(739d) A Quantitative Theory of Adsorptive Separation for the Electronic Sorting of Single-Walled Carbon Nanotubes

High surface area adsorbents, including amide baring surfaces, allow for separation of single walled carbon nanotubes (SWNT) through selective adsorption and desorption of different (n,m) chiral indices.  The mechanistic dependence on surfactant concentration and a full quantitative model of the elution order have not yet been developed. We develop a quantitative theory that describes the separation order and find kinetic rate constants of each SWNT chirality (n,m) based on the surfactant-induced, areal charge density, which ranges from 0.41 e^-/nm for (7,3) in 17mM sodium dodecyl sulfate (SDS) to 3.32 e^-/nm for (6,5) in 105mM SDS.  Adsorption onto the amide baring support is balanced by short distance hard-surface and long distance electrostatic repulsive SWNT/substrate forces, the latter of which we postulate is strongly dependent on surfactant concentration and ultimately leads to gel-based single-chirality semiconducting SWNT separation.  These molecular-scale properties are utilized to derive bulk-phase, forward adsorption rate constants for each SWNT chirality.  The resulting theory quantitatively describes the experimental elution profiles of 15 unique SWNT chiralities as a function of anionic surfactant concentration between 17 and 105mM, as well as phenomenological observations of the impact of varying preparatory conditions such as extent of ultrasonication and ultracentrifugation.  SWNT elution order and separation efficiency are primarily driven by the morphological change of SDS surfactant wrapping on the surface of the nanotube, mediated by SWNT chirality and the ionic strength of the surrounding medium.   This work provides a foundational understanding for high purity, preparative scale separation of as-produced SWNT mixtures into isolated, single-chirality fractions.