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Quantification of interparticle forces by energy controlled fragmentation analysis
Journal of Aerosol Science 84 (2015) 14–20
Contents lists available at ScienceDirect
Journal of Aerosol Science journal homepage: www.elsevier.com/locate/jaerosci
Technical note
Quantification of interparticle forces by energy controlled fragmentation analysis R. Wernet a,n, A.G. Schunck a, W. Baumann b, H.-R. Paur b, M. Seipenbusch a a b
Institute for Mechanical Process Engineering and Mechanics, Karlsruhe Institute of Technology, Karlsruhe, Germany Institute for Technical Chemistry, Karlsruhe Institute of Technology, Karlsruhe, Germany
a r t i c l e in f o
abstract
Article history: Received 24 November 2014 Received in revised form 13 February 2015 Accepted 24 February 2015 Available online 6 March 2015
A molecular beam apparatus (MBA) with an implanted time of flight (tof) measurement cell was used for energy controlled fragmentation experiments on Pt agglomerates. Due to high vacuum conditions, drag forces and stagnation pressure in front of the impaction plate slowing down agglomerates were negligible. Thus, this set-up permitted a precise and convenient detection of the impact velocity of agglomerates. Results on the velocity measurement and the related degree of fragmentation are presented. The current results on fragmentation were compared to the work of Seipenbusch, Toneva, Peukert, and Weber (2007). This was motivated by the question whether the exceedance of the theoretical van der Waals binding energy found in the above-quoted work was caused by calculating the impact velocity with the commonly employed approach of Marple (vimpact ¼ 0.85 vgas). The theoretical van der Waals binding energy was found to exceed the experimentally gained binding energy by the factor of 55.4, which was in good agreement with the comparable published work. & 2015 Elsevier Ltd. All rights reserved.
Keywords: Fragmentation Nanoparticle agglomerates Interparticle forces Energy controlled impaction
1. Introduction The strength of interparticle bonds within agglomerates made of nano-scaled primary particles is a key parameter for the physical properties of powders or composite materials. Especially when processing nano-powders the stability of agglomerates determines the extent of energy consumption e.g. in applications that require dispersion. Another important aspect is product safety in respect to respirable dust that might emerge from powder treatment. Therefore, several techniques have been developed to investigate the mechanical stability of agglomerates. Suh, Prikhodko, and Friedlander (2002) designed the nanostructure manipulation device (NSMD) to study the physical properties of nanoparticle chain aggregates (NCA) that are for instance added to elastomers. It is mounted in a transmission electron microscope (TEM) and allows for applying tension on the NCAs and taking TEM images simultaneously. In this way the deformation of the NCAs can be observed until breakup of the chain occurs. The NSMD and an atomic force microscope (AFM) were utilized by Rong, Pelling, Ryan, Gimzewski, and Friedlander (2004) to estimate the tensile strength and Young's modulus of NCAs. A prevalent device for fragmentation by impaction is the single-stage low pressure impactor (SS-LPI, de la Mora, Rao, and McMurry (1990)). In order to correlate deagglomeration results to the energy of impaction, this approach requires information on the impact velocity. Marple (1970) simulated the impact velocity of particles in a SS-LPI for high Stokes numbers and derived a factor of 0.85 relative to the average velocity of the gas jet. Reuter-Hack, Weber, Rösler, and Kasper (2007) chose a Laser Doppler n
Corresponding author.
http://dx.doi.org/10.1016/j.jaerosci.2015.02.008 0021-8502/& 2015 Elsevier Ltd. All rights reserved.
