A detailed study of the interaction between levitated microspheres and the target electrode in a strong electric ﬁ eld

In this work, we report on an in-depth study of how 10 μ m silica and polystyrene particles interact with a target electrode after they were levitated by applying a strong electric ﬁ eld. The results show that, under these conditions, silica particles unexpectedly have a higher tendency to adhere on a ﬂ uorocarbon coated electrode compared to a bare, non-coated silicon electrode. Relative adherence ratios Γ up to Γ = 4.7 were observed. Using the colloidal probe technique, atomic force microscopy (AFM) and Kelvin probe force microscopy (KPFM), the observations can be explained by a mechanism where particles dissipate their energy through adhesive forces combined with permanent surface deformations during impact and charge transfer through the contact electri-ﬁ cation phenomenon.Allthese processes attributeto increasingthe probability thatlevitatedparticles attainve-locities that are lower than the sticking velocity.


Introduction
A profound description of the electrostatic interaction and charge transfer between particles and bodies of finite sizes is critical to model a variety of fundamental processes in science and engineering [1,2].For this reason, the electrification of particles remains significant to date.Relevant scientific and industrial application of charged particles includes cloud formation in the atmosphere, like-charge attraction in colloidal systems, ion-mediated interactions and self-organization in nucleic acids and proteins, charging of interstellar dust grains, planet formation, toner particles in xerophotographic techniques, dry powder coating, pharmaceuticals, fluidized beds and pneumatic conveying systems [3][4][5][6][7][8].
In laboratory experiments, researchers apply strong electric fields to levitate particles between electrodes [3,[9][10][11], resembling sand/dust storms and dust devils or fluidized bed configurations.If the grains inside the formed particle cloud collide during these natural events, electrical charges accumulate or deplete on these grains as a consequence of contact electrification.Contact electrification or tribocharging is a phenomenon, already discovered by the ancient Greek, in which bodies are electrified upon contact and release.Despite the endeavours of accomplished scientist to unravel this phenomenon, the scientific community remains inconclusive on the exact fundamental mechanism lying at the heart of contact electrification [1,2,[12][13][14].In addition to the occasionally catastrophic natural phenomena it may cause, contact electrification is also important in science and technology, as it excites charged particles to adhere to walls in fluidized beds and pneumatic conveying processes, or stiction of extraterrestrial particles on spacesuits of astronauts or spaceships.Overall, these adhered particles may inflict tremendous damage to all these applications [1].
It is well known that the application of a sufficiently strong electric field in a parallel plate electrodes setup may levitate particles from the lower electrode towards the target electrode.The particles inevitably impacting against the target electrode may rebound and form a particle cloud between the electrodes [15].A multitude of studies has reported on the instantaneous electrostatic phenomena occurring amid the collision of mostly (sub)millimetre-sized particles against metal target plates [2, [16][17][18][19][20], while only a few studies have focused on the impact of microparticles on polymer targets [6,[21][22][23][24][25].The amount of charge transferred during impact depends on the mechanical and electrical properties of the colliding bodies [25], while the empirically established triboseries predicts the direction of charge transfer [1,26].
In the present study, we made an in-depth study of the mechanism of 10 μm powder beads impacting, rebounding and sticking on the target electrode when generating a cloud of microparticles by subjecting them to a strong electric field E ! layer material of the target electrode.Surprisingly, the counterintuitive observation is made that the presence of a CF x -layer (2≤x≤3) [27] on a silicon electrode leads to a stronger adhesion of silica particles than is the case on a bare silicon electrode, whereas in many areas of technology, surfaces are coated with fluorocarbon layers to decrease the adhesive forces [28][29][30].The results obtained in the present study may hence be advantageous to surface cleaning applications in preventing recontamination [31] or the projection of abrasive particles on surfaces [32].

