A cross-linked polymeric material is formed by polymerizing a polyethylene glycol di(meth)acrylate and a sulfonate salt containing a double bond that facilitates covalent bonding of the sulfonate salt to the polyethylene glycol di(meth)acrylate. In the polymeric material, cations from the salt are optionally replaced with metal ions selected from sodium, lithium, aluminum, magnesium, and zinc. Related methods and membranes and batteries including the cross-linked polymeric material are also provided.