Scaling description of the structure factor of fractal soot composites

Sorensen, Christopher M.; Oh, Chang-Hwan; Schmidt, Paul W.; Rieker, T. P.

doi:10.1103/physreve.58.4666

Cited by 37 publications

(48 citation statements)

References 27 publications

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“…The smooth crossover of the power-law region of different structural levels further indicates that primary particles are in contact in the aggregates which in turn are in contact in the agglomerates. 14 The structure factor of interparticle interactions within the aggregates is suppressed by the relatively high polydispersity of primary particles. 24 For the flow rate involved in Fig.…”

Section: Discussionmentioning

confidence: 99%

“…7,8 SAXS is an established technique to elucidate the multilevel structure ͑primary particles, their aggregates, and agglomerates͒ of aerosol systems. [13][14][15][16] The key advantage of SAXS as compared to electron microscopy is that it is a nonintrusive technique-the nucleation and growth condition at the point of observation is not significantly altered. 17,18 In addition, the measured intensity is not influenced by the optical emission from the flame unlike in light scattering.…”

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confidence: 99%

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In situ study of aggregation of soot particles in an acetylene flame by small-angle x-ray scattering

Sztucki

Narayanan

Beaucage

2007

Journal of Applied Physics

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The nucleation and growth of soot particles in an acetylene flame were investigated by synchrotron small-angle x-ray scattering. The scattered intensity spanning over a wide scattering vector (q) range, 10−3nm−1⩽q⩽0.5nm−1, was analyzed using the unified scattering function involving up to three structural levels corresponding to primary particles, aggregates, and agglomerates. The primary particles have a compact morphology with a terminal radius of gyration (Rg) of about 27nm and their growth dynamics is consistent with the nucleation and growth process. The evolution of aggregate Rg reveals a diffusion limited growth mechanism resulting in a fractal dimension (df)≈2 and Rg∼250nm. Although the production of soot dramatically increases with the flow rate, the aggregation dynamics, terminal Rg, and df remain nearly the same. The flow rate used in this study extended to the regime of aerogelation of soot but the aggregation dynamics is found to be similar to the nongelling case.

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Section: Discussionmentioning

confidence: 99%

mentioning

confidence: 99%

In situ study of aggregation of soot particles in an acetylene flame by small-angle x-ray scattering

Sztucki

Narayanan

Beaucage

2007

Journal of Applied Physics

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“…features of wave scattering from a variety of systems, and the reader is encouraged to see Sorensen et al (1998) and Oh and Sorensen (1999) for other examples. It also enhances physical intuition for the scattering process.…”

Section: The Scaling Approach For the Structure Factormentioning

confidence: 99%

“…These facts are outlined schematically in Figure 22. Many examples of optical structure factor measurements on particulate systems exist in the literature (Schaefer et al 1984;Martin et al 1986;Hurd and Flower 1988;Zhang et al 1988;Gangopadhyay et al 1991;Hall 1991, 1992;Dobbins and Megarides 1991;Sorensen et al 1992b;Köylü andFaeth 1994a, 1994b;Köylü 1998;Sorensen et al 1998;Xing et al 1999). …”

Section: The Optical Structure Factormentioning

confidence: 99%

Light Scattering by Fractal Aggregates: A Review

Sorensen

2001

Aerosol Science and Technology

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This paper presents a review of scattering and absorption of light by fractal aggregates. The aggregates are typically diffusion limited cluster aggregates (DLCA) with fractal dimensions of D ' 1:75, which occur frequently in aerosols and colloids, but other types of aggregates are discussed as well. The results of the review are quite general. A scaling description of the scattering of waves forms the basis of our understanding. This description yields the optical structure factor S(q ) of the aggregate, where q is the scattering wavevector, a key quantity. The rigorous approach to the structure factor, the Fourier transform of the density correlation function, is also given and various forms provided in the literature are compared and the best selected. Light scattering is directly related to the structure factor under the assumption of no internal multiple scattering. This so-called Rayleigh -Debye -Gans (RDG) approximation is compared to more rigorous electromagnetic approaches and found to be quite accurate for fractal aggregates. This results despite the presence of internal multiple scattering, which leads to depolarization, and which is also extensively described. For ensembles of aggregates, the effects of aggregate polydispersity on scattering experiments are described and methods for proper analysis are given. A description of optical particle sizing and morphology analysis is given for a complete in situ characterization of the aggregate system. The review relies strongly on straightforward physical reasoning and experimental examples, largely from aerosols, especially those of carbonaceous soot. This paper not only reviews and consolidates, but also presents new results including a scaling analysis of multiple scattering, which leads to depolarization, with a successful comparison to available data and an understanding of structural subtleties; demonstration of the signi cance of a phase shift parameter for evaluating the range of validity of the RDG theory; a Maxwell -Garnet analysis of fractal aggregate scattering; calculations of the albedo and successful comparison to available simulation data; and speculations on multiple scattering and the interior eld. INTRODUCTIONThe purpose of this review is to unify our knowledge of how fractal aggregates scatter (and absorb) light. This is of value for light scattering diagnostics of aerosols and colloids and for understanding the optics of these systems in the environment. The subject has seen able and useful reviews before by Teixeira (1986), Martin and Hurd (1987), Charalampopoulos (1992), and a brief overview by myself (Sorensen 1997). Very recently Fuller and Mackowski (2000) have given an excellent review of the superposition theory of scattering from aggregates. My desire here is to provide an up-to-date and comprehensive review useful for the experimentalist. Any theory that does appear will be based on simple physical arguments rather than detailed mathematical analysis. Many of the general results to be described here apply to nonfractal aggreg...

