Discontinuous powder mixing of nanoscale particles

Chemical Engineering Journal 167 (2011) 377–387

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Discontinuous powder mixing of nanoscale particles Björn Daumann ∗ , Jörg Andreas Weber, Harald Anlauf, Hermann Nirschl Karlsruhe Institute of Technology (KIT), Institute for Mechanical Process Engineering and Mechanics, D-76128 Karlsruhe, Germany

a r t i c l e

i n f o

Article history: Received 4 March 2010 Received in revised form 29 November 2010 Accepted 9 December 2010 Keywords: Powder mixing Fractal dimension Nanoparticles Nano-mixing High shear mixer Nanostructure

a b s t r a c t The study presents an investigation of the nanoparticle mixing in discontinuous high shear mixers to measure the limit of mixing quality. The distinguishing feature of these mixers is high circumferential velocity with very high energy input. This property alone enables the dispersal of the two-component mixtures of commercially available nanoparticles under investigation. During the investigations, the question arose as to which measured variables, besides homogeneity, deliver a characteristic criterion for the determination of the mixing time of nanoparticle mixtures. The agglomerate distribution and the fractal dimension will be measured by a transmission electron microscope. The mass concentration of the solid mixture will be assessed by EDX-spectroscopy to obtain the mixing efficiency. The results indicate that the solid mixtures can be influenced significantly by the addition of an additive. The only correct way to characterize mixtures of particular powders is the determination of mass concentration. The other parameters, such as fractal dimension or agglomerate size, are not significant for the determination of the mixing efficiency. © 2011 Elsevier B.V. All rights reserved.

1. Introduction Various materials are mixed in different sectors of industry, and a variety of process engineering apparatus is available for this purpose. For example, industrial powder mixing processes are found in industries such as ceramics, basic materials, building materials, pharmaceuticals, cosmetics, feeding stuffs and foodstuffs. The mixer market offers a multitude of different units and mixing principles, so that even experts are challenged to identify the best possible solution for the given class of product. It is not just the mixer that needs to be considered when making a selection, but also the necessary infrastructure of bulk material bunkers, conveyor belts or weighing conveyors which turn a powder mixing process into a separate large-scale part of the plant. Regarding industrial considerations, very often the company philosophy, experience and/or investment and operating costs play an important role. In times of rising energy costs, the required energy consumption for a mixing process increasingly comes to the fore. Powder mixing is defined as the dispersion of two or more solid components in a bulk material matrix. Prerequisite for the mixing process, i.e. distribution of the components, is the relative motion between the different products. Strictly speaking, no material conversion takes place in a powder mixing process in relation to physical or chemical particle properties. The desired state or criterion to even describe a mixing process at all is the homogeneity

∗ Corresponding author. Tel.: +49721 608 4139; fax: +49721 608 42403. E-mail address: [email protected] (B. Daumann). 1385-8947/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.cej.2010.12.033

or mixing quality in a user defined sample mass. This target homogeneity has to be achieved in as short a mixing time as possible. This calls for analytical methods which either set forth standards or are user-related measured variables. The assessment of homogeneity is done with the aid of statistical parameters according to [1], which allow different types of mixer to be compared. In general, the finest component in the mixture of solids is the one that is the most difficult to homogenise or distribute. The reason for this is evident from the significantly lower mobility of the fine component. Very coarse bulk material exhibits mixing times of less than 60 s. This mixing task does not present high requirements on the respective powder mixer. Once the proportion of fine material in the mixture is increased from around 10% to 50%, the mixing time increases significantly to more than 300 s, in contrast to the usual figure of 60 s [2]. A major challenge is the dispersion of a low concentration of solids in a finely dispersed powder. To deal with this, mixer manufacturers supply high shear mixers or high performance shear mixers. A characteristic feature of them is a very high energy input as described [3–5], in order to achieve the optimum homogeneity. Over the past 40 years authors in the field of powder mixing have published a multitude of research results concerning the assessment of powder mixtures with particle sizes x > 1 ␮m, chronicled in extensive reviews by [6–12]. In the latest research on powder mixing technology there is a noticeable tendency that ever smaller solid matter particles according to [13] need to be dispersed, which presents a major challenge to the currently available measuring processes. Major advances have been achieved in recent years in the synthesis and application of nanoscale materials. Particle sys-

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Nomenclature Notations ci mass concentration of powder component i [–] c target concentration [–] fractal dimension [–] Df DC diameter of the chopper [mm] DW diameter of mixing tool [mm] mass of the individual component [g] mI mW whole mass of the component [g] n number of self-similar structures [–] nA agitator rotation speed [rpm] chopper rotation speed [rpm] nC nM mixer rotation speed [rpm] nV vessel rotation speed [rpm] number of particles [–] NP NS number of samples [–] Q1 length distribution [%] s2 empirical variance [–] mixing time [s] tM xP primary particle size [nm] xF,50 average agglomerate particle diameter at Q1 = 50% value [nm] x90 /x10 scattering parameter [–] Greek symbols ε linear size of one single structure [-]  variation coefficient [–] B bulk density [kg/m3 ] 2 variance [–] variance of zero mixture [–] 02 S2 systematic variance [–] 2 M variance of measurement value [–] R2 variance of uniform random mixture [–]

