Mass fractal dimension light scattering

Laser diffraction technique is able to generate the envelope diameter distribution of the aggregates in the aerosol cloud, as well as the surface and mass fractal dimensions as explained in Light Scattering under both Boundary and Surface Fractal Dimensions and Mass Fractal Dimension. However, validation of Eq. (25) by comparison studies between the impaction and laser diffraction techniques is required. 

Techniques have been developed to determine the fractal dimension of experimental aggregate particles in solution using small-angle scattering techniques, from x-ray, light, or even neutron sources. In these techniques the scattering intensity, I q), is proportional to the scattering vector, q, raised to the mass fractal dimension by ... 

In some ways, a more robust method of using small-angle light scattering to measure the mass fractal dimension of particle aggregates is to rely on the changing projected area of an assembly of particles as they aggregate, an idea first used by Volker Oles in 1992 [20]. 

Kusters et al. [22] analysed polystyrene latex particles of about 1 p,m diameter aggregated in salt solution in a stirred tank, with samples withdrawn from the tank by pipette for light-scattering measurements. They found mass fractal dimensions of around 2.5 using the volume obscuration method. 

Other possible methods of obtaining fractal dimensions are light- and small-an-gle-X-ray-scattering (SAXS). The first method gives information about mass fractality of aggregates and aggregation kinetics (Fleischmann et al., 1990), whereas the latter allows mass and surface fractals to be differentiated (Schmidt, 1990). 

Much of the current interest in fractal geometry stems from the fact that fractal dimensions are experimentally accessible quantities. For polymers and colloids, the measurement techniques of choice are scattering experiments using X-rays, neutrons, or light. These measurements may be made on liquids or solids and can be performed readily as a function of time and temperature. Both mass and surface fractal structures yield scattering curves that are power laws, the exponents of which depend on the fractal dimension (6). For mass fractal structures the relation is... 

There are two different types of fractals in solid state chemistry (a) mass fractals, sets of solid particles that form aggregates and have as measure their mass that scales as I with 0 < D 3 and (b) surface fractals that consist of interfaces between solids and the vacuum and that have as measure the surface, which also scales as IP with 0 < D < 3. The fractal dimension of an object, composite, or aggregate affects the values of the heat capacity, heat conductivity, electric conductivity, mechanical resistance against deformation, specific mass, and light scattering. 

---