A three-dimensional air-adsorbing structure. The structure has a three-dimensional, unitary, skeletal, porous scaffold, air-adsorbing material particles, and one or more hydrophobic binders that couple air-adsorbing material particles to each other to form agglomerates and couples particles and agglomerates to the scaffold. The structure has structure openings in the agglomerates and structure openings between agglomerates, such structure openings being open to the outside environment. The air-adsorbing material and the agglomerates are coupled to the scaffold by creating a water-based emulsion of air-adsorbing material, agglomerates of the material, and binder, and then impregnating the scaffold with this emulsion. The emulsion is dried at least in part at a temperature below the freezing point of the emulsion.