Setup
Fig. 1 shows a schematic representation of the employed in-house built experimental setup, which consists of two electrodes connected to the terminals of a high-voltage power supply (UltraVolt 15A12-P4 & 15A12-P4, Advanced Energy, USA).An adjustable air gap (distance d) separates the electrodes with a potential difference V applied between the two electrodes, such that an electric field E ! ¼ V d can be applied that is high enough to levitate the particles from the lower electrode (cf.Movie S1).In the experiments, a pile of powder (16 ± 3) mg was scooped on the lower electrode, which was grounded at all times during the experiment.The upper electrode, further referred to as the target electrode of the setup, was normally connected to a +V terminal but could also be switched to a -V terminal to reverse the electric field E ! .The experiments were performed at ambient conditions (T = 21 − 22 ∘ C, RH = 40-52%; measured with Digital Professional Thermo-Hygrometer KLIMA BEE, TFA®, Germany).

Materials and methods
The lower electrode was a 4 in.boron-doped p-type silicon wafer (Si-Mat; Germany).The target electrodes were diced in pieces of 20 × 20 mm from either the CF x -coated or the uncoated silicon wafers.The coated electrodes were fully covered or patterned with the CF x -polymer.The details of the fabrication process of the CF x -coated wafers is described in our recent work [33].The native oxide layer, typically of ca. 3 nm, on uncoated silicon wafers was not removed, as it is known that such a layer does not affect experiments with fields applied in this study.The coated electrodes were uniformly covered or patterned with the CF x -polymer (thickness = 50-75 nm).Prior to each experiment the electrodes were sonicated for 10 min.in acetone followed by an additional 10 min. of sonication in IPA, to eliminate any traces of organic contaminants or dust particles from their surfaces.Experiments were performed using monodisperse hydrophilic silica particles (9.98 ± 0.31) μm as well as hydrophobic polystyrene particles (10.14 ± 0.12) μm.The indicated standard deviation values are provided by the supplier microParticles GmbH (Germany).Table 1 lists the relevant physical properties of the materials (i.e., the Young's modulus Y, the yield stress p yield , the Poisson's ratio μ, the density of the particle ρ p , the relative permittivity ε r , and the electrical resistivity ρ res ) used in this study.
After switching off the high voltage power supply, the target electrodes were inspected using a Zeiss MERLIN HR-SEM to take scanning electron microscopy (SEM) images.To calculate the particle density (mm −2 ) on the target electrodes, the SEM images were postprocessed using ImageJ (NIH Image) [34] to count the number of particles N.
Contact angle measurements were performed on the OCA15+ goniometer (DataPhysics Instruments GmbH, Germany).Microliter water droplets were created by employing a computer-controlled syringe.A camera was used to characterize the droplet shape in terms of dimensions and contact angles [35].
We performed colloidal probe measurements [36] to measure the adhesive force of a silica colloidal probe (CP-NCH-SiO-D-5, NanoAndMore GmbH, Germany) on the CF x -layer and on the silicon surface.The Kelvin probe force microscopy (KPFM) experiments were conducted in a Bruker Icon Atomic Force Microscope (AFM) at ambient conditions with RH = 50-55% (measured with a Digital Professional Thermo-Hygrometer KLIMA BEE, TFA®, Germany).A heavily doped ndoped Si-cantilever (resistivity = 0.01-0.02Ωcm)) with a resonance frequency of 75 kHz and a force constant of 2.8 Nm −1 (SSS-FMR, nanosensors) was used.The FM-KPFM mode was used, using the frequency shift of the cantilever oscillation to detect the electrostatic force gradient.As the tip was grounded during the KPFMmeasurements, the contact potential difference (V CPD ) is determined by: with e the elementary charge and ϕ s and ϕ tip the work function of the sample and tip, respectively.This equation also shows, that a positive (negative) shift in V CPD corresponds to a negatively (positively) charged surface [37].

