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...
