The present disclosure pertains to methods of capturing CO2 from an environment at pressures above 1 bar by associating the environment with a porous material that has a surface area of at least 2,800 m2/g, and a total pore volume of at least 1.35 cm3/g, where a majority of pores of the porous material have diameters of less than 2 nm. The present disclosure also pertains to methods for the separation of CO2 from natural gas in an environment at partial pressures of either component above 1 bar by associating the environment with a porous material that has a surface area of at least 2,200 m2/g, and a total pore volume of at least 1.00 cm3/g, where a majority of pores of the porous material have diameters of greater than 1 nm and less than 2 nm.