Arginine-rich proteins (e.g., lysozyme) or poly-l-arginine peptides have been suggested as solvating and dispersing agents for single-wall carbon nanotubes (CNTs) in water. In addition, protein structure-function in porous and hydrophobic materials is of broad interest. The amino acid residue, arginine (Arg(+)), has been implicated as an important mediator of protein/peptide-CNT interactions. To understand the structural and thermodynamic aspects of this interaction at the molecular level, we employ molecular dynamics (MD) simulations of the protein lysozyme in the interior of a CNT, as well as of free solutions of Arg(+) in the presence of a CNT. To dissect the Arg(+)-CNT interaction further, we also perform simulations of aqueous solutions of the guanidinium ion (Gdm(+)) and the norvaline (Nva) residue in the presence of a CNT. We show that the interactions of lysozyme with the CNT are mediated by the surface Arg(+) residues. The strong interaction of Arg(+) residue with the CNT is primarily driven by the favorable interactions of the Gdm(+) group with the CNT wall. The Gdm(+) group is not as well-hydrated on its flat sides, which binds to the CNT wall. This is consistent with a similar binding of Gdm(+) ions to a hydrophobic polymer. In contrast, the Nva residue, which lacks the Gdm(+) group, binds to the CNT weakly. We present details of the free energy of binding, molecular structure, and dynamics of these solutes on the CNT surface. Our results highlight the important role of Arg(+) residues in protein-CNT or protein-carbon-based material interactions. Such interactions could be manipulated precisely through protein engineering, thereby offering control over protein orientation and structure on CNTs, graphene, or other hydrophobic interfaces.