Characterizing Dispersion and Fragmentation of Fractal, Pyrogenic

Mar 20, 2007 - In this work a synchrotron ultra-small-angle X-ray scattering (USAXS) investigation on diffusion flame and 'Aerosil' silica powders, as...
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Langmuir 2007, 23, 4148-4154

Characterizing Dispersion and Fragmentation of Fractal, Pyrogenic Silica Nanoagglomerates by Small-Angle X-ray Scattering R. Wengeler,† F. Wolf,† N. Dingenouts,‡ and H. Nirschl*,† Institute for Mechanical Process Engineering and Mechanics, UniVersita¨t Karlsruhe (TH), D-76128 Karlsruhe, Germany, and Institute for Technical Chemistry and Polymer Chemistry, UniVersita¨t Karlsruhe (TH), D-76128 Karlsruhe, Germany ReceiVed October 19, 2006. In Final Form: January 30, 2007 Typical characterization of nanoparticle dispersion and compounding processes by dynamic light scattering (DLS) and TEM lack quantitative information on fractal structure, aggregation number, and specific surface area. In this work a synchrotron ultra-small-angle X-ray scattering (USAXS) investigation on diffusion flame and ‘Aerosil’ silica powders, as well as on their desagglomeration by high-pressure liquid dispersion (200-1400 bar) is presented. Primary particle size, polydispersity, and specific surface area are measured for powders, stirred-in dispersions, and after high-pressure processing with identical results, showing the in-situ applicability of USAXS. These parameters, as well as the hard aggregate mass fractal dimension, with typically Df ) 2.15 representing reaction-limited cluster aggregation, are determined by synthesis process conditions. They are unchanged even at the highest hydrodynamic stresses; thus, neither comminution nor agglomerate restructuring nor re-agglomeration occurs. Fragmentation reflects in decreasing radii of gyration, which are compared to mobility equivalent radii from DLS in agreement with theory.

1. Introduction Nanocomposites improve optical, mechanical, thermal, or handling properties of coatings like UV protection1 or bulk materials as, i.e., dental materials.2 Often, inorganic nanoparticles are used as the disperse phase, where pyrogenic synthesis leads to agglomerated powders. Thus, production of nanocomposites requires redispersion of dry particles in an aqueous or monomer solution.3,4 The degree of agglomeration, fractal structure, and specific surface area strongly affect material performance and depend on synthesis5 and redispersion process conditions. Redispersion of nanoscale particles is achieved by imposing very high stresses onto the agglomerates. Typical process equipments for nanoagglomerate dispersion include high shear mixing, high-pressure homogenization, ultrasonication, and nanomilling like in stirred ball mills.15 High-pressure dispersion * To whom correspondence should be addressed. E-mail: [email protected]. Phone: +49 (721) 608 2400. Fax: +49 (721) 608 2405. † Institute for Mechanical Process Engineering and Mechanics. ‡ Institute for Technical Chemistry and Polymer Chemistry. (1) Hwang, D. K.; Moon, J. H.; Shul, Y. G.; Jung, K. T.; Kim, D. H.; Lee, D. W. J. Sol-Gel Sci. Tech. 2003, 26, 783. (2) Nirschl, H. AdV. Eng. Mater. 2003, 5, 1. (3) Kickelbick, G. Prog. Polym. Sci. 28 2003, 1, 83-114. (4) Nussbaumer, R. J.; Caseri W. R.; Smith P.; Tervoort T. Macromol. Mater. Eng. 2003, 1, 44. (5) Pratsinis, S. E. Progr. Energy Combust. Sci. 1998, 3, 197. (6) Hurd A. J.; Flower W. L. J. Colloid Interface Sci. 1988, 178. (7) Hyeon-Lee J.; Beaucage G.; Pratsinis S. E.; Vemury S. Langmuir 1998, 14, 5751. (8) Beaucage G.; Kammler H. K.; Mueller R.; Strobel R.; Agashe N.; Pratsinis S. E.; Narayanan T. Nat. Mater. 2004, 6, 370. (9) Beaucage G.; Kammler H. K.; Pratsinis S. E. J. Appl. Crystallogr. 2004, 523. (10) Kammler H. K.; Beaucage G.; Mueller R.; Pratsinis S. E. Langmuir 2004, 20, 1915. (11) Kammler H. K.; Beaucage G.; Kohls D. J.; Agashe N. J.; Ilavsky J. J. Appl. Phys. 2005, 054309. (12) Pohl, M.; Hogekamp, S.; Hoffmann, N. Q.; Schuchmann, H. P. Chem. Ing. Technol. 2004, 76, 392. (13) Mandzy, N.; Grulke, E.; Druffel, T. Powder Technol. 2005, 121. (14) Mu¨ller, F.; Peukert, W.; Polke, R.; Stenger, F. Int. J. Miner. Proc. 2004, 1, S31. (15) Wengeler, R.; Teleki, A.; Vetter, M.; Pratsinis, S. E.; Nirschl, H. Langmuir 2006, 22, 4928.

