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Not just fractal surfaces, but surface fractal aggregates: Derivation of the expression for the structure factor and its applications

DOI: 10.1063/1.4960953 DOI Help

Authors: Rogier Besselink (Helmholtz Centre Potsdam GFZ German Research Centre for Geosciences, University of Leeds) , Tomasz Stawski (Helmholtz Centre Potsdam GFZ German Research Centre for Geosciences, University of Leeds) , Alexander E. S. Van Driessche (Université Grenoble Alpes, CNRS) , Liane G Benning (Helmholtz Centre Potsdam GFZ German Research Centre for Geosciences, University of Leeds)
Co-authored by industrial partner: No

Type: Journal Paper
Journal: The Journal Of Chemical Physics , VOL 145

State: Published (Approved)
Published: December 2016
Diamond Proposal Number(s): 9904

Open Access Open Access

Abstract: Densely packed surface fractal aggregates form in systems with high local volume fractions of particles with very short diffusion lengths, which effectively means that particles have little space to move. However, there are no prior mathematical models, which would describe scattering from such surface fractal aggregates and which would allow the subdivision between inter- and intraparticle interferences of such aggregates. Here, we show that by including a form factor function of the primary particles building the aggregate, a finite size of the surface fractal interfacial sub-surfaces can be derived from a structure factor term. This formalism allows us to define both a finite specific surface area for fractal aggregates and the fraction of particle interfacial sub-surfaces at the perimeter of an aggregate. The derived surface fractal model is validated by comparing it with an ab initio approach that involves the generation of a “brick-in-a-wall” von Koch type contour fractals. Moreover, we show that this approach explains observed scattering intensities from in situ experiments that followed gypsum (CaSO4 ⋅ 2H2O) precipitation from highly supersaturated solutions. Our model of densely packed “brick-in-a-wall” surface fractal aggregates may well be the key precursor step in the formation of several types of mosaic- and meso-crystals.

Journal Keywords: Fractals, Surface Scattering, Particle Scattering, Surface Structure, Form Factors

Subject Areas: Materials, Chemistry, Physics


Instruments: I22-Small angle scattering & Diffraction

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