Measuring Adhesion Forces in Powder Collectives by Inertial

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Measuring Adhesion Forces in Powder Collectives by Inertial Detachment Stefanie Wanka,† Michael Kappl,*,† Markus Wolkenhauer,‡ and Hans-Jürgen Butt† †

Max Planck Institute for Polymer Research, 55128 Mainz, Germany Boehringer Ingelheim Pharma GmbH & Co. KG, 55216 Ingelheim, Germany

‡

S Supporting Information *

ABSTRACT: One way of measuring adhesion forces in fine powders is to place the particles on a surface, retract the surface with a high acceleration, and observe their detachment due to their inertia. To induce detachment of micrometer-sized particles, an acceleration in the order of 500 000g is required. We developed a device in which such high acceleration is provided by a Hopkinson bar and measured via laser vibrometry. Using a Hopkinson bar, the fundamental limit of mechanically possible accelerations is reached, since higher values cause material failure. Particle detachment is detected by optical video microscopy. With subsequent automated data evaluation a statistical distribution of adhesion forces is obtained. To validate the method, adhesion forces for ensembles of single polystyrene and silica particles on a polystyrene coated steel surface were measured under ambient conditions. We were able to investigate more than 150 individual particles in one experiment and obtained adhesion values of particles in a diameter range of 3−13 μm. Measured adhesion forces of small particles agreed with values from colloidal probe measurements and theoretical predictions. However, we observe a stronger increase of adhesion for particles with a diameter larger than roughly 7−10 μm. We suggest that this discrepancy is caused by surface roughness and heterogeneity. Large particles adjust and find a stable position on the surface due to their inertia while small particles tend to remain at the position of first contact. The new device will be applicable to study a broad variety of different particle−surface combinations on a routine basis, including strongly cohesive powders like pharmaceutical drugs for treatment of lung diseases.

1. INTRODUCTION

Furthermore, existing techniques for measuring particle adhesion forces are experimentally demanding, time-consuming, and of limited practical applicability.14 This includes the two most widely used methods: the colloidal probe technique using an atomic force microscope (AFM)15,16 and the centrifuge method.7,17 For colloidal probe measurements, each single particle has to be attached manually to the end of a microcantilever which limits the number of particles that can be investigated. Moreover, the direction of contact is predetermined and the particle cannot adjust freely like it is the case in real powders. In centrifuge experiments, which have as well been applied to pharmaceutical powders,18−20 adhesion forces of a large number of particles can be measured simultaneously. However, evacuation and spin up/down times for each acceleration value make it a very time-consuming method. Since both techniques are not usable for routine applications, a simple alternative method is needed. Therefore, we developed a new technique that will allow routine measurements of adhesion in ensembles of singly dispersed particles (particle collectives). Adhesion force measurements with our new device are based on particle detachment from a surface caused by inertial forces. The surface

Fine powders usually do not flow easily and are difficult to disperse due to interparticle adhesion that leads to the formation of agglomerates. Knowing about the adhesion forces between particles is indispensable to gain a deeper fundamental understanding of the flow behavior of powders. Many experimental as well as theoretical and numerical studies have been carried out to better describe particle flow properties and mechanics of granular matter.1−5 Knowledge about particle adhesion is relevant for many industrial applications including storage, mixing, and dosing of powders, surface cleaning in semiconductor industry, printing, or food powders processing. Especially in the pharmaceutical industry, control of adhesion forces in powders is mandatory to improve the performance of Dry Powder Inhalers (DPIs) for pulmonary drug delivery. Typically the size of inhalable particles is in the range of 1−5 μm.6 For particles of such size, attractive surface forces are usually by far dominating over inertial forces, making these powders strongly cohesive. So far a full understanding of mechanical microcontacts is lacking. One reason is that even relatively monodisperse powders show wide distributions of adhesion forces rather than a single value. In these powders, adhesion forces of particles can vary by a factor of 2−10,7−9 which is caused by surface roughness and surface heterogeneity.10−13 © 2013 American Chemical Society

Received: October 21, 2013 Revised: December 9, 2013 Published: December 10, 2013 16075

