Experimental studies have demonstrated that nanoparticles can affect the rate of protein self-assembly, possibly interfering with the development of protein misfolding diseases such as Alzheimers, Parkinsons and prion disease caused by aggregation and fibril formation of amyloid-prone proteins. We employ classical molecular dynamics simulations and large-scale density functional theory calculations to investigate the effects of nanomaterials on the structure, dynamics and binding of an amyloidogenic peptide apoC-II(60-70). We show that the binding affinity of this peptide to carbonaceous nanomaterials such as C60, nanotubes and graphene decreases with increasing nanoparticle curvature. Strong binding is facilitated by the large contact area available for xcfx80-stacking between the aromatic residues of the peptide and the extended surfaces of graphene and the nanotube. The highly curved fullerene surface exhibits reduced efficiency for xcfx80-stacking but promotes increased peptide dynamics. We postulate that the increase in conformational dynamics of the amyloid peptide can be unfavorable for the formation of fibril competent structures. In contrast, extended fibril forming peptide conformations are promoted by the nanotube and graphene surfaces which can provide a template for fibril-growth. 