Fused aromatic networks (FANs) are a new generation of porous organic networks (PONs), which are thermodynamic products. FANs are also kinetic products with low crystallinity. Nevertheless, their high physicochemical stability suggests many potential applications. This work reports three structures with their fully fused aromatic units vertically (V), horizontally (H), and three-dimensionally (3D) linked to the growth direction, forming “standing” FAN (VS-FAN), “planar” FAN (HP-FAN), and 3D-FAN, respectively. Their performance as sorbent materials was evaluated. While the VS-FAN has the fastest kinetics for CH4 and I2 adsorption due to the highest segmental freedom, the HP-FAN exhibits the best separation selectivity of the CH4/N2 mixture due to the strongest segmental confinement. The 3D-FAN displays the highest adsorption capacity of CH4 because of the highest specific surface area. The results suggest that the different segmental arrangements may critically affect the sorbent performance of FANs.