Impact-induced generation of single airborne microspheres and the subsequent vacuum-driven assembly of ordered arrays

brushing step is added to remove excess particles in undesired positions on top of the ordered arrays. An asset of the proposed method is that for the investigated particle properties, the same optimized conditions could be used to attain any desired 2-D particle arrangement that can be transferred on soft surfaces, e


A B S T R A C T
A myriad of wet assembly techniques exists to attain ordered arrays of micro-and nanoparticles.The present contribution proposes a universal and rapid (in order of a few seconds) dry assembly strategy that can be employed to assemble ordered arrays of particles with a designed spacing.This method involves shooting agglomerated monodisperse silica, polystyrene or PMMA powder microspheres with diameters ranging between 5-10 μm against an impact plating using pressure exceeding 2.5 bar.Consequently, the fluidized microspheres are attracted towards the pores of a silicon membrane device by applying a vacuum force.Furthermore, a brushing step is added to remove excess particles in undesired positions on top of the ordered arrays.An asset of the proposed method is that for the investigated particle properties, the same optimized conditions could be used to attain any desired 2-D particle arrangement that can be transferred on soft surfaces, e.g., PDMS.

Introduction
Fine to ultrafine powder particles are key building blocks in many contemporary industrial applications as scientists and engineers frequently utilize these particles as catalysts in reactor engineering [1,2] or as arrays assembled in a (non-) close-packed two-dimensional (2D) configuration.These arrays are widely applied in photonic crystals, optical and biological sensors, microlenses, colloidal lithography, and building blocks to devise three-dimensional (3D) packing structures [3][4][5].For some microfluidic applications, e.g., rapid screening assays and liquid chromatography, the assembly of ordered microspheres in a non-closely packed configuration are preferred [6].
Despite their diverse applications, micro-and nanoparticles pose significant challenges due to their high surface area-to-volume ratio.As a result of the latter, the surface forces, e.g., van der Waals, electrostatic and capillary forces, tend to dominate, promoting the formation of agglomerates during the production, transportation or storage of the particles [7].However, having access to single particles is usually a prerequisite, albeit sometimes even challenging, if one is after producing ordered monolayer arrays in the many application mentioned above [8].
To date, a multitude of wet assembly techniques has been predominantly used to disperse powder particles in solvents to attain assembled particle arrays [3].Many of these wet assembly techniques, e.g., convective assembly, capillary assembly, or spin-coating, apply delicate self-assembly processes on (non-) patterned substrates, where a slight deviation in one of the required parameters, such as pH, relative humidity and temperature, can yield defects in the assembled monolayers comprising microspheres or nanospheres [9,10].Other wet assembly techniques use electric and magnetic fields or a vacuumdriven force to attain an ordered monolayer from a dispersion of nanoand microparticles [6,[11][12][13] Recently, it has been shown that these close-packed assembled arrays can be transformed into non-closely packed arrays using reactive ion etching (RIE) to tune the spacing between neighbouring particles [14,15].However, a drawback of this method is that the particle's morphology and surface roughness can be altered by dry etching.In addition, some studies use wet assembly strategies directly on templated surfaces to obtain non-closely packed particles.However, these wet assembly strategies have been predominantly applied in assembling nanospheres, for which gravity effects can be typically neglected [16,17].
On the other hand, dry assembly methods have been less intensely investigated, despite having several advantages over wet assembly techniques.They offer a relatively higher degree of structural freedom and versatility regarding particle size and material, and solvent waste is obsolete.Additionally, dry assembly methods can be faster, more amenable to automation, and have a higher tolerance for small particle dispersity [18].Various studies reported rubbing on patterned (soft) surfaces as a quick and efficient way to produce ordered particle arrays [4,6,[18][19][20].However, as was recently reported by Verloy et al.PDMS debris detaching from the PDMS sheet during rubbing may contaminate the assembled particle arrays [6].Next to this, Khan and Yoon [18] needed a post-treatment step which involved heating the substrate to a temperature of 500 • C to remove the polymer layer that aided the assembly of nanospheres on patterned silicon devices.These temperatures are not suitable for assembling polymer particles.
In an attempt to overcome all of these challenges and find an assembly method that targets a broader spectrum of particles, Van Geite et al. [21] devised a setup in which the polarizability of dielectric particles is leveraged by applying a strong electric field to levitate individual microspheres from an agglomerate and subsequently aspired through vacuum-suction to attain an ordered particle array on a silicon device.However, in comparison to the silica microspheres, it had proven to be much more challenging to disperse the polymer type of microspheres as electric field strengths of at least ±2.5 MVm −1 were required to mobilize particles.Therefore, the present contribution addresses this challenge by investigating a purely mechanical approach to disperse the microspheres devoid of solvents, i.e., proposing another completely dry assembly method.
Vibro-fluidization is a mechanical-based approach in which agglomerated powders or other types of granular materials are vigorously shaken to mobilize the particles.[22][23][24] However, an earlier study reported that 10 μm agglomerated silica particles would stick and form monolayers on a silicon substrate, [8] i.e., single silica particles are not available for assembling particle arrays.On the other hand, a recent study reported that agglomerated silica nanoparticles could be disrupted in smaller agglomerates by letting agglomerates from a fluidized bed impact against a plate with a high-speed jet [25].
Here, we investigate a mechanical-based dry assembly method to produce monolayers of precisely positioned microparticles that is as universal as possible, i.e., applicable for as many different microspheres as possible.Inspired by the work of Nasri et al. [25], agglomerates are first dispersed by shooting them on an impact plate and subsequently aspired towards a perforated silicon device surface (= the ''membrane'') through a vacuum force.This approach can assemble particles on the membrane in a fraction of a second.A brushing step is added as the final step in the assembly process to remove unwanted excess particles from the assembled arrays.Furthermore, the versatility of the proposed assembly strategy is demonstrated by performing experiments with monodisperse 5-10 μm silica, polystyrene or polymethyl methacrylate (PMMA) microspheres.At last, we show that the assembled arrays can be successfully transferred on another substrate, paving the way for printing hierarchical materials.