provides a highly energy efficient technique and highly reproducible sampling. This results from a detailed knowledge of the hydrodynamic stresses imposed from computational fluid dynamics simulations.17 Advancement in processing of nanoscale powders premises characterizing primary particles and agglomerates in flame synthesis, as well as in their dispersion process. Several studies focus on the characterization of particles and agglomerates from flame synthesis by nitrogen adsorption (BET), transmission electron microscopy (TEM), and SAXSssmall-angle X-ray scattering.6-11Even in-situ monitoring of particles in the flame has been possible by SAXS using synchrotron radiation.8,9 However, processing and dispersion of these powders in aqueous solutions has been studied mainly with dynamic light scattering (DLS), ultrasound spectroscopy, and TEM12,13 characterizing the agglomerate size. These methods lack quantitative information on the aggregation number, fractal structure, and specific surface area. However, especially these parameters enable us to assess agglomerate deformation and to distinguish surface erosion and agglomerate break-up.14 In this work we present a synchrotron ultra-SAXS (USAXS) investigation on the desagglomeration and fragmentation by high-pressure dispersion of pyrogenic, nanoscale agglomerates in aqueous suspensions. Here, powders and suspensions are measured using the same method. By characterizing various parameters of interest such as agglomerate size, aggregate structure, primary particle size, and specific surface area with a single method, we yield a more detailed understanding of the dispersion process. 2. Experimental Section 2.1. Particle Characterization and Dispersion. Commercially available pyrogenic silica particles Aerosil 200 and Ox50 from Degussa (Hanau, Germany) and silica particles synthesized in a co-flow diffusion flame (DF) reactor at the Particle Technology Laboratory (ETH Zurich) were used. These particles were synthesized at oxygen flow rates of 2 and 10 L/min,15 which are referred to as (16) Mueller, R.; Kammler, H. K.; Pratsinis, S. E.; Vital, A.; Beaucage, G.; Burtscher, P. Powder Technol. 2004, 140, 40. (17) Wengeler, R.; Nirschl, H. J. Colloid Interface Sci. 2006, 262.

10.1021/la063073q CCC: $37.00 © 2007 American Chemical Society Published on Web 03/20/2007

SAXS Study on Dispersion of Pyrogenic Nanoagglomerates

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Figure 1. TEM images of the powder (A and C) and dispersed at a pressure drop of 1200 bar (B and D) nanoparticles of DF silica S2 (A and B) and S10 (C and D). S2 and S10. As shown by DLS, Aerosil 200 and the DF-silica S10 are strongly agglomerated, whereas agglomerates from DF-silica S2 consist only of a few primary particles, which agrees with Mueller et al.,16 who characterized similar particles as non-agglomerated silica using TEM and SAXS. Additionally, Kammler et al.11 monitored particle growth in situ in a similar flame synthesis reactor using USAXS similar as in this work. The silica particles (0.001 v/v) were stirred into distilled water and stabilized by 0.1 mM Na4P2O7, which yields ζ-potentials of about -70 mV. The aqueous silica suspensions were passed through a high-pressure dispersion apparatus with a detailed description of its design and the experimental method presented by Wengeler et al.15 The dispersion stresses have been assessed using computational fluid dynamics as discussed elsewhere.17 A pressure drop ranging from 200 to 1400 bar was applied by the high-pressure intensifier that was fueled by pressurized air. As the intensifier piston moves down, the dispersion was pressed through the dispersion nozzle

