Single-chirality single walled carbon nanotubes (SWCNTs) have unique optoelectronic properties that can be utilized in specific applications, such as photovoltaics and biosensors. However, due to the large variety of SWCNTs and the difficulty of separation, the application of chiral SWCNTs is still limited. The post-synthesis separation of SWCNTs has been studied with great interest in the past decade. The most promising techniques include the selective adsorption of SWCNTs onto hydrogel stationary phases and aqueous two-phase extraction. In the selective adsorption onto hydrogels, the surfactant structure surrounding the SWCNTs has been shown to play an important role in the separation. While several researchers have successfully achieved separation of the semiconducting fractions by (n,m) type by manipulating the selective adsorption of the nanotubes, these processes often require multiple columns or experimental conditions that are difficult to control. However, the high-fidelity desorption of SWCNTs would provide a simpler approach that minimizes dilution and provides higher yields. Here we report that the desorption of a single-chirality (6,5) fraction in a hydrogel-packed column only occurs once a specific ratio co-surfactant solution is used. High-purity fractions of (6,5) nanotubes are obtained at this ratio even with long elution times, different total co-surfactant concentrations, and moderate temperature changes. The elution of only one (n,m) type at a specific co-surfactant ratio while other types are exposed to more surfactant suggests that each (n,m) type forms a thermodynamically-stable surfactant structure in the co-surfactant solution. These thermodynamic equilibrium states result in entropy-driven desorption at specific co-surfactant ratios, enabling high-fidelity separations of a single (n,m) type in a single column.