Setup & main experimental procedure
Fig. 1a shows a schematic representation of the in-house build experimental setup for the assembly of microspheres on a micromachined membrane.A vacuum force holds this silicon membrane on a chuck (Fig. S1) which is placed on top of the particle fluidization chamber.Particles are scooped on a second membrane chip that acts as a distributor for a pressurized N 2 -jet (Fig. 1b-1) and is positioned at the bottom of the set-up.Subsequently, a pressure pulse ( inlet ) applied for less than a second launches the deposited lump of particles (Fig. 1b-2, 1b-3).The particles subsequently travel towards the target membrane and are directed towards the perforated pores as they are carried along by the vacuum flow (Fig. 1b-4).The travel distance  in the fluidization chamber is defined as the distance between the impact plate and the top membrane.Different fluidization chambers were designed to study the influence of the travel distance and inserts in the fluidization chamber on the supply of particles to the perforated membrane.

De-agglomeration of powder particles
In fluidized bed systems, an essential parameter is the minimal fluidization velocity (  ) needed to transform a fixed bed of particles into a fluidized bed.This implies that as soon as the fluid's upward velocity exceeds   , which represents the point where the drag force of the gas is in equilibrium with the weight of the particles in the bed, and particle entrainment begins.However, this parameter depends on various factors, e.g., the density of the particles and gas respectively, the particle diameter, the porosity of the fixed bed at minimal fluidization, and the sphericity of the particles.Many empirical relations are derived in the literature that attempt to predict the minimal fluidization velocity [26].However, in practice,   is typically higher than the predicted value, as was recently reported for the fluidization of 5 μm silica microspheres.In this case, due to the intra-particle cohesion forces, a 1500× higher   than expected from theory was needed [27].The average diameter of the agglomerates measured at the topside of the bed was 210 μm, with a minimum of 133 μm.
The particles used in this study are classified as Geldart C group (≤ 30 μm) and considered highly challenging, if not nearly impossible, to fluidize [28].For example, Chaouki et al. [29] observed that Group C particles can be fluidized in smaller agglomerates rather than their primary constituents.This is because the interaction forces, e.g., van der Waals, and capillary, are significantly strong among these cohesive powder particles.Various concepts have been proposed in the literature to break compact, agglomerated powder particles.
Another way cohesive agglomerates can be fragmented and fluidized is by shooting them against an impact plate.This impact process has been extensively modelled and studied in the literature [30][31][32].When the agglomerate hits the impact plate, a compressive wave propagates through the agglomerate.The latter transmits a force through the agglomerate that depends on its kinetic energy when impacting the plate.If this force is sufficiently strong to overcome the friction forces among the particles and concomitantly induce a sliding motion between them, the agglomerate can be fragmented into smaller agglomerates, or even individual particles [30,31].
A recent study demonstrated that by shooting agglomerated silica nanoparticles against an impact plate, the average agglomerate size could be reduced from 131 nm to 55 nm.The latter corresponds to small agglomerates comprising three nanoparticles [25].Thus, the deagglomeration of cohesive powder can be enhanced by including an impact plate in a fluidized chamber.

