Functionalized carbon nanoparticles (CNPs) show great promise for various drug delivery applications. These CNPs have distinct physical and chemical properties, such as low solubility, very high conductivity, and drug loading capability, and are thus important nanodevices for cancer therapy. Cancer is a highly challenging disease, because its therapy involves distinguishing diseased cells from healthy ones. This study aimed to determine the ability of CNPs conjugated with a chemotherapeutic agent to inhibit cancer cell growth. We developed two models to determine the effectiveness of paclitaxel (PTX) as an antitumor agent bonded to single-walled carbon nanotubes (SWCNTs) varying in radius (r). The models were used to mathematically evaluate the energy arising from the PTX-SWCNT interaction. The first model divided the PTX molecule into 15 subcomponents: 4 imidazole rings, 1 group of atoms forming a cylindrical nanotube, 6 methyl groups (small spheres represented as individual CH₃ molecules), 3 carboxyl groups (medium-sized spheres represented as individual CO₂ molecules), and 1 large sphere. In the second model, PTX was modeled as a spherical cage with a spheroidal structure. Next, we determined the minimum interaction energy between each subcomponent and an SWCNT of radius r, and then summed the interactions to determine the total energy (E). The numerical results indicated that SWCNTs can be loaded with PTX. We also determined the critical nanotube r required for acceptance of the PTX molecule. We believe that the findings of this research will encourage the development of new nanodevices capable of delivering larger amounts of drugs, genes, and proteins.