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Mini-Review

Triboelectric Charging of Particles, an Ongoing Matter: From the Early Onset of Planet Formation to Assembling Crystals
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Cite this: ACS Omega 2022, 7, 46, 41828–41839
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https://doi.org/10.1021/acsomega.2c05629
Published October 17, 2022

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Abstract

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Triboelectrification is the spontaneous charging of two bodies when released from contact. Even though its manifestation is commonplace, in for instance triboelectric nanogenerators, scientists find the tribocharging mechanism a mystery. The primary aim of this mini-review is to provide an overview of different tribocharging concepts that have been applied to study and realize the formation of ordered stable structures using different objects on various length scales. Relevance spans from materials to planet formations. Especially, dry assembly methods of particles of different shapes based on tribocharging to obtain crystal structures or monolayers are considered. In addition, the current technology employed to examine tribocharging in (semi)dry environments is discussed as well as the relevant forces playing a role in the assembly process. In brief, this mini-review is expected to provide a better understanding of tribocharging in assembling objects on the nano- and micrometer scales.

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1. Introduction

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Particle assembly, either spontaneous or by human intervention, into patterns or structures offers a rich complexity to feed the perpetual curiosity of scientists to study this multiscale problem relevant to the formation of colloidal crystals or planets. Assembling building blocks into ordered structures hinges on balancing distinct interactions, including gravity, capillary, van der Waals, hydrophobic, and electrostatic interactions. (1) The latter may result from the triboelectric charging phenomenon, which has been ubiquitous since antiquity but is often wrongly credited to the Greek philosopher Thales. There is in fact no evidence that Thales even performed the experiments typically described in many reports, but Plato wrote about electrostatic charging in his Timaeus. (2)
Tribocharging is an interfacial process in which two surfaces exchange electrical charges when rubbed past each other (Figure 1a). Consequently, the bodies may gain opposite polarity, leading to the onset of an electrostatic attraction. Another term frequently introduced in the literature for the charge exchange process between two surfaces is contact electrification, distinguishing between rubbing (triboelectric charging) and touching or collision (contact charging) types of contact. However, this distinction may be misleading, as apparent macroscopic touching can sometimes in reality be considered as localized rubbing of nano asperities on the surface. (3) This emphasizes the conundrum one faces when dealing with this mesoscale phenomenon.

Figure 1

Figure 1. (a) Illustration of the tribocharging phenomenon between a piece of cloth and a plastic rod. (b) An exemplary triboelectric series ranking the material’s tendency to gain a certain polarity. Wood does not tend to tribocharge due to the presence of lignin. (c) A sliding drop exchange charge with a polymer film. (d-1) The charge transfer QSC in a TENG. (d-2) A dusty solar panel of NASA’s InSight Mars lander. (a, d-1) Reproduced with permission from ref (5). Copyright 2019 Elsevier. (b) Reproduced with permission from ref (8). Copyright 2020 American Chemical Society. (c) Reproduced with permission from ref (9). Copyright 2022 Springer Nature. (d-2) Reproduced with permission from ref (10). Copyright 2022 Courtesy NASA/JPL-Caltech.

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The effects of tribocharging are commonly known to bring joy when we play a simple game of rubbing a balloon across our hair or decorating a cat with Styrofoam. These elementary examples would deceivingly give a novice the illusion that it is relatively simple to comprehend this phenomenon, yet the truth is that our fundamental understanding of electrostatic charging may still be in its infancy. For centuries, the scientific community endeavored to unravel this mysterious phenomenon, but currently, there is no consensus among scientists on the exact underlying tribocharging mechanism, particularly when it concerns insulators. A few tribocharging mechanisms proposed so far include electron transfer, material transfer, ion transfer, density of states, mechanochemistry, and water layers. (4,5) On the other hand, the empirically established triboelectric series is a guide for scientists in the modern days to determine in which direction the charge will be transferred during the rubbing process (Figure 1b). The triboelectric series rank the materials based on an asymmetry in property such that materials ranked on top of the series charge positively, while materials at the tail gain a negative charge. A critical remark here is that the triboelectric series lacks every fundamental basis as deviating results from the prediction are often obtained. The former is highlighted explicitly by studies that show that identical materials also charge after being in contact. Some scientists are even conjecturing that the triboelectric series are ranked according to the hydrophilicity of the substrate. (3,6) They assume that hydrophilic materials charge more positively, while materials with increasing hydrophobicity are more found toward the tail of the series. The latter coincides with the notion that OH– ions present in the atmosphere or a basic environment act as charge carriers that prefer adhering to hydrophobic surfaces, charging the surface more negatively, (6) as depicted for example in Figure 1c. On the other hand, Shin et al. recently introduced a novel quantitative triboelectric series based on material properties, such as density, specific heat, thermal conductivity and the Seebeck coefficient. (7) However, this model also fails to predict the direction of charge transfer between surfaces of identical materials.
Despite that the scientific community is still puzzled by its exact mechanism, the concept of tribocharging has already been leveraged for decades in applications, such as photocopying, electrospraying, electrochemistry, separation of particles, lignin as antistatic agents in polymers (CF. Figure 1b), and, more recently, as triboelectric nanogenerators (TENGs) employed as sensors, or energy harvesters. For example, these energy harvesters may benefit from recent findings that sliding droplets generate electrical charges spontaneously on hydrophobic surfaces as shown in Figure 1c. (9) However, tribocharging can also inflict damage or reduce application efficiency when particles stick on fluidized beds’ walls and dust particles cover solar panels on Earth or Mars (Figure 1d-2). Tribocharging is also relevant to processes such as agglomeration in granular materials, powder blending in the pharmaceutical industry, conveyor belts, and crystal formation.
Therefore, the present contribution focuses explicitly on the tribocharging of beads ranging from the millimeter size down to the size of colloidal particles. To this end, the different interaction forces relevant to each scale are first qualitatively discussed. A key part of this mini-review sheds light on state-of-the-art technology employed to examine tribocharging. In addition, we cover previous reports that used dry assembly methods based on tribocharging to obtain crystal structures or monolayers. Next, we touch upon tribocharging of identical materials, including induced polarization, applicable to agglomeration or cluster formation in granular systems. Finally, we provide a summary and address various points for future exploration to solve the open questions in particle tribocharging.

2. Surface Interaction Forces

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Classical mechanics dictates that the dynamics of all bodies depend on the forces acting on them in conjunction with their mass m. As far as particulate matter is concerned, the forces acting on the particles can be characterized as long-range and short-range forces.
Gravity is commonly known to pull on all bodies, and for a spherical body with radius R, its magnitude scales as ∝ gR3, where g denotes the acceleration of gravity. Another force that acts on particles carrying charge q is the Coulomb force FC. When charged particles are subjected to an electric field E⃗, the Coulomb force equals FC = qE. Charged particles can also induce Coulomb interactions with each other. In this case FC∝q2R. Consequently, it is inferred from elementary physics that like-charged particles repel each other, whereas oppositely charged bodies attract. However, as we will address in section 5, it is plausible that under certain conditions, an electrostatic attraction exists between beads that carries the same polarity on their surface. Gravity and Coulomb forces dominate the long-range interactions among relatively large spherical particles.
On the other hand, as the size of the beads decreases, short-range cohesion forces could become more prominent, causing particles to stick to each other and form aggregates. Potential sources contributing to cohesive interactions include van der Waals, contact mechanics, and capillary forces. The latter is mainly prevalent when it involves hydrophilic particles, as a liquid meniscus is formed between touching particles covered with an adsorbed water layer. The van der Waals force originates from electromagnetic interactions between neutral molecular dipoles, while the contact mechanics force stemming from the van der Waals interactions accounts for the elastic deformation present at the interface of two contacting particles, e.g., JKR Theory. (11) All these cohesive interaction forces Fcoh scale as γR, in which γ denotes the interfacial energy that depends on the material and temperature. For example in the case of silicates, γ is typical of the order of tens of milli-Newtons m–1, implying that for a silica particle with a radius of 5 μm, the cohesive interactions are of the order of μN, whereas the gravity is only on the order of tens of pN. Note that in practice, the cohesive forces between bodies are significantly reduced, due to the presence of micro or nano asperities on their surface. (11,12)
From the preceding discussion, it can be inferred that only the Coulomb interactions may be repulsive in nature and that in comparison to the cohesive forces Fcoh, gravity can be neglected as the size of the beads is reduced. A caveat is that the particles exhibit surface roughness, reducing the cohesive interactions by at least 2 orders of magnitude. The granular Bond number Bog is a measure of the strength of the cohesive interactions with respect to gravity, i.e., Bog = Fcoh/Gravity, implying that for fine or ultrafine cohesive powder particles Bog > 1, whereas for large beads Bog < 1. It is noteworthy that when the interaction forces cause particles to stick to other surfaces, e.g., flat substrates, they are referred to as adhesion forces. The interested reader is kindly referred to respective studies for a detailed discussion of interaction forces. (11,12)

3. Characterizing Triboelectric Charging

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One of the techniques predominantly employed to measure the electrical charge on millimeter- or sub-millimeter-sized particles or any other type of surface (13) are the Faraday cup and Faraday cage or adaptions thereof. In the Faraday cage setup depicted in Figure 2a, the particles are placed in a metal enclosure that is isolated, while charge is induced in the inner metal wall of the enclosed system. This is induced charge is measured trough the electrical connection with an electrometer, i.e., the current passing through a connected electrometer is recorded. A deficit of the Faraday cup is that when an ensemble of submillimeter particles is flown through the cup, particle–particle or particle–wall interactions before entering the Faraday system can not be prevented from happening, hindering the interpretation and lowering the accuracy of the measured charge on the particles significantly.

Figure 2

Figure 2. Several experimental studies to characterize triboelectric charge. (a) Faraday-cup setup. (b) A submillimeter particle is acoustically levitated between a grounded ultrasonic transducer and a sound-reflecting target plate. A piece of aluminum underneath the target plate is connected to an ac or dc voltage source. The particle was back lit and filmed from the side with a high-speed camera. The whole setup is enclosed in a chamber to control the ambient gas. (c, left) An AFM force–distance curve obtained for a symmetric system; AL = amidine latex, and SL = sulfate latex. (c, right) SEM image of a colloidal AFM probe (colloid diameter 10 μm). (d) Topographic image (1 × 1 μm; scale bar = 250 nm) and the simultaneously obtained potential map of an impact crater created by an impacting silica particle on the CFx coated surface. (e) Triboelectric charge accumulation measured with the KPFM on the SiO2 surface with the increase of the number of repeated rubbing at the same area (20 × 20 μm; scale bar = 5 μm). (a) Reproduced with permission from ref (4). Copyright 2010 Elsevier. (b) Reproduced with permission from ref (6). Copyright 2018 American Physical Society. (c) Reproduced with permission from ref (14). Copyright 2015 American Chemical Society. (d) Reproduced with permission from ref (12). Copyright 2022 Elsevier. (e) Reproduced with permission from ref (15). Copyright 2013 American Chemical Society.

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Another route one may take to study tribocharging effects under controlled conditions, e.g., constant humidity, is forcing a single particle to impact on a target plate. Recently, Lee et al. (6) designed a sophisticated setup shown in Figure 2b where the material-independent acoustic levitation and high-speed imaging are combined to study the dynamics and charge transfer of multiple collisions of single submillimeter microspheres with a diameter of ≈200 μm against a target in a controlled manner. The rationale of this method is that by sequentially applying acoustic levitation wherein a particle is first trapped and subsequently released, a collision is initiated after which the bouncing particle is immediately captured by the acoustic trap. This strategy ensures that exactly one collision occurs between the particle and target. The net charge q on the particle is extracted by tracking the response of the acoustically trapped particle on the application of an oscillating electric field, allowing for measuring the evolution of the net charge q induced on the particles after multiple collisions. However, if one would be interested in measuring the maximum amount of charge that can be exchanged between the particle and target, this method is flawed, as the particle inevitably rotates so that a new spot on the particle surface collides with the target each time. Therefore, measuring the maximum amount of charge can become a daunting task requiring running the experiment for days. Another significant drawback of these methods is that they cannot be employed to study the tribocharging dynamics at high relative humidity conditions or of relatively small microparticles impacting against a target plate. Owing to the interaction forces elaborated on in section 2, impacting particles will not bounce back from but rather stick to the targets, as outlined in a detailed study on particle impacts against target electrodes. (16)
With the introduction of the colloidal probe technique, scientists gained access to an excellent instrument to characterize various interactions of microspheres or colloids with other bodies using atomic force microscopy (AFM) (cf. Figure 2c). The method has become state-of-the-art when measuring friction and surface interaction forces, including long-range electrostatic interactions, (14,17) on the micro- and nanoscales. Different contact geometries can be studied, such as colloids on flat-surfaces and colloid–colloid interactions. In Figure 2c, the difference in electrostatic interaction is observed between two distinct types of latex particles. However, only a few studies have applied this technique to study tribocharging by pressing a probe against a substrate and quantifying the electrostatic force acting on the probe. Tapping the colloidal probe on the same spot addresses the issue of measuring the saturation charge that can be exchanged between a probe and a target under controlled conditions, but the downside is that one is left in the dark in which direction charge transfer occurred, i.e., the polarity of the involved surfaces is unknown.
To this end, Kelvin probe force microscopy (KPFM) measurements, also executed with AFM, are currently scientists’ best bet to characterize the surface potential and polarity of micro- and nanoparticles with high spatial resolution. This technique was initially developed to characterize the local contact potential difference (CPD) between a conductive tip and a metal surface in a closed electrical circuit, thus mapping the work function. On the other hand, the KPFM is also becoming more and more common to identify the surface potential of dielectric particles (12,18) and insulating substrates using a conductive tip (cf. Figure 2d). (16,19) Furthermore, experiments are being reported in which the conductive tip is first rubbed on an area of the insulator substrates, e.g., SiO2, in contact mode. Subsequently, a larger area is scanned to examine the evolution of charge diffusion across the surface on the nanoscale (cf. Figure 2e). (15,20) However, it remains highly complex to retrieve quantitative data on the exact amount of charge present on nonconducting surfaces. As a consequence, only qualitative data, such as the surface’s polarity, after the tribocharging process can be acquired. It has been attempted by Xu et al. to resolve the qualitative KPFM data to calculate the number of charges present on semiconductor surfaces, (21) but for insulators, such methods are unprecedented.