Agglomerate break-up study
As discussed in the preceding sections and corroborated by our previous studies, [8,21] it is challenging to mobilize the massive silica agglomerates (cf.Fig. S1) due to the presence of significantly strong cohesive forces.However, in our quest to attain arrays of ordered microspheres, it is a prerequisite to have single particles.
Based on the aforementioned discussion (cf.Section 3), we explore a strategy in which agglomerated powder is de-agglomerated into individual airborne particles in a chamber in two subsequent steps as depicted in Fig. 1b: firstly, a pressure pulse is applied for less than a second to shoot and fracture the fixed bed of agglomerated powder particles into smaller agglomerates (Fig. 1b-2), and secondly, these smaller agglomerates impact against a plate, where they are reduced to a mixture of single particles and possibly a few smaller clusters (Fig. 1b-3).Subsequently, these individual particles can be attracted with a vacuum force to be assembled on the membrane's pores.
However, the first set of experiments was performed without applying a vacuum force to study the pure break-up process and investigate if the impact process truly fractures the large agglomerates into single microspheres.In addition, the diaphragm (cf.Fig. 1a) was removed from the fluidization chamber.Note that as the membrane surface intrinsically provides an outlet to the system, a net flow is induced, dragging particles towards the top of the fluidized chamber.
The results shown in Fig. 2 confirm that the inclusion of the impact plate in the chamber enhances the fluidization of the large agglomerates into single particles.Next to the single microspheres, clusters of particles (typically ranging from a few to a few tens of particles) can also be observed.The latter implies that either some of the agglomerates were not fluidized into individual microspheres or that re-agglomeration occurred among the single particles.It is noteworthy to mention that at this point, it is incredibly challenging to study the dynamics of the disruption process of the large powder agglomerates with our current setup, as the entire assembly process is swift and lasts a second.
Another important observation that can be made from Fig. 2a is that even though the vacuum force was shut off, many single microspheres reached the membrane while some were even precisely positioned on the pores.Therefore, it was decided to add a diaphragm after the impact plate to reduce the number of particles reaching the membrane pores in the absence of a vacuum force (cf.Fig. 2b).With this approach, it was attempted to decouple the impact process and the aspiration of the particles by the vacuum force.The results obtained with this diaphragm indicate the necessity of applying a vacuum force to promote the attraction of particles, resulting in an improvement in the filling of membrane pores.

