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Dynamical scaling in fractal structures in the aggregation of tetraethoxysilane‐derived sonogels
Author(s) -
Vollet Dimas R.,
Donatti Dario A.,
Ibañez Ruiz Alberto,
De Vicente Fabio S.
Publication year - 2010
Publication title -
journal of applied crystallography
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.429
H-Index - 162
ISSN - 1600-5767
DOI - 10.1107/s0021889810025161
Subject(s) - scaling , exponent , small angle x ray scattering , fractal , fractal dimension , scattering , structure factor , small angle scattering , power law , intensity (physics) , scale invariance , dynamic light scattering , physics , condensed matter physics , mathematics , optics , geometry , mathematical analysis , quantum mechanics , statistics , philosophy , linguistics , nanoparticle
Dynamical scaling properties in fractal structures were investigated from small‐angle X‐ray scattering (SAXS) data of the kinetics of aggregation in silica‐based gelling systems. For lack of a maximum in the SAXS intensity curves, a characteristic correlation distance ξ was evaluated by fitting a particle scattering factor model valid for polydisperse coils of linear chains and f ‐functional branched polycondensates in solution, so the intensity at q = ξ −1 , I (ξ −1 , t ), was considered to probe dynamical scaling properties. The following properties have been found: (i) the SAXS intensities corresponding to different times t , I ( q , t ), are given by a time‐independent function F ( q ξ) = I ( q , t )ξ − D / Q , where the scattering invariant Q has been found to be time‐independent; (ii) ξ exhibited a power‐law behavior with time as ξ≃ t α , the exponent α being close to 1 but diminishing with temperature; (iii) I (ξ −1 , t ) exhibited a time dependence given by I (ξ −1 , t ) ≃ t β , with the exponent β found to be around 2 but diminishing with temperature, following the same behavior as the exponent α. In all cases, β/α was quite close to the fractal dimension D at the end of the studied process. This set of findings is in notable agreement with the dynamical scaling properties.