with a capillary diameter of 125 µm and a length of 10 mm. The dispersion was collected in a second container for particle analysis. The density was measured for the powders being about FP ) 2200 kg/m3 for all products. TEM micrographs of powder samples and suspensions from S2 and S10 are presented in Figure 1a and c. S2 (Figure 1a) shows large primary particles in the range of 50-200 nm which appear non-agglomerated, whereas S10 (Figure 1c) consists of small primary particles, which are strongly agglomerated. In the S2 sample some smaller particles are present, which are agglomerated showing sinter necks between the primary particles. Micrographs (Figure 1b and d) show agglomerates which were dispersed in liquid and prepared for TEM using a Collison nebulizer18 and diffusion drying the aerosol droplets. Clearly, these samples are less agglomerated than the powder samples. Small compact agglomerates of primary particles, especially for the S10 sample (Figure 1d), as (18) May, K. R. J. Aerosol Sci. 1973, 4, 235.

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well as dispersed single primaries are present, especially for the least agglomerated S2 (Figure 1b) dispersion sample. In this study, suspensions were characterized by DLS and powders, and suspensions were measured by SAXS. Mean hydrodynamic agglomerate diameters were obtained from DLS by the standardized unimodal analysis. 2.2. Small-Angle X-ray Scattering. Silica agglomerates were characterized as powders and in liquid suspension by SAXS at the high-brilliance undulator beamline ID02 of the European Synchrotron Radiation Facility (ESRF, Grenoble, France) described by Narayanan et al.19 A quartz capillary sample holder with a capillary diameter of 2 mm is used for suspension samples. Powder samples were prepared collecting particle on a scotch tape placed in fluidized powder. The scattered intensity I(q) is measured as a function of the scattering wave vector q ) (4π/λ) sin(φ/2), where λ is the wavelength of the incident radiation and φ is the scattering angle. A wide q-range (0.002 nm-1 < q < 1 nm-1) was covered using a Bonse-Hart setup for ultra small-angle X-ray scattering (USAXS) at very low q,20 and fast data recovery was enabled by a pinhole setup with different sample-to-detector distances (2 and 10 m) for low to high q. The Bonse-Hart USAXS pattern was obtained with an avalanche photodiode used in photon counting mode. From the rocking curve widths of the horizontal and the vertical analyzer crystals, the absolute scattering intensity was obtained. The two-dimensional pinhole SAXS patterns were recorded with an image-intensified CCD camera. The standard data treatment involved careful detector corrections for flat field response, spatial distortion, and dark current of the CCD, as well as normalization by incident flux, sample transmission, exposure time and the angular acceptance of the detector pixels, 19 thus resulting in absolute scattering intensities. In addition, the absolute intensities were compared to the theoretical intensity using pure water as normalization standard. The intensity of particle scattering is calculated subtracting the scattering patterns from separate measurements of sample and pure water filled cell as particle concentrations were very low. The resulting normalized two-dimensional images were azimuthally averaged to obtain I(q). The scattering curves of Bonse-Hart, pinhole with 2 and 10 m detector distance were joined to give a single scattering curve, which is covering a total q range from about 0.002 to 1.6 nm-1.

3. Data Analysis The specific surface area of the powders and dispersions has been evaluated as an integral parameter using the scattering invariant and the Porod constant. The scattering invariant, Q, defined as

Q)

∫0∞ q2I(q) dq ) 2π2∆F2Vp

(1)

is proportional to the total particle volume, Vp, in the scattering sample, where ∆F2 is the excess electron density of silica in an aqueous solution. The Porod constant CP defined as

Cp ) lim I(q)q4 ) 2π2∆F2Sp qf∞

(2)

accounts for the total particle surface area Sp.21 Therefore, the specific surface area, SSA, is calculated from

SSA )

Sp π Cp ) V pF p F p Q

(3)

The SSA measured by BET directly agrees with the SSA by SAXS. (19) Narayanan, T.; Diat, O.; Boesecke, P. Nucl. Instrum. Methods Phys. Res. A 2001, 1005, 467-468. (20) Diat, O.; Boesecke, P.; Ferrero, C.; Freund, A. K.; Lambard, J.; Heintzmann, R. Nucl. Instr. Methods Phys. Res. A 1995, 566. (21) Glatter, O.; Kratky, O. Small angle x-ray scattering; Academic Press: London, 1982.

