The results for cluster shape anisotropy over a broad range (10)(-3)-10(-1)) of monomer volume fractions, fv values, are presented for both two- (2d) and three-dimensional (3d) simulations of diffusion-limited (DLCA), ballistic-limited (BLCA), and reaction-limited (RLCA) cluster-cluster aggregation classes. We find that all three aggregation classes have different dilute-limit shape anisotropies, with the diffusion-limited model having the largest value of anisotropy and the reaction-limited model having the smallest. The simulation result for the cluster shape anisotropy for each of the three aggregation classes is slightly less than the corresponding prediction of the hierarchial model. In addition, we find excellent agreement between the 2d DLCA simulation results and experimental measurements of shape anisotropy. At late times, shape anisotropy decreases from the dilute-limit value.

Silica (SiO 2 ) aerosol gels were formed via Brownian aggregation of silica nanoparticles in a closed reaction chamber. A sudden and quick detonation reaction of pyrophoric silane (SiH 4 ) with either oxygen or nitrous oxide created silica nanoparticles with diameters ranging from ∼22 to 90 nm in the presence of an inert background gas with a volume fraction of ca. 10 −4 , conditions necessary for gelation. The background gas was necessary for quick thermal quenching of freshly formed silica molecules and molten nanoparticles and some control of the particle size could be achieved by variation of the gas. The silica aerosol gels were found to have very low densities in the range 4-15 mg/cm 3 and high specific surface areas of 300-500 m 2 /g. Wide angle X-ray diffraction showed that the nanoparticles were amorphous silica. Neutron scattering showed that they were arranged in networks with a fractal dimension of 1.75 between 10 and 1000 nm length scales. INTRODUCTIONIn previous work, we presented an aerosol gelation method to produce porous materials with high specific surface area and extremely low density (Dhaubhadel et al. 2007). The method involved the gelation of nanoparticles in the aerosol phase to yield a material that we have named an "aerosol gel." Unlike wellknown aerogel materials which begin with a liquid phase sol-gel step, aerosol gels are made in the gas phase. Simply said a cloud of smoke in a volume gels or freezes to form a volume spanning, very light weight, porous body; truly "frozen smoke." The initial aerosol is composed of nanometer-sized particles produced rapidly by exploding in a chamber a hydrocarbon precursor with an oxidizer, e.g., oxygen. The nanometer particles so produced aggregate and then gel on the order of tens of seconds to form the aerosol gel. The carbon materials we made previously have densities as low as 2.5 mg/cc. The current state-of-the-art Address correspondence to C. M. Sorensen, Department of Physics, Kansas State University, Manhattan, Kansas 66506, USA. E-mail: sor@phys.ksu.edu for manufacture of aerogel materials is the sol-gel/supercriticaldrying method (Brinker and Scherer 1990; Hüsing and Schubert 1998). The gas phase aerosol gelation method is a significantly different than this state-of-the-art and hence might offer advantages because (1) there is no need for a supercritical drying step as for aerogels and (2) the aerosol gel method should be applicable to a greater variety of substances. Disadvantages of our method lie in the current need for a detonation which could be hard to scale up, and it is a batch process.Gelation is a consequence of random aggregation of noncoalescing particles to form ramified fractal aggregates. Fractal aggregates have a mass-size scaling exponent, the fractal dimension D f , that is less than the spatial dimension, d, and this inequality represents a fundamental condition for gelation (Sorensen and Chakrabarti 2011). Because of this, the ratio of aggregate mean nearest neighbor separation to aggregate size declines as the aggreg...