Theory
When particles collide with a target electrode, the surfaces of the bodies may mechanically deform, depending on the nature of the impact and the material properties.In the case of elastic collisions, the surfaces deform elastically, whereas if the impact is inelastic the surface of mechanically the most vulnerable material deforms plastically, i.e. the deformation is permanent.
The threshold velocity v tres characterizing the onset of plastic deformation is related to the mechanical properties of the involved materials and has been derived in the work of Thornton and Ning [38] as: where p yield denotes the yield stress of the weakest material, and k is the modified Young's modulus given by: where Y and μ are the elastic moduli and Poission's ratio of the particle and target material respectively.If the normal impacting velocity v y of a  particle with diameter D p exceeds the threshold velocity, i.e., v y > v tres the corresponding area of permanent surface deformation S per [21] can be calculated using: The energy W sep that is dissipated to separate the surfaces after the impact yields the particle rebound velocity v reb < v i that can be determined from: Next to the plastic surface deformation, attractive adhesive forces between surfaces may also contribute to the energy dissipation during impact.It is well-known that the adhesive forces between microparticles and plane surfaces are substantial [39], such that even in the case of elastic collisions the rebound velocity can be significantly smaller than the impact velocity.In case the impacting velocity is so small that the impact force does not transcend the adhesive surface forces, the particle will stick onto the target electrode (v reb = 0).Following the rationale discussed in the work of Thornton and Ning [38] the upper limit of the sticking velocity v stick is equal to: where F pull is the pull-off force between the particle and the planar surface, m p and R p are the mass and the radius of the particle, respectively.Particles with impact velocity v i ≤ v stick will immediately stick onto the target electrode, regardless whether the collision is elastic or inelastic.

Experiments performed using silica particles with a CF x -patterned target electrode
The first set of experiments was performed with a pile of powder (18 ± 1) mg comprising 10 μm silica particles deposited on the lower electrode with the CF x -patterned silicon target electrodes.The power supply was set to V = +6 kV for a time of t = 10 s, and the distance between the electrodes was adjusted to d = 5 mm.After applying the electric field, a significant fraction of the particles levitated and formed a cloud between the two electrodes.After switching off the power supply, it was observed that the CF x -coated parts of the target electrode were clearly covered much more intensely with irreversibly adhered silica particles than the non-coated parts (Fig. 2).The particle densities on the respective surfaces were measured to quantify this observation.
The particle density on the surface of the target electrode can be quantified using the following equation: where N denotes the counted number of particles on a surface with area A. The ratio Γ between the particle density on the CF x -coated areas σ CFx , and the density on the non-coated silicon area σ Si is then defined as: The ratio Γ for the different cases displayed in Fig. 2 varies (see caption of Fig. 2 for exact values and their standard deviation), but is in all cases clearly significantly larger than Γ = 1, representing the case of an unselective attraction.One possible explanation for the fact that Γ > 1 could be that the patterned target electrode induces a spatial distribution of the particles within the particle cloud, leading to a higher number of particles reaching the CF x -coated vs. the non-coated areas.This is not expected as the thickness of the CF x -layer is significantly less than the air gap between the electrodes.

Experiments performed using silica particles with uncoated silicon target electrodes and the uniformly-coated (with CF x ) target electrodes
Hence, to investigate that the higher particle density measured on the CF x -patterned areas is not merely an effect of the spatial distribution of particles approaching the target electrodes, experiments were performed separately on a silicon target electrode and a silicon target electrode uniformly-coated with the CF x -polymer.Fig. 3 compares target electrodes after an experiment with (a) a uniform silicon electrode and (b) a uniformly-coated CF x -electrode, both conducted at the same field strength (E = 1.2 MVm −1 for t = 10 s).Similar to the patterned electrode case, the surfaces of these uniform target electrodes were also significantly covered with silica particles.The ratio between the measured particle density on the CF x -coated and the non-coated silicon target electrode averaged after three experiments is Γ = 2.7 ± 0.8.Thus, even in this case, there is a significantly higher tendency for the silica particles to adhere to the CF x -patterned electrode compared to the uncoated silicon wafer electrode.Within the large measurement variability, the Γ-ratio measured here is of the same order as the values obtained on the patterned electrodes considered in Fig. 2, such that the hypothesis that the observed particle segregation is caused by a spatial distribution of the particles within the cloud can be largely rejected (within the confidence limits of the measured data).
Another hypothesis that can be formulated to explain the observations, is that the silica particles have a higher tendency to adhere to the CF x -coated surfaces compared to the non-coated silicon surfaces.This is counterintuitive, as surfaces are commonly coated with fluorocarbon layers to decrease the adhesive forces [28][29][30].To investigate this hypothesis, we measured the pull-off force of a silica colloidal probe from the surface of a silicon sample and a CF x -coated sample.The results are shown in Table 2 and prove that the pull-off force of the hydrophilic silica colloidal probe is indeed stronger on the hydrophilic silicon surface than on the hydrophobic CF x -coated surface, which is in good agreement with previous studies [39].The colloidal probe measurements imply that the interaction forces between the hydrophilic silica particles and hydrophilic silicon surface are stronger than the forces between the particle and the hydrophobic CF x -coated surfaces.Following the rationale to reduce particle adhesion, the silica particles would preferentially stick onto the silicon surfaces, whereas in the present study consistently the opposite is observed.We believe the clue to this observation can be found in our recent study [33], where we have shown that rubbing-induced tribocharging leads to a preferential adherence of silica particles to CF x -coated surfaces.As stated before, contact electrification could occur during the collisions between the particles and the target electrode, hence the impact of the particles on the target electrodes was studied in more detail.