R. Wernet et al. / Journal of Aerosol Science 84 (2015) 14–20
15
Anemometer (LDA) to measure the particle velocity in dependence on the distance to the nozzle exit and the pressure drop across the nozzle. Additionally the gas velocity was simulated by CFD and the particle velocity was calculated according to an approach by Brockmann and Rader (1990). For 20 mbar in the impaction chamber, a particle velocity of 0.54 times the gas velocity was found in disagreement with the 0.85 rule. Nevertheless, Marple's rule was commonly used until Rennecke and Weber (2013a, 2013b) developed a new model based on CFD simulation. Their results exhibited an overestimation of slow impact velocities whereas high impact velocities were underestimated. The SS-LPI was utilized to study nano-mechanical properties of agglomerates by Seipenbusch, Froeschke, Weber, and Kasper (2002), Seipenbusch, Toneva, Peukert, and Weber (2007) and Froeschke, Kohler, Weber, and Kasper (2003). Substantial deviations from theoretically predicted to experimentally revealed binding energies were found. The impact velocity was calculated by Marple's rule of 0.85, which might have caused inaccuracies sufficient to raise nonconformities between theory and experiments. In order to shed light on this question, a time of flight (tof) measurement was implanted into a molecular beam apparatus (MBA). This set-up allows for simultaneous fragmentation experiments and the measurement of impact velocity. Due to high vacuum conditions, drag forces acting on particles and stagnation pressure in front of the impaction plate are negligible. Therefore, no correction of the velocity measurement is necessary and the precise determination of impact velocity is suitable to eliminate the uncertainty in the estimation of the impact velocity. Pt soft-agglomerates were fragmented in the MBA and TEM images were analyzed to evaluate the degree of fragmentation. The results of the velocity measurement are shown and the fragmentation experiments are discussed in the context of Weibull statistics. 2. Theory 2.1. Weibull statistics – prediction of the probability of fracture Weichert (1992) modified the work of Weibull (1951) to predict the breakage of brittle material during grinding processes. This modification was continued by Vogel and Peukert (2003) and Seipenbusch et al. (2007) resulting in Eq. (1) that is applicable to calculate the degree of fragmentation. h i S ¼ 1 exp f ðNÞ Uc U v2p v2p; min ð1Þ Hereby S stands for the degree of fragmentation that is influenced by the number of primary particles in the agglomerate N in terms of an undefined function f(N). C is the number of contacts within an agglomerate and vp is the velocity of particles (agglomerates) whereas vp,min is the minimum required velocity of particles (agglomerates) to cause breakage of interparticle bonds by impaction. Inversely Eq. (1) is employed to calculate the vp,min from experimental vp and associated S data. 2.2. Calculation of the binding energy In order to compare the experimentally obtained strength of interparticle bonds to theoretically expected values the binding energy between two primary particles was calculated. Since the investigated agglomerates are expected to be loose and held together in particular by van der Waals forces, Eq. (2) is utilized (Israelachvili, 1991) for the calculation of binding energies. Equation (2) describes the binding energy between two spheres with the same diameter x and a distance of a0 (commonly assumed to be 0.4 nm) between their surfaces. A stands for the material specific Hamaker constant, which is APt ¼2.00 10–19 J (Derjaguin, Rabinovich, & Churaev, 1978). EvdW 11 ¼
A Ux 12 Ua0
ð2Þ
3. Experimental 3.1. Particle generation A spark discharge generator (SDG, Tabrizi, Ullmann, Vons, Lafont, and Schmidt-Ott (2009)) was used to create a Pt aerosol. The applied voltage was 9 kV and the current 4.7 mA. A N2 flow of 1 l min 1 was flushing the space around the electrodes, carrying the flaky agglomerates and aggregates that are formed in the SDG into a sintering furnace. In order to obtain spherical single primary particles a temperature of 1150 1C was chosen. After a residence time of 32 s the primary particles entered an agglomeration tank of 6 l volume. In the tank diffusional coagulation happened under room temperature conditions, therefore no solid contacts were formed between the primary particles and agglomerates would be assumed to be held together by adhesive van der Waals force only. 3.2. Fragmentation setup The fragmentation happened in a molecular beam apparatus (MBA) under high vacuum conditions and the impact velocity of the agglomerates was adjusted by the pre-pressure before the MBA inlet. Figure 1 sketches the agglomerate generation route
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R. Wernet et al. / Journal of Aerosol Science 84 (2015) 14–20
Fig. 1. Experimental arrangement: (1) critical orifice, (2) pre-pressure area, (3) expansion chamber, (4) impaction chamber, (5) velocity measurement cell, and (6) impaction plate and sampling on TEM grid.
Fig. 2. Velocity measurement cell: (1) particles from MBA, (2) photomultiplier, (3) beam trap, (4) impaction plate, and (5) laser and optical components.
that leads to a critical orifice through which the agglomerates were introduced into a low pressure region sustained by a vacuum pump. Since the pre-pressure conditions determined the impaction velocity of the agglomerates, a valve was used upstream of the pump to regulate the pump power. From this pre-pressure area the agglomerates were sucked through a capillary into the MBA. When entering the expansion chamber (p1 in the range of to 5 10 4–3 10 3 mbar) a molecular beam was formed and its center was transferred into the impaction chamber by passing a skimmer. The impaction chamber opened out into the velocity measuring cell where the velocity of agglomerates was measured in a light barrier before they impacted on a plate. On this plate a TEM grid for sampling can be adjusted. The pressure p2 in the impaction chamber and measuring cell was about 10 6–1.2 10 5 mbar. 3.3. Velocity measurement The velocity measurement was implemented into an anodized aluminum cube with openings to five sides (Fig. 2). The measurement was performed with a light barrier employing two laser beams in parallel and a sensor to detect the scattered light. A continuous SSDP-Laser with a wavelength of 457 nm was used (MBL-W-457, PhotonTec Berlin GmbH) as light source and was adjusted to a power of 3 W. The single laser beam passed a polarization device and a beam splitter in series and entered the velocity measuring cell as two parallel and polarized beams. The split beams each had a power of 1.5 W. A beam trap opposite to the laser inlet plane stopped the laser light. Perpendicular to the laser beams a photomultiplier (P30CW5, Sens-Tech Limited) was mounted to detected light that was scattered by passing agglomerates. Background noise from light scattered by windows was reduced by configured anti-reflexion windows and apertures. The photomultiplier was connected to a USB oscilloscope (PicoScope 4224, pico Technology) which recorded the voltage in dependence of time for agglomerates passing the light beam once an arbitrary threshold in voltage was exceeded. Since the intensity of each laser beam was Gauss distributed the peaks were symmetrical in shape and a matlab code determined the time of flight (tof) from the time between two signal peaks. With a tof and the distance between the laser beams of dbeam ¼4.0 mm the particle velocity vp was calculated as follows: vp ¼
tof dbeam
ð3Þ
On the basis of several hundred velocities a velocity distribution was calculated and the arithmetic mean velocity was used for calculating the kinetic energy of the agglomerates. Due to high vacuum conditions, the measured velocity vp was equal to the actual velocity of impaction and no correction of the measurements was required. Impacted agglomerates were sampled on a TEM grid simultaneously (Fig. 1, position 5).