4. Self- and Directed Assembly of Beads on Multiscale: Particles and Substrate Interactions

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As the miniaturized device era emerged, an overwhelming diversity of (self-)assembly techniques have been proposed in the literature to manufacture ordered micro- and nanoparticle arrays used as, e.g., photonic films, structural colors, and colloidal lithography masks. To produce these assembled structures successfully, tuning the particle–substrate and interparticle interactions is paramount. (1) Wet assembly techniques in which particles are dispersed in solvents are usually the preferred choice, as they give the advantage of circumventing and controlling the cohesive interactions (cf. section 2) during assembly, e.g., tuning van der Waals interactions, electrostatic repulsion, or attraction, between the particles and substrates. However, the attained structures’ quality in this case predominantly hinges on highly optimized assembly conditions, e.g., solvent evaporation rate, surface wettability, temperature, and acidity. Any slight deviations from the optimum may lead to tremendous defects, such as cracks in the assembled structures.
On the other hand, dry assembly techniques may offer some benefits as they could potentially be faster, more amenable to automation, and have a higher tolerance for small particle dispersity. Nevertheless, it is incredibly challenging to manipulate and control the interaction forces that cause particles to stick, consequently impairing the assembly of ordered structures under ambient conditions. Therefore, exploiting dry assembly techniques, particularly electrostatic-driven assembly, is a feat hardly undertaken by scientists. However, a limited number of studies applied the tribocharging mechanism with great success to study particle (self-)assembly.
For example, the Whitesides’ group used a chemically directed tribocharging mechanism entailling the transfer of mobile ions (=counterpart of covalently bound ions) from one surface to another upon contact to assemble 3D ordered microstructures under dry conditions. (26) The microstructures are created by agitating large (200 μm) and a substantial excess (at least a factor of 10) of smaller polystyrene spheres (5 μm) in an aluminum dish, whereby the surface of the small and large microspheres had distinct functional groups. When the particles came in contact, the large and small spheres gained opposite polarity, inducing an electrostatic attraction between them. As a consequence, the surface of the large spheres was decorated with a closely packed ordering of small spheres. The latter is remarkable as it indicates that the electrostatic attraction between the large and small spheres must be more substantial than the repulsion among the closely packed small spheres carrying the same polarity. Another explanation is that the attractive induced polarization (cf. section 5) (27) among the small spheres enhances the stability of these equilibrium structures. It is important to comment that if these experiments were performed on a substrate carrying an insulator layer instead, the particles would stick on the dish due to tribocharging, failing to assemble into the desired structure. In addition, it can be argued that, since a massive excess of smaller beads was needed, the method can be considered inefficient due to substantial material loss. The latter is generally the norm for dry assembly methods, whereas the dosage of particles can be better controlled in a wet state.
Instead of using a chemically directed assembly approach, a series of studies utilized two distinct millimeter-sized polymer spheres based on their position in the triboelectric series to attain 2D binary granular crystals by laterally agitating these spheres with a peak acceleration of ≈0.02g inside a container coated various types of material (Figure 3a). (22−24) Note that these experiments represent a complex three-material tribocharged system, as charge exchange can occur between the two different types of spheres, including the bottom and walls of the container. That is, tribocharging of the agitated beads occurs as the beads roll or slide across the container, hitting the container walls and contacting other beads. Despite the inherent complexity of the problem, the results seem promising as steady-state 2D granular lattices with square, pentagonal or hexagonal symmetry are achieved. The type of symmetry depends on the ratio of the distinct particles. Of course, for the formation of crystals spanning a large area, it is essential that the beads acquire opposite charges during agitation, and the electrostatic attraction between the beads must outweigh any interaction between the beads and the container. The dynamics of the crystal formation is underpinned by the existing competition between the charging kinetics of the different materials with each other, i.e., the electrostatic attraction, as well as the particles’ kinetic energy, determine if a certain packing symmetry is attained. Cademartiri et al. measured that these ordered crystal structures contain no net charge, (24) whereas other studies found no such evidence. (22,23) The latter is to be expected as the beads can also exchange charge with the container, such that the net charge of the beads in the granular crystal is not zero. The overall net charge on the beads and container is not only determined by their relative position on the triboelectric series but also by the number of beads, their ratio, their geometry, and their kinetics, illustrating that the results can not be explained merely by the empirically established triboelectric series. (24)

Figure 3

Figure 3. (a) Electrostatic assembly of macroscopic crystals comprising a binary mixture of polymer beads; scale bar = 20 mm. Granular lattice structures self-assembled after agitating a binary mixture of beads with (b, left) one, or (b, right) two conductive plate(s); scale bar = 10 mm. (c) A sequence of the lattice structures after turning the applied electric field on and off between the two conductive plates; scale bar = 10 mm. (d) Assembly of agitated cubic objects; scale bar = 20 mm. KPFM measurements performed after vibration experiments on (e, left) silica microspheres and (e, right) fluorocarbon-coated silicon substrate. Insets represent the corresponding topography scans; scale bar = 5 μm (f) Schematic representation of the electrostatic templated self-assembly of macro-sized spheres; scale bar = 10 mm. (g) Segregation of rubbing-induced silica micropsheres on fluorocarbon-coated glass substrate; scale bar = 50 μm. (a) Reproduced with permission from ref (22). Copyright 2003 Springer Nature. (b, c) Reproduced with permission from ref (23). Copyright 2021 Royal Society of Chemistry. (d) Reprinted with permission from ref (24). Copyright 2012 Royal Society of Chemistry. (e) Reproduced with permission from ref (12). Copyright 2022 Royal Society of Chemistry. (f) Reproduced with permission from ref (25). Copyright 2018, American Chemical Society. (g) Reproduced with permission from ref (19). Copyright 2020, American Chemical Society.

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Lately, Grzybowski’s group reported the formation of these granular crystals on supporting conductive substrates and showed that induced dipole and multipole interactions between the particles and the conductive substrate account for the stability of these granular structures. (23) Interestingly, larger crystal structures were obtained when a second conductive substrate was placed on top of the setup without touching the beads, i.e., charge transfer with the top plate was excluded (cf. Figure 3b). This result implies that the electrostatic assembly of these granular crystals originating from the tribocharging of the system is not purely driven by the Coulomb interactions but also by the polar interactions Fpol ∝ R3 induced by the image charges located in the conductive substrates. Additionally, applying an electric field across the two conductive substrates induces dipoles on the particles which leads to openings in the crystal structures. However, these openings are reversible as soon as the electric field is switched off, implying that the assembled granular crystals can be manipulated in a controlled manner (cf. Figure 3c). (23)
The formation of granular crystals using electrostatic self-assembly is not restricted to spheres but could also be applied to obtain crystals of other millimeter-sized objects such as cubes (cf. Figure 3d) or rods by mechanical agitation. (22)
The aforementioned discussion on granular crystals may give the impression that agitation can easily be adapted to attain similar structures with micro- or nanoparticles. It is precisely the opposite, as significantly more energy should be applied to mobilize these particles with Bog > 1, particularly when agglomerated. The latter is supported by a study performed by Jimidar et al. in which peak accelerations of approximately 30g were required to mobilize the agglomerated monodisperse silica or polystyrene particles with diameters ranging between 3 and 10 μm on bare and fluorocarbon-coated silicon substrates. (12) However, even at these accelerations, the strongly agglomerated hydrophilic silica particles would not fully mobilize compared to the weakly agglomerated hydrophobic polystyrene particles, as the cohesive interactions among the former are substantial compared to the polystyrene ones. On the other hand, the similarity between both types of particles is that they self-organize into monolayers on various substrates. The results are explained by accounting for adhesion and friction forces among the contacting bodies. Additionally, the study found compelling evidence using KPFM measurements that, due to the tribocharging mechanism, the adhesion between the microspheres and fluorocarbon-coated substrate was enhanced, promoting the formation of monolayers. The fluorocarbon-coated substrates locally gained electrical charge, while the polarity of only a few particles reversed after agitation (cf. Figure 3e), implying that charge exchange occurred between the microspheres and the substrate. In contrast to the ordered crystals obtained with millimeter-sized spheres, (22−24) the monolayers comprising the microspheres were highly disordered, as confirmed by analyzing their morphology using the Voronoi approach. The different symmetry structures within the monolayers can possibly be explained by electrostatic repulsion between neighboring particles. Another reason may be that the particles’ kinetic energy was insufficient to overcome the adhesion forces, i.e., particles were stuck on the substrates, implying that it is plausible that higher frequencies and amplitudes were required to achieve ordered crystal structures.
Triboelectrification can also be exploited to direct the assembly of objects into nonclosely packed structures, as has been done elegantly by Wang et al. (25) They obtained arbitrary, predesigned patterns of millimeter-sized nylon beads on a Teflon-coated, templated copper electrode (see Figure 3f). The nylon beads were precharged by shaking them in a Teflon container, while the Teflon coating was charged by rubbing it using aluminum foil. Consequently, the nylon beads were positively charged, while the Teflon coating was negatively charged, as predicted by the triboelectric series. However, positive charges were induced in the grounded copper electrode, screening the negative charge on some parts of the Teflon coating. After gently shaking the beads across the surface, the assembly strategy allows for trapping the positively charged beads solely on the remaining negatively charged regions on the Teflon coating, i.e., an electrostatic attraction emerged between the beads and the zones where the copper electrode was not present underneath the Teflon coating. Note that by tilting the system, excess millimeter-sized beads would just easily roll off the surface due to the gravity force. The applied assembly strategy here is reminiscent of the photocopying technique, which uses the electrostatic attraction of toner particles on a drum.
Next to agitation, manual rubbing is another type of mechanical-based techniques to separate agglomerates into single particles. A recent study applied this method to achieve assembled structures of agglomerated 10 μm silica particles on fluorocarbon-patterned substrates using a polydimethylsiloxane (PDMS) sheet. (19) Note that, generally, surfaces are coated with fluorocarbon to eradicate capillary forces, decreasing the overall adhesion of particles. It was serendipitously observed that the hydrophilic silica microspheres adhered to the hydrophobic fluorocarbon patterns instead of the hydrophilic uncoated zones on the substrates. Despite the circular rubbing motion, the silica particles self-organized into nonclosely packed monolayer structures, matching the geometry of the fluorocarbon features on the substrates as shown in Figure 3g. By probing the fluorocarbon coating and particles using KPFM, it was concluded that they acquired opposite polarity, enhancing the adhesion of particles due to the electrostatic attraction.
In contrast to the study of Wang et al., (25) which leverages gravity to remove the excess particles by simply tilting the substrate, the excess microspheres in the above rubbing study could not be removed in this manner as the adhesion force between particles and uncoated parts of the substrates was considerably stronger than gravity. However, these excess particles could be removed from the uncoated parts by blowing pressurized nitrogen gas, while only a few assembled particles were removed from the fluorocarbon coating. These results show that due to the tribocharging mechanism, the induced electrostatic attraction significantly promotes the adhesion between the particles and the coating such that the particles can withstand the manual rubbing motion and the force exerted by the flow of nitrogen gas.
Compared to mechanical agitation, manual rubbing intrinsically allows for applying substantial shear forces to separate agglomerates into single particles and move them over larger areas. In addition, the assembled structures are attained within a minute (±15 rubbing strokes), whereas agitation takes at least 15 min to obtain large areas covered with monolayers. However, a significant drawback of the manual rubbing method is that the rubbing tool, e.g., the PDMS slab, also interacts with particles and substrate, corresponding to a three-material tribocharged system. Consequently, manual rubbing cannot investigate the pure interaction between the beads and the underlying substrate in contrast to mechanical agitation. In addition, the manual rubbing method is more susceptible to human imprecision and minute differences in applied force.
A key finding of the performed manual rubbing study is that the quality of the assembled monolayers was sensitive to air moisture and the supporting substrate material. The amount of water absorbed on surfaces changes with the relative humidity, possibly affecting the degree of tribocharging and concomitantly electrostatic attraction, as already reported by others. (3,6) Another unexpected but significant finding was that the underlying substrate plays a crucial role in the interfacial charging behavior of the fluorocarbon coating with the particles. This remarkable discovery was first reported by Siek et al. (13) Their study provides compelling evidence that the charge acquired on the polymer surface due to tribocharging is affected by the induced image charges in the supporting substrate, influencing the charge acquired. The thickness of the polymer surfaces varied up to 1 μm.
These examples collectively highlight the rich complexity of tribocharging emerging from mechanically induced friction between dissimilar materials. By perfectly balancing the electrostatic forces with other relevant surface interaction forces at that length scale, one can obtain a wide variety of electrostatically assembled patterns of dielectric objects. However, manipulating these interaction forces is much more challenging for microparticles than for larger beads as cohesion forces tend to dominate the interactions among fine powder particles or between those particles and substrates. Therefore, systematic studies on the dry electrostatic assembly of colloids are lacking, even though there is a myriad of colloidal particle types to be explored. For example, Locatelli et al. showed that a variety of particle arrangements could be achieved when tuning the interactions of heterogeneously charged (patchy) colloids on patterned substrates using Monte Carlo simulations. (28)

5. Granular and Similar Materials Charging

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Up to now, we have elaborated on the tribocharging involving objects with different material compositions. However, particle tribocharging can not be addressed without shedding light on a highly counterintuitive problem: the tribocharging of identical materials. The latter is particularly the case in everyday granular charging events, e.g., sand storms, volcano explosions, and collisions of cosmic grains in early proplanetary formation. (29) The understanding of granular charging is also relevant to engineering applications, (30) such as fluidized beds, the nonuniform blending of pharmaceutical powders, and space explorations.
The charging of identical materials after contact has been studied extensively but is certainly not limited to particles. It is reported that an asymmetry in contact geometry or size leads to tribocharging of identical surfaces. However, the same material tribocharging phenomenon starts to become more mysterious when completely identical materials with the same contact geometries break their surface charge symmetry as soon as they are released. After contact, a charge pattern is observed on the surface, e.g., on two symmetrically rubbed balloons (cf. Figure 4a), or PDMS sheets after conformal contact, implying that it is plausible that local surface heterogeneities or strain fluctuations contribute to charge transfer among the bodies. (31) Surprisingly, charge transfer was not resisted by the Coulomb force as more charge transfer occurred in one direction when the number of repeated contacts was increased. This phenomenon has also been recently addressed by the Waitukaitis group by accounting for the spatial correlations in donor/acceptor properties in their model. (37)

Figure 4

Figure 4. (a) Emerging charge patterns on two identical latex balloons after rubbing them against each other. (b) Segregation of an agitated bidisperse mixture (red = big, blue = small) of PTFE spheres at (left) a RH = 50%, and (right) a RH = 1000%. Time-lapse of (c-1, c-2) a growing, or (c-3) disruption of a cluster after microparticles collided against them. (c-4, left) Dynamic formation of a stable triangular structure comprising two large particles and one small particle. (c-4, right) Possible charge distribution producing these triangular structures. (c) Scale bar: 500 μm (white), and 1 mm (green). (d-1) Precharged agglomerates entering the Bremen tower. (d-2) Impact of a single granule (marked by the black arrow) against a large cluster. (e) Charging of uncharged identical particles in an external electrical field. (f) Time-lapse of vibrated hollow microspheres in the Bremen tower. (a) Reproduced with permission from ref (31). Copyright 2008 Europhysics Letters Association. (b) Reproduced with permission from ref (32). Copyright 2017 Royal Society of Chemistry. (c) Reproduced with permission from ref (33). Copyright 2015 Springer Nature. (d) Reproduced with permission from ref (34). Copyright 2019 Springer Nature. (e) Reproduced with permission from ref (35). Copyright 2010 Springer Nature. (f) Reproduced with permission from ref (36). Copyright 2017 Springer Nature.

