The interface of polyetheretherketone (PEEK) with carbon nanotubes (CNTs) and graphene is investigated using density functional theory and molecular dynamics within the REAXFF-lg interatomic interaction framework. The dependence of PEEK adsorption energy on the polymer chain length, temperature, starting adsorption configuration of the fully stretched conformation, and on the nature of the substrate was investigated. Overall, the interface between graphene and the polymers yield larger adsorption energies than the CNTs. Adsorption energies decrease with increasing temperature while for the CNT substrates, there is a slight dependence on the initial relative orientation between the nanotubes and the extended polymer chain. This is the first study on this interface, to the best of the authors' knowledge, with such a wide spectrum of relevant variables.