NOVELTY - Forming (M1) a polymeric nanocomposite involves combining at least one monomer to form a mixture; adding several carbon fibers to the mixture prior to or concurrently with formation of a polymer from the monomers; polymerizing the monomers to form the polymer; and adding a hydrophobic agent and a plasticizer to the mixture to form the polymer nanocomposite.    USE - For preparation of polymeric nanocomposite for making battery separator or purification device; for making rechargeable battery e.g. lithium ion battery (claimed); in fuel cells.    ADVANTAGE - The polymeric nanocomposites have enhanced mechanical strength and electrochemical properties, are thermally stable, have high ionic conductivity and have high wettability. The battery separator prepared by using the polymeric nanocomposite has an electrolytic ionic conductivity of 0.9x 10-1 to 1.25x 10-1 S-cm-1; a tensile strength of 2100-2200 kg-f-cm-2; and contact angle of 19-23 degrees . The tensile strength of the polymeric nanocomposite is higher than the tensile strength of commercial lithium (Li)-ion battery separators.    DETAILED DESCRIPTION - INDEPENDENT CLAIMS are included for the following:    (1) a polymeric nanocomposite formed by the method (M1);    (2) a polymeric nanocomposite comprising a polymeric material having several hybrid carbon fibers embedded in it, where the hybrid carbon fibers contain carbon microfibers and carbon nanofibers;    (3) a battery separator comprising polyvinyl alcohol having several hybrid carbon fibers embedded in it, where the hybrid carbon fibers comprise carbon microfibers and carbon nanofibers;    (4) a lithium ion battery comprising a battery separator formed of polyvinyl alcohol having several hybrid carbon fibers embedded in it, where the hybrid carbon fibers comprise carbon microfibers and carbon nanofibers; and    (5) a rechargeable battery comprising at least one anode, at least one cathode, at least one battery separator formed of polyvinyl alcohol having several hybrid carbon fibers embedded in it, and an electrolyte in ionic communication with the anode and the cathode through the battery separator.