Nanoscale carbon-based fillers are known to significantly alter the mechanical and electrical properties of polymers even at relatively low loadings. We report results from extensive molecular-dynamics simulations of mechanical testing of model polymer (high-density polyethylene) nanocomposites reinforced by nanocarbon fillers consisting of graphene flakes and fullerenes. By systematically varying filler concentration, morphology, and size, we identify clear trends in composite stiffness with reinforcement. To within statistical error, spherical fullerenes provide a nearly size-independent level of reinforcement. In contrast, two-dimensional graphene flakes induce a strongly size-dependent response: we find that flakes with radii in the 2–4 nm range provide appreciable enhancement in stiffness, which scales linearly with flake radius. Thus, with flakes approaching typical experimental sizes (~0.1–1 μm), we expect graphene fillers to provide substantial reinforcement, which also is much greater than what could be achieved with fullerene fillers. We identify the atomic-scale features responsible for this size- and morphology-dependent response, notably, ordering and densification of polymer chains at the filler–matrix interface, thereby providing insights into avenues for further control and enhancement of the mechanical properties of polymer nanocomposites.

Graphene and other two-dimensional (2D) materials are of emerging interest as functional fillers in polymer-matrix composites. In this study, we present a multiscale atomistic-to-continuum approach for modeling interfacial stress transfer in graphene-high-density polyethylene (HDPE) nanocomposites. Via detailed characterization of atomic-level stress profiles in submicron graphene fillers, we develop a modified shear-lag model for short fillers. A key feature of our approach lies in the correct accounting of stress concentration at the ends of fillers that exhibits a power-law dependence on filler ("flaw") size, determined explicitly from atomistic simulations, without any ad hoc modeling assumptions. In addition to two parameters that quantify the end stress concentration, only one additional shear-lag parameter is required to quantify the atomic-level stress profiles in graphene fillers. This three-parameter model is found to be reliable for fillers with dimensions as small as ∼10 nm. Our model predicts accurately the elastic response of aligned graphene-HDPE composites and provides appropriate upper bounds for the elastic moduli of nanocomposites with more realistic randomly distributed and oriented fillers. This study provides a systematic approach for developing hierarchical multiscale models of 2D material-based nanocomposites and is of particular relevance for short fillers, which are, currently, typical of solution-processed 2D materials.

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