Carbon blacks (CB) demonstrate varied structural features on length scales from angstroms to micrometers. Widely used as fillers in polymers, carbon blacks improve the mechanical and electrical properties of the host material. In general, CB is a low-dimensional mass-fractal aggregate of carbonaceous primary particles. Here we investigate the effect of processing on the interpenetration of aggregates in CB/polymer composites by small-angle X-ray scattering (SAXS). We performed SAXS measurements on a series of N330/EPR and N330/HDPE composites containing different amounts of a commercially available N330 carbon black. N330/HDPE composites were prepared by two different methods. The first method is Brabender dispersion of depelletized N330 in molten polymer; the second method is high-shear mixing of depelletized N330 in HDPE dissolved in a good solvent and subsequent addition of this mixture to a poor solvent for polyethylene. SAXS experiments were performed at the University of New Mexico/Sandia National Laboratories SAXS Laboratory. Data were collected on the Bonse-Hart camera with a q-range of 0.003 < q < 1 nm -1 . This wide q-range probes the structure of both the primary carbon black particles and aggregates of these particles. Depelletized N330 displays two power law regimes from which we deduce a surface-fractal dimension Ds ) 2.3 for the primary particles and a mass fractal dimension Dm ) 1.8 for the aggregate. For pelletized N330, the mass fractal domain vanishes as a result of aggregate interpenetration and, therefore, loss of correlation between primary particles. For N330/HDPE composites prepared by the Brabender method, the SAXS curve is similar to that obtained for the depelletized samples, indicative of little to no interpenetration of the aggregates. For N330/HDPE composites prepared by the solvent method and N330/EPR composites the SAXS curve is similar to that obtained for pelletized N330, indicative of extensive interpenetration of the aggregates.

Small-angle x-ray scattering, nitrogen adsorption, and scanning tunneling microscopy show that a series of activated carbons host an extended fractal network of channels with dimension D p 2.8 3.0 (pore fractal), channel width 15 20 Å (lower end of scaling), network diameter 3000 3400 Å (upper end of scaling), and porosity of 0.3-0.6. We interpret the network as a stack of quasiplanar invasion percolation clusters, formed by oxidative removal of walls between closed voids of diameter of ϳ10 Å and held in registry by fibrils of the biological precursor, and point out unique applications. DOI: 10.1103/PhysRevLett.88.115502 PACS numbers: 61.10.Eq, 47.55.Mh, 61.43.Hv, 81.05.Rm Since the first experimental studies of fractal surfaces of disordered solids [1], it has been conjectured that situations may exist in which the pore space -as opposed to the solid, or the surface alone -is fractal. Such fractal networks of channels crisscrossing the solid, termed pore fractals or "negative image" of mass fractals, have attracted interest as a laboratory for unusual dynamics of confined processes, induced by the long-range correlation of the pore space. The scaling laws predicted relate the dynamic exponents to the fractal and spectral dimensions (spacefilling and branching properties) of the network and include anomalous diffusion, reaction, free motion [2], phase transitions [3], electric conduction of pore fluid [4], and hydrodynamic flow [5]. Here we report the first welldocumented case of a pore fractal.The network is a new member in the family of nanostructured carbons. Its channel width is 15 20 Å, comparable to the width of single-wall carbon nanotubes, but instead of forming an assembly of freestanding tubes or bundle of tubes, the channels are embedded in a solid and connected. The network is of multiple interest: (i) Its synthesis differs vastly from that of isolated nanotubes. Created by controlled oxidation, a mainstay of mass production of porous carbons, it promises to be a low-cost competitor of isolated nanotubes for gas storage. (ii) For gas storage, it has outstanding mechanical stability, nanofluidic properties (rapid transport through branched channels), and capacity (high porosity, condensation in high dimensions) compared to nanotube bundles [6]. (iii) It offers a stage for "chemistry in confined spaces" and control of pathways similar to zeolites and other microscopic vessels [7]. (iv) The extended scaling regime, created by what we believe is invasion percolation, provides a unique platform to compare predicted dynamic exponents with experiment. [8] have been put forth as pore fractals, but these proposals have been controversial or withdrawn [9]. Pore fractals are more challenging to ascertain than mass or surface fractals because they do not reveal their fractality when probed with material yardsticks: the pore-size distribution of a pore fractal is a delta function (mass and surface fractals give a power law), so an intruding nonwetting liquid, capillary condensate, or adsorbed layer will eithe...