Composite materials loaded with nanometer-sized reinforcing fillers are widely believed to have the potential to push polymer mechanical properties to extreme values. Realization of anticipated properties, however, has proven elusive. The analysis presented here traces this shortfall to the large-scale morphology of the filler as determined by small-angle X-ray scattering, light scattering, and electron imaging. We examine elastomeric, thermoplastic, and thermoset composites loaded with a variety of nanoscale reinforcing fillers such as precipitated silica, carbon nanotubes (single and multiwalled), and layered silicates. The conclusion is that large-scale disorder is ubiquitous in nanocomposites regardless of the level of dispersion, leading to substantial reduction of mechanical properties (modulus) compared to predictions based on idealized filler morphology.

Measurement of the fractal dimension, D, of colloidal aggregates of small silica particles is reported. We observe power-law decay of the structure factor [S(k) -k o] by both light and x-ray scattering showing that the aggregates are fractal. D is found to be 2.12+0.05, which is intermediate between recent numerical results for the kinetic models of diffusionlimited aggregation (D = 2.5) and cluster aggregation (D = 1.75), but is rather close to the value for lattice animals (D = 2.0), which are equilibrium structures. PACS numbers: 64.60.Cn, 05.40.+j, 61.10.Fr Understanding aggregation has been a primary goal in the field of colloidal physics for many years. 'In addition to its importance in commercial processes, aggregation is a prototypical example of a complicated random process which may display such features as self-similarity, scaling, and universality. 2 These features have been revealed by computer simulations.It has been shown recently, for example, that the two most popular models, diffusion-limited aggregation3 4 (DLA) and cluster-cluster aggregation 6 (CA), produce ramified structures that are self-similar in that the two-point density-density correlation function p2(r) is of a power-law form, p, (r) -r ", for values of r intermediate between the lattice constant or monomer size a and the cluster size R. Structures described by Eq. (1) are self-similar and are known as fractals; their essential geometric properties are independent of length scale. In ddimensional space, they are characterized by a fractal or Hausdorff-Besicovitch dimension D related to A by D = d -A. An immediate consequence of Eq.(1) is that the radius of gyration of a cluster RG is related to the number of particles it contains N, by N, -RD (2) A uniform object has D = d, while more open structures in which the density decreases with distance from the center have D & d. Numerical simulations have shown D to be -Sd/6 for DLA in d dimensions for both lattice (2~d~6) and nonlattice (d=2, 3) diffusion, independent of sticking coefficient s (0. 1» s~1). Cluster aggregation in which many particles diffuse and stick together to form clusters which also diffuse and stick yields self-similar aggregates having D =1.45 and 1.75 in two and three dimensions, respectively.

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Using small-angle x-ray scattering, we show that porous silica aerogel has a fractal backbone structure. The observed structure is traced to the underlying chemical (polymerization) and physical (colloid aggregation) growth processes. Comparison of scattering curves for aerogel with silica aggregates confirms this interpretation.In spite of the importance of random porous media in nature and in technology, the structure of these materials has eluded characterization.In this paper we show that certain classes of porous materials can be characterized through fractal geometry and that the appropriate geometry can be determined by small-anglex-ray scattering. We report the structure of a silica aerogel prepared by critical-point drying of an alcoholic (sic) silica gel. This material is chosen because of its exceedingly low density (0.09 g/cm3) and concomitant high porosity. We show that the porosity in this material is due to a random colloid aggregation process in the solution precursor. To our knowledge, this is the first time that the structure of a porous material has been explained in terms of random growth. Classical models of porosity-dependent properties are based on highly simplified geometrical structures like packed spheres or bottlenecked bubbles. ' Recently, fractal2 structures (percolation networks, fractal surfaces) have also been postulated to explain fluorescence3 and adsorption4 5 data for porous media. Although there have been many attempts to characterize the microstructure of porous materials, modeldependent geometric assumptions, like those above, have doomed all indirect methods.A primary goal of our work is to establish the existence of a fractally porous solid. To this end, we first outline the expected scattering patterns for simple fractal structures. The key to our interpretation is based on a qualitative distinction between surface and volume fractals. We find that the low-density aerogel has purely mass-fractal character and find no evidence for fractally rough surfaces.Scattering Pom Pactals. -To interpret scattering curves it is useful to distinguish between bulk and surface scattering. In systems without distinct surfaces, such as polymers in solutions, the scattered intensity,

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When the temperature of the gel is lowered, there is a small degree of syneresis between the gel and the confining glass cell.The principal effect of this is to dampen the standing mode observed; the frequency, however, remains unchanged. It must be concluded that the slippage occurring at the boundary is not sufficient to change the nature of the mode. ( 17) L. D. Landau and E. M. Lifshitz, "Theory of Elasticity", Pergamon Press, Oxford, 1970, Chapter 3.

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