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is excited mechanically to provide the acceleration necessary to remove the particles. For detachment, the adhesion force of the particle has to be exceeded by the inertial force provided by the surface, leading to 4 Fad = Fdetach = ρ πR3a 3

(1)

Here, ρ is the particle density, R the particle radius, and a the acceleration of the surface. To achieve detachment of particles in the size range of 1−5 μm, accelerations in the order of 300 000−500 000g are necessary; g = 9.81 m/s2 is the standard acceleration of free fall. Defined accelerations of this magnitude cannot be generated with simple technical systems like piezo actuators or dynamic speakers, which are used in the vibration method,21−23 or systems employing the hammer-anvil principle like a shock pendulum.24 Maximal accelerations with these methods are in the order of 10 000g; therefore, they are limited to relatively large particles of >5 μm. We overcome this limit by using a shock excitation system based on the Hopkinson bar principle. A Hopkinson bar is a bar of titanium which is excited on one end by a bullet from an air gun. The shock wave traveling through the bar causes accelerations up to 500 000g at the free end. This acceleration is a fundamental limit given by the material strength of the system. The first technical application of the Hopkinson bar principle was in 1914 by Hopkinson to measure the pressures arising in detonations.25 This method was developed further by Davies in 1948 and Kolsky in 1949 to investigate material properties.26,27 Kolsky used two bars between which the test object is mounted. Current technical applications of the Hopkinson bar are material characterization at high strain rates or calibration of acceleration sensors.28−31

Figure 1. Experimental setup of the Hopkinson bar system. pneumatically against the left bar end. The projectile is accelerated with pressurized air (4 bar) and retracted with vacuum using magnetic valves in a pneumatic unit that can be controlled electronically. The starting point of the projectile within the guiding tube is defined by a small rod which is inserted into the end of the guiding tube and acts as a stopper during retraction to the starting point. Its position can be varied via a stepper motor. The distance between projectile starting point and the left bar end determines the acceleration length and thus the impact velocity of the projectile. We found a linear dependence between acceleration length and resulting acceleration at the right bar end. Due to this linear relation between starting point of projectile and acceleration, it is possible to generate well-defined accelerations up to 500 000g with a reproducibility of about 5%. The sample surface with particles is attached to the right end of the titanium bar (Figure 1). To optimize the mechanical coupling between bar end and sample and to achieve full transfer of the acceleration, the circular stainless steel plates were screwed to the bar end with a titanium screw with a fixed torque of 3.5 N m. The bar, including sample plate, moves about 0.3 mm forward during the shock pulse due to momentum conservation (Figure 2, left). To allow particle detachment during an acceleration pulse, the sample plate overlaps the bar end by 3 mm and the particles are located on the back side of the overlapping rim (Figure 3). This geometry ensures that particles experience an acceleration away for the surface first and are not first pressed against the surface. The velocity is measured interferometrically with a laser Doppler vibrometer (Polytec OFV-5000-S High Speed) on the front side of the sample plate. The beam is adjusted at the overlapping edge of the plate exactly at the location that is investigated. From the measured velocity of the sample surface during a shock pulse one obtains the displacement and acceleration signal on the sample plate (Figure 2). The displacement signal (Figure 2, left) shows the forward movement of the complete bar including sample plate in the order of 0.3 mm for each shock pulse due to momentum conservation. The small overshot peak (Figure 2, left) originates from the elastic response of the sample plate since the overlapping edges first bend forward and subsequently snap backward during the shock pulse. The relevant part of the acceleration signal (Figure 2, right) causing particle detachment is the first positive peak with a pulse width of 9−13 μs. With current laser Doppler vibrometers velocities up to 20 m/s are detectable, which corresponds to an acceleration of about 300 000g in our system. Higher accelerations cannot be directly measured. Since the acceleration of the sample and starting point of the projectile in the pneumatic guiding tube are linearly related, one can extrapolate the acceleration above 300 000 g from a calibration plot (Supporting Information, Figure SI1). To detect particle detachment events and determine particle diameters we developed an optical system that allows observation of the sample during the experiment (Figure 3, left). It consists of a clamp that is fixed to the bar with foamed rubber. In addition, a gold-

