separator was composed of two electrodes: one at positive 6000 V and the other at negative 6000 V. The polarity of the right and left electrodes were alternated in different trials to ensure that there was no bias from the positioning of the electrodes. The particles fell through the separator under the influence of gravity, and simultaneously migrated in the transverse direction towards the electrode of opposite charge. Bins were placed at positions underneath the electrodes: a bin by the positive electrode to collect negative particles (negative sample), a bin by the negative electrode to collect positive particles (positive sample), and three bins in the middle to collect neutral particles (neutral sample). Here, a similar fluidized bed and electrostatic separator system was set up inside an environmentally controlled chamber (Figure 1) to carry out experiments at prescribed values of relative humidity. The humidity was controlled by mixing a stream of dry air and a stream of wet air at different ratios in the chamber. The dry air was obtained from a compressed air tank and the wet air was made by bubbling dry air through water heated in an Erlenmeyer flask. The humidity was determined inside the chamber by a humidity meter (Fisher Scientific™ Traceable™ Humidity Meter). A fan inside the chamber helped ensure mixing, and the homogeneous humidity was confirmed using multiple probes at different locations in the chamber. The particle bed was fluidized by a separate gas stream of the same humidity as the chamber.


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Particle charging experiments were carried out with soda lime glass (Dragonite) with diameters between 300 and 800 µm. Glass particles were chosen because they are hydrophilic and thus will readily adsorb water from the ambient humidity; we note that quantifying the water adsorbed on the particles is difficult, and we do not precisely know the water content of the particles themselves. The fountain was run for a period of five minutes to reach steady-state charging before transferring particles into the electrostatic separator. After separating by charge polarity, the mass fraction of “large” and “small” particles in each bin was determined by separating with a 600 µm mesh sieve and weighing.

Figure 1. (a) Schematic illustration and (b) 3-D representation of the enclosed humiditycontrolled system. Humidity-controlled air is used to fluidize the particle bed and fill the background of the system. Particles collide with each other and charge in a fountain flow. The charged particles are transferred into the separator by pulses of dry air directed from the fountain toward the separator. The particles are then separated by their charge polarity using two oppositely-biased high voltage electrodes and collected in the bins under the electrodes. MODELING METHODS


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Our model is based on the idea that mobile charge carriers (electrons or ions) can reside in surface states of various energies.31,32,33 At equilibrium, the charge carriers occupy the lowest energy states; however, due to the non-conductive nature of insulating materials, the charge carriers do not relax to the lowest energy states, and thus some remain trapped in high-energy states. Contact could bring a charge carrier trapped in a high-energy state on one surface close to an unoccupied low-energy state on another surface, leading to transfer of the charge carrier between the two surfaces. We have shown that this idea alone leads to triboelectric charging with a particle-size dependence. This particle-size dependence was demonstrated with analysis and simulations, but the underlying basis for the behavior is simple: if all particles begin with the same surface density of charge carriers in high energy states, the larger particles (by virtue of their greater surface area) have a greater number of charge carriers that could be transferred to lower energy states on other particles, and thus larger particles become depleted in charge carriers while smaller particles accumulate them. It is not known whether the charge carriers relevant for triboelectric charging are electrons or ions,1 but this model can apply in either case.36 We note that a recent thermoluminescence spectroscopy study found that non-equilibrium electrons are not in high enough concentration to account for the observed triboelectric charging, suggesting that mobile ions may be the relevant charge carriers.16 Previous authors have suggested that OH- ions in the water layers on particles could be the mobile ions giving rise to triboelectric charging, transferred via water bridges that form as two particles with water layers collide.37 If the charge carriers are negative (electrons or negative ions), the larger particles will tend to charge positively and the smaller particles will tend to charge negatively. To implement this model, we consider a collection of N particles, where each ith particle has radius, Ri. Charge carriers on particle surfaces can reside in high-energy (H) or low-energy (L) states. At time t, the ith particle has the niH(t) charge carries in high-energy states and niL(t) charge carriers in low-energy states. The particles collide with other particles, where the probability of collision for the ith and jth particles are proportional to the collision cross section, (Ri + Rj)2. In a given collision, the probability that a charge carrier is transferred from state α on the ith particle to state β on the jth particle is given by

→ =

(1)

where kαβ is the state-to-state rate constant and α=H or L, β=L or H. Charge carriers can transfer from states on the jth particle to states on the ith particle in an analogous way. Monte Carlo simulations were carried out to determine the behavior that arises from this model. The following procedure was repeated Ncollisions times: (a) Particle i was chosen randomly from the entire set of particles to be a participant in a collision. (b) Particle j was chosen randomly from the remaining particles with probability proportional to (Ri + Rj)2, by choosing a random number r between 0 and ∑ + , and then determining which j-increment in this sum that r falls into.


