The present invention is generally directed to new liquid-liquid extraction methods for the length-based separation of carbon nanotubes (CNTs) and other 1-dimensional nanostructures. In some embodiments, such methods are directed to separating SWNTs on the basis of their length, wherein such methods comprise the steps of: (a) functionalizing SWNTs to form functionalized SWNTs with ionizable functional moieties; (b) dissolving said functionalized SWNTs in a polar solvent to form a polar phase; (c) dissolving a substoichiometric (relative to the amount of ionizable functional moieties present on the SWNTs) amount of a phase transfer agent in a non-polar solvent to form a non-polar phase; (d) combining the polar and non-polar phases to form a bi-phase mixture; (e) adding a cationic donor species to the bi-phase mixture; and (f) agitating the bi-phase mixture to effect the preferential transport of short SWNTs into the non-polar phase such that the non-polar phase is enriched in short SWNTs and the polar phase is enriched in longer SWNTs. In other embodiments, analogous methods are used for the length-based separation of any type of CNT, and more generally, for any type of 1-dimensional nanostructure.