A method of extracting a critical mineral cation from a composition is provided. The composition can be any type of composition having critical minerals. The method can include contacting a polyanion to a composition, wherein the composition includes the critical mineral cation. The method includes complexing the critical mineral cation with the polyanion to form a polyan-ion/cation complex in the composition. The method can include separating the polyanion/cation complex from the composition. The method can also include releasing the critical mineral cation from the polyanion.

A method of extracting a critical mineral cation from a composition is provided. The composition can be any type of composition having critical minerals. The method can include contacting a polyanion to a composition, wherein the composition includes the critical mineral cation. The method includes complexing the critical mineral cation with the polyanion to form a polyan-ion/cation complex in the composition. The method can include separating the polyanion/cation complex from the composition. The method can also include releasing the critical mineral cation from the polyanion.

A method for fixing carbon dioxide may include: circulating a solvent containing a polyol compound through a slag layer formed by charging slag containing calcium in a container; aerating, with a gas containing carbon dioxide, a calcium extract obtained by passage of the solvent through the slag layer in the circulating; and separating, by solid-liquid separation, a precipitate precipitated from a mixed solution obtained in the aerating. In the circulating, the solvent may be circulated at a velocity at which the slag layer does not flow.

A method for fixing carbon dioxide may include: circulating a solvent containing a polyol compound through a slag layer formed by charging slag containing calcium in a container; aerating, with a gas containing carbon dioxide, a calcium extract obtained by passage of the solvent through the slag layer in the circulating; and separating, by solid-liquid separation, a precipitate precipitated from a mixed solution obtained in the aerating. In the circulating, the solvent may be circulated at a velocity at which the slag layer does not flow.