First experiments with vacuum
All subsequent experiments were performed with a vacuum force applied, and concomitantly a flow is induced through the membrane  pores by opening a valve connecting the vacuum channel with a vacuum chamber controlled by a back pressure regulator (BPR), allowing to establish a given pressure difference ( ) across the membrane pores.Pressures inside the vacuum chamber could go to a minimum of 50 mbar.It turned out that the sequence in which the pressure pulse valve and vacuum valve are opened is essential for the assembly process.If the pressure pulse is created first, the number of particles reaching the membrane pores is comparable to the number obtained without vacuum (cf.Fig. 2b vs Fig. S3a).This observation is explained by estimating the travel time of a single microsphere to reach the membrane when the vacuum force is absent.In the latter case, it can be assumed that the microspheres sticking to the membrane must hit the surface with a velocity below 0.1 ms −1 , [33] such that in a 9 cm fluidization chamber, the microspheres impact the membrane after approximately 1 s.Consequently, this time window is too short to manually open the vacuum valve after the pressure pulse.Therefore, the method used in all future experiments described in this study consisted of opening the vacuum valve before forming the particle cloud inside the fluidization chamber by means of the applied pressure pulse (Fig. S3b).
As observed in Fig. 3, the assembly membrane is covered by a large number of unwanted excess single and clustered particles after the vacuum assembly step.This implies that too many particles are supplied.The number of excess particles typically covering a filled membrane is estimated to be 0.5-5 times the number of pores.This also implies that about 90% of the approximately 1 million particles initially contained in the supply cup to feed a membrane with ≈ 8000 pores is lost to the walls of the fluidization chamber.
To corroborate this hypothesis, an experiment was performed in which the lump of about 1 mm 3 of agglomerated powder on the supply membrane was replaced by a fully saturated membrane produced in a previous assembly experiment (Fig. S4 a-1).After the pressure pulse, we noticed that almost all particles were lifted from the bottom membrane pores (Fig. S4a-2).However, it was striking to note that only a few particles eventually reached the top membrane (Fig. S4b).This implies that the material loss during the fluidization step is substantial, presumably due to the fluidization chamber's turbulent flow directing most of the particles to the sidewalls, promoting the adherence of particles to the PLA (polylactic acid) chamber.A visual inspection after the experiment confirmed this hypothesis as a milky layer is visible on the black PLA structure (cf.Fig. S5).Because of this very low fill rate, we kept the supply constant and opted to fill the 1 mm 3 volume of the supply chamber completely.

Parameter optimization
The preceding sections have shown that the pressure pulse effectively breaks up the initial particle lump to produce a sufficient amount of single particles required for the assembly process, but many of the particles do not reach the top of the membrane.Those particles lose impulse and change trajectory due to the many collisions in the particle cloud.Eventually, the turbulent flow in the chamber may cause reagglomeration of the excess particles that form clusters and deposit on the assembled arrays.In an attempt to minimize this effect, the influence of various parameters was studied to investigate and reduce these unwanted excess particles.

Effect of pressure pulse
As highlighted above, the most crucial assembly parameters are the applied vacuum pressure in conjunction with the magnitude of the generated pressure pulse.Therefore, the latter's effect on the quality of the assembled particle arrays was investigated.Fig. 4 displays the results of the different pressure pulse magnitudes with a constant vacuum-pressure difference ) of 800 mbar across the membrane in chambers with different travel distances.The number of vacant pores on the membrane was counted to assess the fill rate of the assembly process.
From Fig. 4a, it can be observed that when a pressure pulse of 1 bar was used, almost 50% of the membrane pores remained vacant.Despite the high standard deviation, it can be concluded that only a few single microspheres reach the membrane pores.A visual inspection of the bottom side of the impact plate revealed that under these conditions, the large powder agglomerate stuck on the impact plate (cf.Fig. 4b).This implies that shooting the large agglomerate with a pressure pulse of 1 bar generates an insufficient amount of kinetic energy to fracture the entire supplied agglomerate, and therefore not enough single microspheres could be produced during impact.The vacancies dropped significantly when the magnitude of the pressure pulse rose to at least 2.5 bar, as can be noticed from the SEM images displayed in Fig. 4c.Clusters are visible on the assembled monolayer for all tested pressures.Pressure pulses of 2.5 and 5 bar were also studied in larger fluidization chambers ( = 11 and 14 cm) with the same vacuum pressure (cf.Fig. 4a).It is seen that the fill rate for both travel distances was comparable to the fill rate for  = 9 cm, indicating that the pressure pulse does not need to be increased for longer distances.However, it should be mentioned that the maximum distance studied here was only 14 cm.