Silica particle impacting on different target electrodes
To characterize the nature of the particle impact on the target electrode both the elastic velocity v tres and the sticking velocity v stick between the silica particle and the silicon target electrode or the CF xcoated target electrode were estimated respectively by substituting the values presented in Table 1 in Eq. 2 and Eq. 6.The outcome is presented in Table 2. Presumably, the silica particles found on the surface of the electrodes are those that attained impacting velocities lower than the sticking velocities.The sticking velocity v stick on the CF xcoated target electrode is higher than on the silicon electrode due to the lower Young's modulus Y of the CF x -polymer.Owing to the lower computed sticking velocity v stick of the silica particles on the silicon electrode compared to the CF x -coated target electrode (cf.Table 2), there is a higher probability of impacting silica particles adhering onto the CF xcoated electrode.Additionally, the computed velocities suggest that the impact between the silica particle and the CF x -coated target electrode may be inelastic, but that the impact with the silicon electrode is definitely elastic.
To confirm that the assumptions hold, it was attempted to record the experiment with a high-speed camera setup.However, due to poor resolution it was difficult to measure the impact velocity of the particles.Therefore, another strategy was followed to estimate the impact velocity.The adhered silica particles have been blown off the target's surface to inspect the surfaces of both the silicon and the CF x -coated target electrodes with the atomic force microscope (AFM).The surfaces of the target electrodes were scanned with the AFM before and after performing the experiment with silica particles that were subjected to an electric field E = 1.2 MVm −1 for t = 10 s.It was observed from the topography scans that the impact inflicted clearly distinguishable craters on the CF x surface, whereas in the case of the silicon electrode, no surface deformations were visible.Fig. 4a clearly shows one of the observed craters on the topography scans of the CF x -coated electrode with its corresponding depth-profile plotted in Fig. 4c.Therefore, it can be concluded that the impact between the silica particle and the CF x -coated target electrode is indeed inelastic.It can be noticed from Fig. 4c that the depth-profile  of the crater slightly deviates from the ideal case in which the maximum deformation should occur in the crater's centre.We can only speculate about the exact origin of this effect.It is plausible that the impacting particle was not perfectly spherical or that it reached the surface with a small incident angle with respect to the normal.A third reason is a fact that the particle has been rotating either during its impact with the surface or during subsequent manipulations of the sample.The schematic cross-section of a crater is displayed in the inset of Fig. 4d with contact diameter a and depth h.For each crater, the surface area A c is computed and using Eq. 4, we have calculated the impact velocities v i of the particles.The values of the measured surface area are within a range of 0.13-0.5 μm 2 .According to Eq. 4, these values respectively correspond to impact velocities between v i = 0.25 − 0.52 ms −1 .These values imply that the impacting velocities of the particles on the target electrode are either higher or lower than v stick (= 0.28 ms −1 ) of the silica particle on the CF x -coated surface.It should be noted that in the case of the 5 μm impacting silica particles, no apparent surface deformation was measured on the CF x -coated surface using the AFM.However, similar to the results of the 10 μm silica particles, a higher particle density of 5 μm silica particles was measured on the CF x -coated surface.
To inspect if any charge is transferred between the particle and the target electrode, KPFM measurements have been conducted on the CF x -coated target electrode and the silicon electrode to measure the contact potential difference V CPD .No change in the V CPD value was measured on the surface of the silicon target electrode.However, from Figs. 4b-c it is noticed that the V CPD value on the CF x layer increased at the impact area with the particle.An increase of the V CPD value indicates that charge is transferred from the silica particle to the CF x -coated target electrode during impact.Therefore, the CF x -coated electrode locally charges negatively, while no charge is transferred to the non-coated silicon parts of the target electrode, which is in agreement with our previous study [33].It could be argued that based on the electrical time constant τ = ρ V × ε 0 ε r these results are expected, where ε 0 denotes the vacuum permittivity.The silicon wafer has a much lower electrical time constant than the CF x layer (compare τ silicon = 10 ps vs. τ CFx = 2 days).Consequently, in contrast to the CF x layer, the silicon wafer would have been completely discharged, such that no difference in V CPD -value can be measured.However, in our previous study [33], it is concluded that even for silicon wafers with thicker oxide layers, no change in V CPD -values on the wafers or the silica particles could be measured, despite the higher electrical time constant of silica τ silica = 1 hour.Therefore, it is assumed that as the silicon wafer has a native oxide layer, limited charge is transferred between the silica particles and the silicon wafer during impact.On the other hand, owing to their position on the triboseries, a significant amount of charge is transferred from the silica particle to the CF x -coated surface.Fig. 4d shows that the V CPD values increase with the surface area of the craters on the CF x -coated target, signifying that charge transfer is intensified during impact with higher velocities [25].