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The inevitable multiple collisions among similar beads add to the complexity of tribocharging in a granular system. Consequently, for bidisperse or polydisperse systems, large particles tend to charge positively, while small particles acquire a negative polarity. For example, a study performed by Schella et al. (32) using a bidisperse system of millimeter-sized polymer beads confined in a container showed that two distinct millimeter-sized PTFE beads gained opposite polarity after shaking this bidisperse system vertically, segregating the bed of particles in the container. Note that there is a chance, albeit minimal, that the particles can collide with the container walls, but the charge on the particles is affected mainly by the particle–particle collisions. A key finding of the study was that the particles’ charge was lower when the humidity levels increased, while the segregation was suppressed at low humidity levels as shown in Figure 4b. In the latter case, the particles acquired more charge, such that the dominant electrostatic attraction among the distinct beads renders a mixed granular system. Thus, it is inferred from this study that various packing structures can be contrived using a mixture of granules by controlling the humidity and concomitantly the charge on the beads.
As mentioned, many multiple head-on collision events occur among identical grains in a granular system. At the moment of the collisions, the granules experience a repulsive collision force Fcol ∝ R3. Note that the attractive gravitation force between two identical particles is Fgrav ∝ R4, while the attractive cohesion forces are Fcoh ∝ R (cf. section 2). The interplay between these short-range and repulsive forces can cause two particles to stick and form dimers that act as seeds in subsequent collisions to form larger agglomerates. Basically, if the attractive forces defy the collision force, particles will stick. Considering the dependency of the forces on the particles’ size, it is inferred that gravity becomes the dominant force for large body stickiness. In contrast, in the case of microparticles or colloids, the cohesive forces tend to become more significant than the collision force, promoting the formation of agglomerates.
Of course, the particle size does not paint the whole picture, as the collision force also pertains to the impacting bodies’ momentum and the coefficient of restitution (COR = ratio of relative velocity magnitude before and after the impact). The latter depends on the bodies’ mechanical properties, e.g., Young’s modulus, and yield stress. (16) Despite the tangled interplay of several factors, the particles’ kinetic energy should surpass the cohesive energy resulting from the short-range forces for them to bounce.
However, a study executed in a tower with a dilute stream of monodisperse zirconium dioxidesilicate grains with a diameter of 274 μm showed that the long-range Coulomb and short-range induced polarization forces continuously attract particles between repeated collisions (Figure 4c-1). (33) Consequently, the formation of clusters was enhanced (Figure 4c-2), but particles with sufficient kinetic energy could also disrupt already existing aggregates (Figure 4b-3). The particles with just a minimal size dispersion obtained a net charge distribution centered around zero, with some particles remarkably acquiring several millions of elementary charges e (1.6 × 10–19 C). In turn, these highly charged particles served as nucleation seeds by attracting lesser charged particles to form densely packed arrangements with multiple particles in contact (cf. Figure 4c-2). The stability of these extraordinary arrangements can be ascribed to the induced polarization forces. These forces are always significantly attractive for particles with a high dielectric constant, even when they carry a charge of the same polarity but with a prominent contrast in magnitude. Therefore, the induced polarization force is essential, as it enhances the likelihood of lattice structure formation at a close approach. The latter is particularly elucidated when experiments were performed with a bidisperse mixture of larges beads (326 μm) and smaller beads (251 μm) of the same material. As expected, the large particles were positively charged, and the smaller beads gained a negatively charged surface. Various stable electrostatically formed structures comprising large and small beads were formed, one of which is depicted in Figure 4c-4. It is observed that the two positively charged large spheres are attracted to each other to form a stable triangular structure with the small particle, which can be attributed to the induced polarization forces. Thus, colliding grains can turn into stable structures, so-called “granular molecules”, by attractive electrostatic interactions provided that their kinetic energy is minimized.
Similarly, the Wurm group observed the spectacular electrostatic driven formation of stable centimeter-sized agglomerates consisting of single monodisperse glass particles (434 μm) in the Bremen tower under microgravity conditions. (34) Prior to releasing the particles in the tower, where an electric field is applied under microgravity conditions, the grains were precharged by shaking them in a container. Consequently, the grains were tribocharged and formed millimeter-sized agglomerates before entering the tower (cf. Figure 4d-1). Strikingly, these agglomerates remained intact even after colliding at speeds of a few decimeters per second. However, due to electrostatic interactions, the agglomerates could deform (cf. Figure 4d-2) or even grow to larger structures.
From a fundamental perspective, this result is highly significant as it demonstrates that millimeter-sized colliding entities can overcome the so-called bouncing barrier relevant to planetesimal formation and growth. Earlier studies reported that uncharged aggregates larger than a few millimeters beyond the bouncing barrier would collide but not stick and may even be fragmented into smaller agglomerates.
Another concept proposed for identical particle charging in particle clouds is the collision of dielectric spheres in the presence of an electric field without accounting for any conductive mechanisms on the particles or the environment. In this model, depicted in Figure 4e, two neutral dielectric spheres are polarized by an external electric field, and their charge gets neutralized at their point of contact. Subsequently, the particles are repolarized after the rebound, such that the particles acquire an opposite polarity. (35) A major concern of this model, as truthfully acknowledged by the authors, is that these external electric fields are nonexisting in natural events.
On the other hand, Yoshimatsu et al. reported that external electric fields are not needed to polarize dielectric spheres. (36) It is shown that the electric field generated by an infinitesimal charged bead is sufficient to polarize neighboring particles, charging them according to the same concept shown in Figure 4f. Surprisingly, the charge on agitated identical particles is amplified and increases exponentially. The latter is corroborated by agitating hollow microspheres with a diameter of ±140 μm also in the microgravity environment of the Bremen tower. From the results shown in Figure 4f, it can be inferred that the trajectory of the spheres leaving the particle bed was parabolic, implying that they only experienced an electrostatic force as gravity effects are nullified in the Bremen tower. In addition, as the acquired charge on the particles increased exponentially, and concomitantly the electrostatic attraction among particles, the levitation of particles from the agitation bed was inhibited.
To sum up, identical materials get tribocharged if an asymmetry exists between the bodies, which can be caused by substantial differences in size, geometry, small fluctuations in strain, surface charge densities, or other surface heterogeneities. These may arise from ambient conditions, such as humidity and environmental ionic species. It is also reported that even on hydrophilic materials water islands are present instead of a continuous layer water, (38) which also may effect the local charging of identical materials. Additionally, several studies highlighted the significance of polarization forces c.q. induced dipoles, even between like-charged particles, making them indispensable when it concerns the charging of similar materials. (27) Consequently, stable granular molecules or large aggregates can be formed, offering insight into the self-assembly of colloidal particles or the formation of planetoids.

6. Summary and Future Outlook

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Spanning the last centuries, a plethora of scientists embarked on a journey to comprehend the omnipresent yet so mysterious, tribocharging phenomenon in which charge is exchanged at the interface between two bodies momentarily in contact. Rubbing balloons or grains using a PDMS sheet may be science’s most straightforward experiment to perform or demonstrate without using expensive equipment. However, as we have highlighted, tribocharging can already be affected by the slightest surface inhomogeneity, which may be considered the Achilles’ heel to arriving at a unifying mechanism explaining this manifestation of charge transfer present since the old days. The different charging mechanisms proposed to date elucidate that we have only scratched the surface of understanding electrostatic charging.
In the present contribution, we have aimed to marry the solid conceptual ideas from chemists, materials scientists and physicists, particularly those working on granular matter, on the tribocharging of different objects at various scales. Considering Richard Feynman’s quote: “there is plenty of room at the bottom”, we envision that these concepts could also be adopted for the dry assembly of crystals comprising microspheres or colloids. Plausibly, the latter can be realized by tuning the surface chemistry of the particles to reduce their tendency to stick on surfaces. Next, advances in contemporary polymer and colloidal chemistry allow synthesizing particles with shape anisotropy, e.g., rods, cubes, ellipsoids, and bespoke chemical functionality such as Janus particles or patchy colloids. (39,40) In addition, these aspherical particles could also be utilized in granular matter studies as, in practice, particles may not be completely spherical. It is expected that the shape anisotropy will affect the surface charge distribution and, consequently, the induced dipoles and assembled structures. Since anisotropic particles are not readily available, systematic studies investigating shape effects on tribocharging at the micro- and nanoscales are lacking. Thus, large gains lie within grasp concerning our understanding of the shape anisotropy of particles or substrates on assembled structures.
Next, as inferred from the rubbing study performed using two identical balloons, a charge pattern existed on their contact area, implying that this is potentially also the case for colliding particles. Thus, instead of only having a net charge q, particles may carry charge patches, as well as water patches, on their surface. Consequently, these patches affect the attractive polarization between neighboring particles, which significantly contributes to the formation of stable electrostatically assembled structures. To gain more insight into the charge distribution on the colliding bead, one can perform, for example, KPFM measurements. However, quantitative data on the charge distribution will remain missing. Therefore, a clear impetus remains to develop methods to produce quantitative data with a nanoscale resolution to take a quantum leap in our understanding of charge transfer among identical materials.
The existing colloidal probe technique has rarely been employed to probe the electrostatic interaction between particles and substrates in the air. Although the acquired polarity of the surfaces can not be retrieved, we believe this technique can be leveraged more frequently to study the electrostatic interaction of particles on surfaces in air. This technique allows the study of tribocharging effects in a controlled manner by varying parameters, e.g., humidity, surface chemistry, load, and concomitantly contact area. These measurements may be relevant to the adhesion of dust particles on solar panels.
Finally, tribocharging encompasses such a rich complexity that unravelling it will be advantageous to the quest for manufacturing novel responsive materials, energy harvesters, wearable materials, more efficient solar panels, as well as our understanding of planet formation. We want to warn those entering the tribocharging field that the triboelectric series is not the holy grail but should be merely treated as a guideline in which direction charge transfer will occur. Moving forward, scientists across all disciplines must contribute to overcoming challenges in understanding the tribocharging of beads, such as synthesizing perfectly identical particles and designing novel experimental techniques that can generate quantitative data under highly controlled and reproducible conditions. These advancements should prevent any asymmetry when studying the charging of completely identical materials. Thus, exciting opportunities lie ahead regarding the dry assembly of structures comprising micro- and nanoparticles.

Author Information

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  • Corresponding Author
    • Ignaas S. M. Jimidar - Department of Chemical Engineering CHIS, Vrije Universiteit Brussel, Brussels1050, Belgium;  Mesoscale Chemical Systems, MESA+ Institute for Nanotechnology, University of Twente, P.O. Box 217, 7500AEEnschede, The Netherlands;  Orcidhttps://orcid.org/0000-0001-9653-1938;  Email: [email protected]
  • Authors
  • Notes
    The authors declare no competing financial interest.

Biographies

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Kai Sotthewes is employed as a researcher at the MESA+ Institute for Nanotechnology and the University of Twente, The Netherlands. He received his MSc degree and his PhD degree in Applied Physics from the University of Twente followed by a postdoctoral study at RWTH Aachen, Germany. His research mainly focuses on contact and transport of low-dimensional materials, functionalized interfaces, and low-energy electronics.

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Han Gardeniers obtained a MSc degree in Chemistry and a PhD in Experimental Solid-State Physics from Radboud University Nijmegen, The Netherlands, in 1985 and 1990, respectively. He joined the Micromechanical Transducers group at the University of Twente, The Netherlands, in 1990. From 2001 until 2003 he has worked in industry, as a senior scientist at Kymata Ltd./Alcatel Optronics and Micronit Microfluidics, after which he rejoined the University of Twente as a member of the Biosensors/Lab-on-a-Chip Group. In 2007 he started his own research group “Mesoscale Chemical Systems”, which focuses on micro- and nanostructures with a focus on chemical applications, including microreactors and microfluidic systems for chemical analysis.

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Gert Desmet has a Master’s degree and PhD in Chemical Engineering from the Vrije Universiteit Brussel (VUB), Brussels, Belgium, where he currently is a full professor in chemical engineering. His research mainly focuses on the miniaturization and automation of separation methods, as well as on the investigation and the modeling of flow effects in chromatographic systems.

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Ignaas Jimidar has a BSc degree in Mechanical Engineering from the Anton de Kom University of Suriname. He obtained his MSc in Applied Physics from the University of Twente, The Netherlands. He holds a PhD from the University of Twente and the Vrije Universiteit Brussel, Belgium. His research mainly focuses on understanding surface interaction forces to study the (self-) assembly of particles. He has studied dry assembly strategies on flat and micromachined substrates. He has applied techniques such as electrostatic levitation and tribocharging to obtain particle arrays that can serve as building blocks in microfluidic applications.

Acknowledgments

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The authors gratefully acknowledge funding from the ERC Advanced Grant “PrintPack” (No. 695067).

