TECHNOLOGY FOCUS - INORGANIC CHEMISTRY - Preferred Method: The nanostructures are to be grown from the catalyst islands by preparing graphite nano-filaments via decomposition of carbon-containing gas mixture precursors on the polymeric structure at an elevated temperature (preferably 500-2000degreesF). The method may involve combining the sol-gel polymerization of precursor mixtures, casing the sol-gel mixtures into a retort, curing the sol-gel mixtures, drying extraction of liquid from the cured sol-gel mixtures, reducing and carbonizing the cured sol-gel mixtures in reducing atmosphere of hydrogen to produce a catalyzed carbon aerogel monolith structure, and growing graphite nano-filaments on the reticulated catalyzed carbon aerogel monolith structures.Preferred Component: The nanostructure comprise a structure of platelet carbon nano-fiber, cylindrical carbon nanostructure, ribbon carbon nano-fiber, faceted tubular carbon nano-fiber, or herringbone carbon nano-fiber. The molecular gas is hydrogen and oxygen. The nanostructures comprise solid fibers or hollow tubes of carbon. The deposited metal catalyst is transition metal consisting of scandium, titanium, vanadium, manganese, iron, cobalt, nickel, copper, and/or zinc. The carbon-containing gas mixture may comprise carbon dioxide, carbon monoxide, or hydrogen. The precursor mixtures are sol-gel catalyst precursors, metal cation salts and organic acid metal salts/polymer sol-gel of acetates, benzoates, carbonates, chlorides, epoxides, formates, hydroxides, isopropoxides, nitrates and/or oxalates of metal precursors. The sol-gel catalyst precursors comprise sodium carbonate, hydrochloric acid, toluenesulfonic acid, and/or phosphoric acid. The oxalates of metal precursors comprise chromium, cobalt, copper, iron, and/or nickel.    TECHNOLOGY FOCUS - MECHANICAL ENGINEERING - Preferred Parameter: The interconnected particles have a diameter of up to 100 Angstrom . The open cells have a size of up to 1000 Angstrom .Preferred Apparatus: The apparatus includes a catalyst disposed on the polymeric structure bonded to carboxyl sites disposed on the polymeric structure to form catalyst islands. The pressure vessel is configured to receive the molecular gas at 77-300K.    TECHNOLOGY FOCUS - METALLURGY - Preferred Composition: The deposed metal catalyst comprises alloy of 70% iron and 30% copper.Preferred Material: The oxalates of metal precursors may comprise alloys of chromium, cobalt, copper, iron, and nickel metals.    TECHNOLOGY FOCUS - ORGANIC CHEMISTRY - Preferred Method: The nanostructures are to be grown from the catalyst islands by preparing graphite nano-filaments via decomposition of carbon-containing gas mixture precursors on the polymeric structure at an elevated temperature (preferably 500-2000degreesF). The method may involve combining the sol-gel polymerization of precursor mixtures, casing the sol-gel mixtures into a retort, curing the sol-gel mixtures, drying extraction of liquid from the cured sol-gel mixtures, reducing and carbonizing the cured sol-gel mixtures in reducing atmosphere of hydrogen to produce a catalyzed carbon aerogel monolith structure, and growing graphite nano-filaments on the reticulated catalyzed carbon aerogel monolith structures.Preferred Component: The nanostructure comprise a structure of platelet carbon nano-fiber, cylindrical carbon nanostructure, ribbon carbon nano-fiber, faceted tubular carbon nano-fiber, or herringbone carbon nano-fiber. The molecular gas is hydrogen and oxygen. The nanostructures comprise solid fibers or hollow tubes of carbon. The deposited metal catalyst is transition metal consisting of scandium, titanium, vanadium, manganese, iron, cobalt, nickel, copper, and/or zinc. The carbon-containing gas mixture may comprise carbon dioxide, carbon monoxide, or hydrogen. The precursor mixtures are sol-gel catalyst precursors, metal cation salts and organic acid metal salts/polymer sol-gel of acetates, benzoates, carbonates, chlorides, epoxides, formates, hydroxides, isopropoxides, nitrates and/or oxalates of metal precursors. The sol-gel catalyst precursors comprise sodium carbonate, hydrochloric acid, toluenesulfonic acid, and/or phosphoric acid. The oxalates of metal precursors comprise chromium, cobalt, copper, iron, and/or nickel.    TECHNOLOGY FOCUS - ORGANIC CHEMISTRY - Preferred Component: The carbon-containing gas mixture comprises gases of acetylene, benzene, or methane. The precursor mixtures may be organic aerogel precursors, or solvent precursors. The organic aerogel precursors comprise resorcinol-formaldehyde (RF), phenolic-furfural (PF), melamine-formaldehyde, or phenolic-novolak resins. The solvent precursors comprise acetic acid, acetone, butane, butyric acid, ethanol, ethyl ether, formic acid, hexane, isopentane, isopropanol, methanol, n-propanol, pentanoic acid, pentane, l-propanol, and/or propionic acid.    TECHNOLOGY FOCUS - POLYMERS - Preferred Material: The polymeric structure of interconnected particles creating open cells comprises a polymeric structure formed from a solution of formaldehyde-resorcinol (RF) or phenolicfurfural (PF). It comprises a carbon aerogel structure having a density of 100 mg/cc and a surface area of 0.2-3000 m2/gm. It comprises a catalyzed carbon aerogel monolith structure.