Carbon nanotubes have attracted considerable interest due to their outstanding physical, electronical and optical properties. Since those properties depends on the chirality, sorting single walled carbon nanotubes (SWCNT) by chirality is essential. Hybrids of DNA and SWCNTs have been used successfully to solve tje long-standing recalcitrant problem of structure-based sorting of complex mixtures of SWCNTs. Recently, it is shown that single stranded DNA coated SWCNTs could be separated effectively into various chiralities using an aqueous two phase system. SWCNT partition in the ATP system is determined by the SWCNT solvation energy difference between the two phases. In this way, we suggest that the ATP process is both a technique for separation and a method by which to evaluate and rank hydration or solvation free energy. In this study, we performed a systematic study of various DNA sequences on different species of SWCNT in ATP systems of two different polymer composition. We observe strong sequence-dependent of partitioning. We developed a model that can phenomenologically describe the experimental observation well and be used to extract a quantitative measure of relative solvation free energy of various DNA/SWCNT hybrids. Furthermore, to investigate a structural basis for experimental findings, we have employed molecular dynamics to examine a few of the ssDNA/CNT combinations.