References

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    Zhou, Y. S.; Liu, Y.; Zhu, G.; Lin, Z.-H.; Pan, C.; Jing, Q.; Wang, Z. L. In situ quantitative study of nanoscale triboelectrification and patterning. Nano Lett. 2013, 13, 2771– 2776,  DOI: 10.1021/nl401006x
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    In Situ Quantitative Study of Nanoscale Triboelectrification and Patterning
    Zhou, Yu Sheng; Liu, Ying; Zhu, Guang; Lin, Zong-Hong; Pan, Caofeng; Jing, Qingshen; Wang, Zhong Lin
    Nano Letters (2013), 13 (6), 2771-2776CODEN: NALEFD; ISSN:1530-6984. (American Chemical Society)
    By combining contact-mode at. force microscopy (AFM) and scanning Kevin probe microscopy (SKPM), the authors demonstrated an in situ method for quant. characterization of the triboelectrification process at the nanoscale. The authors systematically characterized the triboelec. charge distribution, multifriction effect on charge transfer, as well as subsequent charge diffusion on the dielec. surface: (i) the SiO2 surface can be either pos. or neg. charged through triboelec. process using Si-based AFM probes with and without Pt coating, resp.; (ii) the triboelec. charges accumulated from multifriction and eventually reached to satd. concns. of (-150 ± 8) μC/m2 and (105 ± 6) μC/m2, resp.; (iii) the charge diffusion coeffs. on SiO2 surface are (1.10 ± 0.03) × 10-15 m2/s for the pos. charge and (0.19 ± 0.01) × 10-15 m2/s for the neg. charges. These quantifications will facilitate a fundamental understanding about the triboelec. and de-electrification process, which is important for designing high performance triboelec. nanogenerators. The authors demonstrated a technique for nanopatterning of surface charges without assistance of external elec. field, which has a promising potential application for directed self-assembly of charged nanostructures for nanoelectronic devices.
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    Jimidar, I. S.; Sotthewes, K.; Gardeniers, H.; Desmet, G. A detailed study of the interaction between levitated microspheres and the target electrode in a strong electric field. Powder Technol. 2021, 383, 292– 301,  DOI: 10.1016/j.powtec.2021.01.036
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    A detailed study of the interaction between levitated microspheres and the target electrode in a strong electric field
    Jimidar, Ignaas S. M.; Sotthewes, Kai; Gardeniers, Han; Desmet, Gert
    Powder Technology (2021), 383 (), 292-301CODEN: POTEBX; ISSN:0032-5910. (Elsevier B.V.)
    In this work, we report on an in-depth study of how 10μm silica and polystyrene particles interact with a target electrode after they were levitated by applying a strong elec. field. The results show that, under these conditions, silica particles unexpectedly have a higher tendency to adhere on a fluorocarbon coated electrode compared to a bare, non-coated silicon electrode. Relative adherence ratios Γ up to Γ = 4.7 were obsd. Using the colloidal probe technique, at. 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 electrification phenomenon. All these processes attribute to increasing the probability that levitated particles attain velocities that are lower than the sticking velocity.
  17. 17
    Jones, R.; Pollock, H. M.; Cleaver, J. A.; Hodges, C. S. Adhesion forces between glass and silicon surfaces in air studied by AFM: Effects of relative humidity, particle size, roughness, and surface treatment. Langmuir 2002, 18, 8045– 8055,  DOI: 10.1021/la0259196
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    Adhesion Forces between Glass and Silicon Surfaces in Air Studied by AFM: Effects of Relative Humidity, Particle Size, Roughness, and Surface Treatment
    Jones, Robert; Pollock, Hubert M.; Cleaver, Jamie A. S.; Hodges, Christopher S.
    Langmuir (2002), 18 (21), 8045-8055CODEN: LANGD5; ISSN:0743-7463. (American Chemical Society)
    Using the at. force microscope (AFM), the pull-off forces between flat glass or Si surfaces and Si AFM tips or glass microspheres of different sizes were extensively studied as a function of relative humidity (RH) in the range 5-90%, as model systems for the behavior of cohesive powders. The glass and Si substrates were treated to render them either hydrophobic or hydrophilic. All the hydrophilic surfaces gave simple force curves and pull-off forces increasing uniformly with RH. Small contacts (R ∼ 20 nm) gave pull-off forces close to values predicted by simple Laplace-Kelvin theory (∼20 nN), but the values with microspheres (R ∼ 20 μm) fell well below predictions for sphere-flat or sphere-sphere geometry, due to roughness and asperity contacts. The hydrophobic Si surfaces also exhibited simple behavior, with no significant RH dependence. The pull-off force again fell well below predicted values (Johnson-Kendall-Roberts contact mechanics theory) for the larger contacts. Hydrophobic glass gave similar adhesion to Si over most of the RH range, but against both Si tips and glass microspheres, there was an anomalously large adhesion in the RH range 20-40%, accompanied by a long-range noncontact force. The adhesion on fully hydrophilic surfaces and its RH dependence can be mostly explained by current theories of capillary bridges, but the interpretation is complicated by the sensitivity of theor. predictions to contact geometry (and hence to roughness effects) and by uncertainties in the thickness of adsorbed H2O layers. The anomalous behavior on hydrophobic glass surfaces at intermediate values of RH is not fully understood, but possible causes are (1) dipole layers in the partially formed H2O film, giving rise to patch charges and long-range forces, or (2) fixed charges at a reactive glass surface, involving specific bonding reactions. The results may be useful in explaining the behavior of cohesive powders with different coatings or those which show a large humidity dependence (e.g., zeolites) or show electrostatic charging effects (e.g., SiO2 aerogels).
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    Gouveia, R. F.; Galembeck, F. Electrostatic charging of hydrophilic particles due to water adsorption. J. Am. Chem. Soc. 2009, 131, 11381– 11386,  DOI: 10.1021/ja900704f
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    Electrostatic Charging of Hydrophilic Particles Due to Water Adsorption
    Gouveia, Rubia F.; Galembeck, Fernando
    Journal of the American Chemical Society (2009), 131 (32), 11381-11386CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
    Kelvin force microscopy measurements on films of noncryst. silica and aluminum phosphate particles reveal complex electrostatic potential patterns that change irreversibly as the relative humidity changes within an elec. shielded and grounded environment. Potential adjacent to the particle surfaces is always neg. and potential gradients in excess of ±10 MV/m are found parallel to the film surface. These results verify the following hypothesis: the atm. is a source and sink of electrostatic charges in dielecs., due to the partition of OH- and H+ ions assocd. to water adsorption. Neither contact, tribochem. or electrochem. ion or electron injection are needed to change the charge state of the noncryst. hydrophilic solids used in this work.
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    Jimidar, I. S.; Sotthewes, K.; Gardeniers, H.; Desmet, G. Spatial segregation of microspheres by rubbing-induced triboelectrification on patterned surfaces. Langmuir 2020, 36, 6793– 6800,  DOI: 10.1021/acs.langmuir.0c00959
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    Spatial Segregation of Microspheres by Rubbing-Induced Triboelectrification on Patterned Surfaces
    Jimidar, Ignaas S. M.; Sotthewes, Kai; Gardeniers, Han; Desmet, Gert
    Langmuir (2020), 36 (24), 6793-6800CODEN: LANGD5; ISSN:0743-7463. (American Chemical Society)
    Particle (monolayer) assembly is essential to various scientific and industrial applications, such as the fabrication of photonic crystals, optical sensors, and surface coatings. Several methods, including rubbing, have been developed for this purpose. Here, we report on the serendipitous observation that microparticles preferentially partition onto the fluorocarbon-coated parts of patterned silicon and borosilicate glass wafers when rubbed with poly(dimethylsiloxane) slabs. To explore the extent of this effect, we varied the geometry of the pattern, the substrate material, the ambient humidity, and the material and size of the particles. Partitioning coeffs. amounted up to a factor of 12 on silicon wafers and even ran in the 100s on borosilicate glass wafers at zero humidity. Using Kelvin probe force microscopy, the observations can be explained by triboelectrification, inducing a strong electrostatic attraction between the particles and the fluorocarbon zones, while the interaction with the noncoated zones is insignificant or even weakly repulsive.
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    Bai, X.; Riet, A.; Xu, S.; Lacks, D. J.; Wang, H. Experimental and simulation investigation of the nanoscale charge diffusion process on a dielectric surface: effects of relative humidity. J. Phys. Chem. C 2021, 125, 11677– 11686,  DOI: 10.1021/acs.jpcc.1c02272
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    Experimental and Simulation Investigation of the Nanoscale Charge Diffusion Process on a Dielectric Surface: Effects of Relative Humidity
    Bai, Xuejie; Riet, Adriaan; Xu, Song; Lacks, Daniel J.; Wang, Haifeng
    Journal of Physical Chemistry C (2021), 125 (21), 11677-11686CODEN: JPCCCK; ISSN:1932-7447. (American Chemical Society)
    Electrostatic charge generation and diffusion on the nanoscale were studied by at. force microscopy and Kelvin probe microscopy. The charge diffusion coeffs. were obtained by matching exptl. results with numerical solns. of the diffusion equation. The results found that the relative humidity variations could significantly alter both the charge generation and diffusion processes. For the charge generation, the increase in relative humidity led to a decrease in transferred charge amt. between the contact surfaces owing to the presence of the absorbed water film on the tip-sample interface. For the charge diffusion, the increase in relative humidity could accelerate the charge diffusion process laterally, and the diffusion coeff. of higher relative humidity was 3-5 orders of magnitude larger than those under dry air and N2. It was proved that the charge diffusion process for the pos. charge was not necessarily faster than that for the neg. one. In addn., the contribution from atm. water mols. to the surface charge diffusion was distinguished from that of absorbed water films by calcg. the net loss of surface charge, and this effect was found to be more obvious under higher relative humidity. The dominant mechanism for the charge diffusion was discussed, and we argued that the relative humidity could be the main reason, and probably the only reason, for the charge diffusion and decay on the dielec. surfaces.
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    Xu, J.; Li, D.; Chen, D.; Li, W.; Xu, J. Nanoscale Characterization of Active Doping Concentration in Boron-Doped Individual Si Nanocrystals. physica status solidi (a) 2018, 215, 1800531,  DOI: 10.1002/pssa.201800531
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    Grzybowski, B. A.; Winkleman, A.; Wiles, J. A.; Brumer, Y.; Whitesides, G. M. Electrostatic self-assembly of macroscopic crystals using contact electrification. Nat. Mater. 2003, 2, 241,  DOI: 10.1038/nmat860
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    Electrostatic self-assembly of macroscopic crystals using contact electrification
    Grzybowski, Bartosz A.; Winkleman, Adam; Wiles, Jason A.; Brumer, Yisroel; Whitesides, George M.
    Nature Materials (2003), 2 (4), 241-245CODEN: NMAACR; ISSN:1476-1122. (Nature Publishing Group)
    Self-assembly of components larger than mols. into ordered arrays is an efficient way of prepg. microstructured materials with interesting mech. and optical properties. Although crystn. of identical particles or particles of different sizes or shapes can be readily achieved, the repertoire of methods to assemble binary lattices of particles of the same sizes but with different properties is very limited. This paper describes electrostatic self-assembly of two types of macroscopic components of identical dimensions using interactions that are generated by contact electrification. The systems we have examd. comprise two kinds of objects (usually spheres) made of different polymeric materials that charge with opposite elec. polarities when agitated on flat, metallic surfaces. The interplay of repulsive interactions between like-charged objects and attractive interactions between unlike-charged ones results in the self-assembly of these objects into highly ordered, closed arrays. Remarkably, some of the assemblies that form are not electroneutral, i.e., they possess a net charge. The authors suggest that the stability of these unusual structures can be explained by accounting for the interactions between elec. dipoles that the particles in the aggregates induce in their neighbors.
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    Polev, K.; Visyn, V.; Adamkiewicz, W.; Sobolev, Y.; Grzybowski, B. A. Stimuli-responsive granular crystals assembled by dipolar and multipolar interactions. Soft Matter 2021, 17, 8595– 8604,  DOI: 10.1039/D1SM00887K
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    Stimuli-responsive granular crystals assembled by dipolar and multipolar interactions
    Polev, Konstantin; Visyn, Valentin; Adamkiewicz, Witold; Sobolev, Yaroslav; Grzybowski, Bartosz A.
    Soft Matter (2021), 17 (38), 8595-8604CODEN: SMOABF; ISSN:1744-6848. (Royal Society of Chemistry)
    This work describes granular crystals held together by unusual, multipolar interactions and, under the application of an external bias, undergoing reversible structural transitions between closed and open forms. The system comprises two types of polymeric beads agitated on one or between two conductive plates and gradually acquiring charges by contact electrification. The charges thus developed induce a series of electrostatic images in the conductive supports and, in effect, the beads interact via dipolar or multipolar interactions, enabling the stabilization of non-electroneutral crystals. Furthermore, under an applied bias, the beads become polarized and their complex interactions (due to the series of image charges as well as series of image dipoles) result in open-pore crystals which return to compact forms upon bias removal. These effects are rationalized by anal. calcns., and the crystal structures obsd. in the expts. are reproduced by mol. dynamics simulations.
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    Cademartiri, R.; Stan, C. A.; Tran, V. M.; Wu, E.; Friar, L.; Vulis, D.; Clark, L. W.; Tricard, S.; Whitesides, G. M. A simple two-dimensional model system to study electrostatic-self-assembly. Soft Matter 2012, 8, 9771– 9791,  DOI: 10.1039/c2sm26192h
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    A simple two-dimensional model system to study electrostatic-self-assembly
    Cademartiri, Rebecca; Stan, Claudiu A.; Tran, Vivian M.; Wu, Evan; Friar, Liam; Vulis, Daryl; Clark, Logan W.; Tricard, Simon; Whitesides, George M.
    Soft Matter (2012), 8 (38), 9771-9791CODEN: SMOABF; ISSN:1744-683X. (Royal Society of Chemistry)
    This paper surveys the variables controlling the lattice structure and charge in macroscopic Coulombic crystals made from elec. charged, millimeter-sized polymer objects (spheres, cubes, and cylinders). Mech. agitation of these objects inside planar, bounded containers caused them to charge elec. through contact electrification, and to self-assemble. The processes of electrification and self-assembly, and the characteristics of the assemblies, depended on the type of motion used for agitation, on the type of materials used for the objects and the dish, on the size and shape of the objects and the dish, and on the no. of objects. Each of the three different materials in the system (of the dish and of the two types of spheres) influenced the electrification. Three classes of structures formed by self-assembly, depending on the exptl. conditions: two-dimensional lattices, one-dimensional chains, and zero-dimensional rosettes'. The lattices were characterized by their structure (disordered, square, rhombic, or hexagonal) and by the elec. charges of individual objects; the whole lattices were approx. elec. neutral. The lattices obsd. in this study were qual. different from ionic crystals; the charge of objects had practically continuous values which changed during agitation and self-assembly, and depended on exptl. conditions which included the lattice structure itself. The relationship between charge and structure led to the coexistence of regions with different lattice structures within the same assembly, and to transformations between different lattice structures during agitation.