Effect of vacuum pressure
As it is now clear that the pressure pulse used to levitate and break the fed powder lump needs to exceed a certain magnitude, the next question is how strong the vacuum suction force needs to be.Different pressure differences  were applied across the membrane to study the influence of the vacuum force.From the results shown in Fig. 5a, it is inferred that almost half of the pores remains open for a  of 100 mbar, whereas, for  ≥ 500 mbar, only 1% and less of the pores remained vacant.As expected, increasing the vacuum force attracts more particles towards the membrane, readily observed from SEM images displayed in Fig. 5 b-d.The excess particles on top of the assembled monolayer increase from 500 mbar onwards.
Another drawback of an insufficiently strong vacuum force is that some particles get trapped between adjacent membrane pores, thus deviating from the desired ordered configuration (cf.Fig. 5b).It is assumed that when the suction force is too low, the entrainment force that needs to guide the particles towards the assembly membrane pore mouths when they approach the membrane surface is too low, and the particles' inertia makes them miss the pore mouth [19].This leads to misplaced particles, which create a cascade effect because, as they leave the underlying pores partially open, the vacuum force locally persists and keeps attracting more particles, thus locally forming large clusters of excess particles.The imprecise positioning of 10 μm particles was not seen in the monolayer assembled with an applied pressure  ≥ 500 mbar but could be present under these clusters.
Whereas the above mechanism provides one possible explanation for the formation of the observed excess particle clusters, another possible explanation is that, given the large excess number of particles that needs to be supplied in order to attain a fully assembled array, the number of particles attracted by the vacuum force is so high that the probability that multiple particles simultaneously reaching the same pore is very high.Another possibility is that the clusters are formed by attracting small agglomerates remaining intact after the collision with the impact plate.The assembly of these agglomerates on the pores then automatically also leads to the formation of clusters.A third explanation is that the agglomerates forming the observed excess clusters would be generated in the cloud.Due to the turbulent flow in the fluidization chamber, many interparticle collisions may be promoted.Not all collisions are likely pure elastic collisions, and some particles may also undergo inelastic collisions where the colliding particles stick together.Furthermore, the contact electrification mechanism could induce an electrostatic attraction between single colliding particles [19,[34][35][36].It is plausible that all three mechanisms contribute to the re-agglomeration process of single powder microspheres.

Effect of sieve
To rule out that the presence of (small) agglomerates in the particle cloud would contribute to the cluster formation, a sieve was introduced in the middle of the cloud chamber instead of the diaphragm.The sieve is a micromachined silicon device with 13 μm diameter pores, allowing only the passage of single microspheres through a pore, i.e., this device excludes agglomerates.The pores were distributed over an area of 1 × 1 or 2 × 2 mm 2 with a pitch ranging from 10-125 μm.The total surface area where particles can pass decreases from ≈ 12 mm 2 for a 4 mm diaphragm to 1-0.1 mm 2 for a 2 × 2 mm 2 sieve for 10 μm particles with a pitch of 10 μm-125 μm, thus reducing the total open surface area with a factor 10-100.
To study the effect of the micromachined sieve on the assembly process, experiments were performed with the sieve in a fluidization chamber with a 9 cm travel distance.It appeared that 15% of the pores remained vacant (cf.Fig. 6a, orange bars) in the case of the smallest sieve pitches ( = 10 and 15 μm) a 1 × 1 mm 2 sieve membrane.Furthermore, these vacancies were mainly found at the edge of the membrane.Presumably, this is caused by the fact that the pores of the sieve and the membrane are distributed over the same surface area (1 × 1 mm 2 ).Particles passing at the edge of the sieve can divert from their upward trajectory and create a more depleted region in the particle cloud.
Therefore, the area of the sieve was enlarged to 2×2 mm 2 .The vacancies dropped significantly below 1% (cf.Fig. 6a, blue bars).However, the SEM figures corresponding to these experiments (cf.Fig. 6c-d) show that clusters are still present on the monolayer despite the presence of the sieve, which blocked clusters or agglomerates present in the particle cloud formed immediately after the impact plate from reaching the membrane.These observations now imply that the clusters observed on the assembly membrane must be formed in the direct vicinity of the assembly membrane, probably because too many particles arrive too shortly after each other at the same pore mouth.As they cannot abruptly change their trajectory due to their high inertia, they then impact the same pore mouth, thus forming local agglomerates.
In an attempt to further reduce the frequency of particles arriving at the assembly membrane, the pitch between the sieve pores was enlarged.A significant increase in vacancies was noticed for a pitch of 50 μm, with nearly half of the membrane pores remaining vacant.However, increasing the sieve pitch further to 125 μm did not result in a further increase in vacancies.The corresponding SEM images are shown in Figs.6e-f.Interestingly, in Fig. 6e, single particles and small clusters are observed on the assembled array, despite the considerable reduction in particle supply to the membrane.Therefore, it can be safely concluded that reducing the particle supply does not necessarily prevent cluster formation.Since particles are not evenly distributed in the chaotic particle cloud, locally, more particles may still arrive at the membrane simultaneously while other regions are depleted.
Overall, the sieve results indicate that clusters are not attracted from the particle cloud after the impact plate but are formed on the membrane due to an excess number of particles reaching the same pores at once.Reducing the number of pores in the sieve by increasing the pitch between the pores reduced the number of particles travelling towards the membrane but resulted in an unwanted significant number  of vacant pores (±50%), and small clusters and excess particles were found on the assembled particles.

