Theory of structure-based carbon nanotube separations by ion-exchange chromatography of DNA/CNT hybrids

Single-stranded DNA wrap helically around individual single-walled carbon nanotubes to form DNA/CNT hybrids, which are both stable and dispersible in aqueous solution. Subjected to ion-exchange chromatography, a hybrid elutes at an ionic strength that depends on the electronic character and diameter of the core nanotube, thus providing a mechanism for separating nanotubes by chirality. We present a theoretical model for this separation process that explains all the salient features observed experimentally to date, and provides accurate predictions for critical elution salt concentration. The competition between adsorption on the stationary phase and counterion condensation in the mobile phase is characterized by estimating the difference in free energy between the two states of the hybrid. Parametric study of the DNA wrapping geometry, SWNT dielectric properties, hybrid length, and diameter indicate that the elution is most sensitive to the hybrid's effective charge density, primarily governed by the DNA helical pitch. The model correctly predicts hybrids with metallic nanotubes are weaker binding than hybrids with semiconducting nanotubes and larger diameter nanotubes are eluted at later times.