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    Wang, Y.; Wei, X. Y.; Kuang, S. Y.; Li, H. Y.; Chen, Y. H.; Liang, F.; Su, L.; Wang, Z. L.; Zhu, G. Triboelectrification-Induced Self-Assembly of Macro-Sized Polymer Beads on a Nanostructured Surface for Self-Powered Patterning. ACS Nano 2018, 12, 441– 447,  DOI: 10.1021/acsnano.7b06758
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    Triboelectrification-Induced Self-Assembly of Macro-Sized Polymer Beads on a Nanostructured Surface for Self-Powered Patterning
    Wang, Ying; Wei, Xiao Yan; Kuang, Shuang Yang; Li, Hua Yang; Chen, Yang Hui; Liang, Fei; Su, Li; Wang, Zhong Lin; Zhu, Guang
    ACS Nano (2018), 12 (1), 441-447CODEN: ANCAC3; ISSN:1936-0851. (American Chemical Society)
    Here we report an electrostatic-templated self-assembly (ETSA) method for arbitrarily patterning millimeter-sized polymer beads on a nanostructured surface without using an extra voltage source. A patterned electrode underneath an electrification layer generates "potential wells" of the corresponding pattern at predefined window sites, which capture and anchor the beads within the window sites by electrostatic force. Anal. calcn. is combined with numerical modeling to derive the electrostatic force acting on the beads, which is in great agreement with exptl. measured values. The generated pattern is solely detd. by the predefined underlying electrode, making it arbitrarily switchable by using different electrode patterns. By transferring the assembled beads into an elastomer matrix, possible applications of the ETSA in fabricating optical and flexible displays are demonstrated.
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    McCarty, L. S.; Winkleman, A.; Whitesides, G. M. Electrostatic self-assembly of polystyrene microspheres by using chemically directed contact electrification. Angew. Chem., Int. Ed. 2007, 46, 206– 209,  DOI: 10.1002/anie.200602914
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    Electrostatic self-assembly of polystyrene microspheres by using chemically directed contact electrification
    McCarty, Logan S.; Winkleman, Adam; Whitesides, George M.
    Angewandte Chemie, International Edition (2007), 46 (1+2), 206-209CODEN: ACIEF5; ISSN:1433-7851. (Wiley-VCH Verlag GmbH & Co. KGaA)
    Electrostatic charges can be induced in functionalized polystyrene beads. Oppositely charged beads then aggregate to form superstructures. A coat of small beads can self-assemble around a large bead. After annealing, another layer of beads can be added. The technique, based on contact electrification, avoids the use of expensive equipment and enables the use of large quantities of material.
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    Matias, A.; Shinbrot, T.; Araújo, N. Mechanical equilibrium of aggregates of dielectric spheres. Phys. Rev. E 2018, 98, 062903,  DOI: 10.1103/PhysRevE.98.062903
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    Mechanical equilibrium of aggregates of dielectric spheres
    Matias, A. F. V.; Shinbrot, T.; Araujo, N. A. M.
    Physical Review E (2018), 98 (6), 062903CODEN: PREHBM; ISSN:2470-0053. (American Physical Society)
    Industrial as well as natural aggregation of fine particles is believed to be assocd. with electrostatics. Yet like charges repel, so it is unclear how similarly treated particles aggregate. To resolve this apparent contradiction, we analyze conditions necessary to hold aggregates together with electrostatic forces. We find that aggregates of particles charged with the same sign can be held together due to dielec. polarization, we evaluate the effect of aggregate size, and we briefly summarize consequences for practical aggregation.
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    Locatelli, E.; Bianchi, E. Tuning the order of colloidal monolayers: assembly of heterogeneously charged colloids close to a patterned substrate. Soft Matter 2018, 14, 8119– 8136,  DOI: 10.1039/C8SM00691A
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    Tuning the order of colloidal monolayers: assembly of heterogeneously charged colloids close to a patterned substrate
    Locatelli, Emanuele; Bianchi, Emanuela
    Soft Matter (2018), 14 (40), 8119-8136CODEN: SMOABF; ISSN:1744-6848. (Royal Society of Chemistry)
    We study the behavior of neg. charged colloids with two pos. charged polar caps close to a planar patterned surface. The competition between the different anisotropic components of the particle-particle interaction is able by itself to give rise to a rich assembly scenario: colloids with charged surface patterns already form different cryst. domains when adsorbed to a homogeneously charged substrate. Here we consider substrates composed of alternating (neg./neutral, pos./neutral and pos./neg.) parallel stripes and, by means of Monte Carlo simulations, we investigate the ordering of the colloids on changing the no. of the stripes. We show that the addnl. competition between the two different lengths scales characterizing the system (i.e., the particle interaction range and the size of the stripes) gives rise to a plethora of distinct particle arrangements, where some well-defined trends can be obsd. By accurately tuning the substrate charged motif it is possible to, e.g., promote specific particle arrangements, disfavor cryst. domains or induce the formation of extended, open clusters.
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    Poppe, T.; Schräpler, R. Further experiments on collisional tribocharging of cosmic grains. Astronomy & Astrophysics 2005, 438, 1– 9,  DOI: 10.1051/0004-6361:20042327
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    Biegaj, K. W.; Rowland, M. G.; Lukas, T. M.; Heng, J. Y. Surface chemistry and humidity in powder electrostatics: A comparative study between tribocharging and corona discharge. Acs Omega 2017, 2, 1576– 1582,  DOI: 10.1021/acsomega.7b00125
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    Surface Chemistry and Humidity in Powder Electrostatics: A Comparative Study between Tribocharging and Corona Discharge
    Biegaj, Karolina W.; Rowland, Martin G.; Lukas, Tim M.; Heng, Jerry Y. Y.
    ACS Omega (2017), 2 (4), 1576-1582CODEN: ACSODF; ISSN:2470-1343. (American Chemical Society)
    The correlation between surface chem. groups and electrostatic properties of particulate materials was studied. Glass beads were modified to produce OH, NH2, CN, and F functionalized materials. These materials were sep. charged by friction and conventional corona charging and results were compared. Results from both methods indicated the electrostatic properties were directly related to surface functional group chem.; hydrophobic groups accumulated greater quantities of charge than hydrophilic groups. F-rich surfaces accumulated 5.89 times greater charge upon tribocharging (friction-induced charging) on stainless steel vs. hydroxyl-rich surfaces; however, in contrast to the tribocharging method, charge polarity could not be detd. when corona charging was used. Discharge profiles at different relative humidity levels (25, 50, 75% RH) obtained for each modified surface, showed higher humidity facilitated faster charge decay; however, this enhancement depended on surface chem. By increasing RH from 25 to 75%, charge relaxation times were accelerated 1.6 times for F and 12.2 times for cyano groups. These data confirmed surface functional groups may dictate powder electrostatic behavior and account for obsd. charge accumulation and discharge phenomena.
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    Shinbrot, T.; Komatsu, T. S.; Zhao, Q. Spontaneous tribocharging of similar materials. EPL (Europhysics Letters) 2008, 83, 24004,  DOI: 10.1209/0295-5075/83/24004
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    Schella, A.; Herminghaus, S.; Schröter, M. Influence of humidity on tribo-electric charging and segregation in shaken granular media. Soft Matter 2017, 13, 394– 401,  DOI: 10.1039/C6SM02041K
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    Influence of humidity on tribo-electric charging and segregation in shaken granular media
    Schella, Andre; Herminghaus, Stephan; Schroeter, Matthias
    Soft Matter (2017), 13 (2), 394-401CODEN: SMOABF; ISSN:1744-683X. (Royal Society of Chemistry)
    We study the effect of humidity on the charge accumulation of polymer granulates shaken vertically in a stainless steel container. This setup allows us to control the humidity level from 5% to 100%RH while performing automated charge measurements in a Faraday cup directly connected to the shaking container. We find that samples of approx. 2000 polymer spheres become highly charged at low humidity levels (<30%RH), but acquire almost no charge for humidity levels above 80%RH. The transition between these two regimes does depend on the material, as does the sign of the charge. For the latter we find a correlation with the contact angle of the polymer with only very hydrophilic particles attaining pos. charges. We show that this humidity dependence of tribo-charging can be used to control segregation in shaken binary mixts.
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    Lee, V.; Waitukaitis, S. R.; Miskin, M. Z.; Jaeger, H. M. Direct observation of particle interactions and clustering in charged granular streams. Nat. Phys. 2015, 11, 733– 737,  DOI: 10.1038/nphys3396
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    Direct observation of particle interactions and clustering in charged granular streams
    Lee, Victor; Waitukaitis, Scott R.; Miskin, Marc Z.; Jaeger, Heinrich M.
    Nature Physics (2015), 11 (9), 733-737CODEN: NPAHAX; ISSN:1745-2473. (Nature Publishing Group)
    Clustering of fine particles is of crucial importance in settings ranging from the early stages of planet formation to the coagulation of industrial powders and airborne pollutants. Models of such clustering typically focus on inelastic deformation and cohesion. However, even in charge-neutral particle systems comprising grains of the same dielec. material, tribocharging can generate large amts. of net pos. or neg. charge on individual particles, resulting in long-range electrostatic forces. The effects of such forces on cluster formation are not well understood and have so far not been studied in situ. Here we report the first observations of individual collide-and-capture events between charged submillimeter particles, including Kepler-like orbits. Charged particles can become trapped in their mutual electrostatic energy well and aggregate via multiple bounces. This enables the initiation of clustering at relative velocities much larger than the upper limit for sticking after a head-on collision, a long-standing issue known from pre-planetary dust aggregation. Moreover, Coulomb interactions together with dielec. polarization are found to stabilize characteristic mol.-like configurations, providing new insights for the modeling of clustering dynamics in a wide range of microscopic dielec. systems, such as charged polarizable ions, biomols. and colloids.
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    Steinpilz, T.; Joeris, K.; Jungmann, F.; Wolf, D.; Brendel, L.; Teiser, J.; Shinbrot, T.; Wurm, G. Electrical charging overcomes the bouncing barrier in planet formation. Nat. Phys. 2020, 16, 225– 229,  DOI: 10.1038/s41567-019-0728-9
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    Electrical charging overcomes the bouncing barrier in planet formation
    Steinpilz, Tobias; Joeris, Kolja; Jungmann, Felix; Wolf, Dietrich; Brendel, Lothar; Teiser, Jens; Shinbrot, Troy; Wurm, Gerhard
    Nature Physics (2020), 16 (2), 225-229CODEN: NPAHAX; ISSN:1745-2473. (Nature Research)
    In protoplanetary disks, solid objects (so-called planetesimals) are formed from dust. Micrometre-sized dust grains grow into millimetre-sized aggregates. Once those aggregates have diams. exceeding a few centimetres, they become subject to concn. mechanisms such as the streaming instability, permitting the formation of self-gravitating clusters, which might eventually collapse into kilometre-sized planetesimals. However, for the streaming instability to set in, clumps spanning sizes from centimetres to decimetres are required in the center of a protoplanetary disk. In the size range between millimetres and centimetres, aggregates bounce off each other rather than sticking together, and growth is stalled. Here we show in microgravity expts. that collisions between millimetre-sized grains lead to sufficient elec. charging for aggregation to bridge this gap between the bouncing barrier and the onset of the streaming instability. We computationally simulate aggregation and find that models agree with the exptl. data only if elec. charging is present. We therefore propose that collisional charging may promote early growth in the size gap that current models of planetesimal formation cannot account for.
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    Pähtz, T.; Herrmann, H. J.; Shinbrot, T. Why do particle clouds generate electric charges?. Nat. Phys. 2010, 6, 364– 368,  DOI: 10.1038/nphys1631
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    Yoshimatsu, R.; Araújo, N. A.; Wurm, G.; Herrmann, H. J.; Shinbrot, T. Self-charging of identical grains in the absence of an external field. Sci. Rep. 2017, 7, 1– 11,  DOI: 10.1038/srep39996
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    Emergence of Quantum Critical Behavior in Metallic Quantum-Well States of Strongly Correlated Oxides
    Kobayashi, Masaki; Yoshimatsu, Kohei; Mitsuhashi, Taichi; Kitamura, Miho; Sakai, Enju; Yukawa, Ryu; Minohara, Makoto; Fujimori, Atsushi; Horiba, Koji; Kumigashira, Hiroshi
    Scientific Reports (2017), 7 (1), 1-7CODEN: SRCEC3; ISSN:2045-2322. (Nature Research)
    Controlling quantum crit. phenomena in strongly correlated electron systems, which emerge in the neighborhood of a quantum phase transition, is a major challenge in modern condensed matter physics. Quantum crit. phenomena are generated from the delicate balance between long-range order and its quantum fluctuation. So far, the nature of quantum phase transitions has been investigated by changing a limited no. of external parameters such as pressure and magnetic field. We propose a new approach for investigating quantum criticality by changing the strength of quantum fluctuation that is controlled by the dimensional crossover in metallic quantum well (QW) structures of strongly correlated oxides. With reducing layer thickness to the crit. thickness of metal-insulator transition, crossover from a Fermi liq. to a non-Fermi liq. has clearly been obsd. in the metallic QW of SrVO3 by in situ angle-resolved photoemission spectroscopy. Non-Fermi liq. behavior with the crit. exponent α = 1 is found to emerge in the two-dimensional limit of the metallic QW states, indicating that a quantum crit. point exists in the neighborhood of the thickness-dependent Mott transition. These results suggest that artificial QW structures provide a unique platform for investigating novel quantum phenomena in strongly correlated oxides in a controllable fashion.
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    Grosjean, G.; Wald, S.; Sobarzo, J. C.; Waitukaitis, S. Quantitatively consistent scale-spanning model for same-material tribocharging. Physical Review Materials 2020, 4, 082602,  DOI: 10.1103/PhysRevMaterials.4.082602
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    Quantitatively consistent scale-spanning model for same-material tribocharging
    Grosjean, Galien; Wald, Sebastian; Sobarzo, Juan Carlos; Waitukaitis, Scott
    Physical Review Materials (2020), 4 (8), 082602CODEN: PRMHBS; ISSN:2475-9953. (American Physical Society)
    By rigorously accounting for mesoscale spatial correlations in donor/acceptor surface properties, we develop a scale-spanning model for same-material tribocharging. We find that mesoscale correlations affect not only the magnitude of charge transfer but also the fluctuations-suppressing otherwise overwhelming charge-transfer variability that is not obsd. exptl. We furthermore propose a generic theor. mechanism by which the mesoscale features might emerge, which is qual. consistent with other proposals in the literature.
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  • Abstract

