Microscopic Measurement of the Homogeneity of Nanoscale Mixtures

Dec 15, 2010 - E-mail: [email protected](B.D.); [email protected] (H.N.). ... Björn Daumann , Jörg Andreas Weber , Harald Anlauf , Herma...
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Ind. Eng. Chem. Res. 2011, 50, 877–882

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Microscopic Measurement of the Homogeneity of Nanoscale Mixtures B. Daumann* and H. Nirschl* Karlsruhe Institute of Technology (KIT), Institute for Mechanical Process Engineering and Mechanics, D-76128 Karlsruhe, Germany

Powder mixing is a typical operation in particle technology. This work presents a method for the determination of the homogeneity of dry nanoparticle powder mixtures to measure the limit of mixing quality. The research results given here reflect the experimental effort required to study nanoscale solid mixtures consisting of a two-component system of Aerosil 200 and the titanium dioxide additive P25. The experimental effort can be evaluated by means of statistical methods. The parameter measured is the so-called homogeneity or mixing efficiency. It is determined by means of an energy-dispersive X-ray spectroscopy detector attached to a transmission electron microscope. The results will show that the optimal homogeneity depends on the additive concentration, the magnification of the transmission electron microscope, and the number of agglomerates, which have to be analyzed. 1. Introduction Dry particle systems are mixed in diverse industrial sectors and various technical devices are available for this purpose. For instance, industrial solid mixing processes are applied in the ceramics, basic chemical, construction materials, pharmaceuticals, cosmetics, feed stuff, and food industries. In cases where a high mixing homogeneity is required high-shear mixers are the machines which are in general used for this purpose. In these high-shear mixers,1-3 the strong interactions of van-der-Waals forces and electrostatic forces can be specifically influenced. Solid mixing is in general defined as the distribution of one or several solid components in a bulk matrix. In the past 40 years, numerous research results have been published relating to powder mixtures with particle sizes of higher than 1 µm in comprehensive reviews.4-9 1.1. Reference over Nanoscale Mixing and Measurements. The first authors10 to discuss nanoscale powder mixing demonstrate that it is very difficult to get homogeneous solid mixtures from particle sizes of smaller than 1 µm in high shear mixers. All known measurement methods of nanotechnology have been applied for the studies in this work. A result of these studies was that the RESS-process (Rapid Expansion of Supercritical Solutions) has emerged as an alternative process for the generation of homogeneous mixtures of very fine particles. The authors have shown in another publication that in the comprehensive studies, defined particle sizes can be adjusted in particle mixtures by the RESS-process.11-13 In other studies, the authors used a defined impact of influence on the nanoparticle structure14 in the gas phase to modify particles. In a study of mixtures of particles higher than 1 µm plus Aerosil, nanoparticles have been evaluated using atomic force microscope (AFM).15,16 Mixing efficiency is reflected by the decreasing adhesive force. Other authors17,18 have used host particles with guest particles by using electric fields to generate coated particles. It was found that the energy introduced by the impact changes the distribution of the nanoparticles and structural properties. These studies17,18 were not concerned with the homogeneity of the mixture. * Address correspondence to either author. Phone: +49721-6082400. Fax: +49721-608-2403. E-mail: [email protected](B.D.); [email protected] (H.N.).