The radius of gyration, RG, of the agglomerates is the most important characteristic of the dispersion process. Guinier22 deduced an expression to characterize the scattering curve at low q values, known as Guinier law (eq 4).

(

I(q) ) I(0) exp -

)

q2RG2 3

(4)

Scattering of a multiparticle system is composed of the primary particle scattering I0(q) and scattering due to interference between the primary particle scattering intensities representing the spatial distribution or structure of the primary particles. Primary particle scattering is characterized by the form factor

P(q) ) I0(q)/I0(0)

(5)

which is standardized by I0(0). A structure factor is defined by the particles’ spatial distribution, which is characterized by the distance vectors brij between particles i and j. It is calculated from interference of the primary particle scattering leading to an additional contribution to the intensity

S(q) ) 1 +

cos(q bb r ij) ∑j ∑ i*j

(6)

For polydisperse primary particles the structure factor cannot be defined independently from the form factor. However, an analogous definition to monodisperse systems can be found.23 Typical structure factors for fractal aggregates have the form S(q) ∝ (qRG)-Df 24 using the mass fractal dimension Df. The structure factor has to be limited by the maximum and minimum dimensions of the fractal structure, which are the agglomerate and primary particle size, respectively. The low-q limit of the structure factor is described by a Guinier law (eq 4) defining the agglomerate size. The form and structure factor combine to the agglomerate scattering curve

I(q) )

NP VPI0(0)

P(q)S(q)

(7)

The form factor is constant P(q) ) 1 for qRG,P , 1, where RG,P is the primary particle radius of gyration, while S(q) is constant for qRG,P . 1. To characterize the agglomerates, the radii of gyration of the agglomerates and primaries are determined as well as mass and surface fractal dimension of the agglomerates and primaries, respectively. Due to size differences between primaries and agglomerates, each of these parameters is related to different structural features of the scattering curve at differing q values.24 Thus they can be determined independently; nevertheless, interference has to be given attention. The unified approach to small angle scattering proposed by Beaucage25 allows for the determination of structures consisting of different fractally related structural levels using a single formula. Each structural level is characterized by an exponential regime accounting for its size and an associated power-law regime (eq 8) characterizing its internal structure. Fractal agglomerates consisting of spherical primary particles are an ideal two level system. For these the unified equation results in (22) Guinier, A. Ann. Phys. 1939, 12, 161. (23) Moonen, J. A.; de Kruif, C.; Vrij, A. Colloid Polym. Sci. 1988, 266, 1068. (24) Sorensen, C. M. Aerosol. Sci. Technol. 2001, 35, 648. (25) Beaucage, G. J. Appl. Crystallogr. 1995, 28, 717.

SAXS Study on Dispersion of Pyrogenic Nanoagglomerates

(

)

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q2RG22 + 3 D q2RG12 {erf(qRG2/x6)}3 f + B2 exp 3 q 6q2RG12 {erf(qRG1/x6)}3 + Cp Dsf (8) G1 exp 3 q

I(q) ) G2 exp -

( (

)[ ) [

]

]

Here, G1 and G2 are the Guinier prefactors for primary particles and agglomerates, respectively, corresponding to I(0) in the Guinier law (eq 4). B2 is the power law prefactor for the agglomerates, and CP, the Porod constant, is equivalent to the power law prefactor of the primaries. RG1 and RG2 are the radii of gyration of the primary particles and agglomerates. High-q and low-q cutoff functions for the power-law regime are related to the superior and inferior structural levels incorporating their radii of gyration (eq 8) and do not introduce any new parameter.25 The slope of the power law regime, P, is accounting for its fractal structure with P ) 2Df - Dsf, with Df denoting the mass fractal and Dsf the surface fractal dimension. In fractal structures all constituting particles are on the surface Df ) Dsf, yielding P ) Df,24 as in eq 8. Surface fractal dimensions were observed to differ from fractally smooth spheres for colloidal silica and silica aerogels.26,27 While agglomerates of smooth (Dsf ) 2) and homogeneous spheres (Df ) 3) exhibit P ) 6 - Dsf ) 4 as predicted by Porod. Small agglomerates can be identified by TEM and DLS, where no statistically significant power-law regime is visible in the scattering pattern. The unified approach enables characterization even of such agglomerates.16

Figure 2. Scattering curves of Aerosil Ox50, Aerosil 200, and DF silica S2. In the insert, the unified fit according to Beaucage is shown to represent well the measurement data. For clarity, only Aerosil Ox50 scattering is shown.