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    Figure 1

    Figure 1. (a) Illustration of the tribocharging phenomenon between a piece of cloth and a plastic rod. (b) An exemplary triboelectric series ranking the material’s tendency to gain a certain polarity. Wood does not tend to tribocharge due to the presence of lignin. (c) A sliding drop exchange charge with a polymer film. (d-1) The charge transfer QSC in a TENG. (d-2) A dusty solar panel of NASA’s InSight Mars lander. (a, d-1) Reproduced with permission from ref (5). Copyright 2019 Elsevier. (b) Reproduced with permission from ref (8). Copyright 2020 American Chemical Society. (c) Reproduced with permission from ref (9). Copyright 2022 Springer Nature. (d-2) Reproduced with permission from ref (10). Copyright 2022 Courtesy NASA/JPL-Caltech.

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    Figure 2

    Figure 2. Several experimental studies to characterize triboelectric charge. (a) Faraday-cup setup. (b) A submillimeter particle is acoustically levitated between a grounded ultrasonic transducer and a sound-reflecting target plate. A piece of aluminum underneath the target plate is connected to an ac or dc voltage source. The particle was back lit and filmed from the side with a high-speed camera. The whole setup is enclosed in a chamber to control the ambient gas. (c, left) An AFM force–distance curve obtained for a symmetric system; AL = amidine latex, and SL = sulfate latex. (c, right) SEM image of a colloidal AFM probe (colloid diameter 10 μm). (d) Topographic image (1 × 1 μm; scale bar = 250 nm) and the simultaneously obtained potential map of an impact crater created by an impacting silica particle on the CFx coated surface. (e) Triboelectric charge accumulation measured with the KPFM on the SiO2 surface with the increase of the number of repeated rubbing at the same area (20 × 20 μm; scale bar = 5 μm). (a) Reproduced with permission from ref (4). Copyright 2010 Elsevier. (b) Reproduced with permission from ref (6). Copyright 2018 American Physical Society. (c) Reproduced with permission from ref (14). Copyright 2015 American Chemical Society. (d) Reproduced with permission from ref (12). Copyright 2022 Elsevier. (e) Reproduced with permission from ref (15). Copyright 2013 American Chemical Society.

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    Figure 3

    Figure 3. (a) Electrostatic assembly of macroscopic crystals comprising a binary mixture of polymer beads; scale bar = 20 mm. Granular lattice structures self-assembled after agitating a binary mixture of beads with (b, left) one, or (b, right) two conductive plate(s); scale bar = 10 mm. (c) A sequence of the lattice structures after turning the applied electric field on and off between the two conductive plates; scale bar = 10 mm. (d) Assembly of agitated cubic objects; scale bar = 20 mm. KPFM measurements performed after vibration experiments on (e, left) silica microspheres and (e, right) fluorocarbon-coated silicon substrate. Insets represent the corresponding topography scans; scale bar = 5 μm (f) Schematic representation of the electrostatic templated self-assembly of macro-sized spheres; scale bar = 10 mm. (g) Segregation of rubbing-induced silica micropsheres on fluorocarbon-coated glass substrate; scale bar = 50 μm. (a) Reproduced with permission from ref (22). Copyright 2003 Springer Nature. (b, c) Reproduced with permission from ref (23). Copyright 2021 Royal Society of Chemistry. (d) Reprinted with permission from ref (24). Copyright 2012 Royal Society of Chemistry. (e) Reproduced with permission from ref (12). Copyright 2022 Royal Society of Chemistry. (f) Reproduced with permission from ref (25). Copyright 2018, American Chemical Society. (g) Reproduced with permission from ref (19). Copyright 2020, American Chemical Society.

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    Figure 4

    Figure 4. (a) Emerging charge patterns on two identical latex balloons after rubbing them against each other. (b) Segregation of an agitated bidisperse mixture (red = big, blue = small) of PTFE spheres at (left) a RH = 50%, and (right) a RH = 1000%. Time-lapse of (c-1, c-2) a growing, or (c-3) disruption of a cluster after microparticles collided against them. (c-4, left) Dynamic formation of a stable triangular structure comprising two large particles and one small particle. (c-4, right) Possible charge distribution producing these triangular structures. (c) Scale bar: 500 μm (white), and 1 mm (green). (d-1) Precharged agglomerates entering the Bremen tower. (d-2) Impact of a single granule (marked by the black arrow) against a large cluster. (e) Charging of uncharged identical particles in an external electrical field. (f) Time-lapse of vibrated hollow microspheres in the Bremen tower. (a) Reproduced with permission from ref (31). Copyright 2008 Europhysics Letters Association. (b) Reproduced with permission from ref (32). Copyright 2017 Royal Society of Chemistry. (c) Reproduced with permission from ref (33). Copyright 2015 Springer Nature. (d) Reproduced with permission from ref (34). Copyright 2019 Springer Nature. (e) Reproduced with permission from ref (35). Copyright 2010 Springer Nature. (f) Reproduced with permission from ref (36). Copyright 2017 Springer Nature.

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      Jimidar, I. S.; Sotthewes, K.; Gardeniers, H.; Desmet, G.; van der Meer, D. Self-organization of agitated microspheres on various substrates. Soft Matter 2022, 18, 3660– 3677,  DOI: 10.1039/D2SM00432A
      12
      Self-organization of agitated microspheres on various substrates
      Jimidar, Ignaas S. M.; Sotthewes, Kai; Gardeniers, Han; Desmet, Gert; van der Meer, Devaraj
      Soft Matter (2022), 18 (19), 3660-3677CODEN: SMOABF; ISSN:1744-6848. (Royal Society of Chemistry)
      The vibration dynamics of relatively large granular grains is extensively treated in the literature, but comparable studies on the self-assembly of smaller agitated beads are lacking. In this work, we investigate how the particle properties and the properties of the underlying substrate surface affect the dynamics and self-organization of horizontally agitated monodisperse microspheres with diams. between 3 and 10μm. Upon agitation, the agglomerated hydrophilic silica particles locally leave traces of particle monolayers as they move across the flat uncoated and fluorocarbon-coated silicon substrates. However, on the micromachined silicon tray with relatively large surface roughness, the agitated silica agglomerates form segregated bands reminiscent of earlier studies on granular suspensions or Faraday heaps. On the other hand, the less agglomerated hydrophobic polystyrene particles form densely occupied monolayer arrangements regardless of the underlying substrate. We explain the observations by considering the relevant adhesion and friction forces between particles and underlying substrates as well as those among the particles themselves. Interestingly, for both types of microspheres, large areas of the fluorocarbon-coated substrates are covered with densely occupied particle monolayers. By qual. examg. the morphol. of the self-organized particle monolayers using the Voronoi approach, it is understood that these monolayers are highly disordered, i.e., multiple symmetries coexist in the self-organized monolayers. However, more structured symmetries are identified in the monolayers of the agitated polystyrene microspheres on all the substrates, albeit not all precisely positioned on a hexagonal lattice. On the other hand, both the silica and polystyrene monolayers on the bare silicon substrates transition into less disordered structures as time progresses. Using Kelvin probe force microscopy measurements, we show that due to the tribocharging phenomenon, the formation of particle monolayers is promoted on the fluorocarbon surface, i.e., a local electrostatic attraction exists between the particle and the substrate.
    13. 13
      Siek, M.; Adamkiewicz, W.; Sobolev, Y. I.; Grzybowski, B. A. The influence of distant substrates on the outcome of contact electrification. Angew. Chem., Int. Ed. 2018, 57, 15379– 15383,  DOI: 10.1002/anie.201806658
      13
      The Influence of Distant Substrates on the Outcome of Contact Electrification
      Siek, Marta; Adamkiewicz, Witold; Sobolev, Yaroslav I.; Grzybowski, Bartosz A.
      Angewandte Chemie, International Edition (2018), 57 (47), 15379-15383CODEN: ACIEF5; ISSN:1433-7851. (Wiley-VCH Verlag GmbH & Co. KGaA)
      The magnitudes of the charges developed on contact-electrified polymers depend on not only the properties of these materials but also the nature of distant substrates on which the polymers are supported. In particular, image charges induced in conductive substrates can decrease charges on the polymers by arc discharge through the surrounding gas. This mode of charge dissipation occurs on timescales of milliseconds and can be prevented by insulating the sharp edges of the conductive supports.
    14. 14
      Montes Ruiz-Cabello, F. J.; Trefalt, G.; Maroni, P.; Borkovec, M. Accurate Predictions of Forces in the Presence of Multivalent Ions by Poisson–Boltzmann Theory. Langmuir 2014, 30, 4551– 4555,  DOI: 10.1021/la500612a
      14
      Accurate Predictions of Forces in the Presence of Multivalent Ions by Poisson-Boltzmann Theory
      Montes Ruiz-Cabello, F. Javier; Trefalt, Gregor; Maroni, Plinio; Borkovec, Michal
      Langmuir (2014), 30 (16), 4551-4555CODEN: LANGD5; ISSN:0743-7463. (American Chemical Society)
      Forces between pos. and neg. charged colloidal particles across aq. salt solns. contg. multivalent ions are measured directly with the at. force microscope (AFM). The measurements are interpreted quant. with Poisson-Boltzmann (PB) theory. Thereby, the surface potentials and regulation properties of the particle surfaces are extd. from sym. measurements between the same types of particles. This information is used to predict force profiles in the asym. situations involving different types of particles without any adjustable parameters. These predictions turn out to be very accurate, which demonstrates that the mean-field PB theory is reliable down to distances of about 5 nm. While various reports in the literature indicate that this theory should fail due to neglect of ion correlations, such effects seem important only at higher concns. and smaller distances.