1.2. Reasons for This Study. Frequently, a nanoscale particle component is applied as an additive, i.e., it is mixed with a coarser scale particle matrix. The structure of the nanoparticles also has a significant influence on the resulting interactions.19 According to current studies of powder mixing technology, the solid particles20 to be distributed tend to become smaller and measurement methods are consequently facing considerable challenges. In recent years, significant progress has been achieved in the synthesis and use of nanoscale materials. In the meantime, such particle systems have become an integral constituent in the fabrication of innovative products in plastics technology, electrical engineering, and biotechnology. The current study could potentially provide a decisive criterion for evaluating the quality of products generated by industrial mixing processes. The experiments described are intended to show how ultrafine solid components with defined structures can lead to improved mixing efficiencies and product properties. Investigations will be made into the way in which dry nanocomposites at interfaces can be influenced, such that a specific mixing structure and homogeneity result. Demixing effects in powder mixtures, i.e., undesired dust formation during mixing or undesired adhesive forces of nanoparticles on vessel walls, often cause deterioration in product properties and reduced product yields. To evaluate mixtures of nanoparticles, it is reasonable to couple transmission electron microscopy (TEM) with an image evaluation and energy-dispersive X-ray spectroscopy (EDX). This mixing study of nanoscale dry particle systems should be a fundamental characterization method to measure mass concentration according to the theory for powder mixtures. An application of this basic method is the lacquer industry18 and mixtures of lithium-ion batteries21 to measure the mixing quality after high shear mixing. In the appendix, the established theory of powder mixing is discussed. Equations 1-3 may be applied to the removal of samples from a powder mixer. Weighing of the solid components is a very frequently used method if the components have free-flowing conditions. The difference to nanoscale products is this weighing method cannot be used to find an optimal sample. The reason is the very fine particle size. All sample sizes that can be balanced are too large to find a difference in homogeneity. If the balance method at every mixing time is applied, then the result will be a random mixture. For nanoscale mixing, the authors defined the agglomerate size

10.1021/ie1013579  2011 American Chemical Society Published on Web 12/15/2010

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Figure 2. Illustration of the two high shear mixing tools for the high shear mixer 1: (a) star agitator, (b) pin agitator.

Figure 1. Illustration of the high shear mixer 1.

as a limit of powder mixing. In the subsequent sections, the authors explain the experimental effort that is necessary to characterize nanoscale mixtures. 2. Test Apparatus, Test Product for the Experiments 2.1. Design of High Shear Mixer 1. A high shear mixer 1 (Eirich-high shear mixer, Hardheim, Germany), as shown in Figure 1 is used to carry out the mixing tests. The volume V of the high shear mixer is around five liters (V ) 5 L). The mixer consists of a rotating mixing vessel (1), a fast rotating eccentric mixing tool (2) and a wall scraper (3). Both the revolutions per minute nV ) 5-87 rpm at the mixing vessel and nA ) 250-4800 rpm at the mixing tool are independently infinitely variable. The most notable feature of the high shear mixer is the very high circumferential velocity of the agitator which is up to 40 m/s. The control of the high shear mixer allows the agitator to be operated in counter-current flow as well as in cocurrent-flow to the mixing vessel. By the rotation of the mixing vessel, the product under test is transported into the intensive zone, i.e., toward the mixing tool. The wall scraper is a static tool that prevents and removes any product which may become stuck to the vessel wall. Two differently shaped mixing tools as depicted in Figure 2 are used in the investigations. Figure 2a shows the star agitator and Figure 2b the pin agitator. The diameter of the mixing tools are DW ) 135 mm and DW ) 125 mm, respectively. The star agitator produces a radial mixing action with cutting- and impact stress. The pin agitator produces an axial mixing action that subjects the product to high shear stress. 2.2. Design of High Shear Mixer 2. The second high shear mixer has a nominal volume of 0.5 L. It is illustrated in Figure 3. The producer of this mixer is the Diosna Dierks & So¨hne GmbH, Osnabru¨ck, Germany. The mixer consists of two mixing tools which are mounted in a mixing vessel. The three-bladed mixing tool imparts a circulatory motion to the material being mixed. The horizontally rotating mixing tool brings about an intense fluidization of the product. The three-bladed horizontally rotation central mixing tool in Figure 3a has a diameter of DW ) 109 mm by a circumferential velocity of 1.4 m/s. The coneshaped product vessel in the upper section is aimed at further

Figure 3. Illustration of the high shear mixer 2.

