Polyamines with lengths carefully tailored to the framework dimensions are appended to metal-organic frameworks such as Mg2(dobpdc) (dobpdc4-=4,4′-dioxidobiphenyl-3,3′-dicarboxylate) with the desired loading of one polyamine per two metal sites. The polyamine-appended materials show step-shaped adsorption and desorption profiles due to a cooperative CO2 adsorption/desorption mechanism. Several disclosed polyamine-appended materials exhibit strong ability to capture CO2 from various compositions. Increased stability of amines in the framework has been achieved using high molecular weight polyamine molecules that coordinate multiple metal sites in the framework. The preparation of these adsorbents as well as their characterization are provided.