Size Effects in a Silica-Polystyrene Nanocomposite: Molecular Dynamics and Surface-enhanced Continuum Approaches

Abstract

Size effects in a system composed of a polymer matrix with a single silica nanoparticle are studied using molecular dynamics and surface-enhanced continuum approaches. The dependence of the composite’s mechanical properties on the nanoparticle’s radius was examined. Mean values of the elastic moduli obtained using molecular dynamics were found to be lower than those of the polystyrene matrix alone. The surface-enhanced continuum theory produced a satisfactory fit of macroscopic stresses developing during relaxation due to the interface tension and uniaxial deformation. Neither analytical nor finite-element solutions correlated well with the size-effect in elastic moduli predicted by the molecular dynamics simulations.

Keywords:

• Molecular dynamics
• Nanocomposite
• Size effect
• Surface energy
• Surface-enhanced continuum

Notes

¹ In [5] the authors concluded that NCs might have viscoelastic behavior. Thus, the averaged stresses and the resulting elastic moduli could also depend on the chosen relaxation time.

Fig. 2. Illustration of different deformation modes considered in this study. Solid and dashed lines denote initial and deformed configurations, respectively.

² For nonlinear cases, the resulting standard deviation of the normal distribution could be estimated by sampling random variables. However, in order to keep on figures easy to digest, we did not indicate results from this approach.

³ For isotropic materials the Hooke’s law reads , where σ is stress, is the strain tensor and I is the second order identity tensor.

⁴ Note the absence of error ranges as the results are obtained at zero temperature.