promoting mobility of the product. A chopper as depicted in Figure 3b (intensive mixing tool) mounted on the side wall of the mixing receptacle breaks up any agglomerates that form by generating a high impact stress. This mixing tool has a diameter of DW ) 15 mm. Revolutions per minute is infinitely variable up to nM ) 1200 rpm for the three-bladed mixing tool and up to nC ) 2200 rpm for the chopper. The mixing time is likewise freely selectable. 2.3. Dry Nanoparticle Powders and Measurement Mixing Quality. In this work, Aerosil 200 is used as a filler material, while the other nanoparticle component, titanium dioxide P25, is applied as an additive. The reason for the two nanoscale components is that many authors10,22 worked with these components to compare their research works with the present study. The additive mass concentration varies between c ) 1% and c ) 10%. With these well-known nanoscale components the authors will test whether a limit of mixing can be measured with EDX-spectroscopy by different parameter conditions. Table 1 lists the product properties, such as the primary particle diameter xP, the agglomerate diameter xF,50 (maximum Feret diameter), the solid density FS and bulk density FB of the material. Titanium dioxide P25 possesses hydrophilic properties at the interface, while Aerosil 200 possesses hydrophilic silanol groups. Both nanomaterials show strong interparticle interactions, arising from van-der-Waals and electrostatic forces.18 Titanium dioxide P25 possesses both free and bridged OHgroups, indicating that titanium dioxide is of hydrophilic nature. Electrostatic and van-der-Waals interactions also are strong in titanium dioxide. The products mentioned are manufactured by Evonik Degussa GmbH, Germany. The agglomerate size, distribution, and fractal dimension23 are determined from the digital images recorded by a transmission electron microscope (TEM) made by Philips CM12 (Company Fei) with the help of

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Table 1. Material Parameters of the Nanoparticles

Figure 4. Determination of the mass-related concentration of (a) Aerosil 200 and titanium dioxide P25 from a mapping result, (b) example of an EDX-spectrum of the two components for around 10-20 agglomerates.

the Image J program and the Frac-Lac algorithm.24 The agglomerates counted for each measurement point vary between 3000 and 8000 particles.23 The main agglomerate size from mixing this nanoscale powders is in the size range of 120-200 nm. The agglomerate number in this work exists for all particles which are significant greater than the primary diameter. The measuring accuracy24,25 is mainly influenced by the EDX-detector. The limit for measuring mass concentrations of agglomerates is ∼50 nm. In the mixing experiments performed, mixing times tM are investigated up to a maximum of tM ) 450 s. Every measurement point consists of a single mixing test with at least three repetitions. Mass-related concentration of the mixtures can be determined using an energy-dispersive X-ray detector (EDXdetector), type Xflash 5030, made by Bruker AXS, Berlin in Germany. 3. Results and Discussion by Using EDX-Spectroscopy 3.1. Sample Preparation and Influence Parameter to Characterize Nanoscale Products. The EDX-detector is attached to a transmission electron microscope (TEM). For the measurement of the TEM-grids, a low-background sample holder is used, which reduces backscattering via a beryllium window. The sample is installed under a tilt angle of 15° to the horizontal of the detector. Pole shoe alignment of the transmission electron microscope (TEM) is of the twin lens type. The TEM-grids are made of copper and a polymer film. The calculation of the measurement time per EDX-spectra has two conditions, one of which has to be fulfilled. The abort criteria are 2 min measurement time or the sum of the count rate from titanium and silicium peaks of more than 10 000 counts per electron voltage (eV). It is known from preliminary experiments that sample preparation on the TEM-grid could be crucial, since it is not possible for the user to control how many particles are, or how high the loading is, on the grid. The above product properties of the nanoparticles have a decisive influence on the interfaces and, hence, on the mixing result. Consequently, the products have to be prepared prior to every experiment, such that air humidity, for instance, does not affect subsequent results. When using high-shear mixers, gaseous nitrogen is fed into the mixing volume prior to the experiment. Controlled boundary conditions of humidity and

