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

https://www.phys.ksu.edu/personal/sor/publications/2001/light.pdf

Light Scattering by Fractal Aggregates: A Review

Although Portland cement concrete is the world’s most widely used manufactured material, basic questions persist regarding its internal structure and water content, and their effect on concrete behaviour. Here, for the first time without recourse to drying methods, we measure the composition and solid density of the principal binding reaction product of cement hydration, calcium–silicate–hydrate (C–S–H) gel, one of the most complex of all gels. We also quantify a nanoscale calcium hydroxide phase that coexists with C–S–H gel. By combining small-angle neutron and X-ray scattering data, and by exploiting the hydrogen/deuterium neutron isotope effect both in water and methanol, we determine the mean formula and mass density of the nanoscale C–S–H gel particles in hydrating cement. We show that the formula, (CaO)1.7(SiO2)(H2O)1.80, and density, 2.604 Mg m−3, differ from previous values for C–S–H gel, associated with specific drying conditions. Whereas previous studies have classified water within C–S–H gel by how tightly it is bound, in this study we classify water by its location—with implications for defining the chemically active (C–S–H) surface area within cement, and for predicting concrete properties.

/pdf/composition-and-density-of-nanoscale-calcium-silicate-26znkzlx6c.pdf

Composition and density of nanoscale calcium–silicate–hydrate in cement

We give a brief overview of the impact of fractal geometry on physical sciences. In particular we will describe the prototype of fractal growth models and the recent developments in the direction of the formulation of an analytical theory that allows to understand why natural phenomena often give rise to fractal structures. Finally we will show that the large scale properties of the matter distribution in the universe need a radical revision on the of light of these new concepts.

Fractals in physics

Surface modifications for the effective dispersion of carbon nanotubes in solvents and polymers

The structure of temperature-sensitive poly(N-isopropylacrylamide) microgels in dilute suspension was investigated by means of small-angle neutron scattering. A direct modeling expression for the scattering intensity distribution was derived which describes very well the experimental data at all temperatures over an extensive q range. The overall particle form as well as the internal structure of the microgel network is described by the model. The influence of temperature, cross-linking density, and particle size on the structure was revealed by radial density profiles and clearly showed that the segment density in the swollen state is not homogeneous, but gradually decays at the surface. The density profile reveals a box profile only when the particles are collapsed at elevated temperatures. An increase of the cross-linking density resulted in both an increase of the polymer volume fraction in the inner region of the particle and a reduction of the smearing of the surface. The polymer volume fraction inside the colloid decreased with increasing particle size. The structural changes are in good agreement with the kinetics of the emulsion copolymerization used to prepare the microgel colloids.

Small-angle neutron scattering study of structural changes in temperature sensitive microgel colloids

Small-angle neutron scattering from normal, compressed, and water-suspended powders of aggregates of fine silica particles has been studied. The samples possessed average densities ranging from 0.008 to 0.45 g/${\mathrm{cm}}^{3}$. Assuming power-law correlations between particles and a finite correlation length \ensuremath{\xi}, we derive the scattering function S(q) from specific models for particle-particle correlation in these systems. S(q) was found to provide a satisfactory fit to the data for all samples studied. The fractal dimension ${d}_{f}$ corresponding to the power-law correlation was 2.61\ifmmode\pm\else\textpm\fi{}0.1 for all dry samples, and 2.34\ifmmode\pm\else\textpm\fi{}0.1 for the water-suspended samples. The intensity of scattering was found to scale with the correlation length in the manner expected for a fractal system.

Power-law correlations and finite-size effects in silica particle aggregates studied by small-angle neutron scattering.

We have studied small angle neutron scattering on normal, compressed and water-suspended powders of aggregates of fine silica particles. The samples studied possessed average densities ranging from 0.009 gm/cm3 to 0.45 gm/cm3. A universal function S(k) assuming power law correlations between particles and a finite correlation length ξ was found to provide a satisfactory fit to the data for all the samples studied. The fractal dimension D corresponding to the power law correlation was 2.52 ± 0.05 for all samples studied. The normalized scattering per particle scales as ξD as required by the model.

Observation of Power-Law Correlations in Silica-Particle Aggregates by Small Angle Neutron Scattering

We describe briefly the concept of fractal dimension as applied to both mathematical and statistical fractals. We then discuss the scattering of radiation from fractals and describe the results of small angle neutron scattering studies of the aggregation of small particles in fractal clusters.

S. K. Sinha

Papers

Power-law correlations and finite-size effects in silica particle aggregates studied by small-angle neutron scattering.

Observation of Power-Law Correlations in Silica-Particle Aggregates by Small Angle Neutron Scattering

Neutron scattering from fractals