2. THE HOPKINSON BAR METHOD Experimental Setup. The main component of a Hopkinson bar system is a long slender titanium bar. A shock pulse is excited by shooting a projectile pneumatically against one of the bar’s ends. This mechanical impact generates an elastic wave that propagates through the bar and is reflected at the other free end. Superposition of incoming and reflected wave leads to a doubling of displacement and acceleration:32

a(t ) = 2

c0 dF(t ) EA dt

(2)

with the propagation velocity c0 of the wave, Young’s modulus E, cross section area A of the rod and the acting force F during the mechanical impact. By varying the speed of the projectile and therefore the force pulse dF/dt, the acceleration at the bar’s end can be controlled. In our device, the sample surface with adhering particles is attached to the free end of the Hopkinson bar. The particles are deposited on the backside of the overlapping edge so that the initial acceleration leads to a detaching force. Stepwise increase of the acceleration leads to detachment of the particles from the surface as soon as the inertial forces exceed the adhesion force. The sample acceleration is measured via laser Doppler vibrometry and particle detachment events are detected by optical video microscopy. The images are automatically analyzed and a statistical distribution of adhesion forces is obtained. We use a Hopkinson bar shock excitation system (SPEKTRA Schwingungstechnik and Akustik GmbH, Dresden)33,34 with a cylindrical titanium bar of 1 m in length and 10 mm in diameter (Figure 1). The bar is mounted on an aluminum frame using clamps lined with foam rubber so that the elastic wave can propagate unimpeded. The projectile consisting of a mushroom-shaped steel core and a Teflon liner is loaded into a guiding tube in which it can be shot 16076

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Figure 2. Displacement signal (left) and acceleration signal (right) on the sample plate during a shock pulse measured with the laser Doppler vibrometer.

Figure 3. Schematic of the optical system to detect particle detachment and particle diameters (left, side view). Air stream with low flow rate for horizontal dislocation of detached particles (right, top view).

Figure 4. Microscope images (after removal of brightness gradient and contrast enhancement) showing detachment of spherical silica particles (diameter 5 μm) with increasing acceleration of the substrate.

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Figure 5. Polystyrene particle on a polystyrene surface (left) and porous silica particles (right) observed with a SEM.

FDMT = 4πγsR

coated glass plate acting as a mirror was attached magnetically to the clamp under 45°. Via the mirror the sample surface can be observed with a video microscope consisting of a tube system (Navitar 6.5× UltraZoom, coaxial illumination), a 10× objective (Mitutoyo, Japan) with a working distance of 33.5 mm, and a CCD camera (uEye UI 2280 SE monochrome, 2448 × 2048 pixels). To avoid reattachment of particles, especially due to the backward movement of the overlapping edges of the sample plate during a shock pulse, a lateral air stream with low flow rate (10−50 l/min in the tube) was applied next to the sample plate (Figure 3, right). This air flow leads to horizontal dislocation of already detached particles away from the surface. The flow rate in the tube was measured with a flow meter (TSI 4000 Series). Measuring Procedure. First, particles are dispersed on the sample surface to achieve a dense coverage of the substrate while still avoiding agglomeration. The sample plate is then screwed to the bar’s end. A series of shock pulses with stepwise increasing acceleration is applied. Acceleration step size was 5000−20 000g, corresponding to the shock pulse reproducibility. When the inertial force exceeds the adhesion force, particles detach from the surface. After each shock pulse a video microscope image is recorded (Figure 4). Before and after images were compared with an automated image analysis program to identify detached particles and determine their diameters. From the acceleration values recorded by the laser Doppler vibrometer, the adhesion force for each detached particle can be calculated. In this way adhesion values of up to some hundred particles can be measured in a single experiment, depending on the surface coverage within the field of view of the video microscope. The microscope images taken after each shock pulse are analyzed with automatic image processing, based on ImageJ (Version 1.46r). After subtracting illumination gradients and removing irregularities like scratches, the images are converted from gray scale to black and white images. Particles above a predefined size threshold and with a given circularity range can then be identified automatically to determine their coordinates and diameters. We developed a program that compares the images from the consecutive shock pulses, giving out a list of detached particles that can also be cross-checked by eye. Analysis: Forces Acting on the Particles. Considering a single particle on a flat surface which is exposed to a shock pulse, several forces are acting on the particle. The adhesion force is in general a combination of different contributions such as van der Waals forces, electrostatic forces, chemical bonding and capillary forces.35−37 In our model system, van der Waals forces are expected to dominate. Capillary forces can be neglected in our case, since the investigated particles and the surface were mostly hydrophobic and particles were exposed to an air stream with low relative humidity of less than 20%. Theoretical predictions of the required force to separate the particle from the substrate can be obtained with the Johnson−Kendall− Roberts (JKR) model38 and the Derjaguin−Muller−Toporov (DMT) model39 that both take the interplay of surface forces and elastic surface deformation into account:

FKJR = 3πγsR

(4)

For both models, the force depends linearly on the particle radius R and the surface energy γs. The JKR model considers only adhesive forces within the contact zone of particle and wall whereas the DMT model considers forces outside the contact zone. The former is appropriate for large, soft spheres, and the latter for small, hard spheres. However, these two models are only valid if we assume perfectly smooth surfaces. Roughness of particle and surface has a strong influence on adhesion forces. Rabinovich et al.40 developed a model which takes the presence of surface asperities into account by using the root-mean-square roughness. According to this model, van der Waals interaction between a particle and a rough substrate leads to an adhesion force of

Fadh

⎡ AH R ⎢ 1 ⎢ =− + 6D0 2 ⎢ 1 + 32cRr2 rms λ ⎢⎣

1

⎤ ⎥ ⎥ 2 ⎥ ⎥⎦

(1 + ) crrms D0

(5)

with root-mean-square roughness rrms of the interacting surfaces, the average lateral distance λ between asperities (λ ≫ rrms), Hamaker constant AH, particle radius R, the atomic distance D0 for closest approach between surfaces, and a proportionality factor c = 1.817. Assuming an independent statistical combination of the two contact surfaces, the rrms value for the total system is given by rrms =

rrms 2 (particle) + rrms 2 (substrate)

(6)

Gravitational forces on the particle can be neglected for micrometer sized particles, since they are much lower than the surface forces (Table SI1, Supporting Information). The reflected shock wave at the bar’s end causes a force pulse acting on the sample surface and therefore on the particle. This inertial force is given by eq 1. Due to the air stream that is used for removal of detached particles, fluid forces like lift and drag forces are acting on the particle as well. The lift force on a particle near a flat wall in a linear air flow field in a tube can be described with a model by Leighton and Acrivos41 which is in accordance with the results of McLaughlin and Cherukat:42

Flift

2 d 4 ⎛ 6ηair cmean ⎞ ⎟ ⎜ = 0.576ρair 3 ⎜ ⎟ νair ⎝ hρair ⎠

(7)

with the density of air ρair, particle diameter d, the dynamic and kinematic viscosity of air ηair and vair, the mean air velocity cmean, and the height of the tube h. The drag force can be estimated according to O’Neill:43 Fdrag = 5.1027πηair dc(y)

(8)

where c(y) is the air velocity at the particle center. Estimation of lift and drag forces acting on the particles in a laminar air stream with low flow rates that were used in our experiments (measured in the tube)

(3) 16078

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shows a negligible contribution compared to adhesion forces (Table SI2, Supporting Information). Since the particles are not located inside but behind the air tube, the air velocity and thus the aerodynamic forces should be even smaller.