Theoretical model
With the observations made in the previous sections, we can now propose the following theoretical model.Fig. 5 illustrates how the applied potential difference +V over the two electrodes generates an electric field E ! that induce a large electrical charge on the top layer of a pile of silica particles [9,10,40] occupying the lower electrode.Consequently, depending on the permittivity and resistivity of the particles [41] a high number of particles at the top layer of the pile attain a net negative charge and are levitated (e.g.particle #1), after which they impact on the target electrode.Particles having a velocity that is lower than the sticking velocity will immediately stick onto the target electrode, while particles with an excess velocity will rebound from it.These particles (particle #1, 2, and 4) will return to the bottom electrode where they can be (partly) recharged after which they can be levitated again, thus leading to the formation of a particle cloud comprising levitated and rebounding particles between the electrodes (cf.Movie S1).The trajectory of the levitated particles is predominantly affected by the electrostatic force, drag force and the gravitational force.For simplicity, the equation of motion of a single particle in the y-direction is considered: where q is the electrical charge on the particle, η is the dynamic viscosity of air, D p is the diameter of the particle and v y = v i cos θ is the instantaneous velocity of the particle.
With the computed impacting velocities v i , the acquired charge on the silica particle before impact was estimated by solving Eq. 9.The estimated values attained by the silica particles are within a range of 0.2-0.8fC, which are well below the saturation charge q s = 3.6 f. silica particles may acquire when placed in an electric field E = 1.2 MVm −1 [34].Under these conditions, the electrostatic force on the particle and the image force [42] between the particle and the target electrodes are ~10 −9 N (at least 10 3 × smaller than the measured pull-off force F pull in Table 2).Moreover, reversing the electric field to E = −1.2MVm −1 , subsequently, after the experiment, did not result in the removal of the adhered negatively charged silica particles from the target electrodes.Hence, it can be interpreted that the adhesive forces between the particles and the electrodes are truly dominant in comparison to the electrostatic and gravitational forces.
The observation that silica particles adhered to the target electrodes (particle #3-4 in Fig. 5) can be explained by a mechanism, where due to the substantial adhesive forces, energy is progressively dissipated during subsequent collisions.As a consequence, the velocity of the rebounding particles gradually decreases until some eventually reach an impact velocity v i ≤ v stick , upon which they are irreversibly arrested at the top electrode.The mechanism resembles a bouncing tennis ball that finally comes to rest on a gravel tennis court.On the silicon electrode energy is dissipated, albeit the elastic nature of the collision (particle #4), by means of the adhesive forces until the impact velocity v i ≤ v stick ≈ 0.12 ms −1 which causes particles to stick onto the silicon electrode (particle #5).The higher silica particle density observed on the CF x -coated electrode can hence be understood from the fact that the probability of having an impact velocity v i ≤ v stick is higher on the CF x -coated electrode than on the silicon electrode.Next to the adhesive forces, particles are also slowed down and brought in the range v i ≤ v stick ≈ 0.28 ms −1 by the fact that during the inelastic collision between the silica particle and the CF x -electrode, the CF x -surface is permanently deformed locally (particle #1-2 in Fig. 5) and their kinetic energy is dissipated.Furthermore, because of the contact charge transfer mechanism (particle #1-3) occurring during the impact with the CF x -coated electrode, the silica particles rebounding from the CF x -coated target can be expected to lose part of their negative charge (particle #1 in Fig. 5), while a few of the silica particles may even carry a net positive charge after impact (particle #2).Consequently, particles attaining a lower negative charge during the impact will reach lower consecutive impact velocities, while the positively charged particles will move in the direction of the electric field towards the other electrode.As a consequence of the former, the probability of particles having impacting velocities lower than the sticking velocities increases.As can be inferred from Fig. 4d, the charge transfer between the silica particles and the CF x surfaces increases with the area of surface deformation (compare particle #1, 3 with #2 in Fig. 5).