R. Wernet et al. / Journal of Aerosol Science 84 (2015) 14–20
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Fig. 3. Voltage signals of tof measurements.
3.4. Determination of the degree of fragmentation The degree of fragmentation was determined by the analysis of TEM images. By diffusion reference agglomerates were sampled to ascertain that they were representative for the unfragmented initial state. Impacted and fragmented agglomerates were collected on TEM grids on the impaction plate. For both cases the number of interparticle contacts within an agglomerate and the number of primary particles were investigated by TEM image analysis. The degree of fragmentation S was calculated by Eq. (4). The ratio of the number of primary particles to the number of interparticle contacts is a measure for the intactness of the agglomerates. The quotient of this ratio for impaction to reference describes the percentage fraction of unbroken contacts. number of primary particles=number of interparticle contacts impaction S ¼ 1 ð4Þ number of primary particles=number of interparticle contacts ref erence
3.5. Agglomerate characterization In order to validate the assumption of aerodynamic transparency, the free software Image J was used to perform a fractal box count analysis on the reference agglomerates. For Pt agglomerates a fractal dimension Df of 1.76 was revealed. Hence the agglomerates exhibit an aerodynamic behavior that is determined by the primary particle size (Reuter-Hack et al., 2007). The energy available for the breakup of interparticle bonds is the kinetic energy of the primary particles and is calculated by Ekin ¼ ¼
1 π U U x3 U ρp Uv2p 2 6 50;0
ð5Þ
From TEM image analysis the particle size distribution of primary particles was obtained and x50;0 gathered from it. The density of the bulk material ρPt ¼21.45 g cm 3 was utilized.
3.6. Results – velocity In Fig. 3 representative voltage peaks of the velocity measurement over time are depicted. A shift to shorter flight times, respectively higher vp, with increasing pre-pressure is observed. Figure 4 shows the resulting vp in dependence on the prepressure. vp behaves inversely proportional to ppre since a lowered gas density provides less molecules for momentum transfer that is responsible for particle acceleration. The range of adjustable velocity was limited by the pre-pressure. The atmospheric pre-pressure set the upper limit for the velocity whereas the lower limit was determined by the power of the pump generating the pre-pressure. The primary particle mass and the range of pre-pressure confine the range of kinetic energies achievable for fragmentation experiments.
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R. Wernet et al. / Journal of Aerosol Science 84 (2015) 14–20
Fig. 4. Particle velocity adjusted by pre-pressure.
Fig. 5. Fragmentation of Pt.
Table 1 Theoretical and experimental energies.
Pt Pta a
x50,0 (nm)
vmin (m s 1)
Ekin,min, 10 19 J
E vdW 11, 10 19 J
E kin; min =E vdW 11 (dimensionless)
23.3 24
27.6 27.4
537.1 582.8
9.7 10.0
55.4 58.3
Seipenbusch et al. (2007).