3. MATERIALS Test Particles and Surfaces. To validate our new measurement system, we have used two model systems: polystyrene and silica particles. These systems have the advantage of a well-defined surface chemistry and spherical topography. We used spherical polydisperse polystyrene particles (diameter 1− 50 μm, polystyrene DVB, Duke Scientific Corp., density 1.052 g/mL, rrms = (0.57 ± 0.06) nm) and porous silica particles (diameter 3.5 and 5 μm, Kromasil 100 SIL, density 0.738 g/mL, rrms = (4.67 ± 1.27) nm). Roughness parameters of the particles were determined by atomic force microscopy (AFM) imaging in tapping mode (scanning area 1 × 1 μm2, VEECO Dimension 3100, Supporting Information Figures SI2 and SI3). Figure 5 shows the particle morphology imaged by scanning electron microscopy (SEM) with a LEO 1530 Gemini instrument (Zeiss, Oberkochen, Germany). As sample surface we use a polished spherical stainless steel plate (16 mm diameter, 2 mm thickness) with a polystyrene coating (MW = 703 200 g/mol). Stainless steel was chosen since it is not only robust to stand the high accelerations with only small deformations, but also elastic enough to avoid brittle failure during the shock pulse. In all experiments, temperature and relative humidity were measured with a hygrometer. All experiments were carried out under ambient conditions (temperature 20−25 °C, relative humidity 30−46% in laboratory) with low flow rate of the lateral air stream (10−50 l/min, relative humidity 20%). Sample Preparation. The steel substrate was first polished using a polishing machine (Buehler Phoenix 4000) with a diamond suspension to obtain an optically flat surface, which is necessary for a reliable optical detection of the particles. The polished surface was afterward cleaned with acetone and ethanol in an ultrasonic bath, dried with nitrogen and spin-coated with a polystyrene layer (SüssMicrotec spin coater, 1500 rpm, 30 s, toluene as solvent). The polystyrene layer had a thickness of (18 ± 2) nm and a root-mean-square roughness of rrms = (0.55 ± 0.10) nm determined by AFM imaging (scanning area 1 × 1 μm2). Experiments were carried out with untreated and hydrophilized polystyrene surfaces. The polystyrene was hydrophilized by O2 plasma treatment (FEMTO plasma cleaner, Diener electronic, power: 10 W, oxygen flow rate: 0.5 sccm, 36 s) after spin coating a film with a thickness of (565 ± 16) nm. Here, a thicker polystyrene layer was used since plasma treatment removes several nanometers of the film.44 The actual film thickness of the polystyrene has no influence on the adhesion force of particles, provided that the layer is thick enough that the van der Waals forces are dominated by the polystyrene and not by the metal underneath. This is the case for all used samples (Table SI3, Supporting Information). Surface roughness of the polystyrene layer did not change considerably after the plasma treatment, which was verified by AFM measurements. Water on hydrophilized polystyrene had an average static contact angle of (18 ± 2)° compared to (99 ± 1)° for the untreated polystyrene measured by the sessile drop method (1−3 μL, water) at different positions on the sample surface. Particles were deposited onto the surface using a sealed steel chamber (Supporting Information, Figure SI4) in which the sample is placed. After evacuation of the chamber, a spatula tip full of powder is placed into a small funnel on top of a pneumatic shutter. When opening the shutter, particle agglomerates are efficiently dispersed by the inflowing air stream, leading to separate individual particles on the sample surface after sedimentation.

Figure 6. Adhesion forces (red ranges) of polystyrene particles on a polystyrene coated surface (untreated) measured with the Hopkinson bar in comparison with theoretical values from JKR model (black line) and Rabinovich approach (green range). Each red adhesion range represents a different single particle (particle diameter 4−10 μm, RH = 45%, T = 25 °C).

