Fractal Geometry of Silica Condensation Polymers

Schaefer, Dale W.; Keefer, Keith D.

doi:10.1103/physrevlett.53.1383

Cited by 278 publications

(131 citation statements)

References 8 publications

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“…10 As found for the acetone-exchanged wet gel studied in this work, the SAXS intensity departs from the powerlaw regime at low-q values due to the finite correlation range of the mass fractal structure, and at high-q values due to the surface fractal characteristic of the primary particles ͑mi-croclusters͒ composing the structure. We first analyze the SAXS intensity at the low-and medium-q regions in which it can be fitted by 11 I͑q ͒ϭB sin͓͑DϪ1 ͒arctan͑ q ͔͒/͑ 1ϩq 2 …”

Section: Interpretation Of the Saxs Datamentioning

confidence: 80%

Small-angle x-ray scattering study of the structural evolution of the drying of sonogels with the liquid phase exchanged by acetone

et al. 2004

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The structural evolution on the drying of wet sonogels of silica with the liquid phase exchanged by acetone, obtained from tetraethoxisilane sonohydrolysis, was studied in situ by small-angle x-ray scattering ͑SAXS͒. The periods associated to the structural evolution as determined by SAXS are in agreement with those classical ones established on basis of the features of the evaporation rate of the liquid phase in the obtaining of xerogels. The wet gel can be described as formed by primary particles ͑microclusters͒, with characteristic length a ϳ0.67 nm and surface which is fractal, linking together to form mass fractal structures with mass fractal dimension Dϭ2.24 in a length scale ϳ6.7 nm. As the network collapses while the liquid/vapor meniscus is kept out of the gel volume, the mass fractal structure becomes more compacted by increasing D and decreasing , with smoothing of the fractal surface of the microclusters. The time evolution of the density of the wet gels was evaluated exclusively from the SAXS parameters , D, and a. The final dried acetone-exchanged gel presents Porod's inhomogeneity length of about 2.8 nm and apparently exhibits an interesting singularity D →3, as determined by the mass fractal modeling used to fit the SAXS intensity data for the obtaining of the parameters and D.

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Section: Interpretation Of the Saxs Datamentioning

confidence: 80%

Small-angle x-ray scattering study of the structural evolution of the drying of sonogels with the liquid phase exchanged by acetone

et al. 2004

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“…Figure 6 shows images of the aerogel microstructure obtained from SEM. It is clear from these images that the reaction pH value has a significant effect on aerogel morphology [2,3]. The images of the pH = 1 as well as pH = 3 aerogels show parallel ridges that rise out of the fracture surface, while the pH = 2 sample is composed of branched clusters of smaller particles.…”

Section: Surface Area and Pore Size Measurementsmentioning

confidence: 78%

“…Since the 1980s, researchers have extensively studied their fractal structures and mechanisms of formation in sol-gel processes, such as noteworthy works by Schaefer and Keefer [2,3]. Problems concerning the self-organization of these systems have also been thoroughly reviewed in surveys by Roldugin [4,5].…”

Section: Introductionmentioning

confidence: 99%

“…These nanoglobules form homogeneously throughout the sol and then aggregate to form structures during the final stages of growth whose size is determined by diffusion-limited aggregation [6]. Gelation is followed by the drying of the wet gel in an autoclave under supercritical conditions for CO 2 , a process that leads to a pure, homogeneous product with low density, high specific surface area, and high porosity [7,8]. This potentially allows them to be used in numerous applications, such as catalysis, fuel storage tanks, low dielectric constant materials, and fine particle collection [9,10].…”

Section: Introductionmentioning

confidence: 99%

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Tuned optical transmittance in single-step-derived silica aerogels through pH-controlled microstructure

et al. 2017

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We have systematically studied the relationship between synthesis pH and morphological and optical properties of silica aerogels. We have determined through SEM and BET that there is a systematic correlation between the pH of the initial silica solution and the surface area, porosity, and pore size of the resulting aerogel. We find that optical transmittance, particularly its wavelength dependence (dispersion), is strongly governed by the microstructure and, therefore, synthesis pH. We have determined that the microstructure of the aerogels fall into three broad categories: monostructural, which is characterized by repeating elongated microstructural features; fractal, which shows a distinctive structure that is emulated on multiple length scales; and isotropic, which is characterized by having no distinct features in its microstructure. Simply by controlling the pH of the synthesis environment, we can tune the optical properties of silica aerogels through pH controlled the microstructural modification. We have found that pH = 1-5 gives high dispersion, pH = 6-7 results in low transmittance and low dispersion, pH = 8 shows the highest transmittance with the lowest dispersion, and pH = 9-10 transitions back to lower transmittance and higher dispersion.

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“…5 The SAXS intensity departs from the power-law regime at low-q values due to the finite-correlation range of the mass-fractal structure, thus, an approach can be cast as 6 …”

Section: Methodsmentioning

confidence: 99%

Mass fractal characteristics of silica sonogels as determined by small-angle x-ray scattering and nitrogen adsorption

Donatti

Vollet²,

Ruiz³

et al. 2005

Phys. Rev. B

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A sample series of silica sonogels was prepared using different water-tetraethoxysilane molar ratio ͑r w ͒ in the gelation step of the process in order to obtain aerogels with different bulk densities after the supercritical drying. The samples were analyzed by means of small-angle x-ray-scattering ͑SAXS͒ and nitrogen-adsorption techniques. Wet sonogels exhibit mass fractal structure with fractal dimension D increasing from ϳ2.1 to ϳ 2.4 and mass-fractal correlation length diminishing from ϳ13 nm to ϳ 2 nm, as r w is changed in the nominal range from 66 to 6. The process of obtaining aerogels from sonogels and heat treatment at 500°C, in general, increases the mass-fractal dimension D, diminishes the characteristic length of the fractal structure, and shortens the fractal range at the micropore side for the formation of a secondary structured particle, apparently evolved from the original wet structure at a high resolution level. The overall mass-fractal dimension D of aerogels was evaluated as ϳ2.4 and ϳ2.5, as determined from SAXS and from pore-size distribution by nitrogen adsorption, respectively. The fine structure of the "secondary particle" developed in the obtaining of aerogels could be described as a surface-mass fractal, with the correlated surface and mass-fractal dimensions decreasing from ϳ2.4 to ϳ 2.0 and from ϳ2.7 to ϳ 2.5, respectively, as the aerogel bulk density increases from 0.25 ͑r w =66͒ up to 0.91 g / cm 3 ͑r w =6͒.

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Fractal Geometry of Silica Condensation Polymers

Cited by 278 publications

References 8 publications

Small-angle x-ray scattering study of the structural evolution of the drying of sonogels with the liquid phase exchanged by acetone

Small-angle x-ray scattering study of the structural evolution of the drying of sonogels with the liquid phase exchanged by acetone

Tuned optical transmittance in single-step-derived silica aerogels through pH-controlled microstructure

Mass fractal characteristics of silica sonogels as determined by small-angle x-ray scattering and nitrogen adsorption

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