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(c) For each of the eight ways that a charge carrier can transfer between these two particles, we determined if the transfer occurs by calculating → and choosing a random number r between 0 and 1; if r< → , then a single charge carrier was transferred from state α on particle i to state β on particle j. The simulations were run with N=1000 particles, where half of the particles have Ri=1 and the other half have Ri=0.5. The simulations were carried out for up to Ncollisions=50x106. Regarding initial conditions, we considered the situation that all particles initially have the same surface densities in each state (denoted ρΗ0 and ρL0, respectively), and so 0 = 4 . The initial surface densities were such that the sum ρΗ0 + ρL0=2000/π, and we varied the fraction in the high energy state, φΗ0=ρΗ0/(ρΗ0 + ρL0). On physical grounds, we expect the rate of transfer would be greatest for transitions from H to L states, negligible for transitions from L to H states, and intermediate for transitions between same energy states. Therefore, we used the rate parameters kHL=0.5, kLH=0, kHH=kLL=0.05. The qualitative results of the simulations are independent of the particular choices of these values provided kHL>> kHH, kLL >>kLH; we chose the particular values described above because, as we show below, they give results quantitatively similar to those found in the experiments. RESULTS Experiments Experiments were carried out to examine the triboelectric charging due to particle-particle collisions under various relative humidities from 2% to 58%. More than ten trials were carried out under each humidity condition. We collected samples of positive and negative particles in these experiments, and characterized their size distribution by the mass fraction of large particles (>600 µm) in each sample. As shown in Figure 2, at 0-10% relative humidity, the positive sample is enriched in larger particles, and the negative sample is depleted in larger particles. Thus, in this case, the larger particles are tending to charge positive, and the smaller particles are tending to charge negative. A t-test shows that this effect is statistically significant (probability of null hypothesis that values are the same is P ~0). As discussed in the Introduction, this particle-size dependence of charge polarity has been found in many previous experiments8-17 and inferred from electric field measurements in dust systems.18-26


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Figure 2. (a) Experimentally-measured mass fraction of large particles in triboelectricallycharged soda lime glass particles as a function of background relative humidity and (b) difference between positive sample and negative sample mass fraction as a function of relative humidity. Each data point corresponds to an average of numerous points within that bin of humidity.


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This particle-size dependence of charge polarity becomes smaller as humidity increases. At 2030% humidity, the positive sample is still found to be enriched in the large particles, and the negative sample depleted in large particles, but the difference in the compositions of the samples is much smaller; a t-test shows that the difference is probably not statistically significant (P ~26%). At 50-60% humidity, there is no significant difference in the composition of the positive and negative samples (P~56%). There are two possible explanations for our finding that the particle-size dependence of charge polarity diminishes at high humidity. The first possible explanation is that the particles remain electrostatically charged, but without any dependence of the charge on particle size. The second possible explanation is simply that the particles lose their charge (i.e. particles become neutralized). Experiments were performed to distinguish between these two possible explanations. We determined the mass of particles collected in the “side bins”, which are the outer bins closest to the positive and negative electrodes; note that in the presence of an electric field, charged particles will be drawn to the electrodes, and thus would fall into these side bins. Figure 3 shows the mass fraction of particles collected in these side bins as a function of the magnitude of the voltage on the electrodes, at both 5% humidity and 55% humidity. At zero voltage, about 22% of the particles fall into these side bins, due to the initial trajectories of the particles blown into the separator. As the voltage increases, significantly more particles are collected in the side bins; these additional particles are drawn to a side bin because they have charges opposite to the electrode polarity and the attractive force alters their trajectory towards the respective electrodes and into the side bins. The results at 5% humidity and 55% humidity are the same within experimental error, thus showing that the extent of charging is the same in these two cases. Thus, we conclude that at high humidity the particles are electrostatically charged, but without any dependence of the charge on particle size.


