DNA-wrapped single walled carbon nanotubes (SWNTs) have found a widespread use in a variety of nanotechnology applications. Yet, the relationship between structural conformation, binding affinity and kinetic stability of these polymers on SWNTs remains poorly understood. Here, we used molecular dynamics (MD) simulations and experiments to explore this relationship for short oligonucleotides adsorbed on SWNTs. First, using classical MD simulations of oligonucleotide-(9,4)-SWNT hybrid complexes, we explored the relationship between ssDNA and ssRNA surface conformation and sequence chemistry. We screened the conformation of 36 sequences of short ssDNA and ssRNA polymers on (9,4) SWNT, where the contour lengths were selected so the polymers can, to a first approximation, wrap once around the SWNT circumference. From these screens, we identified structural motifs that we broadly classified into "rings" and "non-rings." Then, several sequences were selected for detailed investigations. We used temperature replica exchange MD calculations to compute two-dimensional free energy landscapes characterizing the conformations of select sequences. "Ring" conformations seemed to be driven primarily by sequence chemistry. Specifically, strong (n,n+2) nucleotide interactions and the ability of the polymer to form compact structures, as for example, through sharp bends in the nucleotide backbone, correlated with ring-forming propensity. However, ring-formation probability was found to be uncorrelated with free energy of oligonucleotide binding to SWNTs (∆Gbind). Conformational analyses of oligonucleotides, computed free energy of binding of oligonucleotides to SWNTs, and experimentally determined kinetic stability measurements show that ∆Gbind is the primary correlate for kinetic stability. The probability of the sequence to adopt a compact, ring-like conformation is shown to play a secondary role that still contributes measurably to kinetic stability. For example, sequences that form stable compact rings (C-rich sequences) could compensate for their relatively lower ∆Gbind and exhibit kinetic stability, while sequences with strong ∆Gbind (such as (TG)3(GT)3) were found to be kinetically stable despite their low ring formation propensity. We conclude that the stability of adsorbed oligonucleotides is primarily driven by its free energy of binding and that if ring-like structural motifs form, they would contribute positively to stability.