      PMID: 24735066

    15. 15
      Zhou, Y. S.; Liu, Y.; Zhu, G.; Lin, Z.-H.; Pan, C.; Jing, Q.; Wang, Z. L. In situ quantitative study of nanoscale triboelectrification and patterning. Nano Lett. 2013, 13, 2771– 2776,  DOI: 10.1021/nl401006x
      15
      In Situ Quantitative Study of Nanoscale Triboelectrification and Patterning
      Zhou, Yu Sheng; Liu, Ying; Zhu, Guang; Lin, Zong-Hong; Pan, Caofeng; Jing, Qingshen; Wang, Zhong Lin
      Nano Letters (2013), 13 (6), 2771-2776CODEN: NALEFD; ISSN:1530-6984. (American Chemical Society)
      By combining contact-mode at. force microscopy (AFM) and scanning Kevin probe microscopy (SKPM), the authors demonstrated an in situ method for quant. characterization of the triboelectrification process at the nanoscale. The authors systematically characterized the triboelec. charge distribution, multifriction effect on charge transfer, as well as subsequent charge diffusion on the dielec. surface: (i) the SiO2 surface can be either pos. or neg. charged through triboelec. process using Si-based AFM probes with and without Pt coating, resp.; (ii) the triboelec. charges accumulated from multifriction and eventually reached to satd. concns. of (-150 ± 8) μC/m2 and (105 ± 6) μC/m2, resp.; (iii) the charge diffusion coeffs. on SiO2 surface are (1.10 ± 0.03) × 10-15 m2/s for the pos. charge and (0.19 ± 0.01) × 10-15 m2/s for the neg. charges. These quantifications will facilitate a fundamental understanding about the triboelec. and de-electrification process, which is important for designing high performance triboelec. nanogenerators. The authors demonstrated a technique for nanopatterning of surface charges without assistance of external elec. field, which has a promising potential application for directed self-assembly of charged nanostructures for nanoelectronic devices.
    16. 16
      Jimidar, I. S.; Sotthewes, K.; Gardeniers, H.; Desmet, G. A detailed study of the interaction between levitated microspheres and the target electrode in a strong electric field. Powder Technol. 2021, 383, 292– 301,  DOI: 10.1016/j.powtec.2021.01.036
      16
      A detailed study of the interaction between levitated microspheres and the target electrode in a strong electric field
      Jimidar, Ignaas S. M.; Sotthewes, Kai; Gardeniers, Han; Desmet, Gert
      Powder Technology (2021), 383 (), 292-301CODEN: POTEBX; ISSN:0032-5910. (Elsevier B.V.)
      In this work, we report on an in-depth study of how 10μm silica and polystyrene particles interact with a target electrode after they were levitated by applying a strong elec. field. The results show that, under these conditions, silica particles unexpectedly have a higher tendency to adhere on a fluorocarbon coated electrode compared to a bare, non-coated silicon electrode. Relative adherence ratios Γ up to Γ = 4.7 were obsd. Using the colloidal probe technique, at. 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 electrification phenomenon. All these processes attribute to increasing the probability that levitated particles attain velocities that are lower than the sticking velocity.
    17. 17
      Jones, R.; Pollock, H. M.; Cleaver, J. A.; Hodges, C. S. Adhesion forces between glass and silicon surfaces in air studied by AFM: Effects of relative humidity, particle size, roughness, and surface treatment. Langmuir 2002, 18, 8045– 8055,  DOI: 10.1021/la0259196
      17
      Adhesion Forces between Glass and Silicon Surfaces in Air Studied by AFM: Effects of Relative Humidity, Particle Size, Roughness, and Surface Treatment
      Jones, Robert; Pollock, Hubert M.; Cleaver, Jamie A. S.; Hodges, Christopher S.
      Langmuir (2002), 18 (21), 8045-8055CODEN: LANGD5; ISSN:0743-7463. (American Chemical Society)
      Using the at. force microscope (AFM), the pull-off forces between flat glass or Si surfaces and Si AFM tips or glass microspheres of different sizes were extensively studied as a function of relative humidity (RH) in the range 5-90%, as model systems for the behavior of cohesive powders. The glass and Si substrates were treated to render them either hydrophobic or hydrophilic. All the hydrophilic surfaces gave simple force curves and pull-off forces increasing uniformly with RH. Small contacts (R ∼ 20 nm) gave pull-off forces close to values predicted by simple Laplace-Kelvin theory (∼20 nN), but the values with microspheres (R ∼ 20 μm) fell well below predictions for sphere-flat or sphere-sphere geometry, due to roughness and asperity contacts. The hydrophobic Si surfaces also exhibited simple behavior, with no significant RH dependence. The pull-off force again fell well below predicted values (Johnson-Kendall-Roberts contact mechanics theory) for the larger contacts. Hydrophobic glass gave similar adhesion to Si over most of the RH range, but against both Si tips and glass microspheres, there was an anomalously large adhesion in the RH range 20-40%, accompanied by a long-range noncontact force. The adhesion on fully hydrophilic surfaces and its RH dependence can be mostly explained by current theories of capillary bridges, but the interpretation is complicated by the sensitivity of theor. predictions to contact geometry (and hence to roughness effects) and by uncertainties in the thickness of adsorbed H2O layers. The anomalous behavior on hydrophobic glass surfaces at intermediate values of RH is not fully understood, but possible causes are (1) dipole layers in the partially formed H2O film, giving rise to patch charges and long-range forces, or (2) fixed charges at a reactive glass surface, involving specific bonding reactions. The results may be useful in explaining the behavior of cohesive powders with different coatings or those which show a large humidity dependence (e.g., zeolites) or show electrostatic charging effects (e.g., SiO2 aerogels).
    18. 18
      Gouveia, R. F.; Galembeck, F. Electrostatic charging of hydrophilic particles due to water adsorption. J. Am. Chem. Soc. 2009, 131, 11381– 11386,  DOI: 10.1021/ja900704f
      18
      Electrostatic Charging of Hydrophilic Particles Due to Water Adsorption
      Gouveia, Rubia F.; Galembeck, Fernando
      Journal of the American Chemical Society (2009), 131 (32), 11381-11386CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
      Kelvin force microscopy measurements on films of noncryst. silica and aluminum phosphate particles reveal complex electrostatic potential patterns that change irreversibly as the relative humidity changes within an elec. shielded and grounded environment. Potential adjacent to the particle surfaces is always neg. and potential gradients in excess of ±10 MV/m are found parallel to the film surface. These results verify the following hypothesis: the atm. is a source and sink of electrostatic charges in dielecs., due to the partition of OH- and H+ ions assocd. to water adsorption. Neither contact, tribochem. or electrochem. ion or electron injection are needed to change the charge state of the noncryst. hydrophilic solids used in this work.
    19. 19
      Jimidar, I. S.; Sotthewes, K.; Gardeniers, H.; Desmet, G. Spatial segregation of microspheres by rubbing-induced triboelectrification on patterned surfaces. Langmuir 2020, 36, 6793– 6800,  DOI: 10.1021/acs.langmuir.0c00959
      19
      Spatial Segregation of Microspheres by Rubbing-Induced Triboelectrification on Patterned Surfaces
      Jimidar, Ignaas S. M.; Sotthewes, Kai; Gardeniers, Han; Desmet, Gert
      Langmuir (2020), 36 (24), 6793-6800CODEN: LANGD5; ISSN:0743-7463. (American Chemical Society)
      Particle (monolayer) assembly is essential to various scientific and industrial applications, such as the fabrication of photonic crystals, optical sensors, and surface coatings. Several methods, including rubbing, have been developed for this purpose. Here, we report on the serendipitous observation that microparticles preferentially partition onto the fluorocarbon-coated parts of patterned silicon and borosilicate glass wafers when rubbed with poly(dimethylsiloxane) slabs. To explore the extent of this effect, we varied the geometry of the pattern, the substrate material, the ambient humidity, and the material and size of the particles. Partitioning coeffs. amounted up to a factor of 12 on silicon wafers and even ran in the 100s on borosilicate glass wafers at zero humidity. Using Kelvin probe force microscopy, the observations can be explained by triboelectrification, inducing a strong electrostatic attraction between the particles and the fluorocarbon zones, while the interaction with the noncoated zones is insignificant or even weakly repulsive.
    20. 20
      Bai, X.; Riet, A.; Xu, S.; Lacks, D. J.; Wang, H. Experimental and simulation investigation of the nanoscale charge diffusion process on a dielectric surface: effects of relative humidity. J. Phys. Chem. C 2021, 125, 11677– 11686,  DOI: 10.1021/acs.jpcc.1c02272
      20
      Experimental and Simulation Investigation of the Nanoscale Charge Diffusion Process on a Dielectric Surface: Effects of Relative Humidity
      Bai, Xuejie; Riet, Adriaan; Xu, Song; Lacks, Daniel J.; Wang, Haifeng
      Journal of Physical Chemistry C (2021), 125 (21), 11677-11686CODEN: JPCCCK; ISSN:1932-7447. (American Chemical Society)
      Electrostatic charge generation and diffusion on the nanoscale were studied by at. force microscopy and Kelvin probe microscopy. The charge diffusion coeffs. were obtained by matching exptl. results with numerical solns. of the diffusion equation. The results found that the relative humidity variations could significantly alter both the charge generation and diffusion processes. For the charge generation, the increase in relative humidity led to a decrease in transferred charge amt. between the contact surfaces owing to the presence of the absorbed water film on the tip-sample interface. For the charge diffusion, the increase in relative humidity could accelerate the charge diffusion process laterally, and the diffusion coeff. of higher relative humidity was 3-5 orders of magnitude larger than those under dry air and N2. It was proved that the charge diffusion process for the pos. charge was not necessarily faster than that for the neg. one. In addn., the contribution from atm. water mols. to the surface charge diffusion was distinguished from that of absorbed water films by calcg. the net loss of surface charge, and this effect was found to be more obvious under higher relative humidity. The dominant mechanism for the charge diffusion was discussed, and we argued that the relative humidity could be the main reason, and probably the only reason, for the charge diffusion and decay on the dielec. surfaces.
    21. 21
      Xu, J.; Li, D.; Chen, D.; Li, W.; Xu, J. Nanoscale Characterization of Active Doping Concentration in Boron-Doped Individual Si Nanocrystals. physica status solidi (a) 2018, 215, 1800531,  DOI: 10.1002/pssa.201800531
      There is no corresponding record for this reference.
    22. 22
      Grzybowski, B. A.; Winkleman, A.; Wiles, J. A.; Brumer, Y.; Whitesides, G. M. Electrostatic self-assembly of macroscopic crystals using contact electrification. Nat. Mater. 2003, 2, 241,  DOI: 10.1038/nmat860
      22
      Electrostatic self-assembly of macroscopic crystals using contact electrification
      Grzybowski, Bartosz A.; Winkleman, Adam; Wiles, Jason A.; Brumer, Yisroel; Whitesides, George M.
      Nature Materials (2003), 2 (4), 241-245CODEN: NMAACR; ISSN:1476-1122. (Nature Publishing Group)
      Self-assembly of components larger than mols. into ordered arrays is an efficient way of prepg. microstructured materials with interesting mech. and optical properties. Although crystn. of identical particles or particles of different sizes or shapes can be readily achieved, the repertoire of methods to assemble binary lattices of particles of the same sizes but with different properties is very limited. This paper describes electrostatic self-assembly of two types of macroscopic components of identical dimensions using interactions that are generated by contact electrification. The systems we have examd. comprise two kinds of objects (usually spheres) made of different polymeric materials that charge with opposite elec. polarities when agitated on flat, metallic surfaces. The interplay of repulsive interactions between like-charged objects and attractive interactions between unlike-charged ones results in the self-assembly of these objects into highly ordered, closed arrays. Remarkably, some of the assemblies that form are not electroneutral, i.e., they possess a net charge. The authors suggest that the stability of these unusual structures can be explained by accounting for the interactions between elec. dipoles that the particles in the aggregates induce in their neighbors.
    23. 23
      Polev, K.; Visyn, V.; Adamkiewicz, W.; Sobolev, Y.; Grzybowski, B. A. Stimuli-responsive granular crystals assembled by dipolar and multipolar interactions. Soft Matter 2021, 17, 8595– 8604,  DOI: 10.1039/D1SM00887K
      23
      Stimuli-responsive granular crystals assembled by dipolar and multipolar interactions
      Polev, Konstantin; Visyn, Valentin; Adamkiewicz, Witold; Sobolev, Yaroslav; Grzybowski, Bartosz A.
      Soft Matter (2021), 17 (38), 8595-8604CODEN: SMOABF; ISSN:1744-6848. (Royal Society of Chemistry)
      This work describes granular crystals held together by unusual, multipolar interactions and, under the application of an external bias, undergoing reversible structural transitions between closed and open forms. The system comprises two types of polymeric beads agitated on one or between two conductive plates and gradually acquiring charges by contact electrification. The charges thus developed induce a series of electrostatic images in the conductive supports and, in effect, the beads interact via dipolar or multipolar interactions, enabling the stabilization of non-electroneutral crystals. Furthermore, under an applied bias, the beads become polarized and their complex interactions (due to the series of image charges as well as series of image dipoles) result in open-pore crystals which return to compact forms upon bias removal. These effects are rationalized by anal. calcns., and the crystal structures obsd. in the expts. are reproduced by mol. dynamics simulations.
    24. 24
      Cademartiri, R.; Stan, C. A.; Tran, V. M.; Wu, E.; Friar, L.; Vulis, D.; Clark, L. W.; Tricard, S.; Whitesides, G. M. A simple two-dimensional model system to study electrostatic-self-assembly. Soft Matter 2012, 8, 9771– 9791,  DOI: 10.1039/c2sm26192h
      24
      A simple two-dimensional model system to study electrostatic-self-assembly
      Cademartiri, Rebecca; Stan, Claudiu A.; Tran, Vivian M.; Wu, Evan; Friar, Liam; Vulis, Daryl; Clark, Logan W.; Tricard, Simon; Whitesides, George M.
      Soft Matter (2012), 8 (38), 9771-9791CODEN: SMOABF; ISSN:1744-683X. (Royal Society of Chemistry)
      This paper surveys the variables controlling the lattice structure and charge in macroscopic Coulombic crystals made from elec. charged, millimeter-sized polymer objects (spheres, cubes, and cylinders). Mech. agitation of these objects inside planar, bounded containers caused them to charge elec. through contact electrification, and to self-assemble. The processes of electrification and self-assembly, and the characteristics of the assemblies, depended on the type of motion used for agitation, on the type of materials used for the objects and the dish, on the size and shape of the objects and the dish, and on the no. of objects. Each of the three different materials in the system (of the dish and of the two types of spheres) influenced the electrification. Three classes of structures formed by self-assembly, depending on the exptl. conditions: two-dimensional lattices, one-dimensional chains, and zero-dimensional rosettes'. The lattices were characterized by their structure (disordered, square, rhombic, or hexagonal) and by the elec. charges of individual objects; the whole lattices were approx. elec. neutral. The lattices obsd. in this study were qual. different from ionic crystals; the charge of objects had practically continuous values which changed during agitation and self-assembly, and depended on exptl. conditions which included the lattice structure itself. The relationship between charge and structure led to the coexistence of regions with different lattice structures within the same assembly, and to transformations between different lattice structures during agitation.
    25. 25
      Wang, Y.; Wei, X. Y.; Kuang, S. Y.; Li, H. Y.; Chen, Y. H.; Liang, F.; Su, L.; Wang, Z. L.; Zhu, G. Triboelectrification-Induced Self-Assembly of Macro-Sized Polymer Beads on a Nanostructured Surface for Self-Powered Patterning. ACS Nano 2018, 12, 441– 447,  DOI: 10.1021/acsnano.7b06758
      25
      Triboelectrification-Induced Self-Assembly of Macro-Sized Polymer Beads on a Nanostructured Surface for Self-Powered Patterning
      Wang, Ying; Wei, Xiao Yan; Kuang, Shuang Yang; Li, Hua Yang; Chen, Yang Hui; Liang, Fei; Su, Li; Wang, Zhong Lin; Zhu, Guang
      ACS Nano (2018), 12 (1), 441-447CODEN: ANCAC3; ISSN:1936-0851. (American Chemical Society)
      Here we report an electrostatic-templated self-assembly (ETSA) method for arbitrarily patterning millimeter-sized polymer beads on a nanostructured surface without using an extra voltage source. A patterned electrode underneath an electrification layer generates "potential wells" of the corresponding pattern at predefined window sites, which capture and anchor the beads within the window sites by electrostatic force. Anal. calcn. is combined with numerical modeling to derive the electrostatic force acting on the beads, which is in great agreement with exptl. measured values. The generated pattern is solely detd. by the predefined underlying electrode, making it arbitrarily switchable by using different electrode patterns. By transferring the assembled beads into an elastomer matrix, possible applications of the ETSA in fabricating optical and flexible displays are demonstrated.
    26. 26
      McCarty, L. S.; Winkleman, A.; Whitesides, G. M. Electrostatic self-assembly of polystyrene microspheres by using chemically directed contact electrification. Angew. Chem., Int. Ed. 2007, 46, 206– 209,  DOI: 10.1002/anie.200602914