tems of this kind have now become a permanent feature in the manufacture of innovative products in plastics technology, electronics and also biotechnology. Very often a nanoscale particle component is also used as an additive, i.e. it has to be mixed with a more coarse-scale particle matrix. According to [14] the structure of the nanoparticle also has a decisive effect on the resulting properties. In [15] and [16] assessments have been made of particle mixtures for particle sizes x < 1 ␮m and x > 1 ␮m with the help of an atomic-force microscope (AFM). The quality of the mixing process can be seen in the progressive fall in adhesive force. Other authors such as [17,18] show that it is very difficult to maintain homogeneous powder mixtures of particle sizes x < 1 ␮m in currently available powder mixers. The methods of assessment used here are the principal known measurement methods of nanotechnology. The RESS-process (Rapid Expansion of Supercritical Solution) turns out to be a suitable mixing method, producing very homogeneous end results from ultra-fine particles. As a result of further investigations by [19] and [20,21] it is possible to establish defined agglomerate and particle sizes in particle mixtures using the RESSprocess. Other authors such as [22,23] coated carrier particles (host particles) and nanoparticles (guest particles) with electric fields, thereby producing defined particle composites. In [24] different particle sizes have been investigated for defined impact stressing of nanoparticles in the gas phase. From this it is evident that the energy consumption by the impact process alters not only the distribution of nanoparticles but also the structural properties. However, none of the investigations sheds any light on how the structure of nanoparticles forms, how homogeneity evolves over

time, or how nanoparticles can be manipulated at the bounding surface. This mixing study of nanoscale dry particle systems should be a fundamental characterisation method to measure mass concentration according to the theory of powder mixtures. Furthermore, the progression of the structure of agglomerates and average agglomerate size are investigated according to these high energy consumptions. To determine the quality of nanoparticle mixtures, it is necessary to know which measured variables constitute a suitable instrument for determining the mixing time. An application of this basic method is the lacquer industry [25] and mixtures of lithium-ion batteries [26] to measure the mixing quality after high shear mixing. The established theory of powder mixing is discussed in Appendix and the following section. Weighing of the solid components is a very frequently applied method if the components have free flowing properties. The difference to nanoscale products is that 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 establish a difference in homogeneity. If the balance method at every mixing time is applied, the result will be a random mixture. For nanoscale mixing the authors defined the agglomerate size as a limit of powder mixing. In the subsequent sections, the authors explain the experimental effort that is necessary to characterize nanoscale mixtures.

2. Theoretical basis for this nanoparticle study 2.1. Determining the homogeneity from measurements of concentration The variance  2 exists only theoretically since the number of samples NS that need to be taken to determine should be infinite. Since in practice only a limited number of samples NS can be examined, the mixing quality must be estimated by the empirical variance s2 according to Eq. (1). This is justified due to the high cost and considerable time that is needed to make a determination. As the number of samples NS increases, the empirical variance approaches the theoretical value: 1  · (ci − c)2 . Ns Ns

 2 ≈ s2 =

(1)

i=1

According to [1] the empirical variance s2 as per Eq. (2) is composed of three variances. The variance of the measuring process 2 comprises the reproducibility of the measured-value acquisiM tion and is determined by preliminary tests. As a rule this should be so small that only the variance of the uniform random mixture 2 has an influence on the system, and hence the variance R2  M 2 can be ignored. The systematic variof the measuring process M 2 ance s is time dependent and in its final stationary state has the value  2 = 0, i.e. the mixing process has finished. Reference should be made to [1] for calculation of the systematic variance s2 . A longer mixing time does not result in any further improvement in the mixing quality. During the mixing process the systematic variance is diminished by the single particle size mI and the sample mass mW . The variance  2 (ci ,tM ) is calculated by forming the sum of the squares of deviation of the target concentration c for the individual samples NS , which also emerges from Eq. (2a). By determining the empirical standard deviation s and dividing by the target concentration c, the variation coefficient  (relative deviation) of the mixing efficiency can be calculated according to Eq. (2b). Sampletaking strategies are suggested in [1] so that an assessment can be

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made of a sample’s homogeneity over the mixing time: 1  · (ci − c)2 Ns Ns

 2 (ci , tM ) ≈ s2 =

i=1



2 = R2 + M + 1−

 v=

 2 (ci , tM ) c

mI mW



· s2 (tM ),

(2a)

√ ≈

s2 c

  Ns   (1/Ns )· (ci − c)2 = 2 + 2 +(1−(mI /mW )) · s2 (tM ) R

=

M

i=1

c

. (2b)

