Diameter-dependent elastic properties of carbon nanotube-polymer composites: Emergence of size effects from atomistic-scale simulations

Abstract

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

“Semiconductor” Model of the “Polymer-CNTs” Composite Strengthening

“…Figure 5b shows dependences of relative IR reflectance R/R 0 of composite "polybutadiene rubber-carbon nanotube" on the carbon nanotube content in the area of CH 3 (curve 1, 2844 cm -1 ) and CH 2 (curve 2, 2914 cm -1 ) valence vibrations and relative tensile strength N/N 0 for two types of composites (curves 3-4). Figure 5b became almost linear and proportional to CNTs surface in composite according to [8] and [18] results.…”

Generally cylindrical orthotropic constitutive modeling of matrix-filled carbon nanotubes: Transverse mechanical properties and responses

“…The third boundary condition equation (6c) states that the radial stress of the outside tube at the outer surface is equal to the radially applied uniform external pressure, which again is related to the equilibrium of the system. Substituting equations (4) and (5) into the strain relations given by equation (3) and then substituting the results into the stress relations given by equation (2), the strain and stress equations for both inside and outside tubes can be rewritten in terms of e, C ij , r, A i, A o, and B o (see equations (36) to (39) in Appendix 1 for details).…”

“…Similarly, equations (7) and (10) can be substituted into strain relations (i.e., equations (36) and (37) in Appendix 1) to obtain the exact analytical solutions for the strain components, that is, axial, circumferential, and radial strains, within the domain of each concentric cylinder, as…”

Glass-Reinforced Plastic Filled by Multiwall Carbon Nanotubes and Their Modified Forms

“…As a rule, the addition of any nanosized filler, including CNT's, in the astringent of the composite system increases its physical and mechanical characteristics. The theoretical analysis carried out in various models, for example [19] [20], shows that such a change in properties is due to the characteristics of various phases formed on the interface between the nanofiller and the bulk polymer. Modeling by methods of molecular dynamics [19] demonstrates the formation of an ordered layer of a polymer matrix around CNT's.…”

“…The theoretical analysis carried out in various models, for example [19] [20], shows that such a change in properties is due to the characteristics of various phases formed on the interface between the nanofiller and the bulk polymer. Modeling by methods of molecular dynamics [19] demonstrates the formation of an ordered layer of a polymer matrix around CNT's. This layer, known as interphase one, plays a central role in the overall mechanical response of the composite.…”