The disclosed subject matter provides a filter that is modified by a polymer-carbon based nanomaterial nanocomposite intended to significantly enhance the performance of filtration, separation, and remediation of a broad variety of chemicals, heavy metal ions, organic matters, and living organisms. Polymeric materials, such as but not limited to poly-N-vinyl carbazole (PVK), are combined with (1) graphene (G) and/or graphene-like materials based nanomaterials and (2) graphene oxide (GO) chemically modified with a chelating agent such as but not limited to EDTA. The nanocomposite is homogenously deposited on the surface of the membrane.