Detailed information on the statistic theory of mixing can be found in Appendix. 2.2. The concept of fractal dimension In fractal geometry, the fractal dimension Df , is a statistical quantity that gives an indication of how completely a fractal appears to fill space as one zooms down to ever finer scales. There are many specific definitions of fractal dimension. The most important theoretical fractal dimension is the box-counting dimension and correlation dimension is widely used for areas or volumes, partly due to their ease of implementation. Although for some classical fractals all these dimensions do coincide, in general they are not equivalent. The term “fractal dimension” is sometimes used to refer to what is more commonly called the capacity dimension of a fractal, which is, roughly speaking, the exponent Df in the expression. In Eqs. (3a,b) n the number of self-similar structures and ε the linear size of one single structure that needs to cover the fractal structure. However, it can more generally refer to any of the dimensions commonly used to characterize fractals. In this research paper our limit ε stand for one image pixel. The algorithms of this complex theory found in the literature [27,28] and is to be programmed in the tool image J (http://rsbweb.nih.gov/ij/): n = εDf Df =

log(n) log(1/)

(3a)

Fig. 1. Illustration of the high shear mixer 1.

of the agglomerate is approximately similar to the entire agglomerate. The fractal dimension is therefore exact to any desired degree. The fractal dimension Df for a volume ranges between Df = 1 for linear chains of particles and Df = 3 for densely packed, spherical agglomerates. The digital recordings show the agglomerates in their most stable situation, projected onto a plane. On account of the two-dimensional projection, the fractal dimension of the evaluated agglomerates ranges between Df = 1 till Df = 2, i.e. Df = 1 for a chain and Df = 2 for an inherently closed surface.

(3b)

There are two main approaches to the generation of fractal structures. One is the growing of an object, and the other is the construction, from subsequent divisions, of an original structure. Here we follow the second approach to define the dimension of fractal structures. Since structural properties are just as important an influencing variable as homogeneity for nanoparticles, the fractal dimension reflects the shape of the agglomerates formed. For this purpose [29,30] introduced the fractal dimension to express the structures using real numbers. The majority of physical laws hold true only in “ideal” conditions. In solid-state physics, the notion of “ideal” is linked to regular structure and form, e.g. cube or ball shaped particles, cylindrical voids or a smooth particle surface. Of course, none of these prerequisites are normally fulfilled by the majority of existing substances. The introduction of form factors to describe irregular structures brought no significant advances, since there is no standard definition for form factors, and these are scale invariant. The fractal dimension presupposes a subordinate independence. According to [29], every portion of a form resembles the entire structure. This is also fulfilled by agglomerates of the finest particles, since a magnification of any given part

3. Test apparatus, test product and the use of metrology 3.1. Design of high shear mixer 1 A high shear mixer 1, as shown in Fig. 1 is used to carry out the mixing tests. The volume V of the high shear mixer is around five litres (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 rotation speed nV = 5–87 rpm of 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 is up to 40 m/s. The total quantity of product in this mixer in tests is around 200 g, which is to be stressed at speeds of nA = 250 rpm up to nA = 4000 rpm. The speed of the mixing vessel, which uses the co-current-flow mixing principle, is fixed at nV = 50 rpm. The control of the high shear mixer allows the agitator to be operated in counter-current flow as well as in co-current-flow to the mixing vessel. By the rotation of the mixing vessel the product under test is transported into the intensive zone, i.e. towards the mixing tool. The wall scraper is a static tool that prevents and

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Fig. 2. Illustration of the two high shear mixing tools for the high shear mixer 1. (a) Star agitator and (b) pin agitator.

removes any product which may become stuck to the vessel wall. Two differently shaped mixing tools as depicted in Fig. 2 are used in the investigations. Fig. 2a shows the star agitator and Fig. 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. 3.2. Design of high shear mixer 2 The second high shear mixer has a nominal volume of 0.5 L. It is illustrated in Fig. 3. 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 fluidisation of the product. The three-bladed horizontally rotation central mixing tool in Fig. 3a has a diameter of DW = 109 mm by a circumferential velocity of 1.4 m/s. The cone-shaped product vessel in the upper section is aimed at further promoting mobility of the product. A chopper as depicted in Fig. 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 DC = 15 mm. Unfortunately, a quantification of the impact stress is not directly possible but only via the integral of energy consumption. The agitator can attain a circumferential velocity of up to 2 m/s. Rotation speed 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. The total quantity of product in the mixer in these tests is around 15 g, which is to be stressed at the intensive mixing tool rotation speed of nC = 500 rpm up to nC = 2000 rpm. At lower rotation speeds not enough energy is available for homogenisation. The mixing tool’s rotation speed is around nM = 250 rpm. Higher speeds of the radial mixing tool cause a marked centrifugation of the product and prevent the chopper from imparting sufficient energy into the product. 3.3. Dry nanoparticle powders In this study, Aerosil® 200 is used as a filler material, while the other nanoparticle components, titanium dioxide P25 and Aerosil® R972, are applied as an additive. The reason for the two nanoscale components is that many authors [17,22] worked with these com-

Fig. 3. Illustration of the high shear mixer 2. Side view of the mixing vessel, plan view of the mixing vessel, radial mixing tool, and Intensive mixing tool.

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Table 1 Material parameters of the nanoparticles.