3.7. Results – fragmentation For Pt agglomerates fragmentation experiments under vacuum conditions have been performed. In Fig. 5 the degree of fragmentation is plotted over the mass specific kinetic energy. The maximum degree of fragmentation is 73%. Noticeable is the decrease in the degree of fragmentation raising the energy input from 11.5 to 14.5 kJ kg 1. Considering the range of error it is debatable how much attention should be paid to this observation. On the other hand, rebound of particles after impaction is an investigated incident (e.g. Rennecke & Weber (2013b), Ihalainen, Lind, Arffman, Torvela, & Jokiniemi, 2014) and it is assumed to cause the observed behavior. Recoiling primary particles might evade the TEM image analysis, leading to an underestimation of the degree of fragmentation. 2 Nevertheless, a Weibull fit corresponding to Eq. (1) was employed. By plotting ln(1 S) over vp the minimum impact velocity vmin necessary to break an interparticle bond can be determined. In order to estimate the error in vmin, the standard deviation endpoints of the measured velocities were used for two further Weibull fits. The mean vmin was found to be 27.6 m s 1 (þ0.7 m s 1, 21.1 m s 1). With Eq. (2) the theoretical binding energy according to van der Waals for two spherical particles was calculated. The required Ekin,min exceeds the theoretical value EvdW 11 by the factor of 55.4 (Table 1). The error estimation delivers an excess by the factor of 58.2 for the upper error, respectively 3.1 for the lower error. A slightly raised need of energy for bond breaking can be explained by the energy transformation during impaction since plastic deformation occurs before breakage of interparticle bonds sets in. As TEM images show, energy is spent on the deformation of the TEM grid surface as well (Fig. 6). Furthermore it is considered that parts of the energy are converted into heat during impaction.
R. Wernet et al. / Journal of Aerosol Science 84 (2015) 14–20
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Fig. 6. (Left) cracked carbon film after impaction of Pt agglomerates; vp ¼ 116 m s 1 and (right) Pt agglomerate.
Therefore, there are energy transforming mechanisms acting besides deagglomeration. However, the Ekin,min exceeds the EvdW 11 55 times which might not be caused by additional energy consumption alone. Due to the inert nature of Pt, the surface of Pt agglomerates is expected to be pure even under non-reducing N2 conditions (Seipenbusch, Weber, Schiel, & Kasper, 2003). Therefore, oxidic impurities will not retard sintering and the formation of small material bridges between primary particles might occur even under room temperature conditions. However, high resolution TEM images of Pt agglomerates could not reveal material bridges to confirm this theory (Fig. 6). A comparison of the present results to the work of Seipenbusch et al. (2007) gives good agreement regarding the Ekin,min to EvdW 11 ratio (Table 1). In contrast to the present work, the cited authors calculated the impact velocity by the 0.85 rule of Marple's. As both methods lead to similar results, an adequate precision of Marple's rule of 0.85 for the calculation of the impact velocity is concluded. 3.8. Summary A MBA was employed to conduct impact fragmentation experiments on Pt soft-agglomerates under high vacuum conditions. The Pt aerosol was created by a spark discharge generator, a sintering furnace and an agglomeration tank to obtain loose agglomerates. The degree of fragmentation was gained from TEM image analysis whereas the particle velocity was measured via a light barrier in front of the impaction plate. The tof measurement provided precise registration of the particle velocity, which was adjusted by variation of the pre-pressure. The experimentally gained binding energy exceeded the theoretical van der Waals energy by the factor of 55.4. Sintering of pure Pt surfaces under room temperature conditions, leading to material bridges between primary particles, was suspected to strengthen Pt agglomerates but could not be detected by TEM images. Certainly energy consuming mechanisms like plastic deformation and heating through impaction are responsible for a raised Ekin,min. However, the result showed good agreement with the work of Seipenbusch et al. (2007), suggesting a satisfying accuracy in the determination of the impact velocity by applying Marple's rule of 0.85.
Acknowledgment The authors acknowledge the financial support from the German Research Foundation (SE 1782/4-1) and the collaboration with the joint research project MPaC. References Brockmann, J.E., & Rader, D.J. (1990). APS response to nonspherical particles and experimental determination of dynamic shape factor. Aerosol Science and Technology, 13(2), 162–172. de la Mora, J.F., Rao, N., & McMurry, P.H. (1990). Inertial impaction of fine particles at moderate reynolds numbers and in the transonic regime with a thin-plate orifice nozzle. Journal of Aerosol Science, 21(7), 889–909. Derjaguin, B.V., Rabinovich, Y.I., & Churaev, N.V. (1978). Direct measurement of molecular forces. Nature, 272, 313–318. Froeschke, S., Kohler, S., Weber, A.P., & Kasper, G. (2003). Impact fragmentation of nanoparticle agglomerates. Journal of Aerosol Science, 34(3), 275–287. Ihalainen, M., Lind, T., Arffman, A., Torvela, T., & Jokiniemi, J. (2014). Break-up and bounce of TiO2 agglomerates by impaction. Aerosol Science and Technology, 48(1), 31–41. Israelachvili, J.N. (1991). Intermolecular and Surface Forces. Academic Press: London. Marple, V.A. (1970). A fundamental study of inertial impactors PhD thesis. University of Minnesota. Rennecke, S., & Weber, A.P. (2013a). A novel model for the determination of nanoparticle impact velocity in low pressure impactors. Journal of Aerosol Science, 55, 89–103.