Silica particles levitated at varied electric field strengths
To test the validity of the proposed model, experiments were performed with silica particles and two different target electrodes subjected to other electric fields E ! for a time of t = 10 s.Fig. 6a gives an overview of the measured particle density on the non-coated silicon target electrode (open symbols) and the CF x -coated target electrode (closed symbols) for varying electric field strengths E. The latter were achieved by changing the applied voltage V for a specific air gap distance The breakdown voltage and the specification of the highvoltage power supply limit the applied voltage V for a specific gap distance d.
In agreement with the previous data, the obtained results show that, in all considered cases, the number of silica particles adhered onto the CF x -coated electrode is substantially higher compared to the noncoated silicon electrode.In addition, these results confirm our proposed mechanism as the particle density on the electrodes decreases when the electric field strengths are intensified, resulting in a considerable amount of silica particles attaining velocities that exceed the sticking criterion v i > v stick .Consequently, a significant number of particles rebound from the target electrodes.The data presented in Fig. 6b supports the latter, as the particle density on the target electrodes is consistently higher for E = 1.2 MVm −1 compared to E = 2.5 MVm −1 .For the inelastic collision between the silica particle and CF x -coated electrode, this result is not so trivial, as higher impacting velocities lead to larger surface deformations, more energy dissipation during impact, and lower rebound velocities [38].However, these results suggest that these larger surface deformations do not outweigh the effect of higher initial impacting velocities of the silica particles attained at stronger electric field strengths.Hence, the probability of having velocities lower than the sticking velocity decreases.
We also reversed the direction of the electric field E ! , by applying a voltage V = −5 kV to a system with a gap d = 5 mm (E = −1 MVm −1 ).It was remarkable to see that, even under these conditions, silica particles were levitated after t = 4 − 5 s from the pile.This implies that the particles acquired a net positive charge.When the electric field is reversed, the polarization vector is also reversed aligning in the same direction as the electric field.Consequently, owing to their dielectric properties, a net positive charge may be induced on the top layer of the pile, while the particles in the lower part of the pile are screened from this effect [9,10].It should be noted that the number of silica particles levitated in this reversed field is much smaller because the silica particles carry an intrinsic net negative charge, and only those at the top layer of the pile can gradually attain a net positive charge, due to their resistivity.This also explains why in this case particles were not immediately levitated and why no stable particle cloud was formed between the two electrodes.Furthermore, it can be observed from the data in Fig. 6a that the density of particles on the target electrode is significantly lower when the electric field is reversed (E = −1 MVm −1 ) compared to the case when the same electric field strength is applied in the positive y-direction (E = 1 MVm −1 ).This can be readily assessed by comparing the closed data point at E = −1 MVm −1 with the closed data points for positive E = 1 MVm −1 , and repeating this for the open data points.
It was determined from experiments that the duration of the stable particle cloud that is obtained when applying strong electric fields E ! in the direction of the +y ! is limited by two factors.Firstly, particles with an impacting velocity lower than the sticking velocity will not rebound from the target electrode, and are hence no longer available to form a stable particle cloud.Secondly, weak convective flows in the systems were perceived as another source for the depletion of particles to maintain the particle cloud.This was evidenced by the fact that particles were also found outside the boundaries of the projected area of the target electrode on the lower electrode.Experiments performed with (20.3 ± 0.2) mg silica particles showed that a stable particle cloud existed for t = 12 s and t = 16 s for E = 1.2 MVm −1 (d = 5 mm) and E = 2.5 MVm −1 (d= 2 mm), respectively.
To study the temporal evolution of the particle density on the target electrodes, experiments were performed at respectively E = 1.2 MVm −1 and E = 2.5 MVm −1 during different time intervals t.It is expected that, as time progresses, the applied electric field will slightly induce more charge on the particles occupying the lower electrode, in turn leading to higher impacting velocities of the particles with the target electrodes.The measured density of the particles adhered on the silicon electrode (open symbols) and the uniformly CF x -coated electrode (closed) symbols are presented as a function of the time interval t in Fig. 6b.This figure shows that the particle density on the CF x -coated electrode gradually increases, whereas the density on the bare silicon electrode is approximately constant after t = 2 s.The former is in agreement with the proposed model, as the silica particles dissipate a significant amount of their kinetic energy during each collision with the CF x -coated electrode such that gradually more and more particles reach a velocity that is lower than the sticking velocity.Hence, the time-dependency of the upper two curves in Fig. 6.This gradual energy dissipation does not occur, at least not to a significant extent on the silicon electrode, as in this case the collisions are of a more elastic nature.According to the proposed model, particles rebounding from the silicon electrode can gain extra velocity as these particles have a longer timeof-flight compared to the ones rebounding from the CF x -surfaces, causing the applied electric field E ! to induce more charge on the particles.Consequently, as the velocity of the particles increases, the probability of particles having an impacting velocity that is smaller than the sticking velocity decreases with time, explaining why in this case the particle density on the silicon electrode remains constant after t = 2 s.