Product Primary particle size xP Agglomerate diameter xF,50 Fractal dimension Df Bulk density B Other properties Usage

Aerosil® 200 12 nm 292.5 nm ± 3% ≈1.91 ≈40 g/dm3 Hydrophilic Filler medium

ponents 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, fractal dimension and agglomerate size by different parameter conditions. All of these applied powders should be used and filled under an extractor hood. Table 1 lists the respective product properties such as the primary particle diameter xP , agglomerate diameter xF,50 (maximum Feret diameter), bulk density of the material B and interfacial property of the material. The titanium dioxide P25 is hydrophilic and the Aerosil® R972 hydrophobic at the surface. The property of differing hydrophobicity with the nanoparticles can be attributed to differing surface functionalisation. The Aerosil® 200 has hydrophilic silanol groups while the Aerosil® R972 has hydrophobic methyl silane groups. According to [22] both Aerosils have intermolecular interactions such as the Van-der-Waals forces and electrostatic interactions. The titanium dioxide P25 has free as well as bridged OH-groups. This shows that titanium dioxide has a hydrophilic character. Electrostatic and Van-der-Waals interactions are likewise pronounced in the case of titanium dioxide. The manufacturer of the products mentioned is Evonik Degussa GmbH. Digital images obtained via a transmission electron microscope (TEM voltage 120 kV) CM12 made by Philips (Company Fei) can be used to determine the respective measured variables from the projected areas via the Image J program and the Frac-Lac algorithm (http://rsbweb.nih.gov/ij/plugins/fraclac/fraclac.html). 3.4. Preliminary experiments of nanoparticle mixtures In the mixing tests carried out the maximum mixing time tM was around 450 s. Each measuring point consists of a single mixing test with at least three repetitions in each case. In determining the measured variables, the existing agglomerate size x50 can be determined from a longitudinal distribution Q1 and the scattering parameter x90 /x10 resulting from this. The change in the fractal dimension Df is also investigated. Via the time characteristic of these variables, a comparison is to be made against the required mixing efficiency from measurements of concentration. A determination of the mass-related concentration from the mixtures is possible using an EDX-detector (Energy Dispersive X-ray Detector) of type Xflash 5030 made by Bruker AXS. The detector is connected to a transmission electron microscope (TEM). A low-background probe holder with a beryllium window for reduced backscattering is used to measure the TEM-grids. The tilt angle of the probe is

Titanium dioxide P25 21 nm 141.5 nm ± 6% ≈1.79 ≈50 kg/dm3 Hydrophilic Additive

Aerosil® R972 16 nm 141 nm ± 6% ≈1.9–2 ≈45 kg/dm3 Hydrophobic Additive

around 15◦ to the horizontal for the detector. The pole shoe alignment of the transmission electron microscope is of the twin lens type. The TEM-grids used here consist of copper support grids and a carbon film. The calculation of the measurement time per EDXspectra 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). When determining the agglomerate size (Feret diameter) the resolution of the transmission electron microscope is always left at 7000-fold magnification. The resolution for a pixel then lies in the region of about 4 nm. The magnification is at around 25,000fold when determining the mass-related concentration and the fractal dimension. The minimum spatial resolution falls to approximately 1 nm per pixel. The reason for the different magnifications is that, when determining the agglomerate distribution, very small nanoparticles as well as very large conglomerations of particles contribute to this. A higher resolution is better suited for examining fine structure and concentrations because the spatial resolution increases. When making the determination, care has been taken to ensure that the exposure by the electron beam is always at about the same strength. Only via these means is it at all possible to have an automated image evaluation. To allow statistically reliable statements to be made for each measured variable, roughly 3000 to 8000 (depending on the magnification) agglomerates have been analysed per measuring point. The higher the magnification, the fewer particles can be analysed. This corresponds to the necessary number of particles that [31] recommends for determining the particle size distribution on the transmission electron microscope. A more detailed representation of the method to determine nanoscale mixture is to be found in [32]. 3.5. Sample preparation and influence parameter to characterize nanoscale products 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 the number of particles or the level of loading 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 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 the experiment. Controlled boundary conditions of humidity and temperature are applied

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Fig. 4. Measurement results of median values x50 over the mixing time tM with a concentration of additives c = 1% and the star agitator mixing tool in the high shear mixer 1 with varied agitator rotational speed, (a) pure Aerosil® 200, (b) mix of Aerosil® 200 and titanium dioxide P25, and (c) mix of Aerosil® 200 and Aerosil® R972.

