Scaling of binding affinities and cooperativities of surfactants on carbon nanotubes

High-end applications of single-walled carbon nanotube (SWNT) require detailed understanding of their binding affinity (K_d) with surfactants. Here, we quantitatively determined the comprehensive K_d and aggregation number (γ) of nine nonionic and anionic surfactants according to SWNT chirality. Photoluminescence (PL)-based titration using flavin mononucleotide (FMN)-SWNT complexes showing the largest redshifted optical transition enabled quantitative comparison of the surfactants and displayed distinct first and second regimes which correspond to partial and full replacements of FMN, respectively. Especially, the second transition exhibited sigmoidal PL change whose middle point denoted by the inverse of K_d slightly differs from critical micelle concentration of surfactant alone, depending on its functional groups. Moreover, nonionic surfactants displayed larger K_d and lower γ values than the anionic did. Specifically, K_d values between Pluronic F108 and sodium dodecyl sulfonate differ by four orders of magnitude. Such differences were rationalized in terms of the occupied volume of the micelle based on the hydrodynamic volume and γ. During the replacement, K_d and γ were affected by the degree of surfactant rearrangement induced by aging process, leading to more stable complex. Scaling the interactions between surfactant and SWNT provides useful guidelines to design novel SWNT sorting method using more than two surfactants.