4. Results and Discussion 4.1. Scattering Curve Description. The scattering curves I(q) for Aerosil Ox50, Aerosil 200, and DF-silica S2 are shown in Figure 2 for suspensions dispersed at a pressure drop of 1200 bar. Since all suspensions have the same particle volume concentration (0.001 v/v), absolute scattering intensities can be compared. All patterns are characterized by four regions corresponding to the two structural levels. For clarity, only the curve of Aerosil 200 (squares) is described in detail. At low q < 0.01 nm-1; the curves level off approaching a finite value, which is described by the prefactor I(0) in eq 4. Associated to this structural level is a power law region (0.02 nm-1 < q < 0.2 nm-1) reflecting the internal structure of the agglomerates. This power law region is also detected for the DF-silica S10, while no pronounced power law regime at DF-silica S2 (triangles) reflects weakly or non-agglomerated nanoparticles. Above q ) 0.2 nm-1, an inflection in the curve indicates the Guinier regime of the primary particles. For q > 0.4 nm-1 a Porod regime is detected with a constant slope of q-4. This high-q scattering is described by a form factor for a primary particle size distribution, which strongly depends on the polydispersity. The scattering curve of Aerosil Ox50 (circles) shows the same characteristics. In the insert, the unified approach using the eq 5 agrees well with the experimental data. Here, only Aerosil Ox50 is shown for clarity, while the unified fit shows good agreement with the other experimental data as well. The unified fit can be applied with good numerical accuracy to all agglomerate scattering patterns, when agglomerates are constituted of a large number of primary particles. (26) Martin, J. E.; Hurd, A. J. J. Appl. Crystallogr. 1987, 20, 61. (27) Jarzebski, A. B.; Lorenc, J.; Pajak, L. Langmuir 1997, 13, 1280.

Figure 3. Scattering curves of DF-silica S2 and S10 are presented for powders and suspensions, where powder scattering intensities are standardized by the corresponding suspensions’ Porod constant.

Scattering curves of powder samples (filled symbols) and suspensions after high-pressure dispersion at 1400 bar (open symbols) are compared in Figure 3 for the DF-silicas S2 (triangles) and S10 (diamonds). Powder scattering curves are standardized by the corresponding suspensions’ Porod constant. Differences between powders and suspensions are visible for agglomerate scattering at q < 0.1 nm-1, while primary particle characteristics such as SSA (Table 1) and RG1 agree. However, the inflection in the scattering curve reflecting a primary particle Guinier regime is more pronounced for powder samples. At very low q < 0.01 nm-1, powder samples show a power law behavior with a slope of -3, while the suspension’s scattering curves level off. Thus, larger structures are present in the powder, which are observed as grainy form by optical microscopy, a homogeneous porosity is indicated by the q-3 scattering. These grains mostly disintegrate already by stirring the powder into water and therefore are no longer present in the dispersed suspensions. Since the specific surface area is unchanged between powders and suspension, the scattering invariant has to be equal, explaining the reduced scattering intensity at intermediate q values. In the S10 powder, fractal scattering characterized by a power law behavior with a

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Table 1. Surface Area Measurements by SAXS at the ESRF in Suspension and BET Yield Comparable Results for ‘Aerosil’ and DF-silicasa powder material

SSABET [m2/g]

Aerosil 200 Aerosil Ox50 DF silica S2 DF silica S10

191.6 44.4 ( 2.1 53.1 ( 2.0 210.5 ( 5.7

dispersion

SSASAXS,Powder [m2/g]

SSASAXS,Susp [m2/g]

51.1 218.6

190.0 ( 1.3 49.9 ( 3.6 53.6 ( 3.5 207.3 ( 2.9

a Addtionally, the SSA from SAXS on S2 powders is given for comparison.