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0.35 5% 55%

Mass fraction in side cups

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0.30

0.25

0.20

0

2

4 6 Voltage (kV)

8

10

Figure 3. Experimentally-measured mass fraction of particles collected in the bins closest to the two electrodes. Black squares are results at 5% humidity, and red circles are results at 55% humidity. Thus, the experimental results show that at lower humidity, particle charging occurs such that larger particles tend to charge positively while smaller particles tend to charge negatively. However, the particle-size dependence of the polarity of charge becomes smaller and ultimately becomes negligible as the humidity increases. Simulations To understand the charging behavior as a function of humidity, we first discuss in detail the results of a Monte Carlo simulation with φΗ0= 0.015. Initially all particles are neutral and have the same surface density of charge carriers, with the fraction of charge carriers, φΗ0, being in the H state and the fraction (1- φΗ0) being in the L state. Note the larger particles, by virtue of their larger surface area, have a greater number of charge carriers, 0 and 0. As the simulation proceeds, the particles collide with one another and exchange charge carriers according to probabilities described by Equation 1. We examine separately the two sets of particles: the set of particles that experience a net gain of charge carriers, and the set of particles that experience a net loss of charge carriers. The results for the number fraction of large particles in each of these sets, as a function of number of collisions, are shown in Figure 4. The set of particles that gains charge carriers is composed mostly of small particles, and the set of particles


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that loses charge carriers is composed mostly of large particles. The magnitude of this sizedependence effect initially increases with the number of collisions, but then decreases with further collisions.

0.8 Number fraction of large particles

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Particles losing species

0.7 0.6 0.5 0.4 0.3 0.2

Particles gaining species

0

1 2 3 4 Number of collisions (x 107)

5

Figure 4. Simulation results for number fraction of large particles that lost charge carriers (red) or gained charge carriers (black), as a function of the number of particle collisions for the case φΗ0= 0.015. The results in Figure 4 can be understood by considering the consequences of the different types of transitions: (a) HL transitions. These transitions are “one-way” (since the rate of LH transitions are zero), and lead to the key charge carrier dynamics. To develop an intuition of the behavior, consider what would happen if a given large and small particle, in their initial states, undergo two consecutive collisions. In the first collision, it is equally likely that a charge carrier is transferred from the H state on the large particle to the L state on the small particle as it is that a charge carrier is transferred from the H state on the small particle to the L state on the large !,# particle, because the term is equal in magnitude. For arguments sake, we assume both

transitions occur. After these two transitions occur, each particle has the original number of charge carriers, but with one less charge carrier in the H state and one more in the L state. Now,


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the situation is different for the second collision, because the quantity

!,# $%

%

!,# = − is

greater for the large particle than for the small particle. Thus, on the second collision, it is more likely for a charge carrier to be transferred from the H state on the large particle to the L state on the small particle, than for a charge carrier to be transferred from the H state on the small particle to the L state on the large particle. Thus, the small particles accumulate charge carriers and the large particles become depleted of charge carriers. (b) HH and LL transitions. These transitions are “two-way” and can thus act to bring the system to the maximum entropy state of constant surface density of mobile charge carriers on all particles. The effects of the HL transitions dominate at a low number of collisions and cause small particles to gain charge carriers and large particles to lose charge carriers. In this case, the set of particles that gain charge carriers will be composed mostly of small particles. The effects of the LL transitions dominate at a high number of collisions, and eventually bring the system to the maximum entropy configuration where all particles have the same surface density of charge carriers and thus are at equilibrium. Thus, in the limit of large number of collisions, there is no particle size dependence for the charge polarity. This limit should be equilibrium, and is characterized by an equal density of charge carriers on the particles, which corresponds to maximum entropy and is, thus, self-consistent with equilibrium. We note triboelectric charging is an inherently non-equilibrium phenomenon (again, as equilibrium corresponds to uncharged surfaces); we propose that the triboelectrically charged state corresponds to the state at intermediate time scales.” Simulations were carried out with various values of φΗ0. Figure 5 shows the number fraction of large particles that gain charge carriers and that lose charge carriers as a function of φΗ0. At large φΗ0, there is a strong particle size dependence in that the smaller particles tend to accumulate charge carriers and the large particles tend to become depleted of charge carriers. However, this particle size effect decreases as φΗ0 decreases; i.e., at a small value of φΗ0 the set of particles that gains charge carriers and the set of particles that lose charge carriers have similar particle size distributions. The particle size effect depends on φΗ0 because it is the HL transitions that cause small particles to accumulate charge carriers, but as φΗ0 becomes small, the number of charge carriers in the H state becomes too small to have an appreciable effect. We have thus far described the model in terms of generic charge carriers. If the simulated charge carrier is a negative species, the result would be that the large particles tend to have a net positive charge and the small particles tend to have a negative charge, which agrees with the experimental observations.


