Surface modification of graphene oxide has been performed using diamine moieties with varying chain length and subsequently chemically grafted with long chain polyurethane for wrapping up of graphene sheet with large polymer chains. Functionalization of graphene and its subsequent grafting have been verified through spectroscopic measurements like NMR, FTIR and UV-visible spectroscopy and the uniform dispersion of graphene sheet in polyurethane matrix is achieved. Nanohybrids exhibit better thermal and mechanical responses along with greater self-assembly as compared to pure polymer. Nanometer dimension molecular sheet to gradual increased size of the order of tens of nanometer, hundreds of nanometer to micron scale assembly has been captured through XRD, small angle neutron scattering, AFM and optical microscopy, respectively. Nature of self-assembly associated with stronger interactions sustain the release of embedded drug (anticancerous dexamethasone) from nanohybrid and larger size of in homogeinities for longer spacer length further sustain the drug release and thereby able to control the release rate of drug by articulating the chemistry of graphene modifications with suitable spacer length of diamine. Biocompatibility of the nanohybrids is verified with cell line studies using human breast cancer cells MDA-MB-231 in terms of cell viability, cell adhesion, fluorescence image, reactive oxygen species and mitochondrial tracker measurements indicating better responses of nanohybrid vis-a-vis pure polyurethane. Thus, the control release of the dexamethasone drug from the nanohybrids along with better biological responses clearly suggests a novel biomaterial for the drug carrier. (C) 2016 Elsevier Ltd. All rights reserved.