Two-dimensional nanofiber mats based on a mixture of polybenzimidazole with telechelic oligoperoxide are obtained by the method of electrospinning. It is shown that the reactive peroxide groups on the surface of nanofibers can be modified by the initiation of radical polymerization and grafting of various polymeric chains. The phenomenon of "negative" capacitance is detected for the impedance dependences of synthesized nanofibers. The influence of grafting of various polymeric chains to the surface of nanofibers on the polarization characteristics of nanocomposites is investigated. It is shown that some of the obtained structures are characterized by a combination of a low (< 1) tangent of dielectric losses in the infralow-frequency region (0.001-0.1 Hz) and high values of the dielectric permittivity (similar to 10(6)). The possibilities of application of materials of this kind in the production of quantum batteries are discussed.