slope of -Df is no longer found. In the relevant q range, aggregate scattering interferes with scattering of the larger grainy structure indicating that the fractal form is not preserved. This would be the case for entangled fractal aggregates. From the S2 scattering no fractal structure can be determined neither within the powder (filled triangles) nor for suspensions (open triangles). The development of the scattering pattern of Aerosil 200 by high-pressure dispersion at different pressure drops is shown in Figure 4. High-pressure dispersion only has an impact on the low-q range, representing the Guinier regime of the agglomerates. Suspensions before high-pressure dispersion and at a low-pressure drop of 200 bar show no pronounced Guinier regime. Here, larger structures are present. These can be attributed to remaining grainy structures of constant porosity resulting in a power law regime with q-3 at very low q. At higher pressure drops the slope toward low q decreases, showing the reduced size of maximum agglomerates. Thus a Guinier fit can by applied to determine their RG. The inlet shows a close up of the power law region. Here the order of the scattering intensities is inversed compared to the Guinier region, where maximum intensities in the Guinier regime (0 and 200 bar) are lowest in the corresponding power law region, while low intensities for dispersed agglomerates (1400 bar) are highest. This stems from the constant primary particle sizes requiring a constant scattering-invariant Q. In the Porod regime the curves join into a single line. Hence, the primary particles are not affected and the Porod constant remains unchanged. The rest of the scattering pattern is insensitive to dispersion. Thus the corresponding parameters as mass (Df ) 2.15), surface fractal dimension (Dsf ) 2.0), primary particle size, and their polydispersity are unchanged. 4.2. Characteristics of Primary Particle Size and Agglomerate Structure. 4.2.1. Primary Particle Characteristics. The SSA measured by nitrogen adsorption using the BET method and SAXS using a powder and liquid suspensions sample are shown in Table 1 for ‘Aerosil’ and DF silica. The SSA by SAXS is calculated from eq 3 using the scattering invariant and Porod constant. Both measurement techniques are in mutual agreement with 2.3), which are found in diffusion-limited agglomeration (DLA) processes as proposed by Meakin,30 in turbulent restructuring31 or sintering.32 However, Baron and Willeke33 state that only diffusion-limited cluster agglomeration (DLCA), yielding Df ) 1.8, instead of DLA processes occur in nature. S10 is produced in a hot flame with a short, high-temperature region and fast cooling, where no complete coagulation is realized, the increased Df compared to the other silicas might be attributed to truncated sintering-coagulation processes, as presented by Schmid.32 Similar fractal dimensions have been found for pyrogenic silica by others,7,10 who additionally detected lower fractal dimensions of Df ) 1.8, as observed for DLCA, when large agglomerates were produced. Low fractal dimensions have not been found for any suspension in this study, yet these values show the range of fractal dimensions (1.7 < Df < 2.5) which are accessible to product design in flame synthesis. For suspensions with large primary particles, Aerosil Ox50 and S2, surface fractal dimensions differ from homogeneous spheres (Dsf ) 2). Thus, fractally rough surface structures are observed, which also have previously been found for silica aerogels.27 These variations can be caused by nonspherical particle shape, as found on TEM images of these powders. Since surface fractal dimension are properties associated to the primary particles, they are insensitive to dispersion, yet variations are small and will not have a strong impact on product properties. 4.3. Characteristics of Dispersion and Fragmentation. The agglomerate structure is additionally characterized by its fractal dimension throughout high-pressure dispersion. Studies for all products showed no change in Df with increasing fragmentation as qualitatively shown in Figure 4. Since Df does not change even under highly turbulent flow conditions with Re > 40 000,17 no turbulent restructuring within high-pressure dispersion occurs, which would lead to increasing Df. This indicates that aggregates are stiff with strong van der Waals and chemical bonding between the primary particles. Thus, dispersion does not alter the fractal (29) Weitz, D. A.; Huang, J. S.; Lin, M. Y.; Sung, J. Phys. ReV. Lett. 1985, 17, 1657. (30) Meakin, P. Phys. ReV. Lett. 1983, 51, 1119. (31) Soos, M.; Sefcik, J.; Morbidelli, M. Chem. Eng. Sci. 2006, 61, 2349. (32) Schmid, H.-J.; Al-Zaitone, B.; Artelt, C.; Peukert, W. Chem. Eng. Sci. 2006, 61, 293. (33) Baron, P. A.; Willeke, K. Aerosol Measurement: Principles, Techniques, and Applications; Wiley: New York, 2005.

