Chapter 10:Modeling of Stiffness,Strength,and Structure 467 Fig.10.5.SEM images of crosslinked silica aerogels.The clusters of secondary nanoparticles (round particles)and the mesopores (dark spots)are clearly visible: (a)30%strain-no appreciable change in mesoporous structure,(b)45%strain- gradual decrease in the mesoporosity,few dark spots,and (c)77%strain appreciable loss of porosity,particles are squeezed closer to one another The shape of clusters or cluster configuration,the existence of voids of all sizes,and the gradual loss of connectivity among mesoporous particles suggest that a fractal dimension can be attributed to the x-aerogel structures as a useful descriptive parameter [5].The fractal dimension of a mesoporous structure can be determined from its particle orientation within a sphere of a given radius or from the slope of a radial distribution function.It was reported in the literature [5]that not only the mass of aerogel but also other properties,such as vibrational dynamics,scale according to aerogel's fractal dimension.In general,due to its inherent porosity,the aerogel morphology represents a fractal dimension of less than 3;and its fractal dimension decreases with decreasing cluster densities,as presented later in this chapter. In this study,a three-dimensional distinct element analysis (DEA) simulation was performed to determine the structure-property relationship of nanostructured x-aerogel material.The model attempted to incorporate microscale effects-such as particle bond stiffness,bond strength,particle frictional coefficient,initial cluster porosity (or density),and density ofFig. 10.5. SEM images of crosslinked silica aerogels. The clusters of secondary nanoparticles (round particles) and the mesopores (dark spots) are clearly visible: (a) 30% strain – no appreciable change in mesoporous structure, (b) 45% strain – gradual decrease in the mesoporosity, few dark spots, and (c) 77% strain – appreciable loss of porosity, particles are squeezed closer to one another In this study, a three-dimensional distinct element analysis (DEA) simulation was performed to determine the structure–property relationship of nanostructured x-aerogel material. The model attempted to incorporate microscale effects – such as particle bond stiffness, bond strength, particle frictional coefficient, initial cluster porosity (or density), and density of Chapter 10: Modeling of Stiffness, Strength, and Structure The shape of clusters or cluster configuration, the existence of voids of all sizes, and the gradual loss of connectivity among mesoporous particles suggest that a fractal dimension can be attributed to the x-aerogel structures as a useful descriptive parameter [5]. The fractal dimension of a mesoporous structure can be determined from its particle orientation within a sphere of a given radius or from the slope of a radial distribution function. It was reported in the literature [5] that not only the mass of aerogel but also other properties, such as vibrational dynamics, scale according to aerogel’s fractal dimension. In general, due to its inherent porosity, the aerogel morphology represents a fractal dimension of less than 3; and its fractal dimension decreases with decreasing cluster densities, as presented later in this chapter. 467