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“…2.6, which we have shown can occur in dense aerosols near the gel point (Sorensen et al 2003;Kim et al 2004Kim et al , 2006. On the other hand, this could also be an artifact of the collapsing of the aerosol gel while shipping and handling to NCNR (Sorensen et al 1998b).…”

Section: Morphology Of the Silica Aggregatesmentioning

confidence: 94%

Synthesis of Silica Aerosol Gels via Controlled Detonation

Dhaubhadel

Rieker

Chakrabarti

et al. 2012

Aerosol Science and Technology

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Silica (SiO 2 ) aerosol gels were formed via Brownian aggregation of silica nanoparticles in a closed reaction chamber. A sudden and quick detonation reaction of pyrophoric silane (SiH 4 ) with either oxygen or nitrous oxide created silica nanoparticles with diameters ranging from ∼22 to 90 nm in the presence of an inert background gas with a volume fraction of ca. 10 −4 , conditions necessary for gelation. The background gas was necessary for quick thermal quenching of freshly formed silica molecules and molten nanoparticles and some control of the particle size could be achieved by variation of the gas. The silica aerosol gels were found to have very low densities in the range 4-15 mg/cm 3 and high specific surface areas of 300-500 m 2 /g. Wide angle X-ray diffraction showed that the nanoparticles were amorphous silica. Neutron scattering showed that they were arranged in networks with a fractal dimension of 1.75 between 10 and 1000 nm length scales. INTRODUCTIONIn previous work, we presented an aerosol gelation method to produce porous materials with high specific surface area and extremely low density (Dhaubhadel et al. 2007). The method involved the gelation of nanoparticles in the aerosol phase to yield a material that we have named an "aerosol gel." Unlike wellknown aerogel materials which begin with a liquid phase sol-gel step, aerosol gels are made in the gas phase. Simply said a cloud of smoke in a volume gels or freezes to form a volume spanning, very light weight, porous body; truly "frozen smoke." The initial aerosol is composed of nanometer-sized particles produced rapidly by exploding in a chamber a hydrocarbon precursor with an oxidizer, e.g., oxygen. The nanometer particles so produced aggregate and then gel on the order of tens of seconds to form the aerosol gel. The carbon materials we made previously have densities as low as 2.5 mg/cc. The current state-of-the-art Address correspondence to C. M. Sorensen, Department of Physics, Kansas State University, Manhattan, Kansas 66506, USA. E-mail: sor@phys.ksu.edu for manufacture of aerogel materials is the sol-gel/supercriticaldrying method (Brinker and Scherer 1990; Hüsing and Schubert 1998). The gas phase aerosol gelation method is a significantly different than this state-of-the-art and hence might offer advantages because (1) there is no need for a supercritical drying step as for aerogels and (2) the aerosol gel method should be applicable to a greater variety of substances. Disadvantages of our method lie in the current need for a detonation which could be hard to scale up, and it is a batch process.Gelation is a consequence of random aggregation of noncoalescing particles to form ramified fractal aggregates. Fractal aggregates have a mass-size scaling exponent, the fractal dimension D f , that is less than the spatial dimension, d, and this inequality represents a fundamental condition for gelation (Sorensen and Chakrabarti 2011). Because of this, the ratio of aggregate mean nearest neighbor separation to aggregate size declines as the aggreg...

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Scaling description of the structure factor of fractal soot composites

Cited by 37 publications

References 27 publications

In situ study of aggregation of soot particles in an acetylene flame by small-angle x-ray scattering

In situ study of aggregation of soot particles in an acetylene flame by small-angle x-ray scattering

Light Scattering by Fractal Aggregates: A Review

Synthesis of Silica Aerosol Gels via Controlled Detonation

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