steps one obtains an adhesion force range for each detached particle. The lower limit of that range corresponds to the last shock pulse, where the particle still adhered. The upper limit corresponds to the pulse after which the particle was detached. Each adhesion range in Figure 6 corresponds to an individual particle with a specific diameter. In this particular experiment one particle was detected with a diameter of 4 μm, 4 particles with a diameter of 5 μm etc. The error bars resulted from the combined error of the laser Doppler vibrometer (±1.5%) and the error of particle diameter (±0.5 μm). The latter was estimated comparing microscope images of particles with images from scanning electron microscopy. For particles that detached at accelerations higher than the measuring limit of the vibrometer, the acceleration error corresponds to the shock pulse reproducibility of 5%. Experimental adhesion forces increased with increasing particle diameter. When comparing the measured adhesion forces with predictions from JKR model (eq 3, assumed surface energy γs = 30 mN/m), Figure 6 shows good qualitative agreement concerning the dependence of adhesion on particle size, especially for the smaller particles. However, calculated values overestimated adhesion forces, presumably because surface roughness is not considered. In order to take the roughness into account, adhesion forces were calculated using the Rabinovich approach. Roughness parameters were determined from several AFM scans of the polystyrene surface and the polystyrene particles. To estimate the lateral distance λ between two asperities 24 horizontal and vertical sections of the AFM images were considered. The rrms value of the particle/ surface combination is given by eq 6. The metal underneath the polystyrene film of 18 nm thickness has no considerable influence on the adhesive force of a particle, since the distance is too large. The following parameters were used to calculate adhesion forces of polystyrene particles on a polystyrene surface: AH = 6.6 × 10−20 J, D0 0.17 nm, rrms (substrate) = (055 ± 0.10) nm, rrms (particle) = (057 ± 0.06) nm, λ = (214 ± 48). An upper and a lower limit of the theoretical adhesion force were calculated with the Rabinovich approach of eq 5 using the higher and the lower limits of rrms values and higher and lower limits of distance λ (Figure 6, green range). For the smaller particle sizes, the measured adhesion force values are within the

4. RESULTS AND DISCUSSION Polystyrene Particles. A typical result of a measurement with polydisperse polystyrene powder (51 particles) on a polystyrene coated steel surface (untreated) is shown in Figure 6. Since the acceleration on the sample is increased in discrete 16079

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determined range. However, the increase of adhesion with increasing particle diameter is stronger than theoretically predicted by the Rabinovich model. One reason could be an increasing plastic flattening of the microasperities in the inner contact zone with increasing diameter. Furthermore, as we discuss below, larger particles tend to reorient in a way that maximum contact is achieved which leads to higher adhesion. Both effects are not considered in the Rabinovich model. Comparison with the Colloidal Probe Technique. Comparing measurements with the colloidal probe technique (VEECO Dimension 3100) using seven probes with polystyrene particles of 6, 7, 10, 11, and 13 μm in diameter are shown in Figure 7. The adhesion values were measured at 8−15 Figure 8. Adhesion forces of silica particles on a hydrophilic (blue ranges) and an untreated (red ranges) polystyrene surface measured with the Hopkinson bar in comparison with theoretical values from the Rabinovich approach (green range). Each adhesion range represents a different single particle (RH = 36−39%, T = 22−24 °C).

the 6 μm particles, we measured an adhesion force of F̅adh(6 μm) = (75 ± 13) nN on the untreated and F̅adh(6 μm) = (142 ± 29) nN on the hydrophilic polystyrene. The forces were calculated from the mean values of minimum and maximum adhesion measured for each detached particle. Thus, adhesion forces on the hydrophilic polystyrene were stronger than on the untreated polystyrene surface. This can be explained with the higher surface energy of the hydrophilic surface. In addition, capillary forces are expected to contribute on the hydrophilic surface. Theoretical values were calculated with the Rabinovich model (Figure 8, green range). As the model describes van der Waals forces without considering capillary forces, it can only give reasonable predictions for adhesion on the untreated polystyrene surface (red ranges in Figure 8) where capillary forces play a negligible role. Roughness parameters were determined from several AFM scans of the untreated polystyrene surface and the silica particles. Since porous silica with a low density was used (0.738 g/mL), the Hamaker constant of the silica−air−polystyrene combination, AH = 12 × 10−20 J, was scaled down according to AH ∼ ρ. The following parameters were used to calculate adhesion forces of silica particles on a polystyrene surface: AH = 4 × 10−20 J, D0 = 0.17 nm, rrms (substrate) = (0.55 ± 0.10) nm, rrms(particle) = (4.67 ± 1.27) nm, λ = (214 ± 48). Measured forces of the silica particles on the untreated polystyrene surface agreed with theoretical values (Figure 8) for the smaller particles. However, again larger particles exhibit slightly higher adhesion force values than expected from the Rabinovich model. This is the same trend as measured for the polystyrene particles. We explain the increase in adhesion for diameters above 6− 10 μm in the following way: Particles and substrate surface are rough and heterogeneous on the nanoscale. Some regions have a stronger tendency to adhere than others. Roughness and heterogeneity may influence the adhesion of small and large particles differently. If a small particle gets into contact with the substrate, it probably remains at the point of first contact kept in position, for example, by van der Waals forces. Inertia is too weak to overcome rolling friction. Thus, they typically only attach to the first asperity. This is also the case for a particle glued to a cantilever, as used in the colloidal probe technique (Figure 9a). Hence, for small particles the measured adhesion forces agree well with those obtained from theory and colloidal

