Abstract: Methods and apparatuses for forming carbon nanostructures from a polymer mixture. The methods include the steps of mixing the pre-formed polymer with a liquid to form a polymer mixture, freezing the polymer mixture at an effective freezing rate greater than or equal to 103 Kelvin per second to form a polymer cast within the frozen liquid, separating the polymer cast from the frozen liquid by sublimating the frozen liquid, and carbonizing the polymer cast to form a carbon nanostructure. Variations of these methods are included in the scope of the invention and produce materials with varying properties. Through control of the freezing process, the nanomorphology of the resultant structure may be modulated. Nanostructures formed according to these methods are also claimed.