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Rennecke, S., & Weber, A.P. (2013b). The critical velocity for nanoparticle rebound measured in a low pressure impactor. Journal of Aerosol Science, 58, 135–147. Reuter-Hack, K., Weber, A.P., Rösler, S., & Kasper, G. (2007). First LDA measurements of nanoparticle velocities in a low-pressure impacting jet. Aerosol Science and Technology, 41(3), 277–283. Rong, W., Pelling, A.E., Ryan, A., Gimzewski, J.K., & Friedlander, S.K. (2004). Complementary TEM and AFM force spectroscopy to characterize the nanomechanical properties of nanoparticle chain aggregates. Nano Letters, 4(11), 2287–2292. Seipenbusch, M., Froeschke, S., Weber, A.P., & Kasper, G. (2002). Investigations on the fracturing of nanoparticle agglomerates – First results. Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering, 216–219. Seipenbusch, M., Toneva, P., Peukert, W., & Weber, A.P. (2007). Impact fragmentation of metal nanoparticle agglomerates. Particle & Particle System Characterization, 24, 193–200. Seipenbusch, M., Weber, A.P., Schiel, A., & Kasper, G. (2003). Influence of the gas atmosphere on restructuring and sintering kinetics of nickel and platinum aerosol nanoparticle agglomerates. Journal of Aerosol Science, 34(12), 1699–1709. Suh, Y.J., Prikhodko, S.V., & Friedlander, S.K. (2002). Nanostructure manipulation device for transmission electron microscopy: Application to titania nanoparticle chain aggregates. Microscopy and Microanalysis, 8(6), 497–501. Tabrizi, N.S., Ullmann, M., Vons, V.A., Lafont, U., & Schmidt-Ott, A. (2009). Generation of nanoparticles by spark discharge. Journal of Nanoparticle Research, 11, 315–332. Vogel, L., & Peukert, W. (2003). Breakage behaviour of different materials – Construction of master curve for the breakage probability. Powder Technology, 129, 101–110. Weichert, R. (1992). Theoretical prediction of energy-consumptionand particle-size distribution in grinding and drilling of brittle materials. Zement-KalkGips, 45, 1–8. Weibull, W. (1951). A statistical distribution function of wide applicability. Journal of Applied Mechanics, 9, 293–297.
Contents lists available at ScienceDirect
Journal of Aerosol Science journal homepage: www.elsevier.com/locate/jaerosci
Technical note
Quantification of interparticle forces by energy controlled fragmentation analysis R. Wernet a,n, A.G. Schunck a, W. Baumann b, H.-R. Paur b, M. Seipenbusch a a b
Institute for Mechanical Process Engineering and Mechanics, Karlsruhe Institute of Technology, Karlsruhe, Germany Institute for Technical Chemistry, Karlsruhe Institute of Technology, Karlsruhe, Germany
a r t i c l e in f o
abstract
Article history: Received 24 November 2014 Received in revised form 13 February 2015 Accepted 24 February 2015 Available online 6 March 2015
A molecular beam apparatus (MBA) with an implanted time of flight (tof) measurement cell was used for energy controlled fragmentation experiments on Pt agglomerates. Due to high vacuum conditions, drag forces and stagnation pressure in front of the impaction plate slowing down agglomerates were negligible. Thus, this set-up permitted a precise and convenient detection of the impact velocity of agglomerates. Results on the velocity measurement and the related degree of fragmentation are presented. The current results on fragmentation were compared to the work of Seipenbusch, Toneva, Peukert, and Weber (2007). This was motivated by the question whether the exceedance of the theoretical van der Waals binding energy found in the above-quoted work was caused by calculating the impact velocity with the commonly employed approach of Marple (vimpact ¼ 0.85 vgas). The theoretical van der Waals binding energy was found to exceed the experimentally gained binding energy by the factor of 55.4, which was in good agreement with the comparable published work. & 2015 Elsevier Ltd. All rights reserved.
Keywords: Fragmentation Nanoparticle agglomerates Interparticle forces Energy controlled impaction
1. Introduction The strength of interparticle bonds within agglomerates made of nano-scaled primary particles is a key parameter for the physical properties of powders or composite materials. Especially when processing nano-powders the stability of agglomerates determines the extent of energy consumption e.g. in applications that require dispersion. Another important aspect is product safety in respect to respirable dust that might emerge from powder treatment. Therefore, several techniques have been developed to investigate the mechanical stability of agglomerates. Suh, Prikhodko, and Friedlander (2002) designed the nanostructure manipulation device (NSMD) to study the physical properties of nanoparticle chain aggregates (NCA) that are for instance added to elastomers. It is mounted in a transmission electron microscope (TEM) and allows for applying tension on the NCAs and taking TEM images simultaneously. In this way the deformation of the NCAs can be observed until breakup of the chain occurs. The NSMD and an atomic force microscope (AFM) were utilized by Rong, Pelling, Ryan, Gimzewski, and Friedlander (2004) to estimate the tensile strength and Young's modulus of NCAs. A prevalent device for fragmentation by impaction is the single-stage low pressure impactor (SS-LPI, de la Mora, Rao, and McMurry (1990)). In order to correlate deagglomeration results to the energy of impaction, this approach requires information on the impact velocity. Marple (1970) simulated the impact velocity of particles in a SS-LPI for high Stokes numbers and derived a factor of 0.85 relative to the average velocity of the gas jet. Reuter-Hack, Weber, Rösler, and Kasper (2007) chose a Laser Doppler n
Corresponding author.
http://dx.doi.org/10.1016/j.jaerosci.2015.02.008 0021-8502/& 2015 Elsevier Ltd. All rights reserved.
