Fractal growth of carbon schwarzites

The potential energy, the thermodynamic properties and the growth conditions of random carbon schwarzites are theoretically investigated in connection with their topological properties and self-affine structure. An analysis based on numerical simulations of transmission electron microscopy images permits to assign certain carbon foam, recently produced by means of supersonic cluster beam deposition, to self-affine random schwarzites. It is shown that self-affinity makes their thermodynamic properties non-extensive. The fractal growth exponent is shown to be related to the parameter q-1 of the Tsallis non-extensive entropy.