Figure 7. Comparison of adhesion values measured with the bar system (red ranges), measured with the colloidal probe technique (black symbols), and determined theoretically with JKR model (black line) and Rabinovich model (green range).

locations on the polystyrene surface (black symbols). Each data point corresponds to a mean value of about 80−100 force curves measured at this location, whereas each symbol represents one colloidal probe. The colloidal probe measurements show good agreement with the adhesion values measured with the Hopkinson bar up to a particle diameter of roughly 10 μm. For larger diameters, adhesion forces measured with the bar system tend to higher adhesion forces than those measured with colloidal probe. This could be explained by the fact that the direction of contact is predetermined in a colloidal probe measurement and the particle cannot adjust freely. In the case of the Hopkinson bar, the particles, in particular the larger ones, can rotate when they are deposited on the surface and during a shock pulse and therefore rearrange. This usually leads to a larger contact area and therefore to higher adhesive forces. Silica Particles. In Figure 8, the measured adhesion forces of 4−7 μm sized porous silica particles on a hydrophilic (blue) polystyrene surface are shown in comparison with the forces measured on the untreated (red) polystyrene surface. During each experiment, about 60−100 particles were tested. For the 4 μm particles, we measured an average adhesion force of F̅adh(4 μm) = (33 ± 6) nN on the untreated polystyrene and F̅adh(4 μm) = (64 ± 6) nN on the hydrophilic polystyrene. For the 5 μm particles, the average adhesion force on the untreated surface was F̅adh(5 μm) = (54 ± 12) nN and on the hydrophilic surface F̅adh(5 μm) = (109 ± 25) nN. For 16080

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this size in this experiment. For better overview, error bars are not shown. From the mean value of minimum and maximum adhesion, the average adhesion force of the 3 and 4 μm silica particles was calculated: F̅adh(3 μm) = (20 ± 2) nN and F̅adh(4 μm) = (43 ± 8) nN. Since high accelerations are necessary to detach particles, the question of a possible dependence of adhesion force on detachment velocity may occur. One such possible scenario is described by the so-called Bell−Evans theory,45 where the detachment force depends on the force loading rate due to the different times the system has to thermally overcome the energy barrier between adhering and detached state. This can influence the detachment force for single molecules45 or nanocontacts.46 However, in our situation, the adhesion energies of the particles are many orders of magnitude higher than the thermal energy and therefore such a mechanism can be excluded. Other possible causes for a velocity dependence might result from velocity dependent viscous dissipation. However, for the relatively hard materials used in the study, this is also not likely. Furthermore, for the small particles, which should have a higher detachment velocity compared to larger ones due to their small inertia, we observed best agreement of measured adhesion forces with theoretical values as well as colloidal probe measurements. Thus, there is no indication that the detachment velocity has an influence on adhesion forces of particles in our experiment.