temperature are applied during the mixing experiments. After a displacement phase and waiting time, a nitrogen atmosphere develops. At an air humidity of e50%, however, the nitrogen atmosphere has no influence on the test results, according to detailed studies23 carried out. According to the literature,26,27 however, an influence on the interactions by capillary condensation can only be measured at a relative air humidity of g50%. Adhesive forces, such as van-der-Waals interactions, are no longer dominant at high relative air humidity. Consequently, the products have to be dried prior to each experiment. In this way, adsorption of humidity in the fine capillaries (Kelvin effect) does not have any influence on the particle properties and mixing results. To determine microscopic mixing efficiency, detailed imaging is required for the individual agglomerates formed. Figure 4a shows the two-component mixture described, consisting of Aerosil 200 and titanium dioxide. It is evident from this figure that the additive particles are not distributed homogeneously. An agglomerate number of around 3000 was found to be necessary to make a statistically reliable statement with regard to homogeneity. At an additive concentration of c ) 1%, this corresponds to a minimum variation coefficient of the ideal random mixture of νZ ≈ 18%. Evaluation of the spectra according to Figure 4b reveals the concentration differences. Having the high number of EDXspectrograms, it is not possible to determine the concentration from a single agglomerate. The agglomerate number varies between 10 and 20 per EDX-spectrum. To determine the homogeneity, the total agglomerate number should be nearly constant at each measurement point. This determination of concentration with EDX-detector constitutes a compromise between magnification, measurement time for each EDXspectrum and the signal-to-noise ratio. The carbon peak in the spectrogram according to Figure 4b was caused by the polymer film of the TEM-grid. 3.2. Limitation and Influence Parameters to Measure the Homogenicy of Nanoscale Powders. In a first step, in Figure 5a, magnification of the transmission electron microscope was varied in order to attain the optimal magnification for the analysis of a high number of agglomerates. The error determined by the studies is the variation coefficient of the ideal random mixture νZ. If the magnification factor is chosen to be 7000-fold, the number of agglomerates which should be measured is ∼8000. The ideal random mixture according to eq 3 in this case is reduced to approximately VZ ≈ 12%. See Appendix. When determining the spectra, it is found that the backscattering of the sample excited by the electron beam is not sufficient to reach high intensity for these materials. An optimal signal-to-noise ratio can be attained with a magnification factor of 25 000×. At a magnification of

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Figure 5. Influence of the magnification of the transmission electron microscope on the determination of mixing efficiency at nA ) 3000 rpm and an additive concentration of c ) 1%. (a) mixing efficiency (not normalized) and (b) mixing efficiency (normalized).

Figure 6. Mixing efficiency in high-shear mixers of varying energy consumption at an additive concentration of c ) 1%, (a) high-shear mixer 1 and (b) high-shear mixer 2.

7000×, the spectra always exhibit stronger demixing (higher variation coefficients). At increased resolution, background scattering is reduced, which results in a reduced variation coefficient, because the high background scattering. When increasing the magnification factor to 53 000×, the spectrograms reveal the agglomerate number to be too small. The ideal random mixture increases to νZ ≈ 63% for the maximum of 250 agglomerates. The magnification 53 000× was not selected because the number of agglomerates seemed from a statistical point of view too small. This result is also obtained when evaluating the mixing efficiencies starting with Figure 5b. This variation coefficient is normalized to the variation coefficient determined by (ν)/ (νZ). The highest resolutions can apparently be reached at high magnification, but this resolution depends on the variation coefficient of the ideal random mixture νZ. The value of this variation coefficient νZ by 53 000× is higher than by lower magnification. The result is that the ratio between the variation coefficient ν and the variation coefficient νZ is smaller compared to the other magnifactions. The local resolution of the EDX-detector for the respective sample and the number of agglomerates to be evaluated are important for the determination of the microscopic mixing efficiency of nanoscale mixtures. For a reasonable determination of mixing efficiencies of dry nanoparticles in highshear mixers, a resolution factor of 25 000× was chosen, as this is the range at which homogeneity is achieved. Figure 6a,b shows the respective mixing efficiencies of two different high-shear mixers.23 Both high-shear mixers differ in the energy supplied to the nanocomposites. Energy input can be varied by the rotation speed, as shown in Figure 6a. The results reveal that a certain energy input is needed for the homogenization of the nanoparticle mixture. It appears that a maximum of application of energy exists, since the value of the homogeneity cannot be reduced by a rotation speed higher

