A Kinetic Model for the Deterministic Prediction of Gel-Based Single-Chirality Single-Walled Carbon Nanotube Separation

We propose a kinetic model that describes the separation of single-chirality semiconducting carbon nanotubes based on the chirality-selective adsorption to specific hydrogels. Experimental elution profiles of the (7,3), (6,4), (6,5), (8,3), (8,6), (7,5), and (7,6) species are well described by an irreversible, first-order site association kinetic model with a single rate constant describing the adsorption of each SWNT to the immobile gel phase. Specifically, we find first-order binding rate constants for seven experimentally separated nanotubes normalized by the binding site molarity (<i>M</i>_θ): <i>k</i>_7,3 = 3.5 × 10^–5 M_θ^–1 s^–1, <i>k</i>_6,4 = 7.7 × 10^–8 M_θ^–1 s^–1, <i>k</i>_8,3 = 2.3 × 10^–9 M_θ^–1 s^–1, <i>k</i>_6,5 = 3.8 × 10^–9 M_θ^–1 s^–1, <i>k</i>_7,5 = 1.9 × 10^–11 M_θ^–1 s^–1, <i>k</i>_8,6 = 7.7 × 10^–12 M_θ^–1 s^–1, and <i>k</i>_7,6 = 3.8 × 10^–12 M_θ^–1 s^–1. These results, as well as additional control experiments, unambiguously identify the separation process as a selective adsorption. Unlike certain chromatographic processes with retention time dependence, this separation procedure can be scaled to arbitrarily large volumes, as we demonstrate. This study provides a foundation for both the mechanistic understanding of gel-based SWNT separation as well as the potential industrial-scale realization of single-chirality production of carbon nanotubes