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 (M(θ)): k₇,₃ = 3.5 × 10⁻⁵ M(θ)⁻¹ s⁻¹, k₆,₄ = 7.7 × 10⁻⁸ M(θ)⁻¹ s⁻¹, k₈,₃ = 2.3 × 10⁻⁹ M(θ)⁻¹ s⁻¹, k₆,₅ = 3.8 × 10⁻⁹ M(θ)⁻¹ s⁻¹, k₇,₅ = 1.9 × 10⁻¹¹ M(θ)⁻¹ s⁻¹, k₈,₆ = 7.7 × 10⁻¹² M(θ)⁻¹ s⁻¹, and k₇,₆ = 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.