Effect of total travel distance
Several fluidization chambers were designed with different lengths to study the effect of the total travel distance (5, 9 and 14 cm) on the quality of the assembled particle arrays (Fig. 7).
No vacant pores were observed for the short travel distance of 5 cm.However, the assembled array was substantially covered with multiple excess layers.It should be mentioned that it cannot be excluded that a few vacancies would still be present underneath the massive excess layers.Furthermore, a slight increase in vacancies was noted for a travel distance of 9 cm, whereas a more significant increase in vacant pores was noted for 14 cm (Fig. 7a, blue bars).As can be seen from the SEM images in Fig. 7b, the majority of vacant pores is situated at the side of the perforated membrane, while the number of excess powder microspheres also reduces with increasing travel length.Due to the latter, it can be inferred that the particle aspiration with the vacuum force is weaker above the diaphragm in chambers with longer travel distances.Particles experience a weaker upward pull and, as a result, have more time to divert from their vertical trajectory to the membrane, especially at the edge of the cloud.Consequently, the pores at the side of the membrane attract individual microspheres from a more depleted region in the cloud.

Effect of particle size and material
In contrast to our recently published dry assembly study [21], which exploited the degree of electrification (electrical conductivity and permittivity) of various particle materials, the currently proposed method is purely mechanical.It only relies on finetuning a few process parameters: a pressure pulse strong enough to break up the supplied agglomerate and a suction force generated by a vacuum pump to direct the particles towards the orifice of the pores.As already mentioned, the former assembly strategy required applying approximately three times stronger electric field strengths to electrostatically levitate and subsequently assemble polymer-type particles instead of silica ones.Therefore, the current pressure pulse method was tested with 10 μm polystyrene (PS), polymethyl methacrylate (PMMA) particles, and 5 μm silica particles to examine its versatility.Figs.8a, and 8b show that the proposed assembly strategy can be successfully applied to assemble PS or PMMA particles using the same optimized conditions as for the 10 μm silica particles displayed in Fig. 4e.
Figs. 8c-d show the assembly of 5 μm silica particles assembled with suitable parameters to fill the membrane in a reproducible way for 10 μm silica microspheres.In Fig. 3, it was observed that a pressure pulse of 2.5 bar was sufficient for 10 μm silica particles.It is seen in Fig. 8 that with a pressure shock of 2.5 bar, a relatively large number of pores remained vacant for 5 μm particles.Increasing the pressure pulse to 5 bar, on the other hand, results in 400 a membrane with approximately 32,000 pores occupied.This observation is in line with the fact that the cohesive forces among 5 μm silica microspheres are at least four times stronger [8], and therefore, the agglomerate must hit the impact plate with an increased velocity which can be obtained by increasing the pressure pulse.Potentially, a higher-pressure pulse would be needed to assemble even smaller particles.
It is noteworthy that the pressure pulse method is clearly inferior to the electrostatic levitation strategy [21] in terms of assembly and capture efficiency as a significant number of initially supplied powder is lost in the process.In addition, the pressure shock method is slightly less reproducible than the electrostatic levitation assembly concept.This may be ascribed to the fact that the cloud formation after the impact plate is less controllable.