R. Wernet et al. / Journal of Aerosol Science 84 (2015) 14–20
15
Anemometer (LDA) to measure the particle velocity in dependence on the distance to the nozzle exit and the pressure drop across the nozzle. Additionally the gas velocity was simulated by CFD and the particle velocity was calculated according to an approach by Brockmann and Rader (1990). For 20 mbar in the impaction chamber, a particle velocity of 0.54 times the gas velocity was found in disagreement with the 0.85 rule. Nevertheless, Marple's rule was commonly used until Rennecke and Weber (2013a, 2013b) developed a new model based on CFD simulation. Their results exhibited an overestimation of slow impact velocities whereas high impact velocities were underestimated. The SS-LPI was utilized to study nano-mechanical properties of agglomerates by Seipenbusch, Froeschke, Weber, and Kasper (2002), Seipenbusch, Toneva, Peukert, and Weber (2007) and Froeschke, Kohler, Weber, and Kasper (2003). Substantial deviations from theoretically predicted to experimentally revealed binding energies were found. The impact velocity was calculated by Marple's rule of 0.85, which might have caused inaccuracies sufficient to raise nonconformities between theory and experiments. In order to shed light on this question, a time of flight (tof) measurement was implanted into a molecular beam apparatus (MBA). This set-up allows for simultaneous fragmentation experiments and the measurement of impact velocity. Due to high vacuum conditions, drag forces acting on particles and stagnation pressure in front of the impaction plate are negligible. Therefore, no correction of the velocity measurement is necessary and the precise determination of impact velocity is suitable to eliminate the uncertainty in the estimation of the impact velocity. Pt soft-agglomerates were fragmented in the MBA and TEM images were analyzed to evaluate the degree of fragmentation. The results of the velocity measurement are shown and the fragmentation experiments are discussed in the context of Weibull statistics. 2. Theory 2.1. Weibull statistics – prediction of the probability of fracture Weichert (1992) modified the work of Weibull (1951) to predict the breakage of brittle material during grinding processes. This modification was continued by Vogel and Peukert (2003) and Seipenbusch et al. (2007) resulting in Eq. (1) that is applicable to calculate the degree of fragmentation. h i S ¼ 1 exp f ðNÞ Uc U v2p v2p; min ð1Þ Hereby S stands for the degree of fragmentation that is influenced by the number of primary particles in the agglomerate N in terms of an undefined function f(N). C is the number of contacts within an agglomerate and vp is the velocity of particles (agglomerates) whereas vp,min is the minimum required velocity of particles (agglomerates) to cause breakage of interparticle bonds by impaction. Inversely Eq. (1) is employed to calculate the vp,min from experimental vp and associated S data. 2.2. Calculation of the binding energy In order to compare the experimentally obtained strength of interparticle bonds to theoretically expected values the binding energy between two primary particles was calculated. Since the investigated agglomerates are expected to be loose and held together in particular by van der Waals forces, Eq. (2) is utilized (Israelachvili, 1991) for the calculation of binding energies. Equation (2) describes the binding energy between two spheres with the same diameter x and a distance of a0 (commonly assumed to be 0.4 nm) between their surfaces. A stands for the material specific Hamaker constant, which is APt ¼2.00 10–19 J (Derjaguin, Rabinovich, & Churaev, 1978). EvdW 11 ¼
A Ux 12 Ua0
ð2Þ
3. Experimental 3.1. Particle generation A spark discharge generator (SDG, Tabrizi, Ullmann, Vons, Lafont, and Schmidt-Ott (2009)) was used to create a Pt aerosol. The applied voltage was 9 kV and the current 4.7 mA. A N2 flow of 1 l min 1 was flushing the space around the electrodes, carrying the flaky agglomerates and aggregates that are formed in the SDG into a sintering furnace. In order to obtain spherical single primary particles a temperature of 1150 1C was chosen. After a residence time of 32 s the primary particles entered an agglomeration tank of 6 l volume. In the tank diffusional coagulation happened under room temperature conditions, therefore no solid contacts were formed between the primary particles and agglomerates would be assumed to be held together by adhesive van der Waals force only. 3.2. Fragmentation setup The fragmentation happened in a molecular beam apparatus (MBA) under high vacuum conditions and the impact velocity of the agglomerates was adjusted by the pre-pressure before the MBA inlet. Figure 1 sketches the agglomerate generation route
16
R. Wernet et al. / Journal of Aerosol Science 84 (2015) 14–20
Fig. 1. Experimental arrangement: (1) critical orifice, (2) pre-pressure area, (3) expansion chamber, (4) impaction chamber, (5) velocity measurement cell, and (6) impaction plate and sampling on TEM grid.