during the mixing experiments. The powders and mixers are positioned in a controlled chamber. After a displacement phase and waiting time, a nitrogen atmosphere develops. At an air humidity of ≤50%, however, the nitrogen atmosphere has no influence on the test results. According to the literature [33,34], an influence on the interactions by capillary condensation can only be measured at a relative air humidity of ≥50%. Adhesive forces, such as Vander-Waals interactions, are no longer dominant at high relative air humidity. Consequently, the products have to be dried prior 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 of the individual agglomerates formed. 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 Z ≈ 18%. See Appendix. Having the high number of EDX-spectrograms, it is not possible to determine the concentration from a single agglomerate. The agglomerate number varies between 10 and 20 per EDXspectrum. 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 EDX-spectrum and the signal-to-noise ratio. For the determination of the agglomerate size and fractal dimension the program Image J will be used. The individual images will be reprocessed in the Image J, such that after the setting of a threshold value, only the single agglomerate remains preserved. In the image analysis, the threshold value defines the differentiability. The agglomerates were separated with the help of the image processing program. The threshold value of individual command sequences was defined in the course of prior experiments; these sequences should no longer be altered during the current experiments. It was possible to determine the agglomerate size and fractal dimension. 4. Results and discussion 4.1. Results of agglomerates and nanostructures According to Fig. 4, the stressing of the products by the star agitator in the high shear mixer 1 yields the following measurement results for the characteristic of the median value x50 . The tests showed that a time-dependent behaviour of the median value is yielded only with stressing by pure Aerosil® 200 as in Fig. 4a. It is also evident that increasing the agitator’s rotation speed has only a slight influence on mixing progress for pure Aerosil® 200. The aggregate sizes that form almost independently of the agitator’s rotation speed can be explained on the basis that inter-particle stresses exist which require only very slight shear and impact forces for disintegration. The limit of the particle size can be explained by reference to an agglomerate size which can be broken down

no further, the so-called “hard aggregate”. According to [35] this diameter is in the region of x50 ≈ 150–200 nm for pure Aerosil® 200. A similar test result is yielded by the two mixings with additives. In the mixings with additives as per Fig. 4b/c, the agglomerate size approaches the final value abruptly. The final value of the two hydrophilic particles in the stationary region of the diagram is around x50 ≈ 150 nm. With the mixture of Aerosil® 200 and Aerosil® R972 as in Fig. 4c the final value lies at around x50 ≈ 180–200 nm. The reason for the larger agglomerate size is the different electrical charging behaviour of the two different nanoscale materials, which generates an agglomeration process. The behaviour of the two materials is documented in [36,37,25]. These authors charged particular systems through a mixing process to obtain an agglomerate particle mixture. When a hydrophobic product such as Aerosil® R972 is added to Aerosil® 200, the agglomerate size becomes several nanometres larger. The homogenisation step that ensues parallel to this mixing process can be observed visually as a disintegration process. This becomes visible through an increase in the volume of the test products after every mixing test. This was especially noticeable with the hydrophilic particle mixtures. The effect is not so pronounced when hydrophobic product is added. Fig. 4c indicates a minimum of mixing time of tM = 50 s. The reason is the statistical instability of the determined agglomerates, since the highest error bars exist in Fig. 4a at a mixing time of 50 s. Many more schemas in the same context will follow in the research paper. Illustrations of the time characteristics of the scattering parameters x90 /x10 are omitted here since with all types of mixers and mixtures these are at about the same level as for x90 /x10 ≈ 6–8. When examining the median values as per Fig. 5a during the tests on the high shear mixer 2, it was evident that, as in the case of the high shear mixer 1, a median value of about x50 ≈ 150 nm prevailed. The time characteristic is not so pronounced here as in Fig. 4a, which can be explained by a faster disintegration phase due to the smaller mixing volume. According to Fig. 5b/c agglomerates of comparable size are formed when additives are used. With titanium dioxide these are about x50 ≈ 150 nm and with Aerosil® R972 approximately x50 ≈ 180–200 nm. The measured values as per Fig. 5c reveal a significantly smaller distribution in agglomerate size than those of Fig. 4c. This can be attributed to the smaller volume available in the high shear mixer 2, whereby smaller differences in homogeneity can be achieved. The evaluation of the fractal dimensions as per Fig. 6a–c yields the following measured values for the three mixtures. Only a single fractal dimension in the range 1 ≤ Df ≤ 2 is attainable by evaluation of the projected area. The fractal dimensions given here are median values of a distribution yielded when determining the structures. With the mixture of pure Aerosil® 200 as per Fig. 4a it is evident that the higher agitator rotation speed has low effect on the maximum measured longitudinal extension of the agglomerates. Shearing of the structural branches formed as per Fig. 6a is possible due to the higher agitator rotation speed. The fractal dimension exhibits a time characteristic. It is also clear, however, that the level of fractal dimension as per Fig. 4a at higher agitator rotation

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Fig. 5. Measurement results of the median values x50 over the mixing time tM with a concentration of additive c = 1% in the high shear mixer 2 with varied agitator rotational speed: (a) pure Aerosil® 200, (b) mix of Aerosil® 200 and titanium dioxide P25, and (c) mix of Aerosil® 200 and Aerosil® R972.

Fig. 6. Measurement results of the fractal dimension Df over the mixing time tM with a concentration of additives c = 1% and the star agitator mixing tool in the high shear mixer 1 with varied agitator rotational speed: (a) pure Aerosil® 200, (b) mix of Aerosil® 200 and titanium dioxide P25, and (c) mix of Aerosil® 200 and Aerosil® R972.