Removing excess particles
From all the presented results, it is evident that the assembly process is constantly plagued by the presence of excess particles on the assembled particle array.These excess particle layers can, however, be efficiently removed by applying a brushing step while maintaining the vacuum force on the assembled array of particles.This removal strategy has already been extensively investigated by Van Geite et al. [21].That study showed that the use of profiled membrane surfaces is imperative, as otherwise, the assembled array gets damaged as particles are removed from their position, creating new vacant membrane pores.Next to profiled membranes, the study reported that, in order to remove the excess particles, a vacuum pressure of 950 mbar should be applied on the assembled monolayer, while the brush should be moved two times across the monolayer at a constant velocity of 5 mm s −1 .These optimized conditions resulted in only two misplaced or missing particles on a total of 8000 pores [21].
Fig. 9 shows the results after removing excess particles from assembled layers on profiled membrane surfaces.It can also be inferred from Fig. 9 that, due to the generic nature of the vacuum force, the assembly method allows for a large degree of freedom in the design of the 2D array structure.

Particle transfer
Another advantage of the proposed assembly strategy is that the pressure difference across the assembled monolayer can be simply reversed to transfer the particles to another substrate, i.e., an overpressure instead of a vacuum can be applied across the silicon membrane.Fig. 10 a1-a3 depicts the transfer of an assembled particle array using an overpressure  on a thin 30:1 PDMS sheet (600 μm thick) acting as an adhesive layer attached to a microscope glass, preventing the PDMS surface from extensive deformation that may disturb the successful transfer of the assembled array.To prevent any damage, the PDMS sheet carrying the transferred array is slowly detached from the silicon membrane, keeping the particles in place on the adhesive PDMS sheet.Figs. 10 b-c show that the pitch between the microspheres remains intact after transferring the various geometrical assembled arrays onto the PDMS sheet.

Conclusions
We have devised an alternative route for the dry assembly of 2D ordered particle arrays of 5-10 μm silica, polystyrene or PMMA microspheres on silicon membranes.The fluidization of the agglomerated powder particles is achieved by applying a sufficiently strong pressure pulse (> 2.5 bar) to shoot the particles against an impact plate in a chamber.The established particle cloud is a source to aspire particles towards a silicon membrane using a vacuum force induced by a pressure of at least 500 mbar.Even with the most optimized conditions, inevitably, excess particles are attracted, and more than 90% of the supplied particles are lost inside the chamber.In contrast to the electrostatic levitation experiment, the same optimized conditions could be used to assemble all the distinct particles utilized in this study.The excess particles are removed by including a brush as a cleaning step while maintaining the vacuum force.As a result, nonclosely packed particle arrays without excess particles can be attained within ten seconds on a predetermined lattice.
Regarding other assembly methods, the current dry assembly process does not require any post-treatment steps, and particles can be subsequently transferred to another surface, which is advantageous to soft electronic or wearable devices.In addition, the assembly membranes are manufactured in a batch fabrication process and can be used at least 50 times for the assembly of ordered arrays.This is an advantage compared to other studies where non-closed packed arrays should be fabricated each time after a monolayer of particles is assembled.Furthermore, the particle's surface is not changed or damaged during any step of the assembly process.
As the particles can be transferred, the proposed assembly process can also serve as a platform to print novel hierarchical materials or particle packing structures, e.g., for liquid chromatography, using a layer-by-layer strategy.The present contribution solely explored assembling agglomerated powders comprising microspheres with a diameter of 5 to 10 μm.As the break-up of agglomerated nanospheres has been demonstrated before, we envision that the current assembly strategy can be extended to the assembly of nanoparticles.This can be realized when the diameter of the membrane pores is adjusted to a smaller diameter by using laser-interference lithography (LIL) instead of standard lithography techniques.

Declaration of competing interest
The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: Gert Desmet reports financial support was provided by European Research Council.