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0.58 Number fraction of large particles

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Particles losing species 0.56 0.54 0.52 0.50 0.48 0.46 0.44

Particles gaining species

0.005 0.004 0.003 0.002 0.001 0.000

φΗ0 Figure 5. Simulation results for number fraction of large particles that lost species (red) or gained species (black) as a function of φΗ0 (φΗ0=ρΗ0/(ρΗ0 + ρL0)). The values shown are averaged results between 40 and 50 million collisions. The x-axis is reversed to show that the reduction of φΗ0 decreases the particle size dependence of the charge transfer. DISCUSSION AND CONCLUSION Our experiments show that at low humidity, granular materials exhibit a particle size dependence in triboelectric charging such that small particles tend to charge negative and large particles tend to charge positive, consistent with previous studies.8-17 In the present study, we go further and show that this particle size dependence decreases as humidity increases, such that at high humidity there is no difference in the charge polarity of the small and large particles. We believe the physical basis of this humidity effect can be understood in terms of the nonequilibrium dynamics of charge carriers. The key idea is that charge carriers at the surface of insulators cannot fully equilibrate as insulating materials by their nature allow very limited charge mobility. Therefore, some charge carriers are trapped in high-energy states and are unable to relax to lower energy states elsewhere on the same surface. However, at high humidity, sufficient water adsorbs on the particle surfaces to form a conductive surface layer, and can cause insulator particles to act like conductor particles. This surface conduction is the reason why we do not experience triboelectric effects – such as shocks when touching a doorknob – on days with high humidity. As another example of humidity-dependent surface conductivity, we


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previously showed that nylon spheres sitting on an electrode in an electric field behave like insulators at low humidity, but like conductors at high humidity.34 In regard to the nonequilibrium dynamics, the conducting layer may enable some of the charge carriers trapped in high-energy states to relax to lower energy states on the same particle, and, thus, high humidity conditions correspond to a lower value of φΗ0 in our non-equilibrium dynamics model. Based on this connection between humidity and φΗ0, we can compare the results from our experiments and simulations. The experimental results in Figure 2 show that at low humidity smaller particles tend to charge negative and larger particles tend to charge positive, but this effect goes away at high humidity, even though the particles still charge. Similarly, simulation results in Figure 5 show that at high φΗ0, smaller particles tend to accumulate charge carriers and larger particles tend to become depleted of charge carriers, but that this effect goes away at low φΗ0. If the charge carriers are negative (electrons or negative ions), and the humidity is inversely related to φΗ0, then the experiments and simulations are in agreement. We chose the parameter values for the simulations shown in Figure 5 to fit the magnitude of the effect – i.e., the fraction of large particles in the set of particles that charges positive – is similar to that in the experiments. While this quantitative agreement is of course due to an empirical fit, we note that simulations with any set of model parameters following the rule kHL>> kHH, kLL >>kLH will give results that are qualitatively in agreement with experiment. In conclusion, this study provides support of the idea that non-equilibrium effects play an important role in triboelectric charging of granular systems. We believe the non-equilibrium effects, which are greatest at low humidity, lead to the particle-size dependence of particle charge polarity. The non-equilibrium effects become smaller at high humidity because humidity creates a conductive surface water layer that enables charge carriers to relax to equilibrium states. Thus, as humidity increases, the particle-size dependence of particle charge polarity becomes smaller and ultimately becomes negligible. We expect this humidity effect will be most significant for hydrophilic materials, which have significant water adsorption; for hydrophobic materials we expect that this humidity effect will be smaller (less dependence of φΗ0 on humidity), and the particle-size dependence of particle charge polarity will persist to high humidity. AUTHOR INFORMATION Corresponding Author * Daniel J. Lacks, [email protected] Notes The authors declare no competing financial interest. ACKNOWLEDGMENTS This material is based upon work supported by the National Science Foundation under grant numbers CBET-1235908, CBET-1604909 and DMR-1206480. REFERENCES


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Particle-Size-Dependent Triboelectric Charging in Single-Component

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