speeds than nA = 2000 rpm can be influenced towards smaller fractal dimensions. More rod-shaped agglomerates tend to be formed. This means that the individual branches of agglomerates, which arise due to interactions at higher energy consumptions, shear off or are able to fold into the agglomerate. At agitator rotation speeds nA = 3000 rpm or nA = 4000 rpm the higher energy consumption is no longer able to decisively influence the structure. It is apparently not possible to make the higher energy consumptions influence the structure. When merely c = 1% of additive is added as per Fig. 6b/c, the influencing effect of the agitator’s rotation speed on the structure is less pronounced. The structure of the agglomerates is protected by the titanium dioxide as shown in Fig. 6b. According to Fig. 6c the effect of adding c = 1% of Aerosil® R972 additive, which has hydrophobic interfacial properties, is to increase the fractal dimension. Evidence of this is the formation of a closed surface between hydrophilic Aerosil® 200 and hydrophobic Aerosil® R972. The fractal dimension therefore increases towards Df ≈ 2. The mixing intensity (agitator rotation speed) has no effect on the characteristic of the fractal dimension. At first this was interpreted as a segregation of hydrophilic and hydrophobic nanoparticles. However, [36,37,25] has measured that the two nanomaterials have a differing electrical charging behaviour. Aerosil® 200 is predominantly positively charged due to friction while Aerosil® R972 is negatively charged through contact charging. As a result, the two non-conducting materials are accumulated and activated agglomerates. The closed surface now formed is to be measured at an increased fractal dimension.

A similar characteristic for the fractal dimension is also ascertainable according to Fig. 7a–c with the high shear mixer 2. This is evident in the significantly lower maximum rotational and circumferential velocity of the high shear mixer. The operating method of the intensive mixing tool is unable to influence the structure sufficiently. This can also be observed by the fact that the nanoparticles in this mixer have more of an opportunity to avoid the intensive mixing zone than is the case with the high shear mixer 1. The fluidising solid matter resulting from the constructional geometry and mixing principle is not forced through the intensive zone sufficiently. The mixtures from additives as per Fig. 5b/c exhibit roughly comparable measured values of fractal dimension as for the high shear mixer 1. The addition of titanium dioxide P25 protects the structure. Adding the Aerosil® R972 increases the fractal dimension – an electrostatic charge is the explanation for this. Since the operating method of the high shear mixer 2 is insufficient to greatly influence the structure of the agglomerates, only the measured values of the high shear mixer 1 are investigated in the subsequent mixing tests. On changing the mixing tool from the star agitator to the pin agitator, it is shown that smaller median values can be achieved with a mixture of Aerosil® 200 and titanium dioxide P25 with a concentration c = 1% as per Fig. 8a, at various agitator rotation speeds. All of the median values are around x50 ≈ 125 nm. On account of its shape, the pin agitator can be considered a mixing tool with a good impact of shear stress, which means that smaller agglomerates can be produced. A similar measured value for median values is yielded when the concentration of additive is varied from c = 1% to c = 10%. Thus the median value can-

Fig. 7. Measurement results of the fractal dimension Df over the mixing time tM with a concentration of additives c = 1% in the high shear mixer 2 with varied agitator speed: (a) pure Aerosil® 200, (b) mix of Aerosil® 200 and titanium dioxide P25, and (c) mix of Aerosil® 200 and Aerosil® R972.

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Fig. 8. Measurement results of the median values x50 over the mixing time tM with the pin agitator mixing tool in an high shear mixer 1. The mix is Aerosil® 200 and titanium dioxide P25: (a) constant additive concentration of c = 1% with varied agitator speed and (b) constant agitator speed nA = 3000 rpm with varied additive concentrations.

not be greatly influenced with hydrophilic nanocomposites. This is also due to the fact that products such as Aerosil® 200 and titanium dioxide P25 exhibit a similar mixing behaviour. Comparison of the fractal dimensions as shown in Fig. 9a/b yields a comparable picture to that of the tests with the star agitator shown in Fig. 6b. No major difference compared to the tests with the star agitator is discernible, either when varying the agitator rotation speed or when varying the concentration of additive. This is also confirmed by the measurement results of median values. These cannot be manipulated much by the addition of the hydrophilic material, titanium dioxide. The measurement results also very clearly show that, despite a smaller agglomerate size of x50 ≈ 125 nm with the pin agitator as against x50 ≈ 150 nm with the star agitator, a self-similarity of the resulting structures is present during the disintegration process. Otherwise, roughly comparable fractal dimensions would not result. With the pin agitator and a concentration of around c = 1%, agglomerate sizes around x50 ≈ 150 nm are attainable with variation of the additive concentration c = 1% to c = 10% of Aerosil® R972. The mixing tool is no longer able to achieve such small agglomerates if more additive is added. The agglomerate size increases to roughly x50 ≈ 180 nm at an additive concentration c = 2%, as with the star agitator at an additive concentration c = 1% of Aerosil® R972. At higher concentrations of c = 5% and c = 10%, respectively, the agglomerate size settles down at around x50 ≈200 nm. The agglomerate size can be altered by adding the additive. At higher hydrophobic concentrations, the operating method of the intensive mixing tool is no longer adequate to produce smaller agglomerate sizes. The increase in agglomerate size can also be explained by the different electrostatic charge due to addition of the additive. With the tests in the high shear mixer 2 as per Fig. 7c, the characteristic