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A mechanical dry assembly strategy for microspheres is proposed.• Airborne individual microspheres are produced.• Method uses a pulsed overpressure and mechanical impaction on a plate.• Particles can be assembled in monolayers onto a microstructured membrane.• Any predetermined 2D pattern of particles can be produced and transferred.G R A P H I C A L A B S T R A C T A R T I C L E I N F O

Fig. 1 .
Fig. 1.(a) Schematic representation of the experimental setup: a fluidization chamber (1) with on top a vacuum chuck (2) holding the assembly membrane (3).The chuck is connected to a vacuum pump which induces a flow (red arrow).A diaphragm (diameter = 4 mm) (4) is situated in the fluidization chamber, as well as the impact plate (5) situated above the perforated supply tray where the particles are supplied (6).The complete setup is connected to a pressurized N 2 -gas bottle.The travel distance (d) is the distance between the impact plate and the assembly membrane.(b) Schematic representation of the fluidization and capture process, starting (b-1) with supplying a heap of particles on the perforated device, followed by (b-2 to b-3) the break-up process and ending (b-4) by assembling the particles from the particle cloud on the target membrane.Red arrows denote the vacuum flow.

Fig. 2 .
Fig. 2. SEM images of 10 μm silica particles assembled on the target membrane without vacuum aspiration and a pressure pulse of 5 bar in a fluidization chamber of 9 cm (a) without diaphragm (b) with the diaphragm.Scale bar: green = 200 μm, red = 50 μm.

Fig. 3 .
Fig. 3. SEM image of an assembly of 10 μm silica particles made on the target membrane with a fluidization chamber of d = 9 cm with a P inlet of 5 bar and P = 800 mbar.Excess particles and clusters are visible on top of the monolayer.Scale bar is 200 μm.

Fig. 4 .
Fig. 4. (a) Bar chart representing the fraction of vacant pores on the membrane as a function of the pressure pulse with a constant P of 800 mbar across the membrane.Blue bars represent assemblies with a fluidization chamber with d = 9 cm, orange bars with d = 11 cm and magenta bars with d = 14 cm.No experiments were performed for 1 bar with d = 11 cm and 14 cm.(b) Digital photograph of a remaining agglomerate (highlighted with a red circle) on the impact plate after applying a pressure pulse of 1 bar.SEM images of 10 μm silica particles assemblies corresponding to the blue bars for (c) 1 bar, (d) 2.5 bar and (e) 5 bar.

Fig. 5 .
Fig. 5. (a) Bar chart representing the fraction of vacant pores on the membrane as a function of the pressure difference P for the case of a constant pressure pulse of 5 bar and for d = 9 cm.SEM images of 10 μm silica particles assemblies corresponding to the blue bars on a membrane with pressure difference (b) P = 100 mbar, (c) P = 500 mbar and (d) P = 800 mbar.Red circles indicate misplaced particles, leaving underlying pores open.Scale bar: green = 200 μm, white = 50 μm.

Fig. 6 .
Fig. 6.(a) Bar chart of the fraction of vacant pores as a function of the sieve pore distance for sieves with different surface areas.Experiments were performed with a pressure pulse of 5 bar and a P of 800 mbar.Orange bars represent sieves with pores distributed over 1 x 1 mm 2 , blue bars over 2 x 2 mm 2 .(b) Bar chart of the fraction of vacant pores as a function of the different sieve pore distances (p) for pores distributed over 2 x 2 mm 2 .The value for p = 10 μm in both (a) and (b) is 0. SEM images of 10 μm silica particles assemblies corresponding to different pitches in 2 x 2 mm 2 sieves, (c) p = 10 μm, (d) p = 15 μm, (e) p = 50 μm and (f) p = 125 μm.Scale bar is 200 μm.

Fig. 7 .
Fig. 7. (a) Bar chart of the fraction of vacant pores as a function of different travel distances with a pressure pulse of 5 bar and P = 800 mbar.The value for d = 5 cm is 0. Representative SEM images of 10 μm silica particle assemblies corresponding to the bar chart; (b) d = 5 cm, (c) d = 9 cm, (d) d = 14 cm.Scale bar is 200 μm.

Fig. 10 .
Fig. 10.(a) Schematic representation of the process applied to transfer the assembled microspheres from the membrane onto a PDMS sheet, comprising (a-1) manually pressing the PDMS sheet attached to a microscope slide against the assembled array with a force F ; (a-2) applying an overpressure P across the membrane, and (a-3) gently peeling the elastomeric PDMS sheet containing the transferred array of particles.(b) SEM images of the transferred 10 μm silica particles on a 30:1 PDMS sheet with a thickness of 600 μm.Scale bar is 30 μm.