The invention relates to regenerative, solid sorbents for adsorbing carbon dioxide from a gas mixture, including air, with the sorbent including a modified polyamine and a solid support. The modified polyamine is the reaction product of an amine and an epoxide. The sorbent provides structural integrity, as well as high selectivity and increased capacity for efficiently capturing carbon dioxide from gas mixtures, including the air. The sorbent is regenerative, and can be used through multiple cycles of adsorption-desorption.