Figure 5. Comparative evaluation of the radii of gyration is shown for Aerosil 200 and DF silica S2 for dispersion pressure drops of 200-1400 bar. RG is fitted using Guinier law (eq 4) and the unified exponential/power law approach (eq 8). Table 3. Mass Fractal, Df, and Surface Fractal Dimension, Dsf, Characterize the Agglomerate Structure, Insensitive to High-Pressure Dispersion material

Df

Dsf

Aerosil 200 Aerosil Ox50 DF silica S2 DF silica S10

2.166 ( 0.023 2.199 ( 0.009 2.161 ( 0.016 2.322 ( 0.057

2 2.051 ( 0.054 2.147 ( 0.038 2

agglomerate structure, which indicates that re-agglomeration and reconfiguration by bond deformation in the high-pressure dispersion is negligible. Agglomerate re-agglomeration and reconfiguration would result in increasing Df, while constant Df are found for fragmentation by surface erosion. The influence of high-pressure dispersion on the silica agglomerates is characterized by their radius of gyration measured after dispersion at different pressure drops. Figure 5 shows the radii of gyration for Aerosil 200 (squares) and the DF-silica S2 (triangles) each with eqs 4 and 8 used for fitting. Both suspensions show decreasing radii of gyration from RG,Unified ) 153 to 105 nm for Aerosil at increasing dispersion pressure drops, while S2 yields similar results. As expected, the unified fit (eq 8) and the exponential Guinier fit (eq 4) show comparable results. The Guinier law is valid in the range of qRG < 1 for scattering of homogeneous particles. Here, qRG ranges from 1.35 to 1.5 and scattering curves result from primary particle scattering interference in fractal agglomerates. For the stirred-in DF silica S2 suspension (0 bar), qRG ) 2.0 is ways beyond the valid range, and therefore, RG has not been calculated. Figure 5 shows that both methods agree at high dispersion pressure drops, where large agglomerates are broken and a pronounced Guinier regime is obtained. For further analysis, the radius of gyration from the unified fit is chosen as reference. Additionally, Figure 5 shows the evaluation inherent errors from data fitting for agglomerate sizes. Here, the results differ in average by 9.1%, 10.9%, and 6.9% for Aerosil 200, Aerosil Ox50, and S2, respectively. Repetitions on the scattering curve evaluation show a standard deviation of 7.5% for determining the radius of gyration, thus indicating the USAXS accuracy for agglomerate diameter measurement to be in the range of 10% for pyrogenic suspensions. For validation, these RG are compared to the mobility radius, RM, from DLS, used on diluted suspensions as detailed in

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Also, differences in the fractal structure are observed (Table 3). Thus particle synthesis determines several important particle characteristics which cannot be altered by mechanical processing. For complete primary particle dispersion, sinter necks between primary particles need to be inhibited, which requires a constant temperature-residence time history for all particles allowing for complete coalescence. For defined fractally structured aggregates, a controlled coagulation process at high temperatures is required, where sintering necks are formed which do not break up by hydrodynamic stresses.

5. Conclusions

Figure 6. Radius of gyration measured by SAXS and the hydrodynamic radius from DLS are presented for Aerosil 200 and Aerosil Ox50.

Wengeler et al.15 RM is characterized by the particles’ hydrodynamic mobility. Therefore, the radius of gyration and resulting hydrodynamic radii are plotted in Figure 6 on two different axes with the same scaling. USAXS yields the highest agglomerate radii, while hydrodynamic radii are 10-20% lower. Wang and Sorensen34 and Lattuada et al.35 also compared RG and RM, which are equivalent for monodisperse agglomerates, yet for polydisperse agglomerates they cannot directly be compared representing different moments of the size distribution. For fractal aggregates, they determined the ratio RM/RG ) 0.97,34 0.875,36 and 0.83135 for a self-preserving size distribution at the continuum limit and Df ) 2.15, strongly depending on Df and being independent of the aggregation number NAgg for large agglomerates with NAgg > 50. Here, the ratio RM/RG is 0.835 ( 0.049 for Aerosil 200 comparable to the work of Lattuada et al.35 and 0.808 ( 0.027 for Aerosil Ox50. High-pressure dispersion results in agglomerate size reduction due to fragmentation of nanoscale agglomerates. A continuous decrease in agglomerate size is observed with increasing dispersion pressure corresponding to higher hydrodynamic stresses. USAXS adequately represents agglomerate fragmentation, yet agglomerate sizes of different measurement techniques show differences, requiring focusing one of those techniques. From agglomerate and primary particle radii of gyration, the aggregation number can be obtained8 as

