Cluster fractal porosity

In our studies, we consider several types of aggregated structures such as bispheres, linear chains, plane arrays on a plane rectangular lattice, compact and porous body-centered clusters embedded on the cubic lattice (bcc clusters, the porosity was simulated by random elimination of monomers), and random fractal aggregates (RF clusters). To generate RE clusters, a three-dimensional lattice model with Brownian or linear trajectories of both single particles and intermediate clusters was employed for computer simulations of aggregation process. At the initial time moment, = 50,000 particles are generated at... 

Note that the fractal dimensions discussed here are the fractal dimensions of the excitation transfer paths connecting the hydration centers located on the inner surface of the pores. Due to the low humidity, all of the water molecules absorbed by the materials are bound to these centers. The paths of the excitation transfer span along the fractal pore surface and depict the backbone of clusters formed by the pores on a scale that is larger than the characteristic distance between the hydration centers on the pore surface. Thus the fractal dimension of the paths Dp approximates the real surface fractal dimension in the considered scale interval. For random porous structures, Dp can be also associated with the fractal dimension D, of the porous space Dp = Dr. Therefore, the fractal dimension Dp can be used for porosity calculations in the framework of the fractal models of the porosity. 

A synthetic gel of silica is a two phase solid-liquid material, amorphous and extremely porous (70-99% of porosity). The bulk density of the solid phase is typically in the range of 0.5-0.1 g/cm and the specific surface area is several hundred of m /g [13,14]. The gel network can be described as an assembly of clusters ( 50 nm). The clusters can be fractal (D/ l. 8-2.4), each being composed by aggregates of small particles ( l-2 nm) [20-22] (Chap. 2). 

Textural Evolution. The textural evolution of aerogels with sintering is usually described using the specific surface area, the porous features (porosity, mean pore size distribution) or the solid phase microstructure (fractal dimension, cluster and primary particle... 

The values of the mass fractal dimension (obtained from SAXS [16]) show how the structure of the silicate polymers in the sol varies with the different routes these sols take to the same final dilution, H20/Si ratio and pH. The mass fractal dilnensions are considerably different. We would expect AAB, which is right at the borderline of D = 1.5 for Equation 2, to exhibit different behavior than B2 with D = 2.3. However, Table I shows that both sols exhibit an increase in porosity with sol age (once the pore-plugging species are burned out of B2). The reason for this is the tradeoff between cluster porosity and cluster interpenetration. B2 clusters are less porous but pack less efficiently than AAB clusters. This tradeoff is illustrated schematically in Figure 1. 

Both porosity and fractal dimension of the generated clusters show good agreement with the predicted values resulting from (10.22) to (10.24). Slight differences arise from the accomplished random agglomerate creation process. Furthermore, the determination of the fractal dimension by the box counting method [41] has a limited accuracy for relatively low particle numbers. 

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