than 2000 rpm The minimum rotation speed amounts to approximately 2000 rpm for homogenization in the high-shear mixer used here. It can be easily seen that the possible number of revolutions in the high-shear mixer shown in Figure 6b is not sufficient to achieve a homogeneous end mixture. Otherwise, mixing efficiency would decrease with time and not become stationary after about tM ) 60s mixing time. When increasing the target concentration from c ) 1% to c ) 10%, homogeneity is changed, see Figure 7a. By varying the additive concentration c, both ultimate homogeneity and the ideal random mixture are reduced. This can be explained by the theoretical eqs 1-4. See Appendix. A higher additive concentration causes an increased concentration gradient that promotes concentration balancing. Nanoscale mixtures with higher concentrations exhibit reduced demixing. This result is put into perspective if the variation coefficients ν are normalized to the variation coefficient νZ, as illustrated in Figure 7b. It is found that the values measured at a higher additive concentration are closer to the random mixture. This is explained by the fact that the mixing requirements will be increased with lower concentration to obtain a homogeneous mixture. 4. Conclusions The research results given here reflect the experimental effort required to study nanoscaled solid mixtures consisting of a two-component system. It is determined by means of an energy-dispersive X-ray spectroscopy (EDX) detector attached to a transmission electron microscope (TEM) to characterize the nanoscaled mixture. The measurements of the mass concentration exhibit that it is necessary to comprise the statistic parameters and the measurement boundary conditions of the electron microscope. In this work, the established theory of powder mixing should be used. This

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Figure 7. Mixing efficiency at variable concentrations in the high-shear mixer 1 with a rotation speed of nA ) 3000 rpm High-shear mixers with variable energy consumption at an additive concentration of c ) 1%. (a) Mixing efficiency (not normalized) and (b) mixing efficiency (normalized).

work shows the limit of powder mixing that is possible to define in a sample volume and the homogeneity of a nanoscale powder mixture. The homogeneity by using this equipment depends on the magnification of the electron microscope and the number of agglomerates for the determination of the variation coefficient. The mixtures were stressed in two high shear mixers to measure the statistic values. It is evident that higher shear forces reduce the statistic parameters, which means that lower segregations are measurable. With this method of measurement, it is possible to characterize mixing samples of nanoparticle products. Appendix In this section the established theory of powder mixing to measure mixing qualities is discussed. Homogeneity can be determined from the variance σ2 or the variation coefficient ν by statistical methods of powder mixing technology.28,29 The variance σ2(ci,tM) is calculated by forming the sum of the squares of standard deviations according to eq 1 with the target concentration c for the individual samples NS. The mixing efficiency then results from the determination of the variance σ2(ci,tM) with various mixing times. The variance exists only theoretically because its actual determination requires an infinite number of samples NS, while in practice, only a limited number of samples NS can be studied. Therefore, the mixing quality is estimated by means of the empirical variance s2(ci,tM) on the basis of the existing analyzed samples. The result of the systematic variance σ2syst will be reduced by the mass of individual grain mI and sample mass mS, σ2(ci, tM) ≈ s2(ci, tM) )

1 · NS

NS

∑ (c

i

2 - c)2 ) σM + σ2Z +

i)1

(

1-

)

mI 2 · σsyst (1) mS

The variation coefficient ν is calculated from the quotient of the square root of the empirical variance and the target value concentration c (eq 2), V)

s(ci, tM) c

(2)

The variation coefficient of the ideal random mixture νZ is calculated, according to ref 22, from the mass of the individual particle mI, the sample quantity mW, and the target value c. For particles that have a monodisperse particle size distribution, eq 3 is used according to ref 22

VZ )

σZ ) c

VZ )





(1 - c) mI · c mW

(1 - c) · c

1 FS · · π · xV3 6 ≈ 18.2% 1 NS · FS · · π · xV3 6

(3)

NS ≈ 3000 particles;c ≈ 1% The measurement error is around VM ≈ 1% and has no influence on the steady state. The result clearly shows that the measurement error of the variation coefficient does not dominate the result, because the latter is smaller than the variation coefficient of the ideal random mixture νZ. The variation coefficient of the so-called zero mixture σ20, which, according to eq 4, characterizes the completely de-mixed state of a twin-component mixture, is also calculated from the target concentration c, V0 )

σ0 c

 (1 -c c) ≈ 9.94.