Experiments performed using polystyrene particles with the silicon target electrodes and the fully CF x -coated target electrodes
To study the effect of the nature of the particles on the impact with the target electrodes, experiments were also performed with polystyrene (PS) particles.Preliminary observations revealed that, compared to the silica particles, stronger electric fields are needed to levitate particles from the pile of powder containing polystyrene particles.Moreover, when the electric field was applied, the polystyrene particles were only levitated after t = 4 − 5 s, whereas silica particles are almost instantaneously levitated.We postulate that due to the lower permittivity of polystyrene (ε r , PS < ε r , silica), in conjunction with the higher resistivity (ρ res , PS > ρ res , silica ), equally applied electric fields E ! induce less charge on the polystyrene than on the silica particles for equivalent time-intervals Δt [41], with τ PS ≈ 3τ silica .Fig. 7 shows an example of the results of the polystyrene particles sticking on the silicon and the CF x -coated target electrode after applying an electric field E = 2.5 MVm −1 or E = − 2.5 MVm −1 .Within the investigated domain of the electric field strengths E, the density σ PS of the irreversibly adhered PS particles was, on both electrode surfaces, significantly smaller than the density σ silica of the silica particles (σ PS ≅ σ silica 1:5 on the silicon target electrode and σ PS ≅ σ silica 4 on the CF x -electrode).Considering the ratio between the PS particle densities on the two different surfaces, this was found to lie around unity (Γ = 1.2 ± 0.3) for each electric field strength between E = 1.5 − 3 MVm −1 .These observations can be explained by the fact that, in contrast to the silica particles, only a small fraction of PS particles is levitated.Furthermore, as a consequence of the small induced charge on the PS particles, their corresponding impacting velocity is lower than the lowest sticking velocity v stick on either the silicon or CF x -coated target electrode, such that the rate of adhesion is only determined by the rate of particle levitation which is similar in both cases.
The observed absence of a formed particle cloud between the two electrodes supports this argument, as no particles are rebounding from the surface of the target electrodes.Furthermore, it can also be observed from Fig. 7 that more clusters of PS particles are visible on the target electrodes compared to the silica particle case (cf.Figs. 2 & 3).Presumably, the charge is insufficient for single PS particles to be levitated, due to their lower resistivity.Consequently, mostly larger particle agglomerates that are levitated from the pile in the PS particle case [10].However, it can not be excluded that a stronger adhesion force exists between the PS particles compared to the silica particles.[43,44] The former could, in conjunction with the higher electrical time constant of the PS particles, explain the stronger electric fields and longer times required for levitating the PS particles.The particles are only levitated when the electrostatic force is higher than the adhesion force (the weight can be neglected with respect to the adhesion force).Fig. 8 shows the as-received silica particles and PS particles, and it can be observed that rather large clusters of silica particles are present, where only small clusters of PS are visible.This observation indicates a stronger cohesive interactions between the silica particles compared to the PS particles.As the adhesion force depend on various parameters including surface roughness and relative humidity, [39,44] we can only speculate on the origin of this observation, and intend to study this in more detail in future work.
After scanning the CF x -coated and the bare silicon target electrode with the AFM, apparent surface deformations were absent.However, since polystyrene is the most vulnerable material, surface deformations could be present on the particles themselves [16].