for the fractal dimension in Fig. 10b exhibits a similar behavioural pattern as in the high shear mixer 1 with the star agitator as in Fig. 6c. 4.2. Results of nanoparticle homogeneity The mixing efficiencies have been determined only for the mixture of titanium dioxide P25 and Aerosil® 200. The reason for this is that the mixture of Aerosil® 200 and Aerosil® R972 is not sufficient for the EDX-spectroscopy, since the two products consist of almost identical portions of chemical constituents. Fig. 11a shows the solids mixture with c = 1% titanium dioxide P25 as a function of the mixing time tM at star agitator mixing tool rotation speed nA = 1000 rpm to nA = 3000 rpm. The three mixing efficiencies show that a speed of nA = 1000 rpm is not sufficient to achieve an adequate final homogeneity. This is clear from the very high degree of segregation of the powder mixture. The final homogeneity can be reduced by increasing the mixing tool rotation speed, this being reflected in a drop in mixing efficiency over time. After about tM = 150 s mixing time, only a slight change in the homogeneity is observed. The final homogeneity can no longer be reduced significantly by higher rotation speeds, hence one must assume that the fine agglomerates can no longer be homogenised adequately. Equilibrium is established between disintegration and agglomeration of the nanoparticles. On changing from a high shear mixer 1 to a high shear mixer 2 as in Fig. 11b, there is found to be a significantly higher final homogeneity. Final homogeneity is reached after roughly tM = 60 s. If, as in Fig. 12a, the mixing tool is now changed from the star agitator to the pin agitator, it is found that the higher shearing forces due to this intensive mixing tool bring about a low reduc-

Fig. 9. Measurement results of the fractal dimension Df over the mixing time tM with the pin agitator mixing tool in the high shear mixer 1 from a mix of Aerosil® 200 and titanium dioxide P25: (a) constant additive concentration with c = 1% with varied agitator speed and (b) constant agitator speed nA = 3000 rpm with varied additive concentrations.

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385

Fig. 10. Measurement results of the median values x50 and the fractal dimension Df over the mixing time tM with the pin agitator mixing tool in an high shear mixer 1 from a mix of Aerosil® 200 and Aerosil® R972: (a) median values with constant agitator speed nA = 3000 rpm and with varied concentrations of additive and (b) fractal dimension with constant agitator speed nA = 3000 rpm and varied concentrations of additive.

Fig. 11. Measurement results of the mixing efficiency for the solids mixture of Aerosil® 200 and titanium dioxide P25 with an additive concentration c = 1% at varied agitator speeds: (a) in the high shear mixer 1 with the star agitator and (b) in the high shear mixer 2.

tion in the final homogeneity. The mixing time is neither shortened nor lengthened by the different intensive mixing tool. If the massrelated concentration of titanium dioxide P25 is now increased up to c = 10%, the final homogeneity is found to be smaller as in Fig. 12a. A higher additive concentration causes an increased concentration gradient that that which promotes concentration balancing. Nanoscale mixtures with higher concentrations exhibit reduced demixing. This result is put into perspective if the variation coefficients  are normalised to the variation coefficient Z , as illustrated in Fig. 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. The intensive mixing tool is able to better disperse the higher concentrations of titanium dioxide P25. The smaller the concentration of additive in the solids mixture, the greater the segregation state when the measured values are normalised on the random mixture. A level is formed that most likely corresponds to a basic segregation state and can be reduced no further. A homogeneous random mixture cannot be achieved in all mixing tests, because the operating method is insufficient to inhibit the interactions present due to Van-der-Waals- and electrostatic forces.

Fig. 12. Measurement results of mixing efficiency for the solids mixture of Aerosil® 200 and titanium dioxide P25 with an additive concentration c = 1–10% at constant agitator speed nA = 3000 rpm in the high shear mixer 1: (a) not normalised on random mixing and (b) normalised on random mixing.

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5. Improvement in powder mixing technology for dry nanoparticle mixtures If only the time characteristic of the agglomerate size is compared to the mixing efficiency, then it can be assumed that no relationship exists between the mixing efficiency and the agglomeration characteristic, since the mixing times are absolutely different. The measured values show very clearly that the pin agitator and star agitator mixing tools are able to produce different agglomerate sizes. The solid mixtures can be influenced significantly by the addition of an additive. The results show that the operating method is dependent on the high shear mixers to dissipate sufficient energy consumption into the material being mixed to manipulate the structure, which means that no homogenous mixtures of solids can be produced for the defined sampling region. It can be assumed that the ascertained homogeneity is related to the energy consumption, and is not directly linked to the structure property or agglomerate size. In all of the mixing tests performed on dry powder mixtures with the nanomaterials used, it is clear that the dominant interactions, such as electrostatic and Van-der-Waals forces, can only be influenced in a targeted fashion by materials with altered interfacial properties. Targeted adjustment of a product property is achievable in this range of particle sizes, with the intensive mixers used, mainly by the selective addition of additives. With particle sizes x > 1 ␮m, the main influencing variables for a targeted adjustment of the product property are the machine parameters. A certain energy consumption has to be present with nanoparticle mixtures for an influenceable structure or homogeneity to exist in the first place. Here this is mainly down to the interactions that arise due to electrostatic or Van-der-Waals forces. The results show very clearly that both minimum and maximum energy consumptions are needed for targeted manipulation of the solids mixture. The presumed maximum energy consumption value stems from the high shear mixer being unable to transfer the energy into the solids system and convert it into a lower homogeneity. The user of this type of mixing process needs to appreciate that the measured values obtained are stationary final values at the conclusion of the mixing test. What takes place kinetically during the mixing process cannot be described by the measured values. Selective halting of the kinetic process is not technically achievable with the existing test facilities. In this research work the authors are referring to the limit of powder mixing. The sample limit here is the agglomerate size. The research results indicate a variation coefficient from more than  ≥ 30%. This variation coefficient has to be reduced. If the mixing process should be improved (reducing segregation or variation coefficient), vacuum condition in the mixing vessel is a possible application. To conduct this procedure the Eirich high shear mixer is the first choice. The bulk density of the product and the particle impacts increase with this method. Through the increase of particle mobility in the powder, the likelihood of a homogeneous sample increases.