(4)

These equations will be modified for nanoscale agglomerates. It is not possible to balance a nanoscale product. Instead, the mass of an individual particle or sample mass, the agglomerate numbers will be used in eq 1-3. 6. Notation ci c DF mI mW nA nC nM nV NP NS s2 tM xF,50 xP

mass concentration of powder component i [-] target concentration [-] fractal dimension [-] mass of the individual component [g] whole mass of the component [g] agitator rotation speed [rpm] chopper rotation speed [rpm] mixer rotation speed [rpm] vessel rotation speed [rpm] number of particles [-] number of samples [-] empirical variance [-] mixing time [s] average agglomerate particle diameter at Q1 ) 50% value [nm] Primary particle size [nm]

Greek Symbols ν FB

variation coefficient [-] bulk density [kg/m3]

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σ2 σ20 σ2S σ2M σ2R

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variance [-] variance of zero mixture [-] systematic variance [-] variance of measurement value [-] variance of uniform random mixture [-]

Acknowledgment The authors gratefully acknowledge the financial support of the Deutsche Forschungsgemeinschaft (DFG NI 414/9-1). In addition, the authors would like to thank the company Eirich GmbH (Hardheim, Germany) for supplying the laboratory highshear mixer, in particular Dr.-Ing. S. Gerl and associates. The authors want to thank the Laboratory of the Electron Microscopy at the KIT, particularly its head, Prof. Dr.-Ing. D. Gerthsen and associates Dr. R. Schneider, Dipl.-Phys. W. Send for their technical assistance, in particular the measurement and analysis of the EDX spectrogram. They would also like to thank T. Lebe for assisting in the experimental setup as well as their young apprentice assistants for the particle characterization team. The invaluable advice of Prof. Dr.-Ing. K. Sommer, the leader of the institute process engineering TU Munich, is also gratefully acknowledged. Literature Cited (1) Habermann, R. NobiltasFeststoffmischen mit hohem Energieeintrag Teil 1. Keram. Zeitschr. 2007, 59, 254–259. (2) Habermann, R. NobiltasFeststoffmischen mit hohem Energieeintrag Teil 2. Keram. Zeitschr. 2008, 60, 10–13. (3) Habermann, R. Produktgestaltung von mikro- und nanoskaligen Pulvern durch (Hoch-) Intensivmischen mit hohem Leistungseintrag. Chem. Ing. Technik. 2009, 81, 849–854. (4) Fan, L. T.; Chen, S. J.; Watson, C. A. ANNUAL REVIEW Solids Mixing. Ind. Eng. Chem. 1970, 62, 53–69. (5) Fan, L. T.; Chen, Y.-m.; Lai, F. S. Recent developments in solids mixing. Powder Technol. 1990, 61, 255–287. (6) Pernenkil, L.; Cooney, C. L. A review on the continuous blending of powders. Chem. Eng. Sci. 2006, 61, 720–742. (7) Poux, M.; Fayolle, P.; Bertrand, J.; Bridoux, D.; Bousquet, J. Powder mixing: Some practical rules applied to agitated systems. Powder Technol. 1991, 68, 213–234. (8) Yano, T.; Sato, M.; Terashita, K. Recent work in Japan on the mixing of solids. Powder Technol. 1978, 20, 9–14. (9) Hogg, R. Mixing and Segregation in Powders: Evaluation, Mechanisms and Processes. KONA Powder Part. J. 2009, 27, 3–17. (10) Wei, D.; Dave, R.; Pfeffer, R. Mixing and characterization of nanosized powders: An assessment of different techniques. J. Nanopart. Res. 2002, 4, 21–41. (11) Yang, Y.; Wang, Y.; Dave, R. D.; Pfeffer, R. Mixing of nanoparticles by rapid expansion of high-pressure suspensions. AdV. Powder Technol. 2003, 14, 471–493.