NAgg ) (RG22/RG12)Df/2 Aggregation numbers of the silica agglomerates studied vary strongly. Aerosil 200 form large agglomerates with several hundred primary particles, while NAgg of Aerosil Ox50 decrease from 72.5 before dispersion to 29.0 at 1400 bar representing the fragmentation of the agglomerates. Compared to these commercial products, the DF silica have aggregation numbers of 197-132 (S10) and in the range of 10 for S2. For S2 only small agglomerates exist, accounting to the lack of a pronounced power law regime in the scattering pattern (Figure 2). Thus, variation of production parameters leads to strongly aggregated, as well as almost non-agglomerated, nanoparticles.

Flame synthesis processes lead to agglomerated nanoparticle powders with aggregates and soft agglomerates. High-pressure dispersion allows to reproducibly dispersing agglomerates in aqueous suspension, where hard aggregates are obtained and fragmented at high-pressure drops. SAXS enables a characterization of primary particle size and their polydispersity for powders, as well as stirred-in suspensions with coinciding results. Primary particle sizes determined by SAXS and by nitrogen adsorption agree well, showing that no internal pores exist and that the methods are in good agreement. SAXS on suspensions additionally enables a thorough characterization of agglomerate size and fractal structure within a single measurement. Fractal dimensions indicate that agglomerates are formed by reaction-limited cluster aggregation (RLCA) within the flame. Since dispersion of these powders is an integral part of material processing, the development of agglomerate size and structure by high-pressure dispersion has been studied. Fragmentation could be observed by the radius of gyration and the aggregation number decreasing with increasing hydrodynamic stresses. For the first time it is shown that the specific surface area and the fractal dimension are unchanged throughout the dispersion process, even after exertion of high hydrodynamic stresses. Constant fractal structures of the aggregates are attributed to a surface erosion process with no re-agglomeration or turbulent restructuring. Constant primary particle size and specific surface area show that no comminution of the product occurs. A complete dispersion of primary particles was not achieved, showing the strong influence of sinter necks between the primary particles and residual fractal aggregates after high-pressure dispersion. SAXS has shown to be a versatile tool to study nanoagglomerates throughout their production route. As shown in this work, SAXS allows a complete characterization of powder and liquid suspension in different states of high-pressure processing not possible with other common methods like dynamic light scattering or nitrogen adsorption. Particle parameters are coinciding in the powder, as well as liquid suspension, and results are consistent with literature on the aerosol particle in flame synthesis. Concluding, SAXS provides a basis for the in-situ investigation and integrated process design required for particle processing in nanocomposite materials.

(34) Wang, G. M.; Sorensen, C. M. Phys. ReV. E 1999, 60, 3036. (35) Lattuada, M.; Wu, H.; Morbidelli, M. J. Colloid Interface Sci. 2003, 268,

Acknowledgment. We thank the Particle Technology Laboratory group of Prof. Pratsinis at the ETH Zurich for enabling the use of the outstanding flame synthesis facilities, especially Mrs. Teleki for fruitful discussions and great help. The use of the ID02 beamline at the European Synchrotron Radiation Facility in Grenoble, France was supported in the project ME-1179. Financial support by the German Science Foundation (DFG; No. PAK 75/1) and by the Ministry of Science, Research and the Arts “Baden-Wu¨rttemberg” (No. 7712.14-0903-2) is gratefully acknowledged.

(36) Chen, Z. Y.; Meakin, P.; Deutch, J. M. Phys. ReV. Lett. 1987, 59, 2121.

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