Techniques for separating bundles of carbon nanotubes into homogeneous dispersion are still under development, although a few methods have been successful at the laboratory scale. Understanding the effective interactions between carbon nanotubes in the presence of dispersing agents will provide the necessary information to develop better methods and also to refine the existing ones. We present here results from all-atom molecular dynamics simulations for aqueous flavin mononucleotide (FMN), which has been found experimentally to efficiently separate single-walled carbon nanotubes (SWNTs) based on diameter and chirality. We report results for the aggregate morphology of FMN on SWNTs of different diameters, as well as the potential of mean force between (6,6) SWNTs in the presence of aqueous FMN. The results are compared to the potential of mean force between SWNTs in aqueous sodium dodecyl sulfate (SDS). Our detailed analysis is used to explain the role of FMN, water, and sodium ions in providing a strong repulsive barrier between approaching SWNTs.