Aggregate fractal dimension

FIGURE 6.21 Computer generated aggregate assuming particle-partide aggregation. Fractal dimension of 1.5 in two dimensions made to simulate a fractal dimension of 2.5 in three dimensions. Printed, with permission from Sutherland [72]. 

Particle size and aggregate fractal dimension were measured with a Malvern Instruments Mastersizer/E. A 100 mm lens was used to measure particle sizes between 200 nm and 110 im (the 45 mm lens allowed particle analysis from 50 nm to 80 pm). Measurements were taken immediately after filling the cell to avoid settling effects, and no stirring was applied. 

In Fig. 1.2, the images of the nanocomposites studied, obtained in the force modulation regime, and corresponding to them nanoparticles aggregate, fractal dimension (d distributions are shown. As it follows Ifom the deduced values of dj = 2.40-2.48), nanofiller particles aggregates in the... 

This relationship was used to calculate aggregate fractal dimensions from previous settling rate studies. However, this model was not found to describe the settling behaviour of fractal aggregates adequately due to the perhaps unwarranted assumption that and / are the only variables affecting U, which implies that the drag coefficient will be the same for fractals as for impermeable spheres in the laminar flow region 1). 

Logan and Wilkinson [116] improved the approach of Li and Ganczarczyk [117] by incorporating into the model a relationship between the aggregate projected area A, /, and the 2d aggregate fractal dimension d2f to account for surface area differences between fractals and equivalent-sized spheres. Since the settling velocity U... 

Figure 5.12 Rg versus m I m for aggregates of N primary particles. The circle diameters are directly proportional to the aggregate fractal dimensions A Reproduced by permission of Elsevier.

Raper J.A. and Amal, R. (1993). Measurement of aggregate fractal dimension using static light scattering. Part. Part. Syst. Charact., 10, 239-245. 

Figure la. Fractal aggregate, constructed by computer simulated diffusion limited aggregation. Fractal dimension D = 1.44... 

The aggregate fractal dimension dp is a function of size distribution of constituting particles, solids concentration, temperature, pH, ionic strength and polymer concentration [14, 33-35]. Computer simulation has been applied extensively [36] to study both DLA and RLA and predict aggregate structure by manipulating simulation parameters such as the random walk size [37, 38]. 

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