Fig. 2. Velocity measurement cell: (1) particles from MBA, (2) photomultiplier, (3) beam trap, (4) impaction plate, and (5) laser and optical components.
that leads to a critical orifice through which the agglomerates were introduced into a low pressure region sustained by a vacuum pump. Since the pre-pressure conditions determined the impaction velocity of the agglomerates, a valve was used upstream of the pump to regulate the pump power. From this pre-pressure area the agglomerates were sucked through a capillary into the MBA. When entering the expansion chamber (p1 in the range of to 5 10 4–3 10 3 mbar) a molecular beam was formed and its center was transferred into the impaction chamber by passing a skimmer. The impaction chamber opened out into the velocity measuring cell where the velocity of agglomerates was measured in a light barrier before they impacted on a plate. On this plate a TEM grid for sampling can be adjusted. The pressure p2 in the impaction chamber and measuring cell was about 10 6–1.2 10 5 mbar. 3.3. Velocity measurement The velocity measurement was implemented into an anodized aluminum cube with openings to five sides (Fig. 2). The measurement was performed with a light barrier employing two laser beams in parallel and a sensor to detect the scattered light. A continuous SSDP-Laser with a wavelength of 457 nm was used (MBL-W-457, PhotonTec Berlin GmbH) as light source and was adjusted to a power of 3 W. The single laser beam passed a polarization device and a beam splitter in series and entered the velocity measuring cell as two parallel and polarized beams. The split beams each had a power of 1.5 W. A beam trap opposite to the laser inlet plane stopped the laser light. Perpendicular to the laser beams a photomultiplier (P30CW5, Sens-Tech Limited) was mounted to detected light that was scattered by passing agglomerates. Background noise from light scattered by windows was reduced by configured anti-reflexion windows and apertures. The photomultiplier was connected to a USB oscilloscope (PicoScope 4224, pico Technology) which recorded the voltage in dependence of time for agglomerates passing the light beam once an arbitrary threshold in voltage was exceeded. Since the intensity of each laser beam was Gauss distributed the peaks were symmetrical in shape and a matlab code determined the time of flight (tof) from the time between two signal peaks. With a tof and the distance between the laser beams of dbeam ¼4.0 mm the particle velocity vp was calculated as follows: vp ¼
tof dbeam
ð3Þ
On the basis of several hundred velocities a velocity distribution was calculated and the arithmetic mean velocity was used for calculating the kinetic energy of the agglomerates. Due to high vacuum conditions, the measured velocity vp was equal to the actual velocity of impaction and no correction of the measurements was required. Impacted agglomerates were sampled on a TEM grid simultaneously (Fig. 1, position 5).
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Fig. 3. Voltage signals of tof measurements.
3.4. Determination of the degree of fragmentation The degree of fragmentation was determined by the analysis of TEM images. By diffusion reference agglomerates were sampled to ascertain that they were representative for the unfragmented initial state. Impacted and fragmented agglomerates were collected on TEM grids on the impaction plate. For both cases the number of interparticle contacts within an agglomerate and the number of primary particles were investigated by TEM image analysis. The degree of fragmentation S was calculated by Eq. (4). The ratio of the number of primary particles to the number of interparticle contacts is a measure for the intactness of the agglomerates. The quotient of this ratio for impaction to reference describes the percentage fraction of unbroken contacts. number of primary particles=number of interparticle contacts impaction S ¼ 1 ð4Þ number of primary particles=number of interparticle contacts ref erence
3.5. Agglomerate characterization In order to validate the assumption of aerodynamic transparency, the free software Image J was used to perform a fractal box count analysis on the reference agglomerates. For Pt agglomerates a fractal dimension Df of 1.76 was revealed. Hence the agglomerates exhibit an aerodynamic behavior that is determined by the primary particle size (Reuter-Hack et al., 2007). The energy available for the breakup of interparticle bonds is the kinetic energy of the primary particles and is calculated by Ekin ¼ ¼
1 π U U x3 U ρp Uv2p 2 6 50;0
ð5Þ
From TEM image analysis the particle size distribution of primary particles was obtained and x50;0 gathered from it. The density of the bulk material ρPt ¼21.45 g cm 3 was utilized.