6. Summary Powder mixing is a typical operation in mechanical process technology. This paper deals with an investigation of the mixing behaviour of dry nanoscale particles. The research results given here reflect the experimental effort required to study nanoscaled solid mixtures consisting of a two-component system. The experimental expenditure can be evaluated by means of statistical methods. The parameters measured are the so-called homogeneity or mixing efficiency, the fractal dimension and agglomerate size. It is determined by means of an energy-dispersive X-ray

spectroscopy (EDS) detector attached to a transmission electron microscope (TEM). The properties of a mixture of nanoparticles are already influenceable through minimal changes in concentration. This is evident in an altered agglomerate size and fractal dimension. Evidence was obtained in mixing tests which showed that surface functionalisation of the nanomaterial is a crucial influencing variable in the production of dry nano-mixtures. The machine parameters of a high shear mixer are not a main influencing variable for particle sizes smaller than 1 ␮m. Machine parameters such as rotation speed are responsible for the structure and agglomerate size, but the final value is a stable plateau. The form of the mixing tool can influence agglomerate size but not as decisively as the product attributes. High shear stresses tend to be far better than impact stresses in producing smaller particles. The fractal dimension is more strongly influenceable by the high energy consumptions, since the agglomerate structures which form are able to shear off or fold down more easily than the entire agglomerate length. If a hydrophilic nanomaterial, in this case titanium dioxide P25, is added to a filler, here Aerosil® 200, the fractal dimension can be influenced and can be protected by the additive. The final values of the agglomerate sizes can be actively altered only to a minor extent. In the case of the Aerosil® R972 additive with a hydrophobic surface, the interfacial properties at different concentrations affect both the fractal dimension and the agglomerate size. The agglomerate size tends to be higher than in the case of titanium dioxide P25. The increase in the agglomerate size and fractal dimension can be explained as being due to the electrically differing charging processes of the two nanomaterials. The mixing efficiency of titanium dioxide P25 with Aerosil® 200 can only be influenced to a minor degree by different concentrations and mixing tools. It is evident that higher shear forces reduce the final variation coefficient, which means that lower segregations are measurable. The mixing efficiency results also demonstrate, however, that neither the time characteristic of the agglomerate size and fractal dimension are not linked to the homogeneity characteristic, nor are the mixing times in the characteristics comparable. Decisive in the case of dry nanomixtures and their determining variables is the product property, which influences the measured variables. Acknowledgements The authors gratefully acknowledge financial support by the Deutsche Forschungsgemeinschaft (DFG NI 414/9-1-3007726). In addition, the authors would like to thank the company Eirich GmbH (Hardheim, Germany) for the supply of the laboratory-high shear 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 the technical assistance, the helping for 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 characterisation team. Appendix A. In this section the established theory of powder mixing to measure mixing qualities is discussed. Homogeneity can be determined from the variance  2 or the variation coefficient  by statistical methods of powder mixing technology [1]. The variance  2 (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

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determination of the variance  2 (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 analysed samples. The result of 2 the systematic variance Syst will be reduced by the mass of individual grain mI and sample mass mS . The variation coefficient n is calculated from the quotient between the square root of the empirical variance according to Eq. (4) and the target value concentration c (Eq. (2a)):

v=

s(ci , tM ) . c

(4)

The result clearly shows that the measurement error of the variation coefficient Eq. (5) does not dominate the result, since the latter is smaller than the variation coefficient of the ideal random mixture Z . In determining the variation coefficient , one must therefore consider both the variance of the ideal random mixture Z2 and the 2 have an influence for the variance of the measurement method M steady state:

vM =

M ≈ 1% c

(5)

The variation coefficient of the so-called zero mixture O2 according to Eq. (6) completely de-mixed state of a twin-component mixture, is also calculated from the target concentration c:  v0 = 0 c



1−c ≈ 9.94. c

(6)

The variation coefficient of the ideal random mixture Z is calculated, according to [38], 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. (7) is used according to Stange:

vz =

z = c





=

1 − c mI · c mW . s · (1/6) ·  · xV3 1−c ≈ 18.2% · c NP · s · (1/6) ·  · xV3

NP ≈ 3000 particles;

(7)

c ≈ 1%

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