Achieving long-range order with surface-supported supramolecular assemblies is one of the pressing challenges in the prospering field of non-covalent surface functionalization. Having access to defect-free on-surface molecular assemblies will pave the way for various nanotechnology applications. Here we report the synthesis of two libraries of naphthalenediimides (NDIs) symmetrically functionalized with long aliphatic chains (C-28 and C-33) and their self-assembly at the 1-phenyloctane/highly oriented pyrolytic graphite (1-PO/HOPG) interface. The two NDI libraries differ by the presence/absence of an internal double bond in each aliphatic chain (unsaturated and saturated compounds, respectively). All molecules assemble into lamellar arrangements, with the NDI cores lying flat and forming ID rows on the surface, while the carbon chains separate the 1D rows from each other. Importantly, the presence of the unsaturation plays a dominant role in the arrangement of the aliphatic chains, as it exclusively favors interdigitation. The fully saturated tails, instead, self-assemble into a combination of either interdigitated or non-interdigitated diagonal arrangements. This difference in packing is spectacularly amplified at the whole surface level and results in almost defect-free self-assembled monolayers for the unsaturated compounds. In contrast, the monolayers of the saturated counterparts are globally disordered, even though they locally preserve the lamellar arrangements. The experimental observations are supported by computational studies and are rationalized in terms of stronger van der Waals interactions in the case of the unsaturated compounds. Our investigation reveals the paramount role played by internal double bonds on the self-assembly of discrete large molecules at the liquid/solid interface.