The importance of the role of alkane solvents in the self-assembly process of pi-conjugated molecules is well recognized but hardly understood. Here we present our results on the X-ray diffraction studies that we conducted to gain insight into the supramolecular structure of mixtures of a bipyridine-based molecule (1) with alkanes. Independent of the alkane used (linear or branched), above x(w) > 0.06 (with x(w) being the weight fraction of 1) the mixtures show lyotropic liquid-crystalline behavior. The nature of the lyomesophase depends only on x(w) and not on the nature of the alkane (linear or branched). A columnar rectangular phase is present when x(w) > 0.66. Upon dilution of 1, a columnar hexagonal phase is assigned first (0.50 < x(w) < 0.65), and finally a columnar nematic phase is observed when x(w) < 0.50. Concentration-dependent SAXD measurements revealed that the dilution of I can be viewed as a swelling process. First, solvent molecules occupy space between the columns formed by 1, which are not disrupted. This process can quantitatively be described by a 2D swelling model. Only at lower concentrations does 3D swelling start as the columns start breaking into shorter fragments.