Understanding the interaction of carbon nanomaterials with proteins is essential for determining the potential effects of these materials On health and in the design of biotechnology based on them. Here we leverage explicit-solvent molecular simulation and multidimensional free energy calculations to investigate how adsorption to carbon nanomaterial surfaces, affects the conformational equilibrium of alanine dipeptide, a widely used model of protein backbone structure. We find that the two most favorable structures of alanine dipeptide on graphene (or large carbon nanotubes) correspond to the two amide linkages lying in the same plane, flat against the surface, rather than the nonplanar alpha-helix-like and beta-sheet-like conformations that predominate in aqueous solution. On graphenic surfaces, the latter conformations are metastable and most Often correspond to amide-pi stacking of the N-terminal amide. The calculations highlight the key role of amide-pi interactions in determining the conformational equilibrium. Lesser but significant contributions from hydrogen bonding to the high density interfacial water layer or to the hydroxy groups of hydroxylated graphene also define the most favorable conformations. This work should yield insight on the influence of carbon nanotubes, graphene, and their functionalized derivatives on protein structure.