Sorting single-wall carbon nanotubes (SWCNTs) of different chiralities is both scientifically interesting and technologically important. Recent studies have shown that polymer aqueous two-phase extraction is a very effective way to achieve nanotube sorting. However, works published to date have demonstrated only separation of surfactant-dispersed SWCNTs, and the mechanism of chirality-dependent SWCNT partition is not well understood. Here we report a systematic study of spontaneous partition of DNA-wrapped SWCNTs in several polymer aqueous two-phase systems. We show that partition of DNA SWCNT hybrids in a given polymer two-phase system is strongly sequence-dependent and can be further modulated by salt and polymer additives. With the proper combination of DNA sequence, polymer two-phase system, and partition modulators, as many as 15 single-chirality nanotube species have been effectively purified from a synthetic mixture. As an attempt to provide a unified partition mechanism of SWCNTs dispersed by surfactants and by DNA, we present a qualitative analysis of solvation energy for SWCNT colloids in a polymer-modified aqueous phase. Our observation and analysis highlight the sensitive dependence of the hydration energy on the spatial distribution of hydrophilic functionalities.