Conclusions
Studying the interaction of microparticles levitated by subjecting them to a high electric field strength E ! running between two electrode plates, it was found that not all particles rebounded from the target electrode and that silica particles have a much higher probability to adhere irreversibly to a CF x -coated target electrode than to a bare silicon target electrode, with ratios 2.7 ≤ Γ ≤ 4.7.On the other hand, the measured particle densities on the two different electrode surfaces were similar (Γ ≅ 1.2) when using PS particles.The PS particle density was at least 1.5× lower on the silicon electrode, and even >4× lower on the CF xelectrode compared to the measured silica particle density.Presumably, the PS particles gain less charge owing to their low permittivity and resistivity, which results in lower velocities causing particles to instantly stick regardless of the target electrode.
To study the impact process in more detail, AFM and KPFM measurements were performed.These revealed that, in the case of the silica particles, permanent surface deformations (ineleastic collisions) were present on the CF x -electrode and that during impact charge had been transferred from the silica particle to the CF x -coated target electrode.On the silicon targets, no surface deformation (elastic collision) or charge transfer was measured.Furthermore, due to the adhesive forces between the particles and the electrodes, in conjunction with the inelastic nature of the impact and possible charge transfer mechanism,

Fig. 1 .
Fig. 1.Schematic representation of the experimental setup comprising a bottom and target electrode, both connected to a high voltage power supply.The powder is deposited on the bottom.

Fig. 3 .
Fig. 3. SEM images of the silica particles adhering onto (a) the silicon target electrode, and onto (b) the CF x -coated target electrode.Experiments were performed with an electric field E = 1.2 MVm −1 .Scale bar 20 μm.

Fig. 4 .
Fig. 4. (a) Topographic image (1.5 × 1.5 μm 2 , scale bar 400 nm) and (b) the simultaneously obtained potential map of an impact crater created by an impacting silica particle on the CF xcoated surface.(c) The height (left, black) and contact potential (right, red) profile measured along the dashed line in (a) and (b).(d) The contact potential difference as a function of the paraboloid area (A c ).

Fig. 5 .
Fig. 5. Schematic representation of silica particles levitated from the pile of powder impacting on the CF x -patterned (in black) silicon (in grey) target electrode where they either stick to or rebound of.

Fig. 6 .
Fig. 6.(a) Measured density σ of silica particles on the target electrodes as a function of the different electric field strengths E. Experiments were performed for three different electrode gaps d.Error bars correspond to n = 3 measurements.(b) Particle density of the adhered silica particles as a function of the time interval t.Open symbols correspond to the silicon target electrode, and closed symbols correspond to the uniformly CF x -coated target electrode.

Fig. 7 .
Fig. 7. SEM images of the polystyrene particles adhering on (a-c) the silicon target electrode, and on (b-d) the CF x -coated target electrode.Experiments were performed with an electric field (a-b) E = 2.5 MVm −1 and the reversed field (c-d) E = −2.5 MVm −1 .Scale bar 20 μm.

Table 1
Physical properties of the materials used in the experiment.

Table 2
Computed and measured properties of the silica particle on the silicon target electrode and on the CF x -coated target electrode.