Abstract
Constructing conductive filler networks with high efficiency is essential to fabricating functional polymer composites. Although two-dimensional (2D) sheets have prevailed in nanocomposites, their efficiency in enhancing conductive functions seems to reach the limit, as if merely addressing the dispersion homogeneity. Here, we exploit the unrecognized geometrical curvature of 2D sheets to break the efficiency limit of filler systems. The hyperbolic curvature meditates the incompatibility between 2D topology and 3D filler space and holds the efficient conductive path through face-to-face contact. The hyperbolic graphene framework exhibits the record efficiency in enhancing electrically and thermally conductive functions of nanocomposites. At volume loading of only 1.6%, the thermal and electrical conductivities reach 31.6 W/(mK) and 13,911 S/m, respectively. Nanocomposites with hyperbolic graphene framework exhibit great potentials in thermal management, sensing and electromagnetic shielding. Our work presents a geometrically optimal filler system to break the efficiency limit of multifunctional nanocomposites and broadens the structural design space of 2D sheets by curvature modulation to meet more applications.