      26
      Electrostatic self-assembly of polystyrene microspheres by using chemically directed contact electrification
      McCarty, Logan S.; Winkleman, Adam; Whitesides, George M.
      Angewandte Chemie, International Edition (2007), 46 (1+2), 206-209CODEN: ACIEF5; ISSN:1433-7851. (Wiley-VCH Verlag GmbH & Co. KGaA)
      Electrostatic charges can be induced in functionalized polystyrene beads. Oppositely charged beads then aggregate to form superstructures. A coat of small beads can self-assemble around a large bead. After annealing, another layer of beads can be added. The technique, based on contact electrification, avoids the use of expensive equipment and enables the use of large quantities of material.
    27. 27
      Matias, A.; Shinbrot, T.; Araújo, N. Mechanical equilibrium of aggregates of dielectric spheres. Phys. Rev. E 2018, 98, 062903,  DOI: 10.1103/PhysRevE.98.062903
      27
      Mechanical equilibrium of aggregates of dielectric spheres
      Matias, A. F. V.; Shinbrot, T.; Araujo, N. A. M.
      Physical Review E (2018), 98 (6), 062903CODEN: PREHBM; ISSN:2470-0053. (American Physical Society)
      Industrial as well as natural aggregation of fine particles is believed to be assocd. with electrostatics. Yet like charges repel, so it is unclear how similarly treated particles aggregate. To resolve this apparent contradiction, we analyze conditions necessary to hold aggregates together with electrostatic forces. We find that aggregates of particles charged with the same sign can be held together due to dielec. polarization, we evaluate the effect of aggregate size, and we briefly summarize consequences for practical aggregation.
    28. 28
      Locatelli, E.; Bianchi, E. Tuning the order of colloidal monolayers: assembly of heterogeneously charged colloids close to a patterned substrate. Soft Matter 2018, 14, 8119– 8136,  DOI: 10.1039/C8SM00691A
      28
      Tuning the order of colloidal monolayers: assembly of heterogeneously charged colloids close to a patterned substrate
      Locatelli, Emanuele; Bianchi, Emanuela
      Soft Matter (2018), 14 (40), 8119-8136CODEN: SMOABF; ISSN:1744-6848. (Royal Society of Chemistry)
      We study the behavior of neg. charged colloids with two pos. charged polar caps close to a planar patterned surface. The competition between the different anisotropic components of the particle-particle interaction is able by itself to give rise to a rich assembly scenario: colloids with charged surface patterns already form different cryst. domains when adsorbed to a homogeneously charged substrate. Here we consider substrates composed of alternating (neg./neutral, pos./neutral and pos./neg.) parallel stripes and, by means of Monte Carlo simulations, we investigate the ordering of the colloids on changing the no. of the stripes. We show that the addnl. competition between the two different lengths scales characterizing the system (i.e., the particle interaction range and the size of the stripes) gives rise to a plethora of distinct particle arrangements, where some well-defined trends can be obsd. By accurately tuning the substrate charged motif it is possible to, e.g., promote specific particle arrangements, disfavor cryst. domains or induce the formation of extended, open clusters.
    29. 29
      Poppe, T.; Schräpler, R. Further experiments on collisional tribocharging of cosmic grains. Astronomy & Astrophysics 2005, 438, 1– 9,  DOI: 10.1051/0004-6361:20042327
      There is no corresponding record for this reference.
    30. 30
      Biegaj, K. W.; Rowland, M. G.; Lukas, T. M.; Heng, J. Y. Surface chemistry and humidity in powder electrostatics: A comparative study between tribocharging and corona discharge. Acs Omega 2017, 2, 1576– 1582,  DOI: 10.1021/acsomega.7b00125
      30
      Surface Chemistry and Humidity in Powder Electrostatics: A Comparative Study between Tribocharging and Corona Discharge
      Biegaj, Karolina W.; Rowland, Martin G.; Lukas, Tim M.; Heng, Jerry Y. Y.
      ACS Omega (2017), 2 (4), 1576-1582CODEN: ACSODF; ISSN:2470-1343. (American Chemical Society)
      The correlation between surface chem. groups and electrostatic properties of particulate materials was studied. Glass beads were modified to produce OH, NH2, CN, and F functionalized materials. These materials were sep. charged by friction and conventional corona charging and results were compared. Results from both methods indicated the electrostatic properties were directly related to surface functional group chem.; hydrophobic groups accumulated greater quantities of charge than hydrophilic groups. F-rich surfaces accumulated 5.89 times greater charge upon tribocharging (friction-induced charging) on stainless steel vs. hydroxyl-rich surfaces; however, in contrast to the tribocharging method, charge polarity could not be detd. when corona charging was used. Discharge profiles at different relative humidity levels (25, 50, 75% RH) obtained for each modified surface, showed higher humidity facilitated faster charge decay; however, this enhancement depended on surface chem. By increasing RH from 25 to 75%, charge relaxation times were accelerated 1.6 times for F and 12.2 times for cyano groups. These data confirmed surface functional groups may dictate powder electrostatic behavior and account for obsd. charge accumulation and discharge phenomena.
    31. 31
      Shinbrot, T.; Komatsu, T. S.; Zhao, Q. Spontaneous tribocharging of similar materials. EPL (Europhysics Letters) 2008, 83, 24004,  DOI: 10.1209/0295-5075/83/24004
      There is no corresponding record for this reference.
    32. 32
      Schella, A.; Herminghaus, S.; Schröter, M. Influence of humidity on tribo-electric charging and segregation in shaken granular media. Soft Matter 2017, 13, 394– 401,  DOI: 10.1039/C6SM02041K
      32
      Influence of humidity on tribo-electric charging and segregation in shaken granular media
      Schella, Andre; Herminghaus, Stephan; Schroeter, Matthias
      Soft Matter (2017), 13 (2), 394-401CODEN: SMOABF; ISSN:1744-683X. (Royal Society of Chemistry)
      We study the effect of humidity on the charge accumulation of polymer granulates shaken vertically in a stainless steel container. This setup allows us to control the humidity level from 5% to 100%RH while performing automated charge measurements in a Faraday cup directly connected to the shaking container. We find that samples of approx. 2000 polymer spheres become highly charged at low humidity levels (<30%RH), but acquire almost no charge for humidity levels above 80%RH. The transition between these two regimes does depend on the material, as does the sign of the charge. For the latter we find a correlation with the contact angle of the polymer with only very hydrophilic particles attaining pos. charges. We show that this humidity dependence of tribo-charging can be used to control segregation in shaken binary mixts.
    33. 33
      Lee, V.; Waitukaitis, S. R.; Miskin, M. Z.; Jaeger, H. M. Direct observation of particle interactions and clustering in charged granular streams. Nat. Phys. 2015, 11, 733– 737,  DOI: 10.1038/nphys3396
      33
      Direct observation of particle interactions and clustering in charged granular streams
      Lee, Victor; Waitukaitis, Scott R.; Miskin, Marc Z.; Jaeger, Heinrich M.
      Nature Physics (2015), 11 (9), 733-737CODEN: NPAHAX; ISSN:1745-2473. (Nature Publishing Group)
      Clustering of fine particles is of crucial importance in settings ranging from the early stages of planet formation to the coagulation of industrial powders and airborne pollutants. Models of such clustering typically focus on inelastic deformation and cohesion. However, even in charge-neutral particle systems comprising grains of the same dielec. material, tribocharging can generate large amts. of net pos. or neg. charge on individual particles, resulting in long-range electrostatic forces. The effects of such forces on cluster formation are not well understood and have so far not been studied in situ. Here we report the first observations of individual collide-and-capture events between charged submillimeter particles, including Kepler-like orbits. Charged particles can become trapped in their mutual electrostatic energy well and aggregate via multiple bounces. This enables the initiation of clustering at relative velocities much larger than the upper limit for sticking after a head-on collision, a long-standing issue known from pre-planetary dust aggregation. Moreover, Coulomb interactions together with dielec. polarization are found to stabilize characteristic mol.-like configurations, providing new insights for the modeling of clustering dynamics in a wide range of microscopic dielec. systems, such as charged polarizable ions, biomols. and colloids.
    34. 34
      Steinpilz, T.; Joeris, K.; Jungmann, F.; Wolf, D.; Brendel, L.; Teiser, J.; Shinbrot, T.; Wurm, G. Electrical charging overcomes the bouncing barrier in planet formation. Nat. Phys. 2020, 16, 225– 229,  DOI: 10.1038/s41567-019-0728-9
      34
      Electrical charging overcomes the bouncing barrier in planet formation
      Steinpilz, Tobias; Joeris, Kolja; Jungmann, Felix; Wolf, Dietrich; Brendel, Lothar; Teiser, Jens; Shinbrot, Troy; Wurm, Gerhard
      Nature Physics (2020), 16 (2), 225-229CODEN: NPAHAX; ISSN:1745-2473. (Nature Research)
      In protoplanetary disks, solid objects (so-called planetesimals) are formed from dust. Micrometre-sized dust grains grow into millimetre-sized aggregates. Once those aggregates have diams. exceeding a few centimetres, they become subject to concn. mechanisms such as the streaming instability, permitting the formation of self-gravitating clusters, which might eventually collapse into kilometre-sized planetesimals. However, for the streaming instability to set in, clumps spanning sizes from centimetres to decimetres are required in the center of a protoplanetary disk. In the size range between millimetres and centimetres, aggregates bounce off each other rather than sticking together, and growth is stalled. Here we show in microgravity expts. that collisions between millimetre-sized grains lead to sufficient elec. charging for aggregation to bridge this gap between the bouncing barrier and the onset of the streaming instability. We computationally simulate aggregation and find that models agree with the exptl. data only if elec. charging is present. We therefore propose that collisional charging may promote early growth in the size gap that current models of planetesimal formation cannot account for.
    35. 35
      Pähtz, T.; Herrmann, H. J.; Shinbrot, T. Why do particle clouds generate electric charges?. Nat. Phys. 2010, 6, 364– 368,  DOI: 10.1038/nphys1631
      There is no corresponding record for this reference.
    36. 36
      Yoshimatsu, R.; Araújo, N. A.; Wurm, G.; Herrmann, H. J.; Shinbrot, T. Self-charging of identical grains in the absence of an external field. Sci. Rep. 2017, 7, 1– 11,  DOI: 10.1038/srep39996
      36
      Emergence of Quantum Critical Behavior in Metallic Quantum-Well States of Strongly Correlated Oxides
      Kobayashi, Masaki; Yoshimatsu, Kohei; Mitsuhashi, Taichi; Kitamura, Miho; Sakai, Enju; Yukawa, Ryu; Minohara, Makoto; Fujimori, Atsushi; Horiba, Koji; Kumigashira, Hiroshi
      Scientific Reports (2017), 7 (1), 1-7CODEN: SRCEC3; ISSN:2045-2322. (Nature Research)
      Controlling quantum crit. phenomena in strongly correlated electron systems, which emerge in the neighborhood of a quantum phase transition, is a major challenge in modern condensed matter physics. Quantum crit. phenomena are generated from the delicate balance between long-range order and its quantum fluctuation. So far, the nature of quantum phase transitions has been investigated by changing a limited no. of external parameters such as pressure and magnetic field. We propose a new approach for investigating quantum criticality by changing the strength of quantum fluctuation that is controlled by the dimensional crossover in metallic quantum well (QW) structures of strongly correlated oxides. With reducing layer thickness to the crit. thickness of metal-insulator transition, crossover from a Fermi liq. to a non-Fermi liq. has clearly been obsd. in the metallic QW of SrVO3 by in situ angle-resolved photoemission spectroscopy. Non-Fermi liq. behavior with the crit. exponent α = 1 is found to emerge in the two-dimensional limit of the metallic QW states, indicating that a quantum crit. point exists in the neighborhood of the thickness-dependent Mott transition. These results suggest that artificial QW structures provide a unique platform for investigating novel quantum phenomena in strongly correlated oxides in a controllable fashion.
    37. 37
      Grosjean, G.; Wald, S.; Sobarzo, J. C.; Waitukaitis, S. Quantitatively consistent scale-spanning model for same-material tribocharging. Physical Review Materials 2020, 4, 082602,  DOI: 10.1103/PhysRevMaterials.4.082602
      37
      Quantitatively consistent scale-spanning model for same-material tribocharging
      Grosjean, Galien; Wald, Sebastian; Sobarzo, Juan Carlos; Waitukaitis, Scott
      Physical Review Materials (2020), 4 (8), 082602CODEN: PRMHBS; ISSN:2475-9953. (American Physical Society)
      By rigorously accounting for mesoscale spatial correlations in donor/acceptor surface properties, we develop a scale-spanning model for same-material tribocharging. We find that mesoscale correlations affect not only the magnitude of charge transfer but also the fluctuations-suppressing otherwise overwhelming charge-transfer variability that is not obsd. exptl. We furthermore propose a generic theor. mechanism by which the mesoscale features might emerge, which is qual. consistent with other proposals in the literature.
    38. 38
      Xu, K.; Cao, P.; Heath, J. R. Graphene visualizes the first water adlayers on mica at ambient conditions. Science 2010, 329, 1188– 1191,  DOI: 10.1126/science.1192907
      38
      Graphene Visualizes the First Water Adlayers on Mica at Ambient Conditions
      Xu, Ke; Cao, Peigen; Heath, James R.
      Science (Washington, DC, United States) (2010), 329 (5996), 1188-1191CODEN: SCIEAS; ISSN:0036-8075. (American Association for the Advancement of Science)
      The dynamic nature of the first water adlayers on solid surfaces at room temp. has made the direct detection of their microscopic structure challenging. We used graphene as an atomically flat coating for at. force microscopy to det. the structure of the water adlayers on mica at room temp. as a function of relative humidity. Water adlayers grew epitaxially on the mica substrate in a layer-by-layer fashion. Submonolayers form atomically flat, faceted islands of height 0.37 ± 0.02 nm, in agreement with the height of a monolayer of ice. The second adlayers, obsd. at higher relative humidity, also appear icelike, and thicker layers appear liquidlike. Our results also indicate nanometer-scale surface defects serve as nucleation centers for the formation of both the first and the second adlayers.
    39. 39
      Morgan, A. R.; Ballard, N.; Rochford, L. A.; Nurumbetov, G.; Skelhon, T. S.; Bon, S. A. Understanding the multiple orientations of isolated superellipsoidal hematite particles at the oil–water interface. Soft Matter 2013, 9, 487– 491,  DOI: 10.1039/C2SM26556G
      39
      Understanding the multiple orientations of isolated superellipsoidal hematite particles at the oil-water interface
      Morgan, Adam R.; Ballard, Nicholas; Rochford, Luke A.; Nurumbetov, Gabit; Skelhon, Thomas S.; Bon, Stefan A. F.
      Soft Matter (2013), 9 (2), 487-491CODEN: SMOABF; ISSN:1744-683X. (Royal Society of Chemistry)
      Non-spherical particles have the potential to adopt multiple orientations once adhered to a liq.-liq. interface. In this work we combine simulations and expts. to investigate the behavior of an isolated microscopic hematite particle of superellipsoidal shape. We show that this microparticle can adopt one of three orientations when adhered to a hexadecane-water interface. Two of the orientations, and ests. for their relative populations, could be assigned to two thermodn. min. on the energy landscape as generated through both free-energy minimization and particle trajectory simulations. The third orientation was found to correspond to a kinetically trapped state, existing on certain particle trajectories in a region of a negligible gradient in free energy. To underpin the simulations the individual orientation of a set of 100 isolated particles was explored by means of SEM (SEM) using the gel trapping technique as a tool. Atomic force microscopy (AFM) was addnl. used to support the exptl. findings. This is the first example of such a kinetic metastable state being obsd. for particles at liq.-liq. interfaces.
    40. 40
      Meijer, J.; Rossi, L. Preparation, properties, and applications of magnetic hematite microparticles. Soft Matter 2021, 17, 2354– 2368,  DOI: 10.1039/D0SM01977A
      40
      Preparation, properties, and applications of magnetic hematite microparticles
      Meijer, J. M.; Rossi, L.
      Soft Matter (2021), 17 (9), 2354-2368CODEN: SMOABF; ISSN:1744-6848. (Royal Society of Chemistry)
      A review. Hematite microparticles are becoming increasingly important components in the soft matter field. The remarkable combination of magnetic and photocatalytic properties that characterize them, coupled with the variety of uniform and monodisperse shapes that they can be synthesized in, makes them a one of a kind colloidal model system. Thanks to these properties, hematite microparticles have been recently applied in several important soft matter applications, spanning from novel colloidal building blocks for self-assembly to necessary tools to investigate and understand fundamental problems. In this article we provide a detailed overview of the traditional methods available for the prepn. of hematite microparticles of different shapes, devoting special attention on some of the most common hiccups that could hider a successful synthesis. We furthermore the particles' most important physico-chem. properties and their most relevant applications in the soft matter field.