3.6. Results – velocity In Fig. 3 representative voltage peaks of the velocity measurement over time are depicted. A shift to shorter flight times, respectively higher vp, with increasing pre-pressure is observed. Figure 4 shows the resulting vp in dependence on the prepressure. vp behaves inversely proportional to ppre since a lowered gas density provides less molecules for momentum transfer that is responsible for particle acceleration. The range of adjustable velocity was limited by the pre-pressure. The atmospheric pre-pressure set the upper limit for the velocity whereas the lower limit was determined by the power of the pump generating the pre-pressure. The primary particle mass and the range of pre-pressure confine the range of kinetic energies achievable for fragmentation experiments.
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Fig. 4. Particle velocity adjusted by pre-pressure.
Fig. 5. Fragmentation of Pt.
Table 1 Theoretical and experimental energies.
Pt Pta a
x50,0 (nm)
vmin (m s 1)
Ekin,min, 10 19 J
E vdW 11, 10 19 J
E kin; min =E vdW 11 (dimensionless)
23.3 24
27.6 27.4
537.1 582.8
9.7 10.0
55.4 58.3
Seipenbusch et al. (2007).
3.7. Results – fragmentation For Pt agglomerates fragmentation experiments under vacuum conditions have been performed. In Fig. 5 the degree of fragmentation is plotted over the mass specific kinetic energy. The maximum degree of fragmentation is 73%. Noticeable is the decrease in the degree of fragmentation raising the energy input from 11.5 to 14.5 kJ kg 1. Considering the range of error it is debatable how much attention should be paid to this observation. On the other hand, rebound of particles after impaction is an investigated incident (e.g. Rennecke & Weber (2013b), Ihalainen, Lind, Arffman, Torvela, & Jokiniemi, 2014) and it is assumed to cause the observed behavior. Recoiling primary particles might evade the TEM image analysis, leading to an underestimation of the degree of fragmentation. 2 Nevertheless, a Weibull fit corresponding to Eq. (1) was employed. By plotting ln(1 S) over vp the minimum impact velocity vmin necessary to break an interparticle bond can be determined. In order to estimate the error in vmin, the standard deviation endpoints of the measured velocities were used for two further Weibull fits. The mean vmin was found to be 27.6 m s 1 (þ0.7 m s 1, 21.1 m s 1). With Eq. (2) the theoretical binding energy according to van der Waals for two spherical particles was calculated. The required Ekin,min exceeds the theoretical value EvdW 11 by the factor of 55.4 (Table 1). The error estimation delivers an excess by the factor of 58.2 for the upper error, respectively 3.1 for the lower error. A slightly raised need of energy for bond breaking can be explained by the energy transformation during impaction since plastic deformation occurs before breakage of interparticle bonds sets in. As TEM images show, energy is spent on the deformation of the TEM grid surface as well (Fig. 6). Furthermore it is considered that parts of the energy are converted into heat during impaction.
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Fig. 6. (Left) cracked carbon film after impaction of Pt agglomerates; vp ¼ 116 m s 1 and (right) Pt agglomerate.
Therefore, there are energy transforming mechanisms acting besides deagglomeration. However, the Ekin,min exceeds the EvdW 11 55 times which might not be caused by additional energy consumption alone. Due to the inert nature of Pt, the surface of Pt agglomerates is expected to be pure even under non-reducing N2 conditions (Seipenbusch, Weber, Schiel, & Kasper, 2003). Therefore, oxidic impurities will not retard sintering and the formation of small material bridges between primary particles might occur even under room temperature conditions. However, high resolution TEM images of Pt agglomerates could not reveal material bridges to confirm this theory (Fig. 6). A comparison of the present results to the work of Seipenbusch et al. (2007) gives good agreement regarding the Ekin,min to EvdW 11 ratio (Table 1). In contrast to the present work, the cited authors calculated the impact velocity by the 0.85 rule of Marple's. As both methods lead to similar results, an adequate precision of Marple's rule of 0.85 for the calculation of the impact velocity is concluded. 3.8. Summary A MBA was employed to conduct impact fragmentation experiments on Pt soft-agglomerates under high vacuum conditions. The Pt aerosol was created by a spark discharge generator, a sintering furnace and an agglomeration tank to obtain loose agglomerates. The degree of fragmentation was gained from TEM image analysis whereas the particle velocity was measured via a light barrier in front of the impaction plate. The tof measurement provided precise registration of the particle velocity, which was adjusted by variation of the pre-pressure. The experimentally gained binding energy exceeded the theoretical van der Waals energy by the factor of 55.4. Sintering of pure Pt surfaces under room temperature conditions, leading to material bridges between primary particles, was suspected to strengthen Pt agglomerates but could not be detected by TEM images. Certainly energy consuming mechanisms like plastic deformation and heating through impaction are responsible for a raised Ekin,min. However, the result showed good agreement with the work of Seipenbusch et al. (2007), suggesting a satisfying accuracy in the determination of the impact velocity by applying Marple's rule of 0.85.
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