We propose a computational procedure to assess size effects in nonfunctionalized single-walled carbon nanotube (CNT)-polymer composites. The procedure upscales results obtained with atomistic simulations on a composite unit cell with one CNT to an equivalent continuum composite model with a large number of CNTs. Molecular dynamics simulations demonstrate the formation of an ordered layer of polymer matrix surrounding the nanotube. This layer, known as the interphase, plays a central role in the overall mechanical response of the composite. Due to poor load transfer from the matrix to the CNT, the reinforcement effect attributed to the CNT is negligible; hence the interphase is regarded as the only reinforcement phase in the composite. Consequently, the mechanical properties of the interface and the CNT are not derived since their contribution to the elastic response of the composite is negligible. To derive the elastic properties of the interphase, we employ an intermediate continuum micromechanical model consisting of only the polymer matrix and a three-dimensional fiber representing the interphase. The Young's modulus and Poisson's ratio of the equivalent fiber, and therefore of the interphase, are identified through an optimization procedure based on the comparison between results from atomistic simulations and those obtained from an isogeometric analysis of the intermediate micromechanical model. Finally, the embedded reinforcement method is employed to determine the macroscopic elastic properties of a representative volume element of a composite with various fiber volume fractions and distributions. We then investigate the role of the CNT diameter on the elastic response of a CNT-polymer composite; our simulations predict a size effect on the composite elastic properties, clearly related to the interphase volume fraction.

Molecular-dynamics simulations of single-walled carbon nanotubes (CNTs) embedded in a coarse-grained amorphous monodisperse polyethylene-like model system have been carried out. The roles of nanotube diameter and chirality on the physical and structural properties of the composite are thoroughly discussed for several CNTs with different diameter and chirality. It is shown that the glass-transition temperature of the polymer matrix increases with the diameter of the CNT while chirality effects are negligible. A denser and ordered layered region of polymer matrix is found in the vicinity of the nanotube surface. The density and ordering of this layer increases with the CNT diameter. All simulations indicate that chirality does not affect the atomic structure of the highly ordered layer surrounding the CNTs. Despite the simplicity of the polymer model, results of this study are qualitatively comparable with those obtained from experiments and numerical simulations that consider a chemically specific polymer matrix.