(12) Sanganwar, G. P.; Gupta, R. B. Enhancement of shelf life and handling properties of drug nanoparticles: Nanoscale mixing of itraconazole with silica. Ind. Eng. Chem. Res. 2008, 47, 4717–4725. (13) Sanganwar, G. P.; Gupta, R. B. Nano-mixing of dipyridamole drug and excipient nanoparticles by sonication in liquid CO2. Powder Technol. 2009, 196, 36–49. (14) Froeschke, S.; Kohler, S.; Weber, P. A.; Kasper, G. Impact fragmentation of nanoparticle agglomerates. J. Aerosol Sci. 2003, 34, 275– 287. (15) Meyer, K.; Zimmermann, I. Effect of glidants in binary powder mixtures. Powder Technol. 2004, 139, 40–54. (16) Kurfess, D.; Hinrichsen, H.; Zimmermann, I. Statistical model of the powder flow regulation by nanomaterials. Powder Technol. 2005, 159, 63–70. (17) Linsenbu¨hler, M.; Wirth, K. E. An innovative dry powder coating process in non-polar liquids producing tailor-made micro-particles. Powder Technol. 2005, 158, 3–20. (18) Linsenbu¨hler, M.; Werth, J. H.; Dammer, S. M.; Knudsen, H. A.; Hinrichsen, H.; Wirth, K. E.; Wolf, D. E. Cluster size distribution of charged nanopowders in suspensions. Powder Technol. 2006, 167, 124–133. (19) Wood, J. Mixing nanoparticles for a variety of structures: Nanoparticles. Nano Today 2006, 1, 9. (20) Panagiotis, D. C.; Mingheng, l.; Ma¨dler, L. Control of particulate processes: Recent results and future challenges. Powder Technol. 2007, 175, 1–7. (21) Wu, L.; Li, X.; Wang, Z.; Wang, X.; Li, L.; Wu, J.; Guo, H. Preparation of synthetic rutile and metal-doped LiFePO4 from ilmenite. Powder Technol. 2010, 199, 293–297. (22) Du¨nsch, S. Untersuchung der Wirkungsweise von Nanomaterialien; Ph.D. Thesis, Universita¨t Wu¨rzburg, 2005. (23) Daumann, B. Untersuchungen zum Dispersions-und Transportverhalten von Feststoffmischungen unterschiedlicher Partikelgro¨βen in diskontinuierlichen Feststoffmischern. Ph.D. Thesis, Karlsruhe Institute of Technology (KIT), 2010. (24) Karperien A. Advanced User’s Manual http://rsb.info.nih.gov/ij/ plugins/fraclac/fraclac-manual.pdf. Charles Sturt University Australia, 2004. (25) Vanghan, D. Energy-Dispersive X-Ray Microanalysis An introduction, Thermo Noran (2008). (26) Go¨tzinger, M.; Peukert, W. Dispersive forces of particle-surface interactions: direct AFM measurements and modelling. Powder Technology. 2003, 130, 102–109. (27) Zhou, H.; Go¨tzinger, M.; Peukert, W. The influence of particle charge and roughness on particle-substrate adhesion. Powder Technology. 2003, 135-136, 82–91. (28) Hersey, J. A.; Cook, P.; Smyth, M.; Bishop, E. A.; Clarke, E. A. Homogeneity of multicomponent powder mixtures. J. Pharm. Sci. 1974, 63, 408–411. (29) Sommer, K. Sampling of Powders and Bulk Materials, Springer Verlag Berlin Heidelberg New York: Tokyo, 1986 ISBN 0-387-15891-X (U.S.).

ReceiVed for reView June 25, 2010 ReVised manuscript receiVed October 20, 2010 Accepted November 17, 2010 IE1013579