Figure 9. Small particle or situation in AFM (a): the particle remains at the point of first contact and typically attaches only to the first asperity. A large particle (b) may still move on the surface and adjust, leading to a larger contact area and therefore to stronger adhesion.

probe measurements. Large particles, in contrast, may still be able to roll and adjust on the substrate due to their high inertia upon impact (Figure 9b). Also mechanical vibrations of the substrate have no influence on small particles because their inertia is too low to overcome rolling friction while large particles can roll and adjust. This may lead to more and stronger nanocontacts and thus a stronger adhesion. Since rearrangement is not possible in AFM measurements and this effect is not considered in the Rabinovich model, we observe a deviation of adhesion values for larger particles. A possible plastic deformation of particles undergoing multiple shock pulses, caused by the inverted acceleration pressing them on the surface (negative peak in Figure 2, right), would also lead to higher adhesion forces. However, this could not be experimentally observed. Small particles in the Hopkinson bar setup were generally exposed to more shock pulses compared to larger ones, since higher accelerations were needed to detach them from the surface due to their small inertia. Indeed, the measured adhesion forces of small particles show good agreement with theory and colloidal probe measurements. Thus, in our experiments no indication could be found that the number of shock pulses influences adhesion of a particle. Measurements were also conducted with smaller silica particles (average diameter 3.5 μm, manufacturer’s information) on an untreated polystyrene surface. Here, adhesion forces of 157 particles could be obtained in one experiment. Measured adhesion force ranges of 3 and 4 μm silica particles could be fitted with a Gaussian curve (Figure 10). The particle fraction refers to the total number of measured particles with

5. CONCLUSION We have developed a new method to measure adhesion forces in ensembles of single micrometer-sized particles. It is based on the acceleration exerted by the free end of a Hopkinson bar. The method was validated using polystyrene and silica microspheres with diameters in the range of 3−13 μm on a polystyrene surface. When plotting adhesion force versus diameter of the particles, we find a steep increase around a particle diameter of roughly 7−10 μm. It is steeper than predicted by the model of Rabinovich, and adhesion forces for large particles are stronger than those measured with the colloidal probe technique. We attribute this to an adjustment by inertia of large particles during impact. For smaller particles, the attractive forces such as van der Waals are so strong that particles are unable to roll and adjust. With our new method, adhesion values of more than 150 individual particles can be determined during one experiment, in contrast to the colloidal probe technique where only one single particle can be investigated. Sample preparation and measuring effort are considerably lower compared to the established colloidal probe and centrifuge technique. Therefore, the Hopkinson bar has the potential to be applied as a routine tool for the characterization of a broad variety of particle− surface combinations, even for standard analysis in industrial research.

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ASSOCIATED CONTENT

S Supporting Information *

Further information is provided about the calibration of the measured sample acceleration and powder deposition on the sample plate using a dispersing chamber. Measured AFM images of the used polystyrene and silica particles and the polystyrene surface are shown from which roughness parameters were obtained. An estimation of gravitational, lift and drag forces acting on the particles is presented.

Figure 10. Histogram of the adhesion force of porous silica particles (diameter 3 and 4 μm) on untreated polystyrene. Solid lines are Gaussian fits of the distributions. 16081

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Furthermore, the van der Waals contribution of the metal substrate underneath the polystyrene layer is calculated. This material is available free of charge via the Internet at http:// pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*Mailing address: Max Planck Institute for Polymer Research, Ackermannweg 10, D-55128, Mainz, Germany. E-mail: kappl@ mpip-mainz.mpg.de. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors are grateful to Boehringer Ingelheim Pharma GmbH & Co. KG for cooperation and financial support. We thank SPEKTRA GmbH Dresden for the fruitful discussions and cooperation. We also acknowledge technical support by A. Best, M. Rein, L. Mammen, and G. Schäfer.

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NOMENCLATURE a acceleration A cross section area AH Hamaker constant c proportionality factor (c = 1.817) c(y) velocity at particle center c0 wave propagation velocity cmean mean velocity d particle diameter D0 interatomic distance E Young’s modulus F force Fadh adhesion force F̅adh average adhesion force Fdetach detachment force Fdrag drag force Flift lift force h tube height MW molecular mass R particle radius RH relative humidity rrms root-mean-square roughness t time T temperature γs surface energy η dynamic viscosity λ lateral distance between asperities ν kinematic viscosity ρ particle density

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REFERENCES

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