[en] Neutron scattering experiments have been carried out on low-coverage films of the aromatic p-phenylene oligomer molecules (p-nP, C_6nH_10+4(n-2), where n indicates the number of phenyl units per molecule) physisorbed onto the surface of graphite. The molecular arrangement within these films has been determined as a function of temperature, number of molecular layers, and molecular length. Analysis of the diffraction data reveals two-dimensional film structures consistent for molecules having their long-axis parallel to the underlying substrate. The experimental measurements provide evidence for a melting transition in a monolayer film and thermal expansion of a bilayer film of p-terphenyl (p-3P). The planes of the phenyl rings are approximately parallel to the substrate in the monolayer structure but rotate out of this plane by 60 ± 20^o in the bilayer film of p-3P. As the number of phenyl units is increased from n = 3 to n = 6, bilayer structures are observed having similar packing arrangements of the molecules but with lattice parameters that scale with molecular length.